Question 1 :
State whether the given statement is True or False :<br/>$2\sqrt { 3 }-1 $ is an irrational number.
Question 4 :
Assertion: The denominator of $34.12345$ is of the form $2^n \times 5^m$, where $m, n$ are non-negative integers.
Reason: $34.12345$ is a terminating decimal fraction.
Question 8 :
Determine the HCF of $a^2 - 25, a^2 -2a -35$ and $a^2+12a+35$
Question 9 :
Without actually dividing find which of the following are terminating decimals.
Question 10 :
A rectangular veranda is of dimension $18$m $72$cm $\times 13$ m $20$ cm. Square tiles of the same dimensions are used to cover it. Find the least number of such tiles.
Question 11 :
The greatest number that will divided $398, 436$ and $542$ leaving $7,11$ and $14$ remainders, respectively, is
Question 12 :
The ........... when multiplied always give a new unique natural number.
Question 16 :
Euclids division lemma, the general equation can be represented as .......
Question 17 :
Let $x=\dfrac { p }{ q } $ be a rational number, such that the prime factorization of $q$ is of the form $2^n 5^m$, where $n, m$ are non-negative integers. Then $x$ has a decimal expansion which terminates.
Question 18 :
The statement dividend $=$ divisor $\times$ quotient $+$ remainder is called 
Question 24 :
H.C.F. of $x^3 -1$ and $x^4 + x^2 + 1$ is
Question 25 :
For three irrational numbers $p,q$ and $r$ then $p.(q+r)$ can be
Question 28 :
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is<br>
Question 30 :
Use Euclid's division lemma to find the HCF of the following<br/>16 and 176
Question 31 :
Which of the following irrational number lies between $\dfrac{3}{5}$ and $\dfrac{9}{10}$
Question 32 :
Use Euclid's division algorithm to find the HCF of :$196$ and $38220$
Question 34 :
State whether the following statement is true or not:$\left( 3+\sqrt { 5 }  \right) $ is an irrational number. 
Question 35 :
For finding the greatest common divisor of two given integers. A method based on the division algorithm is used called ............
Question 36 :
State whether the following statement is true or false.The following number is irrational<br/>$6+\sqrt {2}$
Question 37 :
State True or False:$4\, - \,5\sqrt 2 $ is irrational if $\sqrt 2 $ is irrational.
Question 38 :
A number $x$ when divided by $7$  leaves a remainder $1$ and another number $y$ when divided by $7$  leaves the remainder $2$. What will be the remainder if $x+y$ is divided by $7$?
Question 39 :
Using fundamental theorem of Arithmetic find L.C.M. and H.C.F of $816$ and $170$.
Question 40 :
Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion$\displaystyle \frac{7}{210}$
Question 43 :
State whether the following statement is true or false.The following number is irrational<br/>$7\sqrt {5}$
Question 45 :
In a division sum the divisor is $12$  times the quotient and  $5$  times the remainder. If the remainder is  $48$  then what is the dividend?
Question 46 :
$2\times 2\times 2\times 3\times 3\times 13 = 2^{3} \times 3^{2} \times 13$ is equal to
Question 47 :
................. states the possibility of the prime factorization of any natural number is unique. The numbers can be multiplied in any order.
Question 48 :
Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion$\displaystyle \frac{15}{1600}$
Question 50 :
To get the terminating decimal expansion of a rational number $\dfrac{p}{q}$. if $q = 2^m 5^n$ then m and n must belong to .................
Question 52 :
When a natural number x is divided by 5, the remainder is 2. When a natural number y is divided by 5, the remainder is 4. The remainder is z when x+y is divided by 5. The value of $\dfrac { 2z-5 }{ 3 } $ is
Question 54 :
For what value of k does the system of equations$\displaystyle 2x+ky=11\:and\:5x-7y=5$ has no solution?
Question 56 :
Five tables and eight chairs cost Rs. $7350$; three tables and five chairs cost Rs. $4475$. The price of a table is
Question 57 :
If x and y are positive with $x-y=2$ and $xy=24$ , then $ \displaystyle \frac{1}{x}+\frac{1}{y}$   is equal to
Question 58 :
The values of x and y satisfying the two equation 32x+33y=31, 33x+32y=34 respectively will be
Question 59 :
What is the nature of the graphs of a system of linear equations with exactly one solution?
Question 60 :
The unit digit of a number is $x$ and its tenth digit is $y$ then the number will be 
Question 61 :
The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is
Question 62 :
What is the equationof Y-axis? Hence, find the point of intersection of Y-axis and the line $y\,=\, 3x\, +\, 2$.
Question 63 :
In a zoo there are some pigeons and some rabbits. If their heads are counted these are $300$ and if their legs are counted these are $750$ How many pigeons are there?
Question 64 :
If $(a, 3)$ is the point lying on the graph of the equation $5x\, +\, 2y\, =\, -4$, then find $a$.
Question 70 :
The sum of two numbers is $2$ and their difference is $1$. Find the numbers.
Question 71 :
If the system of equation, ${a}^{2}x-ay=1-a$ & $bx+(3-2b)y=3+a$ possesses a unique solution $x=1$, $y=1$ then:
Question 72 :
Some students are divided into two groups A & B. If $10$ students are sent from A to B, the number in each is the same. But if $20$ students are sent from B to A, the number in A is double the number in B. Find the number of students in each group A & B.<br/>
Question 73 :
A choir is singing at a festival. On the first night $12$ choir members were absent so the choir stood in $5$ equal rows. On the second night only $1$ member was absent so the choir stood in $6$ equal rows. The same member of people stood in each row each night. How many members are in the choir?
Question 74 :
The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is
Question 75 :
Let PS be the median of the triangle with vertices $P\left( 2,2 \right), Q\left( 6,-1 \right), R\left( 7,3 \right).$The equation of the line passing through $\left( 1,-1 \right)$and parallel to PS is
Question 76 :
Assem went to a stationary shop and purchased $3$ pens and $5$ pencils for $Rs.40$. His cousin Manik bought $4$ pencils and $5$ pens for $Rs. 58$. If cost of $1$ pen is $Rs.x$, then which of the following represents the situation algebraically?
Question 77 :
If $2x + y = 5$, then $4x + 2y$ is equal to _________.
Question 78 :
If (a, 4) lies on the graph of $3x + y = 10$, then the value of a is
Question 79 :
What is the equation of the line through (1, 2) so that the segment of the line intercepted between the axes is bisected at this point ?
Question 80 :
Solve the following equations:<br/>$x + \dfrac {4}{y} = 1$,<br/>$y + \dfrac {4}{x} = 25$.Then $(x,y)=$
Question 81 :
A line which passes through (5, 6) and (-3. -4) has an equation of
Question 82 :
The linear equation $y = 2x + 3$ cuts the $y$-axis at 
Question 83 :
The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point
Question 84 :
What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes ?
Question 85 :
The  linear equation, such that each point on its graph has an ordinate $3$ times its abscissa is $y=mx$. Then the value of $m$ is<br/>
Question 86 :
The solution of the simultaneous equations $\displaystyle \frac{x}{2}+\frac{y}{3}=4\: \: and\: \: x+y=10 $ is given by
Question 87 :
The graph of the linear equation $2x -y = 4$ cuts x-axis at
Question 88 :
Examine whether the point $(2, 5)$ lies on the graph of the equation $3x\, -\, y\, =\, 1$.
Question 89 :
Equation of a straight line passing through the point $(2,3)$ and inclined at an angle of $\tan^{-1}\dfrac{1}{2}$ with the line $y+2x=5$, is:
Question 90 :
If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is
Question 91 :
A member of these family with positive gradient making an angle of$\frac{\pi }{4}$ with the line3x-4y=2, is
Question 92 :
Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$
Question 94 :
If $p+q=1$ andthe ordered pair (p, q) satisfies $3x+2y=1$,then it also satisfies
Question 95 :
Equation of a straight line passing through the origin and making an acute angle with $x-$axis twice the size of the angle made by the line $y=(0.2)\ x$ with the $x-$axis, is:
Question 96 :
State whether the given statement is true or false:The graph of a linear equation in two variables need not be a line.<br/>
Question 97 :
State whether the given statement is true or false:Every point on the graph of a linear equation in two variables does not represent a solution of the linear equation.<br/>
Question 99 :
Two perpendicular lines are intersecting at $(4,3)$. One meeting coordinate axis at $(4,0)$, find the coordinates of the intersection of other line with the cordinate axes.
Question 101 :
The value of $k$ for which the system of equations $3x + 5y= 0$ and $kx + 10y = 0$ has a non-zero solution, is ________.
Question 103 :
Solve the equations using elimination method:<br>$2x + 3y = 12$ and $4x + 2y = 8$
Question 104 :
Given that $3p + 2q = 13$ and $3p - 2q = 5$, find the value of $p + q$
Question 105 :
Find the value of x and y using cross multiplication method: <br>$3x - 5y = -1$ and $x + 2y = -4$
Question 106 :
If $bx+ay=a^2+b^2$ and $ax-by=0$, then the value of $(x-y) $ is<br/>
Question 107 :
Solve the following pair of simultaneous equations:$\displaystyle\, 4x\, +\, \frac{3}{y}\, =\, 1\,; 3x\, -\, \frac{2}{y}\, =\, 5$
Question 108 :
Solve the following pair of equations:<br/>$\displaystyle \frac{6}{x}+\displaystyle \frac{4}{y}= 20, \displaystyle \frac{9}{x}-\displaystyle \frac{7}{y}= 10.5$
Question 109 :
Solve the following pair of simultaneous equations:$\displaystyle \frac{1}{x}\, +\, \frac{1}{y}\, =\, 5\,;\, \frac{1}{x}\, -\, \frac{1}{y}\, =\, 1$
Question 111 :
Solve the equations using elimination method:<br>$2x + y = 2$ and $x - y = 4$
Question 112 :
If$\displaystyle \frac{x+y}{x-y}=\frac{5}{3}\: and\: \frac{x}{\left ( y+2 \right )}=2$ the value of (x , y) is
Question 113 :
Solve the following pair of equations:<br/>$\displaystyle \frac{9}{x}-\displaystyle \frac{4}{y}= 8$, $\displaystyle \frac{13}{x}+\displaystyle \frac{7}{y}=101$
Question 114 :
The ratio of the present ages of mother and son is $ 12: 5$. The mother's age at the time of the birth of the son was $21$ years. Find their present ages.
Question 115 :
If $y=a+\dfrac { b }{ x } $, where $a$ and $b$ are constants and if $y=1$ when $x=-1$, and $y=5$ when $x=-5$, what is the value of $a+b$?
Question 116 :
Solve the following equations by substitution method.<br/>$\dfrac{1}{x} + \dfrac{2}{y} = 9; \dfrac{2}{x} + \dfrac{1}{y} = 12     (x \neq 0, y \neq 0)$
Question 117 :
To save on helium costs, a balloon is inflated with both helium and nitrogen gas. Between the two gases, the balloon can be inflated up to $8$ liters in volume. The density of helium is $0.20$ grams per liter, and the density of nitrogen is $1.30$ grams per liter. The balloon must be filled so that the volumetric average density of the balloon is lower than that of air, which has a density of $1.20$ grams per liter. Which of the following system of inequalities best describes how the balloon will be filled, if $x$ represents the number of liters of helium and $y$ represents the number of liters of nitrogen ?
Question 118 :
Solve the following pair of linear (simultaneous) equations by the method of elimination:<br/>$0.2x+0.1y= 25$<br/>$2\left ( x-2 \right )-1.6y= 116$
Question 119 :
Is the following situation possible? If so, determine their present ages.<br>The sum of the ages of two friends is $20$ years.Four years ago, the product of their ages in years was $48$.
Question 120 :
Find the value of x and y using cross multiplication method: <br>$5x + 2y = 32$ and $6x + 6y = 42$
Question 121 :
Solve: $\displaystyle \frac{3}{x}-\displaystyle \frac{2}{y}= 0$ and $\displaystyle \frac{2}{x}+\displaystyle \frac{5}{y}= 19$. Hence, find $a$ if $y= ax+3$.
Question 122 :
Solve the following simultaneous equations :$\displaystyle \frac{16}{x + y}\, +\, \frac{2}{x - y}\, =\, 1;\quad \frac{8}{x + y}\, -\, \frac{12}{x - y}\, =\, 7$
Question 124 :
If $2x=t+\sqrt{t^2+4}$ and $3y=t-\sqrt{t^2+4}$ then the value of  $y$ when $x=\dfrac {2}{3}$, is ____.
Question 127 :
Solve the equations using elimination method:<br>$2x - y = 20$ and $4x + 3y = 0$
Question 128 :
Solve the following pairs of equations by reducing them to a pair of linear equations:<br>$\displaystyle \dfrac {7x-2y}{xy}=5, \dfrac {8x+7y}{xy}=15$<br>
Question 129 :
Solve the following simultaneous equations :$\displaystyle \frac{27}{x-2}\, +\, \frac{31}{y + 3}\, =\, 85;\quad \frac{31}{x - 2}\, +\, \frac{27}{y + 3}\, =\, 89$
Question 130 :
If $(3)^{x + y} = 81$ and $(81)^{x - y} = 3$, then the values of $x$ and $y$ are<br>
Question 131 :
Solve the equations using elimination method:<br>$x - 4y = -20$ and $4x + 4y = 20$
Question 132 :
Solve the following pair of simultaneous equations:$\displaystyle\, y\, -\, \frac{3}{x}\, =\, 8\, ;\, 2y\, +\, \frac{7}{x}\, =\, 3$
Question 134 :
In the following system of equation determine whether the system has a unique solution, no solution or infinitely many solution. In case there is a unique solution, find it.<br>$2x+3y=7$<br>$6x+5y=11$<br>
Question 135 :
Find the value of x and y using cross multiplication method: <br/>$x-  2y = 1$ and $x + 4y = 6$
Question 137 :
In the system of equations $4(x + 3) -3(y + 1) =4$ and $3(x -1) + (2y -3) =20$, the values of $x$ and $y$ are:
Question 138 :
Find the solution of $x$ and $y$ using cross multiplication method: $3x - y = 1$ and $x + 2y = 5$<br/>
Question 139 :
Solve the equations using elimination method:<br>$x - 6y = 9$ and $2x - y = 7$
Question 141 :
Find the value of x and y using cross multiplication method: <br>$x + y = 15$ and $x - y = 3$
Question 142 :
Solve: $\displaystyle \frac{3}{x}\, -\, \displaystyle \frac{2}{y}\, =\, 0$ and $\displaystyle \frac{2}{x}\, +\, \displaystyle \frac{5}{y}\, =\, 19$<br/>Hence, find 'a' if $y\, =\, ax\, +\, 3$
Question 143 :
Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$\displaystyle \frac {2}{\sqrt x}+\frac {3}{\sqrt y}=2, \frac {4}{\sqrt x}-\frac {9}{\sqrt y}=-1$<br/>
Question 144 :
Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$\dfrac {10}{(x+y)}+\dfrac {2}{(x-y)}=4, \dfrac {15}{(x+y)}-\dfrac {5}{(x-y)}=-2$<br/>
Question 145 :
The simultaneous equations, $\displaystyle y = x + 2|x| $ & $y = 4 + x - |x|$ have the solution set 
Question 146 :
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:The sum of the digits of a two-dlgit number is $9$. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number<br/>
Question 147 :
Solve the following pair of simultaneous equations:$\displaystyle\,3x\, +\, \frac{1}{y}\, =\, 13\, ;\, \frac{2}{y}\, -\, x\, =\, 5$
Question 148 :
If $1$ is added to each of the two certainnumbers, their ratio is $1:2$; and if $5$issubtracted from each of the two numbers, theirratio becomes $5:11$. Find the numbers.
Question 149 :
Solve each of the following system of equations by elimination method. $65x-33y=97, 33x-65y=1$
Question 150 :
Find the value of $x$ and $y$ using cross multiplication method: <br/>$3x + 5y = 17$ and $2x + y = 9$
Question 151 :
Solve : $\displaystyle \frac{3}{x+y}+\displaystyle \frac{2}{x-y}= 2$ and $\displaystyle \frac{9}{x+y}-\displaystyle \frac{4}{x-y}= 1$
Question 152 :
Solve the following pair of equations by the elimination method and the substitution method:<br/>$3x - 5y - 4 = 0$ and $9x = 2y + 7$<br/>
Question 153 :
Equation of straight line $ax + by + c= 0$, where $3a + 4b + c = 0$, which is at maximum distance from $(1, -2)$,is
Question 154 :
If the equations $y = mx + c$ and $x  \cos  \alpha + y \sin  \alpha = p$ represent the same straight line, then
Question 155 :
Equations of the two straight lines passing through the point $(3, 2)$ and making an angle of $45 ^ { \circ }$ with the line $x - 2 y = 3$, are
Question 156 :
The axes being inclined at an angle of $30^o$, the equation of straight line which makes an angle of $60^o$ with the positive direction of x-axis and x-intercept 2 is
Question 157 :
A straight line $L$ through the point $(3,-2)$ is inclined at an angle $60^{o}$ to the line $\sqrt{3}x+y=1$. lf $L$ also intersects the $x-$axis, then the equation of $L$ is<br>
Question 158 :
The sum of three numbers is $92$. The second number is three times the first and the third exceeds the second by $8$. The three numbers are: 
Question 160 :
The equation of the straight line which passes through $(1, 1)$ and making angle $60^o$ with the line $x+ \sqrt 3y +2 \sqrt 3=0$ is/are.
Question 161 :
Equations $\displaystyle \left ( b-c \right )x+\left ( c-a \right )y+\left ( a-b \right )=0$ and $\displaystyle \left ( b^{3}-c^{3} \right )x+\left ( c^{3}-a^{3} \right )y+a^{3}-b^{3}=0$ will represent the same line if<br>
Question 162 :
Equation of a straight line passing through the point $(2, 3)$ and inclined at an angle of $\tan^{-1} \left(\dfrac{1}{2}\right)$ with the line $y + 2x = 5$ is
Question 163 :
Based on equations reducible to linear equations<br/>Solve for x and y: $\dfrac {16}{x+3}+\dfrac {3}{y-2}=5; \dfrac {8}{x+3}-\dfrac {1}{y-2}=0$<br/>
Question 164 :
Based on equations reducible to linear equations, solve for $x$ and $y$:<br/>$\dfrac {x-y}{xy}=9; \dfrac {x+y}{xy}=5$<br/>
Question 165 :
The equations of two equal sides of an isosceles triangle are $ 3x + 4y = 5 $and $4x - 3y = 15$. If the third side passes through $(1, 2)$, its equation is
Question 166 :
Based on equations reducible to linear equations<br/>Solve for x and y: $\dfrac {24}{2x+y}-\dfrac {13}{3x+2y}=2; \dfrac {26}{3x+2y}+\dfrac {8}{2x+y}=3$
Question 167 :
A line has intercepts $a$ and $b$ on the coordinate axes. When the axes are rotated through an angle $\alpha $, keeping the origin fixed, the line makes equal intercepts on the coordinate axes, then $\tan$ <br> $\alpha $=<br/>
Question 168 :
The cost of an article $A$ is $15$% less than that of article $B.$ If their total cost is $2,775\:Rs\:;$ find the cost of each article$.$ <br>
Question 169 :
A straight line L through the point $(3, - 2)$ is inclined at an angle of 60$^o$ to the line $\sqrt 3 x + y = 1$. If $L$ also intersects the $x-$axis, then the equation of $L$ is
Question 170 :
Father's age is three times the sum of ages of his two children. After $5$ years his age will be twice the sum of ages of two children. Find the age of father.<br/>
Question 171 :
The equation of the line passing through the point $P(1, 2)$ and cutting the lines $x + y - 5 = 0$ and $2x - y = 7$ at $A$ and $B$ respectively such that the harmonic mean of $PA$ and $PB$ is $10$, is
Question 172 :
A line perpendicular to the line $\displaystyle 3x-2y=5$ cuts off an intercept $3$ on the positive side of the $x$-axis. Then 
Question 173 :
The ratio between the number of passangers travelling by $1^{st}$ and $2^{nd}$ class between the two railway stations is 1 : 50, whereas the ratio of$1^{st}$ and $2^{nd}$ class fares between the same stations is 3 : 1. If on a particular day, Rs. 1325 were collected from the passangers travelling between these stations by these classes, then what was the amount collected from the $2^{nd}$ class passangers ?
Question 174 :
The ratio of the areas of two similar triangles is $25:16$. The ratio of their perimeters is ..............
Question 175 :
Triangle A has a base of x and a height of 2x. Triangle B is similar to triangle A, and has a base of 2x. What is the ratio of the area of triangle A to triangle B?
Question 176 :
State true or false:<br/>The ratio of the areas of two triangles of the same height is equal to the ratio of their bases.
Question 177 :
State true or false:<br/>The ratio of the areas of two triangles on the same base is equal to the ratio of their heights.
Question 179 :
 If the two legs of a right angled $\Delta$ are equal and the square of the hypotenuse is $100,$ then the length of each leg is:
Question 180 :
In a right triangle the square of the hypotenuse is equal to twice the product of the legs. One of the acute angles of the triangle is:
Question 181 :
If three sides of a right-angled triangle are integers in their lowest form, then one of its sides is always divisible by
Question 182 :
Which of the following can be the sides of a right angled triangle ?
Question 183 :
In $\triangle{ABC}$, $\angle{B}=90$, $AB=8\:cm$ and $BC=6\:cm$.The length of the median BM is
Question 184 :
In $\Delta$ ABC, $\angle B = 90$, AB = 8 cm and BC = 6 cm. The length of the median BM is<br>
Question 185 :
We use ........... formula to find the lengths of the right angled triangles.
Question 186 :
In the $\triangle LMN$ <b></b>$\displaystyle $, angle L is $\displaystyle { 65 }^{ o }$ $\displaystyle $, angle M is a right angle, what would be angle N?
Question 187 :
A............can never be made up of all odd numbers or two even numbers and one odd number.
Question 188 :
Find hypotenuse of right angled triangle if the sides are $12,4\sqrt 3$
Question 189 :
A right angled triangle has $24,7cm $ as its sides . What will be its hypotenuse?
Question 190 :
Can we construct sets of Pythagorean Triples with all even numbers?
Question 191 :
 A Pythagorean Triplet always...............of all even numbers, or two odd numbers and an even number.
Question 192 :
It is easy to construct sets of Pythagorean Triples, When m and n are any two ............... integers.
Question 193 :
Is it true that a Pythagorean Triple can never be made up of all oddnumbers?
Question 194 :
If the measures of sides of a triangle are $(x^2-1) cm, (x^2 +1) cm$, and $2x cm$, then the triangle will be: 
Question 195 :
In a $\Delta$ABC, if $AB^2\, =\, BC^2\, +\, AC^2$, then the right angle is at:
Question 196 :
The length of the hypotenuse of a right angled $\Delta$ le whose two legs measure 12 cm and 0.35 m is:
Question 198 :
Select the correct alternative and write the alphabet of that following :<br>Out of the following which is the Pythagorean triplet ?
Question 199 :
If the two legs of a right angled triangle are equal and the square of the hypotenuse is $100cm^2$, then the length of each leg is _________.
Question 200 :
A right-angles triangle has hypotenuse $13$ cm, one side is $12$ cm, then the third side is _________.
Question 201 :
If the lengths of the sides of a triangle does not satisfy the rule of $\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$, then that triangle does not contain a
Question 202 :
If the hypotenuse of a right angled triangle is 15 cm and one side of it 6cm less than the hypotenuse, the other side b is equal to.
Question 203 :
Which of the following cannot be the sides a right angle triangle?<br>
Question 204 :
Given the measures of the sides of the triangle , identify which measures are in the ratio 3 : 4 : 5
Question 205 :
In $\Delta ABC,$ if $AB =6\sqrt{3}$ cm, $AC=12$ cm and $BC=6$ cm, then angle B is equal to:<br/>
Question 206 : <p> In a right angle triangle, the hypotenuse is the greatest side. <br/></p><b>State whether the above statement is true or false.</b><br/>
Question 207 :
A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.
Question 208 :
A ladder $13m$ long rests against a vertical wall. If the foot of the ladder is $5m$ from the foot of the wall, find the distance of the other end of the ladder from the ground.
Question 210 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$3cm, 8cm, 6cm$
Question 211 :
The hypotenuse of a grassy land in the shape of a right triangle is $1$ meter more than twice the shortest side. If the third side is $7$ meters more than the shortest side, find the sides of the grassy land.
Question 212 :
In $\Delta$ ABC, angle C is a right angle, then the value<br>of tan $A + tan B $is<br><br>
Question 213 :
Which of the following numbers form pythagorean triplet? <br/>i) $2, 3, 4$<br/>ii) $6, 8, 10$<br/>iii) $9, 10, 11$<br/>iv) $8, 15, 17$
Question 214 :
Which of the following could be the side lengths of a right triangle?
Question 215 :
Triangle ABC is right -angled at C. Find BC, If AB = 9 cm and AC = 1 cm.<br/>In each case, answer correct to two place of decimal. 
Question 216 :
The hypotenuse 'c' and one arm 'a' of a right triangle are consecutive integers. The square of the second arm is:
Question 217 :
There is a Pythagorean triplet whose one member is $6$ and other member is $10$
Question 218 :
In$ \displaystyle \bigtriangleup $ ABC , angle C is a right angle, then the value of$ \displaystyle \tan A+ \tan B is $
Question 219 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$
Question 220 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $b$ when $c=13 \ cm$ and $a=5 \ cm$.
Question 221 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $a$ when $c=25 \ cm$ and $b=7 \ cm$.
Question 222 :
The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$
Question 223 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>
Question 224 :
The sides of a right triangle are $(x-1)$, $x$ and $(x+1)$. Find the sides of the triangle.
Question 225 :
The triangle formed by the vertices $A(1,0,1) \quad B(2,-1,4) $ and $C(3,-4,-1)$ is
Question 226 :
In similar triangles $\triangle ABC$ and $\triangle FDE, DE = 4 cm, BC = 8 cm$ and area of $\triangle FDE = 25 cm^2$. What is the area of $\Delta ABC$?
Question 227 :
Two isosceles triangles have equal vertical angles and their areas are in the ratio $9:16$. Find the ratio of their corresponding heights.
Question 228 :
State true or false:<br/>In parallelogram $ ABCD $. $ E $ is the mid-point of $ AB $ and $ AP $ is parallel to $ EC $<b> </b>which meets $ DC $ at point $ O $ and $ BC $ produced at $ P $. Hence$ BP= 2AD $<br/><br/><br/>
Question 229 :
The corresponding sides of two similar triangles are in the ratio $a : b$. What is the ratio of their areas?
Question 230 :
ABC is an isosceles triangle right angled at B. Similar triangles ACD and ABE are constructed in sides AC and AB. Find the ratio between the areas of $\triangle ABE$ and $\triangle ACD$.
Question 231 :
The sides of a triangle are $5$ cm, $6$ cm and $7$ cm. One more triangle is formed by joining the midpoints of the sides. The perimeter of the second triangle is:<br/>
Question 232 :
If the sides of two similar triangles are in the ratio $2 : 3$, then their areas are in the ratio:
Question 233 :
If $\triangle ABC$ is similar to $\triangle DEF$ such that BC=3 cm, EF=4 cm and area of $\triangle ABC=54 {cm}^{2}$. Determine the area of $\triangle DEF$.
Question 234 :
If $\triangle ABC$ and $\triangle PQR$ are similar and $\dfrac {BC}{QR} = \dfrac {1}{3}$ find $\dfrac {area (PQR)}{area (BCA)}$
Question 235 :
In $\triangle ABC \sim \triangle DEF$ such that $AB = 1.2\ cm$ and $DE = 1.4\ cm$. Find the ratio of areas of $\triangle ABC$ and $\triangle DEF$.
Question 236 :
The perimeter of two similar triangles $\triangle ABC$ and $\triangle DEF$ are $36$ cm and $24$ cm respectively. If $DE=10 $ cm, then $AB$ is :
Question 237 :
State true or false:<br/>Triangle $ABC$ is similar to triangle $PQR$. If bisector of $\angle BAC$ meets $BC$ at point $D$ and the bisector of $\angle QPR$ meets $QR$ at point $M$, Then, $\displaystyle \dfrac{AB}{PQ}=\dfrac{AC}{PM}.$<br/>
Question 238 :
$ABCD$ is parallelogram and $P$ isthe mid point of the side $AD$. The line $BP$ meets the diagonal $AC$ in $Q$. Then the ratio $AQ:QC=$
Question 239 :
The ratio of areas of two similar triangles is $81 : 49$. If the median of the smaller triangle is $4.9\ cm$, what is the median of the other?
Question 240 :
In $\Delta ABC$, DE is || to BC, meeting AB and AC at D and E. If AD = 3 cm, DB = 2 cm and AE = 2.7 cm, then AC is equal to:
Question 241 :
ABC is right angled triangle, right angle at B, $AC=25$, $AB=7$ then BC= ? <br/>
Question 242 :
The perimeter of two similar triangle are $30\ cm$ and $20\ cm$. If one side of first triangle is $12\ cm$ determine the corresponding side of second triangle.
Question 243 :
$\displaystyle \Delta ABC$ and $\displaystyle \Delta DEF$ are two similar triangles such that $\displaystyle \angle A={ 45 }^{ \circ  },\angle E={ 56 }^{ \circ  }$, then $\displaystyle \angle C$ =___.<br/>
Question 244 :
D and E are the points on the sides AB and AC respectively of triangle ABC such that $ DE||BC$. If area of $ \triangle DBC =15 cm^2$, then area of $\triangle EBC $ is:<br/>
Question 245 :
Two angles of triangle ABC are $\displaystyle 85^{\circ}$ and $\displaystyle 65^{\circ}$ whilethe two angles of another triangle DEF are $\displaystyle 30^{\circ}$ and $\displaystyle 65^{\circ}$.Which of the statements is correct?<br>
Question 246 :
Two triangles ABC and PQR  are similar, if $BC : CA : AB = $1: 2 : 3, then $\dfrac{QR}{PR}$ is<br/>
Question 248 :
Aline segment DE is drawn parallel to base BC of $\Delta\,ABC$ which cuts ABat point D and AC at point E. If AB = 5 BD and EC = 3.2 cm. Find the length ofAE.
Question 249 :
A ladder of $3.9m$ length is laid against a wall. The distance between the foot of the wall and the ladder is $1.5m$. Find the height at which the ladder touches the wall.
Question 250 :
State true or false:<br/>In parallelogram $ ABCD $. $ E $ is the mid-point of $ AB $ and $ AP $ is parallel to $ EC $<b> </b>which meets $ DC $ at point $ O $ and $ BC $ produced at $ P $. Hence $ O $ is mid-point of $ AP $.<br/><br/>
Question 251 :
D and F are mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Find AB (in cm), if EF = 4.8 cm.
Question 252 :
The areas of two similar triangles are $49 \ {cm}^{2}$ and $64 \ {cm}^{2}$ respectively. The ratio of their corresponding sides is:
Question 254 :
The lengths of the sides of a right triangle are $5x + 2$, $5x$ and $3x - 1$. If $x > 0$ then the length of each side is?
Question 256 :
For $\Delta ABC$ & $\Delta PQR$, if $m \angle A = m \angle R$ and $m \angle C = m \angle Q$, then $ABC \leftrightarrow$ ............. is a similarity.
Question 257 :
The hypotenuse of a right triangle is $6$ m more than twice the shortest side. If the third side is $2$ m less than the hypotenuse, find the hypotenuse of the triangle.<br>
Question 258 :
The areas of two similar triangles are $81\ cm^{2}$ and $49\ cm^{2}$. If the altitude of the bigger triangle is $4.5\ cm$, find the corresponding altitude of the smaller triangle.
Question 259 :
Two $\triangle sABC $ and DEF are similar. If $ar(DEF)= 243\ cm^2, ar(ABC)=108\ cm^2$ and $BC= 6\ cm$. Find $EF$.
Question 260 :
STATEMENT - 1 : If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar.<br>STATEMENT - 2 : If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.<br>
Question 261 :
D and E are respectively the points on the sides AB and AC of a $\displaystyle \Delta ABC$ such that $AB = 12 cm$, $AD = 8 cm$, $AE = 12 cm$ and $AC = 18 cm$, then
Question 262 :
In Pythagoras theorem triplets the lengths of the sides of the right angled triangle are in the ratio.
Question 263 : <p>Which among the following is/are correct?<br/>(I) If the altitudes of two similar triangles are in the ratio $2:1$, then the ratio of their areas is $4 : 1$.<br/>(II) $PQ \parallel BC$ and $AP : PB=1:2$. Then, $\dfrac{A(\triangle APQ)}{A(\triangle ABC)}=\dfrac{1}{4}$</p>
Question 264 :
In $\Delta ABC \sim  \Delta PQR$, $M$ is the midpoint of $BC$ and $N$ is the midpoint of $QR$. If the area of $\Delta ABC =$ $100$ sq. cm and the area of $\Delta PQR =$ $144$ sq. cm. If $AM = 4$ cm, then $PN$ is:<br/>
Question 265 :
If all the three altitudes of a triangle are equal, the triangle is equilateral.<br/><b>State whether the above statement is true or false.</b><br/>
Question 266 :
If $\Delta ABC \sim \Delta PQR$ and $\displaystyle {{PQ} \over {AB}} = {5 \over 2}$ then area $(\Delta ABC):$ area $(\Delta PQR) = ?$
Question 267 :
The perimeters of two similar triangles are $24$ cm. and $18$ cm. respectively. If one side of first triangle is $8$ cm., what is the corresponding side of the other triangle.<br/>
Question 268 :
In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point in side AC such that AP = 6 cm. Prove that $\Delta\,BPC$ is similar to $\Delta\,ABC$. Also, find the length of BP.
Question 269 :
$\Delta ABC \sim \Delta PQR$ and areas of two similar triangles are $64$sq.cm and $121$sq.cm respectively. If $QR=15$cm, then find the value of side BC.
Question 270 :
Assertion: $\triangle ABC$ and $\triangle DEF$ are two similar triangles such that $BC= 4$ cm, $EF = 5$ cm and $A(\triangle ABC) = 64 \:cm^2$, then $A(\triangle DEF) = 100\:cm^2$.
Reason: The areas of two similar triangles are in the ratio of the squares of the corresponding altitudes.
Question 271 :
In $\Delta ABC$, a line is drawn parallel to $BC$ to meet sides $AB$ and $AC$ in $D$ and $E$ respectively. If the area of the $\Delta ADE$ is $\dfrac 19$ times area of the $\Delta ABC$, then the value of $\dfrac {AD}{AB}$ is equal to:
Question 272 :
Choose and write the correct alternative.<br>Out of the following which is aPythagorean triplet ?<br>
Question 273 :
The perimeter of two similar triangles is 40 cm and 50 cm. Then the ratio of the areas of the first and second triangles is
Question 274 : Match the column.<br/><table class="wysiwyg-table"><tbody><tr><td>1. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P$<br/></td><td>(a) AA similarity criterion </td></tr><tr><td>2. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,<br/>$\displaystyle \angle A=\angle P,\angle B=\angle Q$<br/><br/></td><td>(b) SAS similarity criterion </td></tr><tr><td>3. In $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$<br/>$\angle A=\angle P$<br/></td><td>(c) SSS similarity criterion </td></tr><tr><td>4. In $\displaystyle \Delta ACB,DE||BC$<br/>$\displaystyle \Rightarrow \frac{AD}{BD}=\frac{AE}{CE}$<br/></td><td>(d) BPT</td></tr></tbody></table>
Question 275 :
$\frac{a}{r}$, a, ar are the sides of a triangle. If the triangle is a right angled triangle, then $r^2$ is given by
Question 276 :
Let $\displaystyle \Delta XYZ$ be right angle triangle with right angle at Z. Let $\displaystyle A_{X}$ denotes the area of the circle with diameter YZ. Let $\displaystyle A_{Y}$ denote the area of the circle with diameter XZ and let $\displaystyle A_{Z}$ denotes the area of the circle diameter XY. Which of the following relations is true?
Question 280 :
Solve for $x : 15 x^2 - 7x - 36 = 0$<br>
Question 281 :
The mentioned equation is in which form?$z\, -\, \cfrac{7}{z}\, =\, 4z\, +\, 5$
Question 283 :
Find $ p \in R $ for $x^2 - px + p + 3 = 0 $ has<br/>
Question 284 :
The difference between the product of the roots and the sum of the roots of the quadratic equation $6x^{2} - 12x + 19 = 0$ is
Question 285 :
Is the following equation quadratic?$n^{3}\, -\, n\, +\, 4\, =\, n^{3}$
Question 286 :
If $9y^{2}\, -\, 3y\, -\, 2\, =\, 0$, then $y\, =\, \displaystyle -\frac{2}{3}, \, \displaystyle \frac{1}{3}$.<br/>
Question 287 :
State the following statement is True or False<br/>The digit at ten's place of a two digit number exceeds the square of digit at units place ($x$) by 5 and the number formed is $61$, then the equation is $10\, (x^{2}\, +\, 5)\, +\, x\, =\, 61$.<br/>
Question 288 :
Let x and y be two 2- digit number such that y is obtain by reversing the digits of x.suppose they also satisfy $x^2-y^2=m^2$ for some positive integer m. The value of $x+y+m$ is.
Question 289 :
Which of the following is a quadratic polynomial in one variable?<br>
Question 291 :
Is the following equation a quadratic equation?$\displaystyle 3x + \frac{1}{x} - 8 = 0$
Question 295 :
__________ is true for the discriminant of a quadratic equation $x^2+x+1=0$.
Question 296 :
Is the following equation a quadratic equation?$(x + 2)^3 = x^3 - 4$
Question 297 :
If $3$ is one of the roots $x^2-mx+15=0$. Choose the correct options -<br/>
Question 298 :
When $a = \dfrac {4}{3}$, the value of $27a^{3} - 108a^{2} + 144a - 317$ is
Question 300 :
The expression $21x^2 + ax + 21$ is to be factored into two linear prime binomial factors with integer coefficients. This can be done if a is:
Question 301 :
Before Robert Norman worked on 'Dip and Field Concept', his predecessor thought that the tendency of the magnetic needle to swing towards the poles was due to a point attractive. However, Norman showed with the help of experiment that nothing like point attractive exists. Instead, he argued that magnetic power lies is lodestone. Which one of the following is the problem on which Norman and others worked?
Question 303 :
A quadratic equation in $x$ is $ax^2 + bx + c = 0$, where $a, b, c$ are real numbers and the other condition is<br/>
Question 305 :
Choose the quadratic equation in $p$, whose solutions are $1$ and $7$.<br/>
Question 306 :
Say true or false.If $2y^{2}\, =\, 12\, -\, 5y$, then solution is $\displaystyle \frac{3}{2}\, or\, -4$.<br/>
Question 307 :
If $x^{2} + 10 x = 24,$ where $x>0$, then the value of $x + 5$ is
Question 308 :
Applying zero product rule for the equation $x^{2}- ax - 30 = 0$ is $x = 10$, then $a =$ _____.<br/>
Question 309 :
Choose best possible option.<br>$\displaystyle\left( x+\frac { 1 }{ 2 } \right) \left( \frac { 3x }{ 2 } +1 \right) =\frac { 6 }{ 2 } \left( x-1 \right) \left( x-2 \right)$ is quadratic.<br>
Question 310 :
Which one of the following condition will satisfy the zero product roots of the equation $(x - a)(x - b)$?<br>
Question 311 :
If $x^{2} - 4x + 2 = 0$, then the value of $4x^{2} + 2x + \dfrac {4}{x} + \dfrac {16}{x^{2}}$ is
Question 313 :
Is the following equation a quadratic equation?$\displaystyle \frac{3x}{4} - \frac{5x^2}{8} = \frac{7}{8}$
Question 315 : <p>If the value of '$b^2-4ac$' is less than zero, the quadratic equation $ax^2+bx+c=0$ will have</p><br/>
Question 317 :
If c is small in comparision with l then ${\left( {\frac{l}{{l + c}}} \right)^{\frac{1}{2}}} + {\left( {\frac{l}{{l - c}}} \right)^{\frac{1}{2}}} = $
Question 318 :
The quadratic polynomial whose sum of zeroes is $3$ and product of zeroes is $- 2$ is:<br/>
Question 320 :
If, in the expression $x^2 - 3$, x increases or decreases by a positive amount a, the expression changes by an amount
Question 321 :
Check whether $2x^2 - 3x + 5 = 0$ has real roots or no.<br/>
Question 322 :
If $f(x)$ is a quadratic expression such that $f(1) + f(2) = 0$, and $-1$ is a root of $f(x) = 0$, then the other root of $f(x) = 0$ is :
Question 323 :
The length of a rectangular verandah is $3\:m$ more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter. Taking $x$ as the breadth of the verandah, write an equation in $x$ that represents the above statement.
Question 325 :
Difference between the squares of $2$ consecutive numbers is $31$. Find the numbers.
Question 326 :
If $x^2-36=0$, which of the following could be a value of $x$?
Question 327 :
The set of values of k for which the given quadratic equation has real roots<br/>$2x^2$ + 3x + k = 0 are k $\leq \dfrac{9}{8}$
Question 328 :
If $\alpha, \beta$ are the roots of the equation $2x^2 + 4x-5=0$, the equation whose roots are the reciprocals of $2\alpha -3$ and $2 \beta -3$ is<br>
Question 329 :
The ratio of the roots of the equation $a{ x }^{ 2 }+bx+c=0$ is same as the ratio of the roots of the equation $p{ x }^{ 2 }+qx+r=0$. If ${ D }_{ 1 }$ and ${ D }_{ 2 }$ are the discriminants of $a{ x }^{ 2 }+bx+c=0$ and $p{ x }^{ 2 }+qx+r=0$ respectively, then ${ D }_{ 1 }:{ D }_{ 2 }$ is equal to
Question 330 :
If $'r'$ and $'s'$ are the roots of the equation $ax^2+bc+c=0$, then the value of $\displaystyle\frac{1}{r^2}+\frac{1}{s^2}$ is equal to
Question 331 :
$|x^2 + 6x + p| = x^2 + 6x + p$ $\forall x \in R$ where p is a prime number then least possible value $p$is
Question 332 :
The value of k for which the equation $x^{2} - 4x + k = 0 $ has equal roots is<br/>
Question 333 :
For what value of $k$ will the quadratic equation:  $\displaystyle { kx }^{ 2 }+4x+1=0$ have real and equal roots ?
Question 334 :
If the equations $x^{2}+ax+bc=0$ and $x^{2}+bx+ca=0$ have a common root, then their other roots satisfy the equation<br>
Question 337 :
Find the value of discriminant for the following equation.$x^{2}\, +\, 4x\, +\, k\, =\, 0$<br/>
Question 338 :
In each of the following, determine whether the given values are solutions of the given equation or not :<br/> $x^2 \, - \, 3\sqrt{3x} \, + \, 6 \, = \, 0, \, x \, = \, \sqrt{3}, \, x \, = \, -2\sqrt{3}$
Question 339 :
Minimum possible number of positive root of the quadratic equation${x^2} - (1 + \lambda )x + \lambda - 2 = 0, \in R:$
Question 340 :
The factors of the equation, $(x + k)\left (x + \dfrac{1}{2}\right) = 0$, find the value of $k$.<br/>
Question 341 :
If the equation $\displaystyle \lambda x^{2}-2x+3= 0$has positive roots for some real$\displaystyle \lambda $, then
Question 344 :
Assertion: If $a$ and $b$ are integers and the roots of $x^2+ax+b=0$ are rational then they must be integers.
Reason: If the coefficient of $x^2$ in a quadratic equation is unity then its roots must be integers.
Question 347 :
If one root of the quadratic equation $ax^2+bx+c=0$ is the reciprocal of the other, then<br/>
Question 348 :
Determine the value of $k$ for which the $x = -a$ is a solution of the equation $\displaystyle x^{2}-2\left ( a+b \right )x+3k=0 $<br/>
Question 349 :
The values of $a$ which makes the expression $x^2 -ax + 1 -2a^2$ always positive for real values of $x$ are
Question 350 :
$ax^2 + bx + c = 0,$ where $a, b, c$ are real, has real roots if 
Question 351 :
If the roots of the equation $ax^2+ bx + c = 0$ arereciprocal to each other, then
Question 352 :
The value of $'k'$ for which the roots of equation $(x - 1)(x - 5) + k = 0$ differ by 2 is<br>
Question 353 :
If one root of the equation $\displaystyle (k^{2}+1)x^{2}+13x+4k=0$ is reciprocal of the other, then $k$ has the value
Question 354 :
If the roots of the equation $\displaystyle x^{2}+px-6=0$ are $6$ and $-1$ then the value of $p$ is
Question 355 :
Find all values of parameter $a$ for which the quadratic equation $ \left( a+1 \right) { x }^{ 2 }+2\left( a+1 \right) x+a-2=0 $has two distinct roots.<br><br>
Question 356 :
A shopkeeper buys a certain no. of books for Rs. $960$. If the cost per book was Rs. $8$ less, the no. of books that could be bought for Rs. $960$ would be 4 more. Taking the original cost of each book to be Rs. $x$, write an equation in $x$ and solve it.
Question 357 :
The roots of the equation $(b+c)x^2-(a+b+c)x+a=0$ $(a,b,c\ \epsilon \Q, b+c \neq a)$ are
Question 358 :
The values of k for which the roots are real and equal of the following equation<br/>$4x^2$ - 3kx + 1 = 0 are $k = \pm \dfrac{4}{3}$<br/>
Question 359 :
A certain number of balls were purchased for Rs. $450$. Five more balls could have been purchased for the same amount, if each ball was cheaper by Rs. $15$. Find the number of balls purchased.
Question 360 :
If sum and product of the slopes of lines represented by ${ 4x }^{ 2 }+2hxy-{ 7y }^{ 2 }=0$ is equal then h is equal to :
Question 361 :
Let a, b be non-zero real numbers. Which of the following statements about the quadratic equation $ax^2 + (a+b) x + b = 0$ is necessarily true?<br/>(I) It has at least one negative root.<br/>(II) It has at least one positive root.<br/>(III) Both its roots are real.
Question 362 :
The number of values of $k$ for which $\displaystyle \left \{x^{2}-(k-2)x+k^{2}\right\}+ \left \{x^{2}+kx+(2k-1)\right \}$ is a perfect square is/are
Question 363 :
Find the discriminant of the equation and the nature of roots. Also find the roots.$2x^2 + 5 \sqrt 3x + 6 =0$
Question 365 :
The probability of choosing randomly a number c from the set $\{1, 2, 3, ..........9\} $ such that the quadratic equation $x^2+ 4x +c=0$ has real roots is:
Question 366 :
The value of $a$ for which one root of the quadratic equation $(a^2-5a+3) x^2+(3a-1)x+2=0 $ is twice as large as the other, is :<br/>
Question 367 :
If the ratio of the roots of equation$\displaystyle x^{2}+px+q=0$ be equal to the ratio of the roots of$\displaystyle x^{2}+lx+m=0$ then
Question 368 :
If $x=1$ is common root of equations $ax^{2} +ax+3=0$ and $x^{2}+x+b=0$, then value of $ab$ will be:
Question 369 :
I. lf one root of the equation $5x^{2}+13x+k=0$ is the reciprocal of the other, then $k=5$<br>II. lf the roots of the equation $a(b-c)x^{2}+b(c-a)x+c(a-b)=0$ are equal, then $a, b,c$ are in H.P.<br>Which of the above statement is true?<br>
Question 370 :
A man bought an article for Rs $x$ and sold is for Rs $16$ .If his loss percent was $x$ per cent ,find the cost price of the article.
Question 371 :
State the nature of the given quadratic equation $2x^2 +6x + \cfrac{9}{2} = 0$
Question 372 :
If the graph of $f\left(x\right)=x^{2}+\left(3-k\right)x+k,\left(where\ k\in\ R\right)$ lies above and below $x-axis$, then $k$ cannot be
Question 373 :
Assertion (A): The roots of $(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0$  are real<br/>Reason (R): A quadratic equation with non-negative discriminant has real roots .<br/>
Question 374 :
If $a(p+q)^{2}+2 b p q+c=0$ and $a(p+r)^{2}+2 b p r+c=0$ <br> $(a \neq 0),$ then,
Question 375 :
If (x-a)(x-b)+(x-b)(x-a)=0 has equal roots, then the relation between a, b is 
Question 376 :
In the following, determine whether the given quadratic equation have real roots and if so, find the roots :<br/>$\sqrt{3}x^2 \, + \, 10x \, - \, 8\sqrt{3} \, = \, 0$
Question 377 :
The value of $a$ for which the equation $a ^ { 2 } + 2 a + \csc ^ { 2 } \pi ( a + x ) = 0$ has a solution, is/are
Question 378 :
Let $r,s,t$ be roots of the equation $8x^3+1001x+2008=0$. The value of $(r+s)^3+(s+t) ^3+(t+r) ^3$is
Question 379 :
The rectangular fence is enclosed with an area $16$cm$^{2}$. The width of the field is $6$ cm longer than the length of the fields. What are the dimensions of the field?<br/>
Question 380 :
If $a, b$ and $c$ are in arithmetic progression, then the roots of the equation $ax^{2} - 2bx + c = 0$ are 
Question 381 :
All the values of '$a$' for which the quadratic expression $ax^2+(a-2)x-2$ is negative for exactly two integral values of $x$ may lie in
Question 382 :
For what value of $k$ is $x^2 + kx + 9=(x+3)^2$?
Question 383 :
The coefficient of $x$ in the equation $x^2+px+q=0$ was wrongly written as $17$ in place of$13$ and the roots thus found was $-2$ and $-15$.<br>Then the roots of the correct equation are
Question 384 :
If the equation $\displaystyle\frac{x^{2}-bx}{ax-c}=\frac{m-1}{m+1}$has roots equal in magnitude but opposite in sign, then $m=$<br>
Question 386 :
The number of integral values of $a$ for which the quadratic expression $(x-a)(x-10)+1$ can be factored as a product $(x+\alpha)(x+\beta)$ of two factors $\alpha, \beta, \in I$, is
Question 387 :
 If  the sum of the roots of the quadratic  equation $ax^2+bx+c=0$  is equal to the sum of the square of their reciprocals, then  $\dfrac{a}{c},\dfrac{b}{a}$ and $\dfrac{c}{b}$ are in<br/>
Question 388 :
Given expression is $x^{2} - 3xb + 5 = 0$. If $x = 1$ is a solution, what is $b$?
Question 389 :
If $m_1$ and $m_2$ are the roots of the equation $x^2+\left(\sqrt{3}+2\right)x+\left(\sqrt{3}-1\right)=0$, then the area of the triangle formed by the lines $y=m_1x,y=m_2x$ and $y=2$ is :
Question 390 :
$\alpha ,\beta $ are roots of the equation $2{x^2} - 5x - 6 = 0$ then
Question 391 :
If both the roots of the equation ${ x }^{ 2 }-32x+c=0$ are prime numbers then the possible values of $c$ are
Question 392 :
If <b>p</b> and <b>q</b> are positive then the roots of the equation $x^2-px-q=0$ are-
Question 393 :
If $22^3 +23^3+24^3+.........+88^3 $is divided by 110 then the remainder will be
Question 394 :
The roots of the equation $\displaystyle x^{2}-px+q=0$ are consecutive integers. Find the discriminate of the equation.
Question 396 :
If $\alpha$, $\beta$ are the roots of the equation $a{ x }^{ 2 }+bx+x=0$, then the roots of the equation $\left( a+b+c \right) { x }^{ 2 }-\left( b+2c \right) x+c=0$ are
Question 397 :
If $x = 3t, y = 1/ 2(t + 1)$, then the value of $t$ for which $x = 2y$ is
Question 398 :
$(a^{4}-1)x^{2}-(a^{2}+1)(sin^{-1}sin^{3} 2)x+(cos^{-1}cos2)(a^{2}-1) =0$.<br>.Find the set of values of a so that above equation have roots of opposite in sign.<br><br><br>
Question 399 :
If $|2x + 3|\le 9$ and $2x + 3 < 0$, then
Question 400 :
Number of positive integral values of $b$ for which both roots of the quadratic equation $\displaystyle x^2 + bx - 16 = 0$ are integers, is 
Question 401 :
If a,b,c >0 and $a=2b+3c$, then the roots of the equation $ax^2+bx+c=0$ are real if
Question 402 :
If the quadratic equation $ax^2 + bx + 6 = 0$does not have distinct real roots, thenthe least value of $2a + b$ is
Question 403 :
The coordinates of a point on the line y=x where perpendicular from the line 3x+4y=12 is 4 units, are
Question 405 :
Which of the following are the co-ordinates of the centre of the circle that passes through $P(6, 6), Q(3, 7)$ and $R(3, 3)$?
Question 407 :
The ratio in which the line joining the points $(3, 4)$ and $(5, 6)$ is divided by $x-$axis :
Question 408 :
Slope of the line $AB$ is $-\dfrac {4}{3}$. Co-ordinates of points $A$ and $B$ are $(x, -5)$ and $(-5, 3)$ respectively. What is the value of $x$
Question 409 :
The coordinates of $A, B$ and $C$ are $(5, 5), (2, 1)$ and $(0, k)$ respectively. The value of $k$ that makes $\overline {AB} + \overline {BC}$ as small as possible is
Question 410 :
$M(2, 6)$ is the midpoint of $\overline {AB}$. If $A$ has coordinates $(10, 12)$, the coordinates of $B$ are
Question 411 :
The point which lies in the perpendicular bisector of the line segment joining the points A (-2, -5) and B (2,5) is
Question 412 :
A Cartesian plane consists of two mutually _____ lines intersecting at their zeros.  
Question 413 : <br/>Let $\mathrm{P}(\mathrm{x}_{1},\mathrm{y}_{1})\mathrm{b}\mathrm{e}$ any point on the cartesian plane then match the following lists:<br/> <br/><table class="table table-bordered"><tbody><tr><td> LIST - I    </td><td> LIST - II</td></tr><tr><td> $\mathrm{A})$ The distance from $\mathrm{P}$ to X-axis</td><td>1) $0$</td></tr><tr><td> $\mathrm{B})$ The distance from $\mathrm{P}$ to Y-axis</td><td>2) $|\mathrm{y}_{1}|$</td></tr><tr><td> $\mathrm{C})$ The distance from $\mathrm{P}$ to origin is </td><td> 3) $\sqrt{x_{1}^{2}+y_{1}^{2}}$ </td></tr><tr><td> </td><td>4)$ |x_{1}|$                                   </td></tr></tbody></table>
Question 414 :
If a point $C$ be the mid-point of a line segment $AB$, then $AC = BC = (...) AB$.
Question 415 :
The distance between the points (sin x, cos x) and (cos x -sin x) is
Question 416 :
The coordinates of the point of intersection of X-axis and Y-axis is( 0,0)<br/>State true or false.<br/>
Question 417 :
The line $x+y=4$ divides the line joining the points $(-1,1)$ and $(5,7)$ in the ratio
Question 418 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?
Question 419 :
The coordinates of $A$ and $B$ are $(1, 2) $ and $(2, 3)$. Find the coordinates of $R $, so that $A-R-B$  and   $\displaystyle \frac{AR}{RB} = \frac{4}{3}$.<br/>
Question 420 :
If Q$\displaystyle \left ( \frac{a}{3},4 \right )$ is the mid-point of the line segment joining the points A(-6,5) and B(-2,3), then the value of 'a' is
Question 422 :
Find the distance from the point (2, 3) to the line 3x + 4y + 9 = 0
Question 423 :
The centroid of the triangle with vertices (2,6), (-5,6) and (9,3) is
Question 424 :
If the points (1,1) (2,3) and (5,-1) form a right triangle, then the hypotenuse is of length
Question 425 :
The vertices P, Q, R, and S of a parallelogram are at (3,-5), (-5,-4), (7,10) and (15,9) respectively The length of the diagonal PR is
Question 426 :
How far is the line 3x - 4y + 15 = 0 from the origin?
Question 428 :
A rectangular hyperbola whose cente is C is cut by any circle of radius r in four point P, Q, R, S. The value of$CP^{2}+CQ^{2}+CR^{2}+CS^{2}$ is equal to :
Question 429 :
The point at which the two coordinate axes meet is called the
Question 431 :
The ratio in which the line segment joining (3,4) and (-2,1) is divided by the y-axis is
Question 433 :
If a point $P\left(\displaystyle\frac{23}{5}, \frac{33}{5}\right)$ divides line AB joining two points $A(3, 5)$ and $B(x, y)$ internally in ratio of $2:3$, then the values of x and y will be.
Question 434 :
Find the co-ordinates of the mid point of a point that divides AB in the ratio 3 : 2.
Question 435 :
A line is of length $10$ m and one end is $(2,-3)$, the $x$ - co-ordinate of the other is $8$, then its $y$- coordinate is:
Question 436 :
If A(x,0), B(-4,6), and C(14, -2) form an isosceles triangle with AB=AC, then x=
Question 437 :
Find the distance from the point (5, -3) to the line 7x - 4y - 28 = 0
Question 438 :
Find the value of $x$ if the distance between the points $(2, -11)$ and $(x, -3)$ is $10$ units.
Question 439 :
A student moves $\sqrt {2x} km$ east from his residence and then moves x km north. He then goes x km north east and finally he takes a turn of $90^{\circ}$ towards right and moves a distance x km and reaches his school. What is the shortest distance of the school from his residence?
Question 440 :
Given the points $A(-3, 7)$ and $B(5, -9)$, determine the coordinates of point P on directed line segment that partitions in the ratio $\dfrac{1}{4}$.
Question 442 :
If $P \left( \dfrac{a}{3}, 4\right)$ is the mid-point of the line segment joining the points $Q ( 6, 5) $  and $R( 2, 3)$, then the value of $a$ is <br/>
Question 444 :
The points $(-2, -1), (1, 0),(4, 3),$ and $(1, 2)$ are the vertices
Question 445 :
$P$ is the point $(-5,3)$ and $Q$ is the point $(-5,m)$. If the length of the straight line $PQ$ is $8$ units, then the possible value of $m$ is:
Question 446 :
Given the points $A(-1,3)$ and $B(4,9)$.Find the co-ordinates of the mid-point of $AB$
Question 447 :
A(2,6) and B(1,7) are two vertices of a triangle ABC and the centroid is (5,7) The coordinates of C are
Question 448 :
An isosceles triangle has vertices at (4,0), (-4,0), and (0,8) The length of the equal sides is
Question 449 :
If the distance between the points $(4, p)$ and $(1, 0)$ is $5$, then the value of $p$ is:<br/>
Question 450 :
The coordinates of the midpointof a line segment joining$P ( 5,7 )$ and Q $( - 3,3 )$ are
Question 451 :
The distance between the points $(3,5)$ and $(x,8)$ is $5$ units. Then the value of $x$ 
Question 452 :
A pair of numerical coordinates is required to specify each point in a ......... plane.
Question 453 :
The point which lies on the perpendicular bisector of the line segment joining the points $P(-2,0)$ and $Q(2,5)$ is:
Question 454 :
The coordinate of point which divides the line segment joining points $A(0,0)$ and $B(9,12)$ in the ratio $1:2$, are
Question 455 :
The line joining $(5, 0)$ to $(10\cos\theta, 10\sin\theta)$ is divided internally in the ratio $2:3$ at $P$, then the locus of $P$ is
Question 456 :
The point which divides the line segmentjoining the points (3, 5) and (8, 10) internallyin the ratio 2 :3 is:
Question 457 :
The ratio in which X-axis divides the line segment joining $(3,6)$ and $(12,-3)$ is
Question 458 :
The ratio in which the joint of (-3, 10), (6, -8)is divided by (-1, 6),
Question 459 :
In what ratio does the point P(-2, 3) divide theline segment joining the points A(-3, 5) andB(4, -9) internally?
Question 460 :
There are two point $P(1,-4)$ and $Q(4,2)$. Find a point X dividing the line PQ in the ratio $1:2$
Question 461 :
The mid-point of line segment joining thepoints (3, 0) and (-1, 4) is :
Question 462 :
The point P divides the line segment joining the points $\displaystyle A\left ( 2,1 \right )$ and $\displaystyle B\left ( 5,-8\right )$ such that $ \frac{AP}{AB}=\frac{1}{3}$ If P lies on the line $\displaystyle 2x+y+k=0$<br/>then the value of k is-
Question 463 :
The points $A$ $(x_1, y_1), B (x_2, y_2)$ and $C (x_3, y_3)$ are the vertices of $\Delta $ ABC.<br/>The median $AD$ meets $BC$ at $D$.<br/>Find the coordinates of points Q and R on medians BE and CF, respectively such that $BQ : QE = 2 : 1$ and $CR : RF = 2 : 1$.<br/>
Question 464 :
The ratio in which the line $3x+y-9=0$ divides the line segment joining points (1, 3) and (2, 7) is:
Question 465 :
In what ratio does the point $\begin{pmatrix} \dfrac { 1 }{ 2 },\dfrac { -3 }{ 2 } \end{pmatrix}$ divide the line segment joining the points $(3,5)$ and $(-7,9)$?<br/>
Question 466 :
Find the coordinates of the point $P$ which divides line segment $QR$ internally in the ratio $m:n$ in the following example:<br/>$Q \equiv (6, -5), R \equiv (-10, 2)$ and $m:n = 3:4$
Question 467 :
If X-axis divides the line joining $(3,-4)$ and $(5,6)$ in the ratio $a:b $, then what is the value of $\dfrac{a}{b}$?
Question 468 :
Find the ratio in which the line segment joining the points $(3,5)$ and $(-4,2)$ is divided by y-axis.<br/>
Question 469 :
What is the ratio in which $P(2, 5)$ divides the line joining the points $(8, 2)$ and $(-6, 9)$?
Question 470 :
What is the approximate slope of a line perpendicular to the line $\sqrt{11}x+\sqrt{5}y=2$?
Question 471 : <p>x-axis divides line segment joining points (2, -3) and (5,6) in the ratio</p>
Question 472 :
The ratio by which the line $2x + 5y - 7 = 0$ divides the straight line joining the points $(-4, 7) $ and $(6, -5)$ is
Question 473 :
The straight line $3x+y=9$ divides the line segment joining the points $(1,\,3)$ and $(2,\,7)$ in the ratio
Question 474 :
If the line joining A(2, 3) and B(-5, 7) is cut by X - axis at P, then find AP : PB.
Question 475 :
If the line $2x+y=k$ passes through the point which divides the line segment joining the point $(1,1)$ & $(2,4)$ in the ratio $3:2$ then $k$ equal
Question 476 :
If the point P (2, 1) lies on the segment joining Points A (4, 2) and B (8, 4) then
Question 477 :
Length of the median from B on AC where A (-1, 3), B (1, -1), C (5, 1) is
Question 478 :
The coordinates of one end of a diameter of a circle are $(5, -7)$. If the coordinates of the centre be $(7, 3)$, the co ordinates of the other end of the diameter are
Question 479 :
What will be the value of $y$ if the point $\begin{pmatrix} \dfrac { 23 }{ 5 },y \end{pmatrix}$, divides the line segment joining the points $(5,7)$ and $(4,5)$ in the ratio $2:3$ internally?<br/>
Question 480 :
The coordinates of the point which divides the line segment joining the points $(-7, 4)$ and $(-6, -5)$ internally in the ratio $7 : 2$ is:
Question 481 :
Find the coordinates of the point which divides the line segment joining $(-3,5)$ and $(4,-9)$ in the ratio $1:6$ internally.
Question 482 :
Let $A(-6,-5)$ and $B(-6,4)$ be two points such that a point $P$ on the line $AB$ satisfies $AP=\cfrac{2}{9}AB$. Find the point $P$.
Question 483 :
Find the midpoint of the segment joining the points $(4, -2)$ and $(-8,6)$.
Question 484 :
If $P(2, 2), Q(-2, 4)$ and $R(3, 4)$ are the vertices of $\Delta PQR$ then the equation of the median through vertex R is _______.
Question 485 :
In what ratio is the line segment joining the points $(4, 6)$ and $(-7, -1)$ Is divided by $X$-axis ?
Question 486 :
<i></i>If the coordinates of opposite vertices of a square are $(1,3)$ and $(6,0)$, the length if a side od a square is 
Question 487 :
Find the distance between the points $(-1,-3)$ and the midpoint of the line segment joining $(2,4)$ and $(4,6)$.
Question 488 :
$A(5,1)$, $B(1,5)$ and $C(-3, -1)$ are the vertices of $\Delta ABC$. The length of its median AD is:
Question 489 :
The ratio in which the line $3x+y=9$ divides the line sequent joining the points $(1,3)$ and $(2,7)$ is given by
Question 490 :
If the point $(x_1 + t (x_2 -x_1), y_1+t (y_2-y_1))$ divides the join of $(x_1, y_1)$ and $(x_2, y_2)$ internally, then
Question 491 :
The point which is equi-distant from the points $(0,0),(0,8) and (4,6)$ is 
Question 492 :
If P(x, y) is any point on the line joining thepoints (a, 0) and (0, b) then the value of$\displaystyle \frac{x}{a} + \frac{y}{b}$
Question 493 :
The line segment joining the points $(3, -4)$ and $(1, 2) $ is trisected at the points P and Q. If the and co-ordinates of P and Q are $(p, -2)$ and $(\frac{5}{3}, q)$ respectively, find the value of p and q.
Question 494 :
In how many maximum equal parts, a rectangular cake can be divided using three straight cuts?
Question 495 :
Point $P$ divide a line segment $AB$ in the ratio $5:6$ where $A(0,0)$ and $B(11,0)$. Find the coordinate of the point $P$:
Question 496 :
If we take $11$ points on a ray which is drawn at acute angle to a line segment, then the line segment can be divided into maximum _____ equal points.
Question 497 :
The coordinates of the third vertex of an equilateral triangle whose two vertices are at $(3, 4), (-2 3)$ are ______.
Question 499 :
State whether the following statements are true or false . Justify your answer.<br>Point $ A(-6 , 10) , B(-4 , 6) $ and $ C(3 , -8) $ are collinear such that $ AB = \dfrac{2}{9} AC $ .
Question 500 :
State whether the following statements are true or false . Justify your answer.<br>The points $ (0 , 5) , (0 , -9) $ and $ (3 , 6) $ are collinear .
Question 501 :
Select the correct option.<br>The value of $p$, for which the points $A(3,1) , B (5, p)$ and $C (7, -5)$ are collinear, is
Question 502 :
Number of points with integral co-ordinates that lie inside a triangle whose co-ordinate are (0,0), (0, 21) and (21, 0)
Question 503 :
The vertices of a triangle are $A(3,4)$, $B(7,2)$ and $C(-2, -5)$. Find the length of the median through the vertex A.<br/>
Question 504 :
The mid point of the segment joining $(2a, 4)$ and $(-2, 2b)$ is $(1, 2a+1)$, then value of b is
Question 505 :
If $Q(0, 1)$ is equidistant from $P(5, -3)$ and $R(x, 6)$, find the values of x. Also find the distances QR and PQ.
Question 506 :
If the coordinates of the extermities of diagonal of a square are $(2,-1)$ and $(6,2)$, then the coordinates of extremities of other diagonal are
Question 507 :
$ABC$ is an equilateral triangle. If the coordinates of two of its vertices are ($1, 3)$ and $(-2, 7)$ the coordinates of the third vertex can be<br>
Question 509 :
The points $A\left( {2a,\,4a} \right),\,B\left( {2a,\,6a} \right)\,$ and $C\left( {2a + \sqrt 3 a,\,5a} \right)$ (when $a>0$) are vertices of 
Question 510 :
The points $(-2,2)$, $(8, -2)$ and $(-4, -3)$ are the vertices of a:
Question 511 :
If $a> 0$ and $P(-a, 0), Q(a, 0)$ and $R(1,1) $ are three points such that $\displaystyle \left|(PR)^{2}-(QR)^{2} \right| = 12,$ then<br/>
Question 512 :
If $P\left( x,y,z \right) $ is a point on the line segment joining $Q\left( 2,2,4 \right) $ and $R\left( 3,5,6 \right) $ such that the projections of $OP$ on the axis are $\cfrac { 13 }{ 5 } ,\cfrac { 19 }{ 5 } ,\cfrac { 26 }{ 5 } $ respectively, then $P$ divides $QR$ in the ratio
Question 513 :
The point whose abscissa is equal to its ordinate and which is equidistant from $A(5,0)$ and $B(0,3)$ is
Question 514 :
If two vertices of a parellelogram are $(3,2)$ and $(-1,0)$ and the diagonals intersect at $(2, -5)$, then the other two vertices are:
Question 515 :
Determine the ratio in which the line $3x+y-9=0$ divides the line segment joining the points $(1,3)$ and $(2,7)$<br>
Question 516 :
If the line $2x+y=k$ passes through the point which divides the line segment joining the points $(1, 1)$ and $(2, 4)$ in the ratio $3 : 2$ ,then $k$ equals:
Question 517 :
If $(-6, -4), (3, 5), (-2, 1)$ are the vertices of a parallelogram, then remaining vertex can be
Question 518 :
$\mathrm{P}_{1},\ \mathrm{P}_{2},\ldots\ldots.,\ \mathrm{P}_{\mathrm{n}}$ are points on the line $y=x$ lying in the positive quadrant such that $\mathrm{O}\mathrm{P}_{\mathrm{n}}=n\cdot\mathrm{O}\mathrm{P}_{\mathrm{n}-1}$, where $\mathrm{O}$ is the origin. If $\mathrm{O}\mathrm{P}_1=1$ and the coordinates of $\mathrm{P}_{\mathrm{n}}$ are $(2520\sqrt{2},2520\sqrt{2})$, then $n$ is equal to<br/>
Question 519 :
Find the ratio in  which the point $P(2,y)$ divides the line segment joining the point $A(-2,2)$ and $B(3,7)$. Also find the value of $y$.<br/>
Question 520 :
If $\displaystyle A \left(\frac{2c}{a},\frac{c}{b}\right),B\left(\frac{c}{a},0\right)$ and $\displaystyle C\left(\frac{1+c}{a},\frac{1}{b}\right) $ are three points, then<br/>
Question 521 :
Consider the points $A(0,\ 1)$ and $B(2,\ 0)$, and $P$ be a point on the line $4x+3y+9=0$. The coordinates of $P$ such that $|PA-PB|$ is maximum are
Question 522 :
If $P \left( \dfrac{a}{3},\dfrac{b}{2} \right)$ is the mid-point of the line segment joining $A(-4,3)$ and $B(-2,4)$ then $(a,b)$ is 
Question 523 :
If a line intercepted between the coordinate axes is trisected at a point $A(4, 3),$ which is nearer to $x-$axis, then its equation is
Question 524 :
Three points $\left( {0,0} \right),\left( {3,\sqrt 3 } \right),\left( {3,\lambda } \right)$ from an equilateral triangle, then $\lambda $ is equal to
Question 525 :
If $\displaystyle(-1,2),(2,-1)$ and $\displaystyle(3,1)$ are any three vertices of a parallelogram then the fourth vertex $\displaystyle(a,b)$ will be such that
Question 526 :
The points given are $(1, 1)$, $(-2, 7)$ and $(3, 3)$.Find distance between the points.
Question 527 :
If the three distance points $\left( { t }_{ i\quad }2{ at }_{ i }+{ { at }^{ 3 }_{ i } } \right) \quad for\quad i=1,2,3$ are collinear then the sum of the abscissae of the points is
Question 528 :
Find the point on the x-axis which is equidistant from the points $(-2,5)$ and $(2, -3)$. Hence find the area of the triangle formed by these points<br>
Question 529 :
$ABC$ is an isosceles triangle. If the coordinates of the base are $B(1,3)$ and $C(-2,7)$. The vertex $A$ can be
Question 530 :
The region between an arc and two radii joining the centre to the end points of the arc is called
Question 532 :
The sum of the circumference and diameter of a circle is $116 cm$. Find its radius.
Question 533 :
A rectangular sheet of acrylic is 50 cm by 25 cm . From it 60 circular buttons, each of diameter 2.8 cm have been cut out. The area of the remaining sheet is
Question 534 :
What is the area of the sector of a circle, whose radius is $6\ m$ when the angle at the centre is $42^{\circ}$?
Question 535 :
Which of the following is not a sector of a circle?<br/>
Question 536 :
In a circle of radius 21 cm an arc subtends an angle of $\displaystyle 56^{\circ} $ at the centre of the circle. The length of the arc is
Question 537 :
Find the circumference of the circle with the following radius : 10 cm
Question 538 :
The perimeter of a sector of a circle is 37cm. If its radius is 7cm, then its arc length is
Question 539 :
The circumference of a circular field is $308 m$. Find its radius in metres.
Question 541 :
The diameter of a wheel of a cycle is 21 cm How far will it go in 28 complete revolutions?
Question 542 :
If 'c' be the circumference and 'd' be the diameter then the value of$ \displaystyle \pi $ is equal to-<br>
Question 543 :
A square is inscribed in a circle of radius $7\: cm$. Find area of the square.
Question 544 :
A wire of length $36$ cm is bent in the form of a semicircle. What is the radius of the semicircle?
Question 545 :
The number of circular pipes with an inside diameter of $1$ cm which will carry the same amount of water as a pipe with an inside diameter of $6$ cm is:
Question 546 :
Choose the correct answer from the alternative given.<br/>A can go round a circular path $8$ times in $40$ minutes. If the diameter of the circle is increased to $10$ times the original diameter, the time required by A to go round the new path once travelling at the same speed as before is:
Question 547 :
The area of a circle is $24.64$. $\displaystyle m^{2}$ What is the circumference of the circle ?
Question 548 :
What is the minimum radius $(>1)$ of a circle whose circumference is an integer?
Question 549 :
The radius of a circular wheel is $1.75\ m$. The number of revolutions that it will make in covering $11\ kms$ is:
Question 550 :
The radius of a circle whose area is equal to the sum of the areas of two circles where radii are 5 cm and 12 cm is
Question 551 :
A rope by which a cow is tethered is in reased from 16m to 23m. How much additional ground does it have to graze now?
Question 552 :
The length of a minute hand of a wall clock is $8.4\ cm$. Find the area swept by it in half an hour.
Question 553 :
Size of a tile is $9$ inches by $9$ inches. The number of tiles needed to cover a floor of $12$ feet by $18$ feet is
Question 554 :
If the radius of a circle is tripled, the ares becomes.
Question 556 :
If one side of a square is 2.4 m. Then what will be the area of the circle inscribed in the square?
Question 558 :
The ratio of areas of square and circle is givenn : 1 where n is a natural number. If the ratio of side of square and radius of circle is k :1, where k is a natural number, then n will be multiple of
Question 559 :
If the diameter of a circle is increased by 200% then its area is increased by<br>
Question 560 :
If radius of a circle is increased to twice its original length, how much will the area of the circle increase ?
Question 561 :
$r$ is the radius and $l$  is the length of an arc. The area of a sector is ______.
Question 562 :
Area of a sector having radius 12 cm and arc length 21 cm is
Question 563 :
If a circle is divided into two equal parts, then equal part of the circle is called ________.
Question 564 :
If the area of the circle be $ \displaystyle 154 cm^{2},$ then its radius is equal to:
Question 565 :
The diameter of a circle is divided into n equal parts.On each part a semicircle is constructed. as n becomes very large, the sum of the lengths of the arcs of the semicircles approaches a length:
Question 566 :
The angle of sector with area equal to one fifth of total area of whole circle 
Question 567 :
The distance between the two parallel chords of length 8 cm and 6 cm in a circle of diameter 10 cm if the chords lic on the same side of the centre is
Question 568 :
If the radius of a circle increased by 20% then the corresponding increase in the area of circle is ................
Question 569 :
A cow is tied to a pole, fixed to the midpoint of a side of a square field of dimensions $40\ m\times 40\ m$, by means of $14\ m$ long rope. Find the area that the cow can graze.
Question 570 :
Given, $\displaystyle A = \frac{S}{360}\times \pi r^2$<br/>$A$ is the area of setor, $ S$ is the angle measure in degrees of the sector and $r$ is the radius of the circle. Find $r$ in terms of $A$ and $S$.
Question 571 :
If the difference between the circumference and radius of a circle is 37 cm then its diameter is
Question 573 :
The area of two circles are in the ratio $25 : 36$. Then the ratio of their circumference is _________.
Question 574 :
The area of a sector formed by two mutually perpendicular radii in $\odot \left( 0,5cm \right) $ is ............... ${cm}^{2}$.
Question 575 :
If the number of units in the circumference of a circle is same is same as the number of units in the area then the radius of the circle will be
Question 576 :
If the radius of a circle is $\dfrac{7}{\sqrt{\pi}}$, what is the area of the circle (in $cm^2$)?
Question 577 :
The area of a sector is 1/18th of the area of the circle The sectorial angle is
Question 580 :
Given radius = $11 $ cm, area of the sector is $230 $ $cm^2$. Find the length of the arc $SR$.<br/>
Question 581 :
The radius of a circle is $3.5$ cm and area of the sector is $3.85$ $cm^2$. Find the length of the corresponding arc.
Question 582 :
The area of the part of the square filed in which a horse tied to a fixed pole at one comer by means of a $10\ m$ rope, can graze is 
Question 583 :
If the diameter of a circle is $14$ cm, then its circumference is
Question 584 :
A sector is cut off from a circle of radius $21$ cm The angle of the sector is $\displaystyle 120^{\circ} $ The length of its arc is [Take $\displaystyle \pi =\frac{22}{7} $]
Question 585 :
The difference between circumference and radius of a circle is $37 $m. The circumference of that circle is 
Question 586 :
The minute hand of a clock is $7\ cm$ long. Find the area traced by it on the clock face between $4{:}15$ p.m. and $4{:}35$ p.m.
Question 587 :
A horse is tied to a post by a rope If the horse moves along a circular path always keep the rope tight and describes $88$ metres when it has traced out $\displaystyle 72^{\circ}$ at the center, then the length of rope is 
Question 588 :
A man runs with the speed of $15.84\ km/hr$. He completes $12$ rounds of a circular ground in one hour, find the area of the ground in $sq. m$.
Question 589 :
The area of a sector of a circle of radius $16$ cm cut off by an arc which is $18.5$ cm long is 
Question 590 :
Which of the following shapes of equal perimeter the one having the largest areas is
Question 591 :
The radii of two circles are $25 cm$ and $18 cm$. Find the radius of the circle which has a circumference equal to the sum of the circumference of these two circles.
Question 592 :
Find the area of sector whose length is $30\ \pi$ cm and angles of the sector is $40^o$.
Question 593 :
A sector of $120^{\circ}$cut out from a circlehas an area of $9\displaystyle \frac {3}{7}$ sq cm. The radius ofthe circle is
Question 594 :
What is the area of the circle whose equation is $(x - 3)^{2} + (y + 5)^{2} = 18$?
Question 595 :
A pizza parlor cuts its $14$-inch (diameter) pizzas into $8$ equal slices. What is the size (in square inches) of each slice?
Question 597 :
A circular ground whose diameter is $140$meters is to be fenced by wire three times around its circumference. Find the length of wire needed.<br><br>$[$use $\displaystyle \pi = \frac {22}{7}$ <br> $]$
Question 598 :
The area of a sector with  perimeter as  $45\ cm$ and radius as $6 \ cm$ is
Question 599 :
Ratio of circumference of a circle to its radius is always $2 \pi : 1$
Question 600 :
If the ratio of circumference of two circles is $4 : 9$, then what is the ratio of their areas is?
Question 601 :
In $\bigodot (P, 6)$, the length of an arc is $\pi$. Then the arc subtends an angle of measure ___at the center.
Question 602 :
A running track is the ring formed by two concentric circles. It is $10\ m$ wide. The circumferences of the two circle differ by about.
Question 603 : <p>If the circumference of a circle is $8$ units and arc length of major sector is $5$ units then find the length of minor sector.</p>
Question 604 :
A chord of a circle of radius 6 cm subtends an angle of $\displaystyle 60^{\circ}$ at the centre of the circle. The area of the minor segment is<br/>(use $\displaystyle \pi =3.14$)
Question 605 :
An express train is running between two stations with a uniform speed. If the diameter of each wheel of the train is $42 cm$ and each wheel makes $1200$ revolutions per minute, find the speed of the train.
Question 606 :
A circular wire of radius $7$ cm is cut and bend again into an arc of a circle of radius $12$ cm. The angle subtended by the arc at the centre is<br/>
Question 607 :
The minute hand of a clock is 14 cm long If it moves between 8:00 AM and 8:45 AM What is the area covered by it on the face of the clock?
Question 608 :
Let $\triangle PQR$ is inscribed in the circle ${ x }^{ 2 }+{ y }^{ 2 }=25$. If $Q$ and $R$ have coordinates $(3,4)$ and $(-4,3)$ respectively, then $\angle QPR$ is equal to
Question 609 :
Find the diameter of a wheel that makes $113$ revolutions to go $2 km 26dm$. $ \displaystyle \left ( \pi =\frac{22}{7} \right )$
Question 610 :
Find the area of a sector of a circle with radius $6$cm if angle of the sector is $60^o$.
Question 611 :
A polygon has 44 diagonals, The number of its sides is
Question 612 :
The radius of a circle is increased by 1 cmthen the ratio of the new circumference to the new diameter is
Question 613 :
A sector is cut from a circle of radius $21$ cm. The angle of the sector is $150^o$. Find the length of its arc and area.
Question 614 :
In covering a distance s meters, a circular wheel of radius r m makes $\dfrac{s}{2\pi r}$ revolutions. Is the statement true ? Why ?
Question 615 :
The area of a circle is 314 sq. cm and area of its minor sector is 31.4 sq. cm. Find thearea of its major sector.
Question 616 :
The angle subtended at the centre of a circle of radius $3cm$ by an arc of length $1cm$ is:
Question 617 :
If the radius of a circle is increased $100$%, the area is increased.
Question 618 :
The radii of two circles are in the ratio $3 : 8$. If the difference between their areas is$2695\pi \: cm^{2}$ ,find the area of the smaller circle.
Question 619 :
A wire in the shape of an  equilateral triangle encloses  an area of $s$ $cm^2$. If the same  wire is bent to form a circle,  then the area of the circle will  be<br/>
Question 620 :
If the sector of a circle of diameter $10$ cm subtends an angle of $144^{\circ}$ at the centre, then the length of the arc of the sector is
Question 621 :
The minute hand of a clock is 7 cm long Find the area traced out by the minute hand of the clock between 6 pm to 6:30 pm<br>
Question 622 :
The circumference of a circle exceeds its diameter by $180$ cm. Then  the area of the circle
Question 623 :
State whether True or FalseThe diameter of a circle is $10 cm$. Find the length of the arc, when the corresponding central angle is as given below.  $(\pi =3.14)$<br/>$270^{\circ}$ is 12.56cm<br/>
Question 624 :
Consider a circle with unit radius. There are seven adjacent sectors, $S_1, S_2, S_3, ............ S_7$, in the circle such that their total area is $\dfrac {1}{8}$ of the area of the circle. Further, the area of the $j^{th}$ sector is twice that of the $(j-1)^{th}$ sector, for $j$ $=$ $2, ........... 7$. What is the area of sector $S_1?$<br/>
Question 625 :
The radius of a circle is $14$ m, then the circumference of a circle is 
Question 626 :
The minute hand of a clock is $10$ cm long. Find the area of the face of the clock described by the minute hand between $9$A.M and $9.35$A.M.
Question 627 :
If the circumference of a circle is reduced by $50\%$ the area of the circle is reduced by:
Question 628 :
The area of a circle drawn with its diameter as the diagonal of a cube of side of length 1 cm each is :
Question 629 :
If the diameter of a semicircular protractor is $14cm$ then find its perimeter.
Question 630 :
The perimeter of a quadrant of a circle of radius $\dfrac{7}{2}$ cm is:<br/>
Question 631 :
If a bicycle wheel makes $5000$ revolution in moving $11$ km, then diameter of wheel is
Question 632 :
A wire bent in the form a square incloses an area of 484 $\displaystyle m^{2}$ but if the same wire is bent in the form of a circle the area enclosed will be <br>
Question 633 :
The ratio of the slant height of two right cones of equal base is 3 : 2 then the ratio of their volumes is <br>
Question 634 :
The area of a sector of a circle of angle $\displaystyle 60^{\circ}$ is $\displaystyle \frac{66}{7}cm^{2}$ then the area of the corresponding major sector is<br>
Question 635 :
A sphere with diameter $50$ cm intersects a plane $14$ cm from the center of the sphere. What is the number of square centimeters in the area of the circle formed?
Question 636 :
The remainder when$4{a^3} - 12{a^2} + 14a - 3$ is divided by $2a-1$, is
Question 638 :
State whether True or False.Divide: $x^2 + 3x -54 $ by $ x-6 $, then the answer is $x+9$.<br/>
Question 639 :
Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.$49x^2-81$<br/>
Question 642 :
If the quotient of $\displaystyle x^4 - 11x^3 + 44x^2 - 76x +48$. When divided by $(x^2 - 7x +12)$ is $Ax^2 + Bx + C$, then the descending order of A, B, C is
Question 643 :
What is the remainder, when<br>$(4{x^3} - 3{x^2} + 2x - 1)$ is divided by (x+2)?<br>
Question 644 :
If $\alpha$ and $\beta$ are the zeroes of the polynomial $4x^{2} + 3x + 7$, then $\dfrac{1}{\alpha }+\dfrac{1}{\beta }$ is equal to:<br/>
Question 645 :
If a polynomial $p(x)$ is divided by $x - a$ then remainder is<br/>
Question 646 :
State whether True or False.Divide: $12x^2 + 7xy -12y^2 $ by $ 3x + 4y $, then the answer is $x^4+2x^2+4$.<br/>
Question 650 :
Divide:$\left ( 15y^{4}- 16y^{3} + 9y^{2} - \cfrac{1}{3}y - \cfrac{50}{9} \right )$ by $(3y-2)$Answer: $5y^{3} + 2y^{2} - \cfrac{13}{3}y + \cfrac{25}{9}$
Question 651 :
What must be subtracted from $4x^4 - 2x^3 - 6x^2 + x - 5$, so that the result is exactly divisible by $2x^2 + x - 1$?
Question 652 :
Is $(3x^{2} + 5xy + 4y^{2})$ a factor of $ 9x^{4} + 3x^{3}y + 16x^{2} y^{2} + 24xy^{3}  + 32y^{4}$?<br/>
Question 653 :
Find the expression which is equivalent to : $\displaystyle \frac { { x }^{ 3 }+{ x }^{ 2 } }{ { x }^{ 4 }+{ x }^{ 3 } } $?
Question 654 :
The product of the roots of the quadratic equation $2x^{2}-8x+3=0$ is
Question 656 :
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and their coefficients.$2s^2-(1+2\sqrt 2)s+\sqrt 2$<br/>
Question 658 :
If $\alpha , \beta$ are the zeros of the polynomials $f(x) = x^2+x+1 $ then $\dfrac{1}{\alpha}+\dfrac{1}{\beta}=$________.
Question 659 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$a^2-b^2 ; a-b$
Question 660 :
If the roots of ${ x }^{ 2 }-2mx+{ m }^{ 2 }-1=0$ lie between $-2$ and $4$, then
Question 661 :
State whether true or false:Divide: $4a^2 + 12ab + 91b^2 -25c^2 $ by $ 2a + 3b + 5c $, then the answer is $2a+3b+5c$.<br/>
Question 662 :
Apply the division algorithm to find the remainder on dividing $p(x) = x^4 -3x^2 + 4x + 5$ by $g(x)= x^2 +1 -x.$
Question 664 :
Factorise the expressions and divide them as directed.$4yz(z^2 + 6z-  16)\div  2y(z + 8)$<br/>
Question 667 :
Find the value of a & b, if  $8{x^4} + 14{x^3} - 2{x^2} + ax + b$ is divisible by $4{x^2} + 3x - 2$
Question 668 :
If $a\ne 2$, which of the following is equal to $\cfrac { b\left( { a }^{ 2 }-4 \right) }{ ab-2b } $?
Question 669 :
State whether the following statement is true or false.After dividing $ (9x^{4}+3x^{3}y + 16x^{2}y^{2}) + 24xy^{3} + 32y^{4}$ by $ (3x^{2}+5xy + 4y^{2})$ we get<br/>$3x^{2}-4xy + 8y^{2}$
Question 672 :
If $P=\dfrac {{x}^{2}-36}{{x}^{2}-49}$ and $Q=\dfrac {x+6}{x+7}$ then the value of $\dfrac {P}{Q}$ is:
Question 674 :
Work out the following divisions.<br/>$96abc(3a -12) (5b +30)\div  144(a-  4) (b+  6)$<br/>
Question 676 :
The common quantity that must be added to each term of $a^{2}:b^{2}$ to make itequal to $a:b$ is:
Question 677 :
Simplify:$20(y + 4) (y^2 + 5y + 3) \div 5(y + 4)$<br/>
Question 679 :
What must be added to $x^3-3x^2-12x + 19$, so that the result is exactly divisible by $x^2 + x-6$?
Question 681 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$\displaystyle x^2-\frac{1}{4x^2}; x-\frac{1}{2x}$
Question 682 :
What is $\dfrac {x^{2} - 3x + 2}{x^{2} - 5x + 6} \div \dfrac {x^{2} - 5x + 4}{x^{2} - 7x + 12}$ equal to
Question 683 :
Find the Quotient and the Remainder when the first polynomial is divided by the second.$-6x^4 + 5x^2 + 111$ by $2x^2+1$
Question 684 :
Work out the following divisions.$10y(6y + 21) \div 5(2y + 7)$<br/>
Question 685 :
Choose the correct answer from the alternatives given.<br>If the expression $2x^2$ + 14x - 15 is divided by (x - 4). then the remainder is
Question 686 :
If a and b are such that the quadratic equation$\displaystyle ax^{2}-5x+c=0$ has 10 as the sum of the root and also as the product of the roots find a and b respectively
Question 687 :
Find the product of roots if the quadratic equation $ax^2+bx+c=0$ has exactly one non-zero root.
Question 688 :
Let $ p $and $q $be roots of the equation $x^{2}-2 x+A=0 $and let $r $and $s $be the roots of the equation $x^{2}-18 x+B=0 . $If $p<q< $ <br> $r<s $are in arithmetic progression, then the values of $A $and $B $are
Question 689 :
The value of $m$ for which the equation $\dfrac { a }{ x+a+m } +\dfrac { b }{ x+b+m } =1$ has roots equal in magnitude but opposite in sign is<br>
Question 690 :
If $\alpha, \beta$ are the root of quadratic equation $ax^2+bx+c=0$,then $\displaystyle \left ( a\alpha +b \right )^{-3}+\left ( a\beta +b \right )^{-3}=$
Question 691 :
Divide :$\displaystyle \left[ { x }^{ 4 }-{ \left( y+z \right)  }^{ 4 }\right] \ by \left[{ x }^{ 2 }+{ \left( y+z \right)  }^{ 2 }\right]$
Question 692 :
If $x^4 \, + \, 2x^3 \, - \, 3x^2 \, + \, x \, - \, 1$ is divided by $x - 2$. then the remainder is
Question 693 :
If $ \alpha, \beta $ be the roots of the equation $ a x^{2}+b x+c=0, $ then value of $\dfrac{ \left(a \alpha^{2}+c\right) }{(a \alpha+b)}+\dfrac{\left(a \beta^{2}+c\right)}{ (a \beta+b)} $ is
Question 694 :
Simplify: $\cfrac { { x }^{ 2 }-4x-21 }{ { x }^{ 2 }-9x+14 } $
Question 695 :
The roots of the equation $x^2 + kx -12=0$ will differ by unity only, when
Question 696 :
Find the Quotient and the Remainder when the first polynomial is divided by the second.<br/>$(x^3+1) $ by $(x+1)$
Question 697 :
The condition that the equation $x^2 + px + q = 0$, whose one root is the cube of the other root is :
Question 698 :
If ${(5{x}^{2}+14x+2)}^{2}-{(4{x}^{2}-5x+7)}^{2}$ is divided by ${x}^{2}+x+1$, then the quotient $q$ and the remainder $r$ are given by:
Question 699 :
If $\alpha, \beta$ be the zeros of the quadratic polynomial $2-3x-x^2$, then $\alpha+\beta=$<br>
Question 700 :
If equation $\displaystyle p{ x }^{ 2 }+9x+3=0$ has real roots, then find value of $p$.<br/>
Question 701 :
Using long division method, divide the polynomial$4p^3-4p^2+6p -\displaystyle \frac{5}{2}$ by $2p-1$
Question 702 :
Write whether the following statement is true or false. Justify your answer.A quadratic equation with integral coefficients has integral roots.
Question 703 :
Divide the following and write your answer in lowest terms: $\dfrac{x}{x+1}\div \dfrac{x^2}{x^2-1}$
Question 704 :
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $ax^2+bx+c$, then $\alpha + \beta=\dfrac {-b}{a}$ & $\alpha \beta=\dfrac {c}{a}$.
Question 705 :
If the equation$\displaystyle{ px }^{ 2 }+2x+p=0$ hastwo distinct roots if.
Question 706 :
If $3{p}^{2}=5p+2$ and $3{q}^{2}=5q+2$, where $p\ne q$, then $pq$ is equal to
Question 707 :
Calculate $\left( 6{ p }^{ 2 }+p-12 \right) \div \left( 2p+3 \right) $.
Question 709 :
Workout the following divisions<br/>$11a^3b^3(7c - 35) \div 3a^2b^2 (c - 5)$
Question 711 :
If $a, b$ are the roots of $x^2 + px + 1 = 0$ and $c, d$ are the roots of $x^2 + qx + 1 = 0,$ the value of $E = (a - c)(b - c)(a + d) ( b + d)$ is
Question 712 :
On dividing $x^3-3x^2+x+2$ by polynomial $g(x)$, the quotient and remainder were $x -2$ and $4 - 2x$ respectively, then $g(x)$ is<br/>
Question 714 :
If $\displaystyle \alpha ,\beta$are the roots of the quadratic equation$\displaystyle { x }^{ 2 }-8x+p=0$, find the value of p if$\displaystyle { \alpha }^{ 2 }+{ \beta }^{ 2 }=40$.
Question 715 :
The remainder obtained by dividing$ \displaystyle x^{n}-\frac{a}{b} $ by ax-b is
Question 716 :
If the ratio of the roots of ${x}^{2}+bx+c=0$ is equal to the ratio of the roots of ${x}^{2}+px+q=0$ then ${p}^{2}c-{b}^{2}q=$
Question 717 :
If one factor of the polynomial $x ^ { 3 } + 4 x ^ { 2 } - 3 x - 18$ is $x + 3,$ then the other factor is
Question 718 :
Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.$48y^2-13y-1$<br/>
Question 721 :
Simplify: $\displaystyle 7\left( 4x+5 \right) \left( 2x+6 \right) \div \left( 4x+5 \right) $
Question 722 :
Let $ p $ and $ q $ be real numbers such that $ p \neq 0, p^{3} \neq q $ and $ p^{3} $ $ \neq-q . $ If $ \alpha $ and $ \beta $ are non-zero complex numbers satisfying and $ \alpha+\beta=-p $ and $ \alpha^{3}+\beta^{3}=q, $ then a quadratic equation having $ \dfrac{\alpha}{\beta} $ and $ \dfrac{\beta}{\alpha} $ as its roots is
Question 724 :
The sum and product of zeros of the quadratic polynomial are - 5 and 3 respectively the quadratic polynomial is equal to<br>
Question 725 :
The condition that one root is twice the other root of the quadratic equation$\displaystyle x^{2}+px+q=0$ is
Question 727 :
If the roots of the equation $\dfrac{x^{2}-bx}{ax-c}=\dfrac{m-1}{m+1}$ are equal but opposite in sign, then the value of $m$ will be
Question 728 :
Let $\alpha , \beta \in \mathrm { R }$. If $\alpha , \beta ^ { 2 }$ are the roots of quadratic equation $x ^ { 2 } - p x + 1 = 0$ and $\alpha ^ { 2 } , \beta$ equation $x ^ { 2 } - q x + 8 = 0$, then the value r if $\frac { r } { 8 }$ is the arithmetic means of p and q, is
Question 729 :
Divide the following and write your answer in lowest terms: $\dfrac{x^2+11x+28}{x^2-4x-77}\div \dfrac {x^2+7x+12}{x^2-2x-15}$
Question 730 :
If $\alpha, \beta$ be the zeros of the quadratic polynomial $2x^2+5x+1$, then the value of $\alpha+\beta+\alpha \beta=$<br>
Question 731 :
If the sum of two numbers is $9$ and the sum of their squares is $41$, then the numbers are<br/>
Question 732 :
Evaluate :$\displaystyle \frac { 50xyz\left( x+y \right) \left( y+z \right) \left( z+x \right) }{ 100xy\left( x+y \right) \left( y+z \right) }$
Question 734 :
When $(x^{3} - x^{2} - 5x - 3)$ is divided by $(x - 3)$, the remainder is
Question 735 :
The value of $\displaystyle \frac { 28xy\left( y-5 \right) \left( y+4 \right)  }{ 14y\left( y-5 \right)}$ is 
Question 736 :
If $\cos{\cfrac{\pi}{7}},\cos{\cfrac{3\pi}{7}},\cos{\cfrac{5\pi}{7}}$ are the roots of the equation $8{x}^{3}-4{x}^{2}-4x+1=0$<br>The value of $\sec{\cfrac{\pi}{7}}+\sec{\cfrac{3\pi}{7}}+\sec{\cfrac{5\pi}{7}}=$
Question 737 :
The number of integers $n$ for which $3x^3-25x+n=0$ has three real roots is$?$<br/>
Question 738 :
Suppose $\alpha ,\beta .\gamma $ are roots of ${ x }^{ 3 }+{ x }^{ 2 }+2x+3=0$. If $f(x)=0$ is a cubic polynomial equation whose roots are $\alpha +\beta ,\beta +\gamma ,\gamma +\alpha $ then $f(x)=$
Question 739 :
If the equation<br>$\displaystyle\left( { p }^{ 2 }+{ q }^{ 2 } \right) { x }^{ 2 }-2\left( pr+qs \right) x+{ r }^{ 2 }+{ s }^{ 2 }=0$ has equal rootsthen<br>
Question 740 :
The difference of the roots of$\displaystyle 2y^{2}-ky+16=0$ is 1/3 Find k
Question 741 :
Divide $\displaystyle 10{ a }^{ 2 }{ b }^{ 2 }\left( 5x-25 \right)$ by $15ab\left( x-5 \right) $
Question 742 :
If $\alpha$ and $\beta$ are the roots of the equation $ \displaystyle 5x^{2}-x-2=0, $  then the equation for which roots are $ \displaystyle \dfrac{2}{\alpha }$ and $\dfrac{2}{\beta } $ is
Question 744 :
Let $f(x)=2{ x }^{ 2 }+5x+1$. If we write $f(x)$ as<br>$f(x)=a(x+1)(x-2)+b(x-2)(x-1)+c(x-1)(x+1)$ for real numbers $a,b,c$ then
Question 745 :
Total number of polynomials of the form ${ x }^{ 3 }+a{ x }^{ 2 }+bx+c$ that are divisible by ${ x }^{ 2 }+1$, where $a,b,c\in \left\{ 1,2,3,......10 \right\} $ is equal to
Question 746 :
Divide $\displaystyle x\left( x+1 \right) \left( x+2 \right) \left( x+3 \right)$ by $\left( x+3 \right) \left( x+2 \right) $
Question 747 :
Find the value of p for which the given equation has real roots.<br>$\displaystyle8p{ x }^{ 2 }-9x+3=0$<br>
Question 748 :
The equation $\displaystyle x^{2}+Bx+C=0$ has 5 as the sum of its roots and 15 as the sum of the square of its roots. The value of C is
Question 749 :
State the following statement is True or False<br/>The zeros of the polynomial $(x - 2) (x^{2} + 4x + 3)$ are $2,-1 and -3$
Question 750 :
$x_1$ and $x_2$ are the real roots of $ax^2+bx+c=0$ and $x_1x_2 < 0$. The roots of $x_1(x-x_2)^2+x_2(x-x_1)^2=0$ are<br/>
Question 752 :
Evaluate: $\displaystyle \frac { 35\left( x-3 \right) \left( { x }^{ 2 }+2x+4 \right)  }{ 7\left( x-3 \right)  } $
Question 753 :
If the roots of $ax^2+bx+c=0, \neq 0,$ are p,q ($p \neq q $), then the roots of $cx^2-bx+a=0$ are.
Question 754 :
Let $\alpha$ and $\beta$ be the roots of equation $x^2-6x-2=0$. If $a_n=\alpha^n-\beta^n$, for $n\geq 1$, then the value of $\dfrac{a_{10}-2a_8}{2a_9}$ is equal to?
Question 755 :
If $\alpha, \beta$ be the roots $x^2+px-q=0$ and $\gamma, \delta$ be the roots of $x^2+px+r=0$, then $\dfrac{(\alpha -\gamma)(\alpha -\delta)}{(\beta -\gamma )(\beta -\delta)}=$
Question 756 :
$\displaystyle \frac{x^{-1}}{x^{-1} + y^{-1}} + \frac{x^{-1}}{x^{-1} - y^{-1}}$ is equal to
Question 757 :
Simplify: $\displaystyle \frac { 45\left( { a }^{ 4 }-3{ a }^{ 3 }-28{ a }^{ 2 } \right)  }{ 9a\left( a+4 \right)  } $
Question 758 :
If$\alpha ,\beta $ are roots of the equation $2x^{2}+6x+b=0$ where $b<0$, then find least integral value of$\displaystyle \left ( \dfrac{\alpha ^{2}}{\beta }+\dfrac{\beta ^{2}}{\alpha } \right )$.<br>
Question 760 :
If $\alpha,\beta$ are the roots of $ { x }^{ 2 }+px+q=0$, and $\gamma,\delta$ are the roots of  $ { x }^{ 2 }+rx+s=0$, evaluate $ \left( \alpha -\gamma  \right) \left( \alpha -\delta  \right) \left( \beta -\gamma  \right) \left( \beta -\delta  \right) $ in terms of $p,q,r$ and $s$. <br/>
Question 761 :
Simplify: $\displaystyle \frac { 49\left( { x }^{ 4 }-2{ x }^{ 3 }-15{ x }^{ 2 } \right)  }{ 14x\left( x-5 \right)  } $
Question 762 :
Which of the following is equal to $\sin x \sec x$?
Question 763 :
Eliminate $\theta$ and find a relation in x, y, a and b for the following question.<br/>If $x = a sec \theta$ and $y = a tan \theta$, find the value of $x^2 - y^2$.
Question 764 :
If$\displaystyle \cot A=\frac{12}{5}$ then the value of$\displaystyle \left ( \sin A+\cos A \right )$ $\displaystyle \times cosec$ $\displaystyle A$ is
Question 766 :
As value of $x$ increases from $0$ to $\cfrac{\pi}{2}$, the value of $\cos {x}$:
Question 767 :
Find the value of $\sin^3\left( 1099\pi -\dfrac { \pi  }{ 6 }  \right) +\cos^3\left( 50\pi -\dfrac { \pi  }{ 3 }  \right) $
Question 769 :
$\tan \theta$ increases as $\theta$ increases.<br/>If true then enter $1$ and if false then enter $0$.<br/>
Question 771 :
Value of ${ cos }^{ 2 }{ 135 }^{ \circ  }$
Question 773 :
If $\theta$ increases from $0^0$ to $90^o$, then the value of $\cos\theta$: <br/>
Question 774 :
Find the value of $ \displaystyle  \theta , cos\theta  \sqrt{\sec ^{2}\theta -1}     = 0$
Question 775 :
IF A+B+C=$ \displaystyle 180^{\circ}  $ ,then $  tan A+tanB+tanC $ is equal to
Question 778 :
If $A+B+C=\dfrac { 3\pi }{ 2 } $, then $cos2A+cos2B+cos2C$ is equal to
Question 779 :
If $\displaystyle 5\tan \theta =4$, then find the value of $\displaystyle \frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }$. 
Question 781 :
The expression$ \displaystyle \left (\tan \Theta +sec\Theta \right )^{2} $ is equal to
Question 784 :
The value of $[\dfrac{\tan 30^{o}.\sin 60^{o}.\csc 30^{o}}{\sec 0^{o}.\cot 60^{o}.\cos 30^{o}}]^{4}$ is equal to
Question 786 :
Choose and write the correct alternative.<br>If $3 \sin \theta = 4 \cos \theta$ then $\cot \theta = ?$<br>
Question 788 :
The value of $\sqrt { 3 } \sin { x } +\cos { x } $ is max. when $x$ is equal to
Question 789 :
Simplest form of $\displaystyle \dfrac{1}{\sqrt{2 + \sqrt{2 + \sqrt{2 + 2 cos 4x}}}}$ is
Question 790 :
If $ \alpha \epsilon \left[ \frac { \pi  }{ 2 } ,\pi  \right] $ then the value of $\sqrt { 1+sin\alpha  } -\sqrt { 1-sin\alpha  } $ is equal to
Question 791 :
Solve : $\dfrac { 2tan{ 30 }^{ \circ  } }{ 1+{ tan }^{ 2 }{ 30 }^{ \circ  } } $
Question 793 :
If $\tan \theta = \dfrac {4}{3}$ then $\cos \theta$ will be
Question 794 :
Choose the correct option. Justify your choice.<br/>$\displaystyle 9{ \sec }^{ 2 }A-9{ \tan }^{ 2 }A=$<br/>
Question 798 :
If $sin({ 90 }^{ 0 }-\theta )=\dfrac { 3 }{ 7 } $, then $cos\theta $
Question 800 :
If $3\sin\theta + 5 \cos\theta =5$, then the value of $5\sin\theta -3 \cos\theta $ are 
Question 801 :
The given relation is $(1 + \tan a + \cos a)(\sin a - \cos a )= 2\sin a\tan a - cat\,a\cos a$
Question 802 :
Given $\cos \theta = \dfrac{\sqrt3}{2}$, which of the following are the possible values of  $\sin 2 \theta$?
Question 803 :
$\left( \dfrac { cosA+cosB }{ sinA-sinB }  \right) ^{ 2014 }+\left( \cfrac { sinA+sinB }{ cosA-cosB }  \right) ^{ 2014 }=...........$
Question 804 :
The angle of elevation and angle of depression both are measured with
Question 805 :
find whether ${ \left( \sin { \theta  } +co\sec { \theta  }  \right)  }^{ 2 }+{ \left( \cos { \theta  } +\sec { \theta  }  \right)  }^{ 2 }=7+\tan ^{ 2 }{ \theta  } +\cos ^{ 2 }{ \theta  } $ is true or false.
Question 807 :
If $sec\theta -tan\theta =\dfrac{a}{b},$ then the value of $tan\theta $ is
Question 808 :
The solution of $(2 cosx-1)(3+2 cosx)=0$ in the interval $0 \leq \theta \leq 2\pi$ is-
Question 809 :
The given expression is $\displaystyle \sin { \theta  } \cos { \left( { 90 }^{ o }-\theta  \right)  } +\cos { \theta  } \sin { \left( { 90 }^{ o }-\theta  \right)  } +4 $ equal to :<br/>
Question 810 :
If $\displaystyle x=y\sin \theta \cos \phi ,y=\gamma \sin \theta \sin \phi ,z=\gamma \cos \theta $. Eliminate  $\displaystyle \theta $ and  $\displaystyle \phi $
Question 811 :
Express$\displaystyle \cos { { 79 }^{ o } } +\sec { { 79 }^{ o } }$ in terms of angles between$\displaystyle { 0 }^{ o }$ and$\displaystyle { 45 }^{ o }$
Question 812 :
If$\displaystyle \sin \theta +\sin ^{2}\theta =1$ then the value of$\displaystyle \cos ^{12}\theta +3\cos ^{10}\theta +3\cos ^{8}\theta +\cos ^{6}\theta +2\cos ^{4}\theta +2\cos ^{2}\theta -2$ is _________
Question 813 :
If $\displaystyle \sin \left ( A+B \right ) =\frac{\sqrt{3}}{2}$ and $\displaystyle \cot \left ( A-B \right )=1$, then find $A$
Question 814 :
The value of $\displaystyle { \left( \frac { \sin { { 47 }^{ o } }  }{ \cos { { 43 }^{ o } }  }  \right)  }^{ 2 }+{ \left( \frac { \cos { { 43 }^{ o } }  }{ \sin { { 47 }^{ o } }  }  \right)  }^{ 2 }-4{ \cos }^{ 2 }{ 45 }^{ o }$ is :
Question 817 :
The value of $\cos 1^{\circ}. \cos 2^{\circ}. \cos 3^{\circ} ...\cos 179^{\circ}$ is equal to:
Question 819 :
Choose the correct option and justify your choice:<br>$\displaystyle \frac { 1-{ \tan }^{ 2 }{ 45 }^{ \circ } }{ 1+{ \tan }^{ 2 }{ 45 }^{ \circ } } =$<br>
Question 820 :
$\displaystyle\sin ^{2}\theta= \frac{(x+y)^{2}}{4xy}$, where $\displaystylex\epsilon R,$ <br> $\displaystyle y\epsilon R,$gives real $\displaystyle\theta$ if and only if
Question 821 :
The value of $\cos { \dfrac { \pi }{ 7 } } +\cos { \dfrac { 2\pi }{ 7 } } +\cos { \dfrac { 3\pi }{ 7 } } +\cos { \dfrac { 4\pi }{ 7 } } +\cos { \dfrac { 5\pi }{ 7 } } +\cos { \dfrac { 6\pi }{ 7 } } +\cos { \dfrac { 7\pi }{ 7 } } $ is
Question 823 :
If $\sin \theta = \dfrac {3}{5}$, then the value of $\text{cosec}\, \theta$ is
Question 824 :
Find the value of : $\dfrac {\cos 38^{\circ} \csc 52^{\circ}}{\tan 18^{\circ} \tan 35^{\circ} \tan 60^{\circ} \tan 72^{\circ} \tan 55^{\circ}} =$
Question 825 :
If $sin x cos y=\dfrac 14$ and $3 tan x=4 tan y$, then $sin(x+y)$ is equal to
Question 827 :
If $\text{cosec} \theta-\cot \theta = q,$ then the value of $\text{cosec}\theta$ is<br>
Question 828 :
Write True or False and justify your answerin each of the following :<br>$ cos \theta = \dfrac{a^2 + b^2}{2ab} $ , where $ a$ and $b$ are two distinct numbers such that $ ab > 0 $.
Question 830 :
Evaluate: $\dfrac {\tan 35^{\circ}}{\cot 55^{\circ}} + \dfrac {\cot 78^{\circ}}{\tan 12^{\circ}} = $
Question 831 :
If $\sin A + \sin^{2}A + \sin^{3}A = 1$, then find the value of $\cos^{6}A-4\cos^{4}A + 8\cos^{2}A$ is:
Question 832 :
If $ \sqrt3 \cos \theta + \sin \theta = \sqrt2 , $ then the most general value of $ \theta $ is :
Question 833 :
A right angledtriangle has perimeter of length $7$ and hypotenuse of length $3$. If $\displaystyle \theta $ is the largest non-right angle in the triangle, then the value of $\displaystyle \cos \theta $ equals<br>
Question 834 :
Find the value of $\tan 10^{\circ} \tan 15^{\circ} \tan 75^{\circ} \tan 80^{\circ} $
Question 835 :
If $\displaystyle \cos{ \theta  }=\frac { 12 }{ 13 } $ and $ \theta $ is an acute angle, then $\displaystyle \sqrt { \left( 1+\frac { \sin { \theta  }  }{ \cos { \theta  }  }  \right) \left( 1-\tan { \theta  }  \right)  } $ is :
Question 837 :
If $\displaystyle \frac { x\text{ cosec }^{ 2 }{ 30 }^{ o }{ \sec }^{ 2 }{ 45 }^{ o } }{ 8{ \cos }^{ 2 }{ 45 }^{ o }{ \sin }^{ 2 }{ 90 }^{ o } } ={ \tan }^{ 2 }{ 60 }^{ o }-{ \tan }^{ 2 }{ 45 }^{ o }$, then $x$ is :
Question 838 :
If $\displaystyle x= \frac{2\sin \alpha}{1+\cos \alpha+\sin \alpha}$ then $\displaystyle \frac{1-\cos \alpha+\sin \alpha}{1+\sin \alpha}$ is equal to<br/><br/><br/>
Question 840 :
If $\tan\theta$ = $\dfrac{6}{8}$ and $\theta$ is acute, what is the value of $\cos\theta$?<br/>
Question 842 :
The value of the expression$\displaystyle \frac {tan^2 20^0 - sin^2 20^0}{tan^2 20^0 . sin^2 20^0}$ is
Question 843 :
If $\sin \theta =\dfrac{24}{25} \:and\:\theta $ lies in the second quadrant, then $\sec \theta +\tan \theta =$<br/>
Question 845 :
The value of$ \displaystyle \tan 1^{\circ}\tan 2^{\circ}\tan 3^{\circ}.....\tan 89^{\circ} $ is
Question 846 : <p>Suppose ABC is a triangle with 3 acute angles A, B, and C. The point whose coordinates are (cosB-sinA, sinB-cosA)can be in the-</p>
Question 847 :
Evaluate: $\displaystyle \sin { { 40 }^{ o } } .\sec{ { 50 }^{ o } }-\cfrac { \tan { { 40 }^{ o } }  }{ \cot { { 50 }^{ o } }  } +1$
Question 848 :
The value of the expression $\text{cosec }(75^0+\theta) - \sec (15^0 - \theta) - \tan (55^0 + \theta) + \cot (35^0 - \theta)$, is<br/>
Question 852 :
If $'\theta '$  is in the III quadrant then  $\sqrt{4  \sin^{4}\theta }+4  \cos^{2}\left ( \frac{\pi }{4}-\frac{\theta }{2} \right )=$<br/>
Question 853 :
If $b\tan \theta =a$, then the value of $\dfrac{a\sin \theta -b\cos \theta }{a\sin \theta +b\cos \theta}$<br/>
Question 854 :
The value of   $\displaystyle \sin { \theta  } \cos { \theta  } -\frac { \sin { \theta  } \cos { \left( { 90 }^{ o }-\theta  \right)  } \cos { \theta  }  }{ \sec { \left( { 90 }^{ o }-\theta  \right)  }  } -\frac { \cos { \theta  } \sin { \left( { 90 }^{ o }-\theta  \right)  } \sin { \theta  }  }{ \text{cosec }\left( { 90 }^{ o }-\theta  \right)  } $ is :
Question 856 :
If $x= \sec\phi - \tan\phi $ and  $y= cosec \phi  $ then:
Question 857 :
If $A$ and $B$ are acute angles such that $\sin A=\sin^2 B, 2\cos^2 A=3 \cos^2 B$; then
Question 858 :
Let $\displaystyle a=cosx + cos(x + \frac{2{\pi}}{3}) + cos(x + \frac{4{\pi}}{3})$ and $\displaystyle b=sinx + sin(x + \frac{2{\pi}}{3}) + sin(x + \frac{4{\pi}}{3})$ then which one of the following holds good ?
Question 861 :
If$\displaystyle 2\tan { \theta } =1$, find the value of$\displaystyle \frac { 3\cos { \theta } +2\sin { \theta } }{ 2\cos { \theta } -\sin { \theta } }$
Question 862 :
The number of ordered pairs $(\alpha, \beta)$, where $\alpha, \beta $ $\in$ $(-\pi, \pi)$ satisfying $\cos(\alpha -\beta)=1$ and $\cos(\alpha+\beta)=\dfrac {1}{e}$ is
Question 864 :
If $\text{cosec } \theta = \dfrac {13}{5}$, then $\cos \theta = ......$
Question 865 :
In $\triangle ABC, \angle B = 90^{\circ}, BC = 7$ and $AC - AB = 1$, then $\cos C = .....$
Question 866 :
If $\sin {x}+\sin^{2}{x}+\sin^{3}{x}=1 ,\ \ then \ \  \cos^{6}{x}-4\cos^{4}{x}<br/>+8\cos^{2}{x}$ is equal to<br/>
Question 867 :
If $\displaystyle\frac{\cos^{4}x }{\theta _{1}}+\displaystyle\frac{\sin^{4}x}{\theta _{2}}=\frac{1}{\theta _{1}+\theta _{2}},$ then $\displaystyle\frac{\theta _{2}}{\theta _{1}}$ equals<br>
Question 869 :
The value of the expression $(\tan1^{0} \tan2^{0} \tan 3^{0}...\tan89^{0})$ is equal to<br/>
Question 870 :
If $\sin x + \sin^{2}x=1,$ then the value of $\cos^{12} x + 3 \cos^{10} x + 3 cos^{8} x + cos ^{6} x -1$ is equal to :
Question 871 :
$A$ tower of height $h$' standing at the centre of a square with sides of length $a$' makes the same angle $\alpha$ at each of the four corners then $a^{2}=$
Question 872 :
If $\displaystyle \frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1,\frac{x}{a}\sin \theta-\frac{y}{b}\cos \theta=1,$ then eliminate $\theta $<br>
Question 874 :
<br/>If $a \sin^{2}\theta+b\cos^{2}\theta=a\cos^{2}\phi+b\sin^{2}\phi=1$ and $a \tan\theta=b\tan\phi$, then choose the correct option.<br/>
Question 875 :
In $\displaystyle A_{n}=\cos^{n}\theta+\sin^{n}\theta, n\in N$ and $\displaystyle \theta \in R$<br/><br/>If $\displaystyle A_{n-4}-A_{n-2}=\sin^{2}\theta\cos^{2}\theta A_{\lambda} $ , then $\displaystyle \lambda $ equals<br/>
Question 876 :
If $\cos x + \sec x = - 2$ for a positive odd integer $n$ then $\cos^nx + \sec^nx$ is
Question 877 :
Assertion: Statement 1:If $\displaystyle x+y+z= xyz,$ then at most one of the numbers can be negative.
Reason: Statement 2: In a triangle ABC, $\displaystyle \tan A+\tan B+\tan C= \tan A \tan B \tan C $ ,there can be at most one obtuse angle in a triangle.
Question 878 :
If $\displaystyle X=\tan 1^{0}+\tan 2^{0}+........+\tan 45^{0}$ and $\displaystyle y= -(\cot 46^{0}+\cot 47^{0}+.......+\cot 89^{0})$ then find the value of $(x + y)$.
Question 879 :
In a $\Delta ABC$, if $\cos A \cos B \cos C=\displaystyle\dfrac {\sqrt 3-1}{8}$ and $\sin A. \sin B. \sin C=\displaystyle \dfrac {3+\sqrt 3}{8}$, <br/><br/>then- On the basis of above information, answer the following questions:The value of $ \tan A \tan B + \tan B \tan C + \tan C \tan A$ is:
Question 880 :
The value of the expression $\displaystyle 1\, - \,\frac{{{{\sin }^2}y}}{{1\, + \cos \,y}}\, + \frac{{1\, + \cos \,y}}{{\sin \,y}}\, - \,\frac{{\sin \,y}}{{1\, - \cos \,y}}$ is equal to 
Question 881 :
$\cos { { 1 }^{ o } } .\cos { { 2 }^{ o } } .\cos { { 3 }^{ o } } ......\cos { { 179 }^{ o } } $ is equal to
Question 882 :
If $0\leq x, y\leq 180^o$ and $\sin (x-y)=\cos(x+y)=\dfrac 12$, then the values of $x$ and $y$ are given by
Question 883 :
Find the relation obtained by eliminating$\displaystyle \theta $ from the equation$\displaystyle x=a\cos \theta +b\sin \theta $ and$\displaystyle y=a\sin \theta -b\cos \theta $
Question 884 :
If$\displaystyle \sin \Theta =\frac{3}{5} $ and$\displaystyle \Theta $ is acute then find the value of$\displaystyle \frac{\tan \Theta -2\cos \Theta }{3\sin \Theta +\sec \Theta }$
Question 887 :
If $\sin\theta + \sin^{2}\theta = 1$, then $\cos^{2}\theta + \cos^{4}\theta = ......$
Question 888 :
What is $\left(\dfrac{sec 18^{\circ}}{sec 144^{\circ}} + \dfrac{cosec 18^{\circ}}{cosec 144^{\circ}}\right)$ equals to?
Question 889 :
If $ \cos^{-1}\left ( 4x^{3}-3x \right )= 2\pi -3\cos^{-1}x $, then $ x $ lies in interval
Question 891 :
If the angles of a triangle are in arithmetic progression such that $\sin (2A+B)=\dfrac{1}{2}$, then
Question 892 :
${\cos ^2}{48^ \circ } - {\sin ^2}{12^ \circ }$ is equal to -
Question 894 :
If $x_{1}=1$ and $x_{n+1}=\frac{1}{x_{n}}\left ( \sqrt{1+x_{n}^{2}}-1 \right ),n\geq 1,n \in N$, then $x_{n}$ is equal to :<br>
Question 896 :
If $\sin (\alpha+\beta)=1$ and $\sin(\alpha -\beta)=1/2$ where $\alpha, \beta \epsilon [0, \pi /2]$ then
Question 897 :
If $\displaystyle \frac { \sin { \alpha  }  }{ \sin { \beta  }  } =\frac { \sqrt { 3 }  }{ 2 } $ and $\displaystyle \frac { \cos { \alpha  }  }{ \cos { \beta  }  } =\frac { \sqrt { 5 }  }{ 2 } ,0<\alpha ,\beta <\frac { \pi  }{ 2 } $, then
Question 901 :
If $x = a \cos^{3} \theta \sin^{2} \theta, y = a \sin^{3} \theta \cos^{2} \theta$ and $\dfrac {(x^{2} + y^{2})^{p}}{(xy)^{q}}(p, q\epsilon N)$ is independent of $\theta$, then
Question 902 :
Let $\displaystyle -\frac { \pi }{ 6 } <\theta <-\frac { \pi }{ 12 }$, Suppose$\displaystyle { \alpha }_{ 1 }$ and$\displaystyle { \beta }_{ 1 }$ are the roots of the equation$\displaystyle { x }^{ 2 }-2x\sec { \theta } +1=0$ and$\displaystyle { \alpha }_{ 2 }$ and $\displaystyle { \beta }_{ 2 }$ are the roots of the equation$\displaystyle { x }^{ 2 }+2x\tan { \theta } -1=0$. If$\displaystyle { \alpha }_{ 1 }>{ \beta }_{ 1 }$ and$\displaystyle { \alpha }_{ 2 }>{ \beta }_{ 2 }$, then$\displaystyle { \alpha }_{ 1 }+{ \beta }_{ 2 }$ equals to
Question 905 :
If $\sin (\alpha+\beta)=1$ and $\sin(\alpha -\beta)=1/2$ where $\alpha, \beta \epsilon [0, \pi /2]$ then
Question 907 :
If $\displaystyle \left ( \sec \theta +\tan \theta  \right )\left ( \sec \phi +\tan \phi  \right )\left ( \sec \psi  +\tan \psi  \right )=\tan \theta \tan \phi \tan \psi $ ,then $\displaystyle \left ( \sec \theta -\tan \theta  \right )\left ( \sec \phi -\tan \phi  \right )\left ( \sec \psi  -\tan \psi  \right )$ is equal to <br/>
Question 908 :
If $\displaystyle \frac { \sin ^{ 4 }{ x }  }{ 2 } +\frac { \cos ^{ 4 }{ x }  }{ 3 } =\frac { 1 }{ 5 } ,$ then:
Question 909 :
If $\tan { \theta  } +\sin { \theta  } =m, \tan { \theta - \sin { \theta =n }  } $, then $(m^{2}-n^{2})^{2}=$.<br/>
Question 911 :
If $\cos9 \alpha= \sin \alpha$ and $9 \alpha < 90^{0}$, then the value of $\tan5 \alpha$ is<br/>
Question 912 :
A pair of dice is thrown. Find the probability of getting a sum of $8$ or getting an even number on both the dices.
Question 913 :
If the odd in favour of an event are $4$ to $7$, find the probability of its no occurence.
Question 914 :
If I calculate the probability of an event and it turns out to be $7$, then I surely know that<br/>
Question 915 :
Two dice are thrown. Find the odds in favour of getting the sum $4$.<br/>
Question 916 :
What is the maximum value of the probability of an event?
Question 917 :
Vineeta said that probability of impossible events is $1$. Dhanalakshmi said that probability of sure events is $0$ and Sireesha said that the probability of any event lies between $0$ and $1$.<br>in the above, with whom will you agree?
Question 918 :
Out of the digits $1$ to $9$, two are selected at random and one is found to be $2$, the probability that their sum is odd is
Question 919 :
The probability of an event happening and the probability of the same event not happening (or the complement) must be a <br/>
Question 920 :
Ticket numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?
Question 922 :
If the probability of the occurrence of an event is P then what is the probability that the event doesn't occur.
Question 924 :
A bulb is taken out at random from a box of 600 electricbulbs that contains 12 defective bulbs. Then theprobability of a non-defective bulb is
Question 925 :
A fair dice has faces numbered $0, 1, 7, 3, 5$ and $9$. If it is thrown, the probability of getting an odd number is
Question 926 : A coin is tossed $400$ times and the data of outcomes is below:<span class="wysiwyg-font-size-medium"> <span class="wysiwyg-font-size-medium"><br/><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Outcomes </p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$H$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$T$</p></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Frequency</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$280$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$120$</p></td></tr></tbody></table><p><br/></p><p>Find:</p><p>(i) $P(H)$, i.e., probability of getting head</p><p>(ii) $P (T)$, i.e., probability of getting tail. </p><p>(iii) The value of $P (H) + P (T)$.</p>
Question 927 :
A die is thrown .The probability that the number comes up even is ______ .
Question 928 :
One hundred identical coins each with probability p as showing up heads are tossed. If $0 < p < 1$ and the probability of heads showing on 50 coins is equal to that of heads on 51 coins, then the value of p is
Question 930 :
A pair of dice is thrown once The probability that the sum of the outcomes is less than 11 is
Question 931 :
The probability of guessing the correct answer to a certain test is $\displaystyle\frac{x}{2}$. If the probability of not guessing the correct answer to this questions is $\displaystyle\frac{2}{3}$, then $x$ is equal to ______________.
Question 932 :
The probability of an event $A$ lies between $0$ and $1$, both inclusive. Which mathematical expression best describes this statement?<br/>
Question 933 :
A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number between 1 to 15. What is the probability that it will point to an odd number.
Question 934 :
If the events $A$ and $B$ mutually exclusive events such that $P(A)=\dfrac {1}{3}(3x+1)$ and $P(B)=\dfrac {1}{4}(1-x)$, then the aet of possible values of $x$ lies in the interval:
Question 935 :
A biased coin with probability $p , 0 < p < 1 ,$ of heads is tossed until a head appears for thefirst time. If the probability that the number of tosses required is even, is $2 / 5 ,$ then $p$ equal to
Question 936 :
A bag contains 5 blue and 4 black balls. Three balls are drawn at random. What is the probability that 2 are blueand 1 is black?
Question 937 :
If $P(A) = \dfrac{5}{9}$, then the odds against the event $A$ is
Question 938 :
The probability expressed as a percentage of a particular occurrence can never be
Question 940 :
According to the property of probability, $P(\phi) = 0$ is used for <br>
Question 941 :
A bag contains $15$ cabbages, $20$ carrots, and $25$ turnips. If a single vegetable is picked at random from the bag, what is the probability that it will not be a carrot?
Question 942 :
There are three events $A, B$ and $C$ one of which must and only one can happen ; the odds are $8$ to $3$ against A, the odds are $5$ to $2$ against $B$, find odds against $C$.
Question 943 :
A gumball machine contains $40$ blue gum balls, $20$ red gumballs, $15$ gumballs, and $25$ purple gumballs. What is the probability that a person gets a red gumball?
Question 944 :
The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chance of each event is
Question 945 :
If 10 persons are to sit around a round table, the odds against two specified persons sitting together is
Question 946 :
A determinant is chosen at random from the set of all departments of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is :
Question 947 :
There are three events $A$, $B$ and $C$ out of which one and only one can happen. The odds are $7$ to $3$ against $A$ and $6$ to $4$ against $B$. The odds against C are
Question 948 :
In a tennis tournament, the odds that player A will be the champion is 4 to 3 and the odds that player B will be champion is 1 to 4. What are the odds that either A or B will become the champion?
Question 949 :
In a ODI cricket match, probability of loosing the game is $\dfrac{1}{4}$. What is the probability of winning the game ?
Question 950 :
If odds in favour of a target are $2 : 5$, what is the probability of success?<br/>
Question 951 :
What is the condition if the sample space is finite and an event is $S =$ {$x_1, x_2...x_n$} then<br/>
Question 952 :
Let $A$ and $B$ be two events with $P(A) = \dfrac {1}{3}, P(B) = \dfrac {1}{6}$ and $P(A\cap B) = \dfrac {1}{12}$. What is $P(B|\overline {A})$ equal to?
Question 953 :
One of the two events must occur. If the chance of one is$\displaystyle \frac{2}{3}$ of the other, then odds in favour of the other are
Question 954 :
$A$ and $B$ are two events. Odds against $A$ and $2:1$. Odds in favor of $A\cup B$ are $3:1$. If $x\le P\left( B \right) \le y$, then the ordered pair $(x,y)$ is
Question 955 :
A missile target may be at a point P with probability$\displaystyle \frac{9}{10}$ or at a point Q with probability$\displaystyle \frac{1}{10}$ we have 20 shells each of which can be fired either at point P or Q Each shell may hit the target independently of the other shoot with probability$\displaystyle \frac{2}{3}$ Then number of shells must be fired at point P to hit any target with maximum probability is
Question 956 :
A box contains $9$ tickets numbered $1$ to $9$ inclusive. If $3$ tickets are drawn from the box without replacement. The probability that they are alternatively either {odd, even, odd} of {even, odd, even} is
Question 957 :
If a positive integer $n$ is picked at random from the positive integers less than or equal to $10$, what is the probability that $5n + 3 \leq 14$  ?
Question 958 :
If $10$% of the attacking a air crafts are expected to be shot down before reaching the target, the probability that out of $5$ aircrafts atleast four will be shot before they reach the target is
Question 959 :
A bag contains yellow and black balls. The probability of getting a yellow ball from the bag of balls is $\dfrac23$. What is the probability of not getting a yellow ball?<br/>
Question 960 :
A coin tossed $100$ times. The no. of times head comes up is $54$.What is the probability of head coming up?
Question 961 :
An integer is chosen at random between 1 and 100. Find the probability that it is divisible by 8.<br/>
Question 962 :
A woman has 10 keys out of which only one opens a lock She tries the keys one after the another(keeping aside the failed ones) till she suceeds in opening the lock. What is the chance that it is the seventh key that works?
Question 963 :
The probability of getting head or tail in a throw ofa coin is ______.
Question 964 :
A number is chosen at random from the numbers $10$ to $99$. By seeing the number a man will laugh if product of the digits is $12$. If he choose three numbers with replacement then the probability that he will laugh at least once is
Question 965 :
The odds against the occurrence of an event are <span class="MathJax_Preview"><span class="MJXp-math"><span class="MJXp-mn">5<span class="MJXp-mo">:<span class="MJXp-mn">4<span class="MathJax MathJax_Processed"><span class="math"><span class="mrow"><span class="mn">5<span class="mo">:<span class="mn">4 The probability of its occurrence is?
Question 966 :
The odds in favour of getting atleast one time an even prime when a fair die is tossed three times is
Question 967 :
If $A$ and $B$ are two events such that $ P(A)=\displaystyle \frac{1}{4} $ and $P(B)= P$, the value of $P$ is not ______, if  $A\subset B$.
Question 968 :
A problem in statistics is given to three students whose chance of solving it are $ \dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}$ respectively. The probability that the question is solved is
Question 969 :
$n$ is an integer chosen at random from the set $\{2,5,6 \}$ and $p$ another integer chosen at random from the set $\{6,9,10 \}$. What is the probability that the two numbers $n$ and $p$ are even?
Question 970 :
Two cards are drawn at random from a pack of $52$ cards. The probability of these two being "Aces" is
Question 971 :
A fair die is rolled once.<br>STATEMENT - 1 : The probability of getting a composite number is 1/3<br>STATEMENT - 2 : There are three possibilities for the obtained number (i) the number is a prime number (ii) the number is a composite number (iii) the number is 1, and hence probability of getting a prime number $=$1/3.<br>
Question 972 :
The probability that atleast one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then$P(\bar{A})+P(\bar{B})$ is.
Question 973 :
A coin is tossed $100$ times with following frequency:<br/>Head: $25$, Tail: $75$<br/>Find the probability of not getting a head.
Question 974 :
If x is chosen at random from the set $\left \{2, 3, 4, 5, 6\right \}$, and y is chosen at random from the set $\left \{11, 13, 15\right \}$, find the probability that $xy$ is even.
Question 975 :
If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?<br/>
Question 976 :
Two dice are thrown. Find the odds in favour of getting the sum $6.$
Question 977 :
A die is rolled three times. The probability that the sum of three numbers obtained is $15,$ is equal to :
Question 978 :
$A, B$ are two events of a simple space.Assertion (A):- $A, B$ are mutually exclusive $\Rightarrow P\left ( A \right )\leq P\left ( \bar{B} \right )$Reason (R):- $A, B$ are mutually exclusive  $\Rightarrow P\left ( A \right )+ P\left ( B \right )\leq 1$
Question 979 :
If $a$ and $b$ are chosen randomly from the set consisting of numbers $1,\ 2,\ 3,\ 4,\ 5,\ 6$ with replacement. Then the probability that $\displaystyle \lim _{ x\rightarrow 0 }{ { \left[ \left( { a }^{ x }+{ b }^{ x } \right) /2 \right] }^{ 2/x }=6 }$ is
Question 980 :
If $\dfrac {1 + 3p}{3}, \dfrac {1 - 2p}{2}$ are probabilities of two mutually exclusive events, then p lies the interval
Question 981 :
In a single cast with two dice, the odds against drawing $7$ is
Question 982 :
Two persons $A$ and $B$ have respectively $n + 1$ and $n$ coins, which they toss simultaneously. Then probability $P$ that $A$ will have more heads than $B$ is:
Question 983 :
The sum of the probabilities of the distinct outcomes within a sample space is
Question 984 :
The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second.The chances of the events are
Question 985 :
$A$ and $B$ each throw a dice. The probability that "$B$" throw is not smaller than "$A$" throw, is
Question 986 :
Three different numbers are selected at random from the set $A = \{1,2,3, ...... 10 \}$. The probability that the product of two of the numbers is equal to third is :<br/>
Question 987 :
The probability of students not attending class is $0.24$. What is the probability of students attending class ?
Question 988 :
If $A$ and $B$ are independent events such that $P\left( A \right) =\dfrac { 1 }{ 5 }$, $P\left( A\cup B \right) =\dfrac { 7 }{ 10 }$, then what is $P\left( \bar { B } \right) $ equal to?
Question 990 :
The probability that atleast one of the events A and B occurs, is $0.6$. If A and B occur simultaneously with probability $0.2$, then $P(\bar{A})+P(\bar{B})$ is equal to?
Question 991 :
A man and his wife appear for an interview for two posts. The probability of the man's selection is $\dfrac{1}{5}$ and that of his wife selection is $\dfrac{1}{7}$. The probability that at least one of them is selected, is:
Question 992 :
The odds that a book will be favorably reviewed by three independent critics are $5$ to $2,$ $4$ to $3$ and $3$ to $4$ respectively. What is the probability that of the three reviews a majority will be favorable?<br/>
Question 993 :
There are four letters and four addressed envelopes. The probability that all letters are not dispatched in the right envelope is:<br/>
Question 994 :
There are two bags $A$ and $B$. Bag A contains $3$ white and $4$ red balls whereas bag $B$ contains $4$ white and $3$ red balls. Three balls are drawn at random (without replacement) from one of the bags and are found to be two white and one red. Find the probability that these were drawn from bag $B$.
Question 995 :
There are two events $A$ and $B$. If odds against $A$ are as $2:1$ and those in favour of $ A \cup B$ are $3:1$ , then
Question 996 :
In a group of $13$ cricket players, four are bowlers. Find out in how many ways can they form a cricket team of $11$ players in which atleast $2$ bowlers are included.
Question 997 :
A coin whose faces are marked 3 and 5 is tossed 4 times; what are the odds against the sum of the numbers thrown being less than 15?<br>
Question 998 :
In throwing $3$ dice, the probability that atleast $2$ of the three numbers obtained are same is
Question 999 :
For two events $A$ and $B , P ( B ) = P ( B / A ) = 1 / 3$ and $P ( A / B ) = 4 / 7 ,$ then <br>Option a : $P \left( B ^ { \prime } / A \right) = 2 / 3$<br>Option b : $P \left( A / B ^ { \prime } \right) = 3 / 7$<br>Option c : $A$ and $B$ are mutually exclusive<br>Option d: $A$ and $B$ are independent
Question 1000 :
A fair coin is flipped $5$ times.<br/> The probability of getting more heads than tails is $\dfrac{1}{2}$<br/><br/>
Question 1001 :
If odds against solving a question by three students are $2:1, 5:2$ and $5:3$ respectively, then probability that the question is solved only by one students is
Question 1002 :
A fair coin is tossed five times. Calculate the probability that it lands head-up at least twice.
Question 1003 :
There are only three events $A,B,C$ one of which must and only one can happen; the odds are $8$ to $3$ against $A,5$ to $2$ against $B$; find the odds against $C$
Question 1004 :
X and Y plays a game in which they are asked to select a number from $21-50$. If the two number match both of them wins a prize. Find the probability that they will not win a prize in the single trial.
Question 1005 :
Each of a and b can take values 1 or 2 with equal probability. The probability that the equation $ax^2 + bx + 1 = 0$ hasreal roots, is equal to
Question 1006 :
If $2$ cards are drawn from a pack of $52$, then the probability that they are from the same suit is___
Question 1007 :
A number is randomly selected from the set $\left \{6, 7, 8, 8, 8, 10, 10, 11\right \}$. Find the probability the number will be less than the mean.
Question 1008 :
The probability that an electronic device produced by a company does not function properly is equal to $0.1$. If $10$ devices are bought, then the probability, to the nearest thousandth, than $7$ devices function properly is
Question 1009 :
The chance of an event happening is the square of the chance, of a second event but the odds against the first are the cubes of the odds against thefirst are the cubes of the odds against the second. Find the chance of each.
Question 1010 :
A party of $23$ persons take their seats at a round table. The odds against two specified persons sitting together is
Question 1011 :
In a set of games it is $3$ to $5$ in favour of the winner of the previous game.. Then the probability that a person who has won the first game shall win at least $2$ out of the next $5$ games is ?
