Question 1 :
For what value of k does the system of equations$\displaystyle 2x+ky=11\:and\:5x-7y=5$ has no solution?
Question 2 :
The values of x and y satisfying the two equation 32x+33y=31, 33x+32y=34 respectively will be
Question 3 :
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 4 :
The linear equation $y = 2x + 3$ cuts the $y$-axis at 
Question 5 :
A line which passes through (5, 6) and (-3. -4) has an equation of
Question 9 :
If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is
Question 10 :
The solution of the simultaneous equations $\displaystyle \frac{x}{2}+\frac{y}{3}=4\: \: and\: \: x+y=10 $ is given by
Question 11 :
If $2x + y = 5$, then $4x + 2y$ is equal to _________.
Question 12 :
If $p+q=1$ andthe ordered pair (p, q) satisfies $3x+2y=1$,then it also satisfies
Question 13 :
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 14 :
What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes ?
Question 15 :
Solve the following equations:<br/>$x + \dfrac {4}{y} = 1$,<br/>$y + \dfrac {4}{x} = 25$.Then $(x,y)=$
Question 19 :
The sum of two numbers is $2$ and their difference is $1$. Find the numbers.
Question 20 :
What is the equationof Y-axis? Hence, find the point of intersection of Y-axis and the line $y\,=\, 3x\, +\, 2$.
Question 21 :
The graph of the line $5x + 3y = 4$ cuts the $y$-axis at the point
Question 22 :
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 23 :
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 24 :
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 25 :
Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$
Question 26 :
The survey of a manufacturing company producing a beverage and snacks was done. It was found that it sells orange drinks at $ $1.07$ and choco chip cookies at $ $0.78$ the maximum. Now, it was found that it had sold $57$ food items in total and earned about $ $45.87 $ of revenue. Find out the equations representing these two. 
Question 27 :
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 29 :
A member of these family with positive gradient making an angle of$\frac{\pi }{4}$ with the line3x-4y=2, is
Question 31 :
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 32 :
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 33 :
The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is
Question 34 :
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 35 :
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 36 :
$\dfrac{1}{3}x - \dfrac{1}{6}y = 4$<br/>$6x - ay = 8$<br/>In the system of equations above, $a$ is a constant. If the system has no solution, what is the value of $a$
Question 37 :
If (a, 4) lies on the graph of $3x + y = 10$, then the value of a is
Question 38 :
Examine whether the point $(2, 5)$ lies on the graph of the equation $3x\, -\, y\, =\, 1$.
Question 39 :
If $(a, 3)$ is the point lying on the graph of the equation $5x\, +\, 2y\, =\, -4$, then find $a$.
Question 40 :
The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point
Question 41 :
What is the nature of the graphs of a system of linear equations with exactly one solution?
Question 42 :
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 43 :
If $x + y = 25$ and $\dfrac{100}{x + y} + \dfrac{30}{x - y} = 6$, then the value of $x - y$ is
Question 44 :
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 45 :
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 46 :
The graph of the linear equation $2x -y = 4$ cuts x-axis at
Question 47 :
The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is
Question 48 :
The value of $k$ for which the system of equations $3x + 5y= 0$ and $kx + 10y = 0$ has a non-zero solution, is ________.
Question 49 :
Five tables and eight chairs cost Rs. $7350$; three tables and five chairs cost Rs. $4475$. The price of a table is
Question 53 :
Factorise the expressions and divide them as directed.$12xy(9x^2-  16y^2)\div  4xy(3x + 4y)$
Question 54 :
The remainder when$4{a^3} - 12{a^2} + 14a - 3$ is divided by $2a-1$, is
Question 56 :
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 57 :
State whether True or False.Divide : $a^2 +7a + 12 $ by $  a + 4 $, then the answer is $a+3$.<br/>
Question 58 :
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 59 :
The common quantity that must be added to each term of $a^{2}:b^{2}$ to make itequal to $a:b$ is:
Question 60 :
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 61 :
Find the expression which is equivalent to : $\displaystyle \frac { { x }^{ 3 }+{ x }^{ 2 } }{ { x }^{ 4 }+{ x }^{ 3 } } $?
Question 62 :
The product of the roots of the quadratic equation $2x^{2}-8x+3=0$ is
Question 63 :
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 65 :
Simplify:$20(y + 4) (y^2 + 5y + 3) \div 5(y + 4)$<br/>
Question 66 :
Factorise the expressions and divide them as directed.$4yz(z^2 + 6z-  16)\div  2y(z + 8)$<br/>
Question 68 :
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 72 :
$\alpha $ and $\beta $ are zeroes of polynomial $x^{2}-2x+1,$ then product of zeroes of a polynomial having zeroes $\dfrac{1}{\alpha }$  and    $\dfrac{1}{\beta }$ is
Question 73 :
Is $(3x^{2} + 5xy + 4y^{2})$ a factor of $ 9x^{4} + 3x^{3}y + 16x^{2} y^{2} + 24xy^{3}  + 32y^{4}$?<br/>
Question 74 :
Work out the following divisions.$10y(6y + 21) \div 5(2y + 7)$<br/>
Question 75 :
If $\alpha , \beta$ are the roots of equation $x^2 \, - \, px \, + \, q \, = \, 0,$ then find the equation the roots of which are $\left ( \alpha ^2  \, \beta ^2 \right )  \,  and  \,  \,  \alpha \, + \,\beta $.
Question 76 :
If $a\ne 2$, which of the following is equal to $\cfrac { b\left( { a }^{ 2 }-4 \right) }{ ab-2b } $?
Question 79 :
The degree of the remainder is always less than the degree of the divisor.
Question 80 :
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 81 :
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 83 :
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 84 :
Simplify:Find$\ x(x + 1) (x + 2) (x + 3) \div  x(x + 1)$<br/>
Question 86 :
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 88 :
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 89 :
If $\alpha , \beta $ are the roots of the equation $ax^{2}+bx+c=0$, find the value of $\alpha ^{2}+\beta ^{2}$.
Question 91 :
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 92 :
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 93 :
What is $\dfrac {x^{2} - 3x + 2}{x^{2} - 5x + 6} \div \dfrac {x^{2} - 5x + 4}{x^{2} - 7x + 12}$ equal to
Question 94 :
State whether True or False.Divide: $x^2 + 3x -54 $ by $ x-6 $, then the answer is $x+9$.<br/>
Question 96 :
Work out the following divisions.<br/>$96abc(3a -12) (5b +30)\div  144(a-  4) (b+  6)$<br/>
Question 97 :
Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.$49x^2-81$<br/>
Question 99 :
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 100 :
What is the remainder, when<br>$(4{x^3} - 3{x^2} + 2x - 1)$ is divided by (x+2)?<br>
Question 101 :
The ratio of the areas of two similar triangles is $25:16$. The ratio of their perimeters is ..............
Question 102 :
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 103 :
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 104 :
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 106 :
 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 107 :
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 108 :
If three sides of a right-angled triangle are integers in their lowest form, then one of its sides is always divisible by
Question 109 :
Which of the following can be the sides of a right angled triangle ?
Question 110 :
In $\triangle{ABC}$, $\angle{B}=90$, $AB=8\:cm$ and $BC=6\:cm$.The length of the median BM is
Question 111 :
In $\Delta$ ABC, $\angle B = 90$, AB = 8 cm and BC = 6 cm. The length of the median BM is<br>
Question 112 :
We use ........... formula to find the lengths of the right angled triangles.
Question 113 :
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 114 :
A............can never be made up of all odd numbers or two even numbers and one odd number.
Question 115 :
Find hypotenuse of right angled triangle if the sides are $12,4\sqrt 3$
Question 116 :
A right angled triangle has $24,7cm $ as its sides . What will be its hypotenuse?
Question 117 :
Can we construct sets of Pythagorean Triples with all even numbers?
Question 118 :
 A Pythagorean Triplet always...............of all even numbers, or two odd numbers and an even number.
Question 119 :
It is easy to construct sets of Pythagorean Triples, When m and n are any two ............... integers.
Question 120 :
Is it true that a Pythagorean Triple can never be made up of all oddnumbers?
Question 121 :
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 122 :
In a $\Delta$ABC, if $AB^2\, =\, BC^2\, +\, AC^2$, then the right angle is at:
Question 123 :
The length of the hypotenuse of a right angled $\Delta$ le whose two legs measure 12 cm and 0.35 m is:
Question 125 :
Select the correct alternative and write the alphabet of that following :<br>Out of the following which is the Pythagorean triplet ?
Question 126 :
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 127 :
A right-angles triangle has hypotenuse $13$ cm, one side is $12$ cm, then the third side is _________.
Question 128 :
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 129 :
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 130 :
Which of the following cannot be the sides a right angle triangle?<br>
Question 131 :
Given the measures of the sides of the triangle , identify which measures are in the ratio 3 : 4 : 5
Question 132 :
In $\Delta ABC,$ if $AB =6\sqrt{3}$ cm, $AC=12$ cm and $BC=6$ cm, then angle B is equal to:<br/>
Question 133 : <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 134 :
A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.
Question 135 :
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 137 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$3cm, 8cm, 6cm$
Question 138 :
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 139 :
In $\Delta$ ABC, angle C is a right angle, then the value<br>of tan $A + tan B $is<br><br>
Question 140 :
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 141 :
Which of the following could be the side lengths of a right triangle?
Question 142 :
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 143 :
The hypotenuse 'c' and one arm 'a' of a right triangle are consecutive integers. The square of the second arm is:
Question 144 :
There is a Pythagorean triplet whose one member is $6$ and other member is $10$
Question 145 :
In$ \displaystyle \bigtriangleup $ ABC , angle C is a right angle, then the value of$ \displaystyle \tan A+ \tan B is $
Question 146 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$
Question 147 :
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 148 :
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 149 :
The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$
Question 150 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>
Question 151 :
$M(2, 6)$ is the midpoint of $\overline {AB}$. If $A$ has coordinates $(10, 12)$, the coordinates of $B$ are
Question 152 :
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 154 :
The centroid of the triangle with vertices (2,6), (-5,6) and (9,3) is
Question 155 :
The ratio in which the line joining the points $(3, 4)$ and $(5, 6)$ is divided by $x-$axis :
Question 156 :
Find the distance from the point (2, 3) to the line 3x + 4y + 9 = 0
Question 157 :
The points which trisect the line segment joining the points $(0,0)$ and $(9,12)$ are
Question 158 :
If a point $C$ be the mid-point of a line segment $AB$, then $AC = BC = (...) AB$.
Question 159 :
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 160 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?
Question 161 :
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 162 :
Distance between the points $(2,-3)$ and $(5,a)$ is $5$. Hence the value of $a=$............
Question 164 :
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 166 :
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 167 :
$A=\left(2,-1\right), B=\left(4,3\right)$. If $AB$ is extended to $C$ such that $AB=BC$, then $C=$
Question 168 :
The ratio, in which the line segment joining (3, -4) and (-5, 6) is divided by the x-axis is
Question 169 :
If $A$ and $B$ are the points $(-3,4)$ and $(2,1)$, then the co-ordinates of the point $C$ on $AB$ produced such that $AC=2BC$ are 
Question 172 :
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 173 :
A(3 , 2) and B(5 , 4) are the end points of a line segment . Find the co-ordinates of the mid-point of the line segment .
Question 174 : <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 175 :
Which of the following points is not 10 units from the origin ?
Question 176 :
Find the value of $x$ if the distance between the points $(2, -11)$ and $(x, -3)$ is $10$ units.
Question 177 :
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 178 :
The coordinates of the midpointof a line segment joining$P ( 5,7 )$ and Q $( - 3,3 )$ are
Question 179 :
If the points (1,1) (2,3) and (5,-1) form a right triangle, then the hypotenuse is of length
Question 180 :
The distance between the points (sin x, cos x) and (cos x -sin x) is
Question 181 :
If the distance between the points $(4, p)$ and $(1, 0)$ is $5$, then the value of $p$ is:<br/>
Question 183 :
The distance between the points $(3,5)$ and $(x,8)$ is $5$ units. Then the value of $x$ 
Question 184 :
In what ratio, does $P(4, 6)$ divide the join of $A(-2, 3)$ and $B(6, 7)$
Question 185 :
The ratio in which the line segment joining (3,4) and (-2,1) is divided by the y-axis is
Question 187 :
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 188 :
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 189 :
How far is the line 3x - 4y + 15 = 0 from the origin?
Question 190 :
The points $(-2, -1), (1, 0),(4, 3),$ and $(1, 2)$ are the vertices
Question 191 :
The point which lies in the perpendicular bisector of the line segment joining the points A (-2, -5) and B (2,5) is
Question 192 :
An isosceles triangle has vertices at (4,0), (-4,0), and (0,8) The length of the equal sides is
Question 193 :
Find the co-ordinates of the mid point of a point that divides AB in the ratio 3 : 2.
Question 194 :
Find the distance from the point (5, -3) to the line 7x - 4y - 28 = 0
Question 195 :
Given the points $A(-1,3)$ and $B(4,9)$.Find the co-ordinates of the mid-point of $AB$
Question 198 :
$P$ 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 199 :
A point R (2,-5) divides the line segment joining the point A (-3,5) and B (4,-9) , then the ratio is
Question 200 :
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 202 :
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 203 :
If $A+B+C=\dfrac { 3\pi }{ 2 } $, then $cos2A+cos2B+cos2C$ is equal to
Question 204 :
The expression$ \displaystyle \left (\tan \Theta +sec\Theta \right )^{2} $ is equal to
Question 205 :
If $3\sin\theta + 5 \cos\theta =5$, then the value of $5\sin\theta -3 \cos\theta $ are 
Question 206 :
Choose the correct option. Justify your choice.<br/>$\displaystyle 9{ \sec }^{ 2 }A-9{ \tan }^{ 2 }A=$<br/>
Question 209 :
Simplest form of $\displaystyle \dfrac{1}{\sqrt{2 + \sqrt{2 + \sqrt{2 + 2 cos 4x}}}}$ is
Question 210 :
Express$\displaystyle \cos { { 79 }^{ o } } +\sec { { 79 }^{ o } }$ in terms of angles between$\displaystyle { 0 }^{ o }$ and$\displaystyle { 45 }^{ o }$
Question 211 :
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 212 :
Value of ${ cos }^{ 2 }{ 135 }^{ \circ  }$
Question 216 :
$\left( \dfrac { cosA+cosB }{ sinA-sinB }  \right) ^{ 2014 }+\left( \cfrac { sinA+sinB }{ cosA-cosB }  \right) ^{ 2014 }=...........$
Question 217 :
Given $tan \theta = 1$, which of the following is not equal to tan $\theta$?
Question 218 :
$\tan \theta$ increases as $\theta$ increases.<br/>If true then enter $1$ and if false then enter $0$.<br/>
Question 219 :
Solve : $\dfrac { 2tan{ 30 }^{ \circ  } }{ 1+{ tan }^{ 2 }{ 30 }^{ \circ  } } $
Question 220 :
If $\displaystyle \tan { \theta  } =\frac { 1 }{ 2 } $ and $\displaystyle \tan { \phi  } =\frac { 1 }{ 3 } $, then the value of $\displaystyle \theta +\phi $ is:
Question 221 :
IF $ \displaystyle \tan \theta =\sqrt{2}    $ , then the value of $ \displaystyle \theta     $ is 
Question 222 :
Given $\cos \theta = \dfrac{\sqrt3}{2}$, which of the following are the possible values of  $\sin 2 \theta$?
Question 223 :
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 224 :
If $\displaystyle  \cos A+\cos ^2A=1$ then the value of $\displaystyle  \sin ^{2}A+\sin ^{4}A$ is
Question 225 :
The value of $\sqrt { 3 } \sin { x } +\cos { x } $ is max. when $x$ is equal to
Question 226 :
Solve:$\displaystyle \sin ^{4}\theta +2\cos ^{2}\theta \left ( 1-\frac{1}{\sec ^{2}\theta } \right )+\cos ^{4}\theta $
Question 227 :
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 230 :
Select and wire the correct answer from the given alternatives. <br/>$\cos \left(\dfrac {3\pi}{2}+\theta \right)=$ ____
Question 233 :
As value of $x$ increases from $0$ to $\cfrac{\pi}{2}$, the value of $\cos {x}$:
Question 234 :
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 235 :
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 237 :
Find the value of $\sin^3\left( 1099\pi -\dfrac { \pi  }{ 6 }  \right) +\cos^3\left( 50\pi -\dfrac { \pi  }{ 3 }  \right) $
Question 239 :
If $\sin \theta + \cos\theta = 1$, then what is the value of $\sin\theta \cos\theta$?
Question 240 :
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 243 :
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 244 :
Choose and write the correct alternative.<br>If $3 \sin \theta = 4 \cos \theta$ then $\cot \theta = ?$<br>
Question 245 :
IF A+B+C=$ \displaystyle 180^{\circ}  $ ,then $  tan A+tanB+tanC $ is equal to
Question 248 :
The solution of $(2 cosx-1)(3+2 cosx)=0$ in the interval $0 \leq \theta \leq 2\pi$ is-
Question 249 :
Maximum value of the expression $\begin{vmatrix} 1+{\sin}^{2}x & {\cos}^{2}x & 4\sin2x \\ {\sin}^{2}x & 1+{\cos}^{2}x & 4\sin2x \\ {\sin}^{2}x & {\cos}^{2}x & 1+4\sin2x \end{vmatrix}=$
Question 250 :
Which of the following is equal to $\sin x \sec x$?
Question 251 :
If the probability of the occurrence of an event is P then what is the probability that the event doesn't occur.
Question 252 :
If I calculate the probability of an event and it turns out to be $7$, then I surely know that<br/>
Question 253 :
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 254 :
If $P(A) = \dfrac{5}{9}$, then the odds against the event $A$ is
Question 255 :
If the odd in favour of an event are $4$ to $7$, find the probability of its no occurence.
Question 257 :
A pair of dice is thrown once The probability that the sum of the outcomes is less than 11 is
Question 258 :
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 259 :
A die is thrown .The probability that the number comes up even is ______ .
Question 260 :
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 262 :
The probability of an event happening and the probability of the same event not happening (or the complement) must be a <br/>
Question 263 :
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 264 :
What is the maximum value of the probability of an event?
Question 265 :
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 267 :
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 268 :
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 269 :
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 270 :
The probability of an event $A$ lies between $0$ and $1$, both inclusive. Which mathematical expression best describes this statement?<br/>
Question 271 :
Two dice are thrown. Find the odds in favour of getting the sum $4$.<br/>
Question 272 :
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 273 :
The probability expressed as a percentage of a particular occurrence can never be
Question 274 :
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 276 :
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 277 : 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 278 :
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 279 :
According to the property of probability, $P(\phi) = 0$ is used for <br>
Question 280 :
If radius of a circle is increased to twice its original length, how much will the area of the circle increase ?
Question 281 :
The circumference of a circular field is $308 m$. Find its radius in metres.
Question 282 :
The area of two circles are in the ratio $25 : 36$. Then the ratio of their circumference is _________.
Question 283 :
If the radius and arc length of a sector are 17 cm and 27 cm respectively, then the perimeter is
Question 284 :
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 285 :
A circular disc of radius $10 cm$ is divided into sectors with angles $120^o$ and $150^o$, then the ratio of the area of two sectors is
Question 286 :
Area of a circle with diameter 'm' radius 'n' and circumference 'p' is
Question 287 :
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 288 :
If the radius of a circle increased by 20% then the corresponding increase in the area of circle is ................
Question 289 :
A roller of diameter 70 cm and length 2m is rolling on the ground What is the area covered by the roller in 50 revolutions?
Question 290 :
The angle of sector with area equal to one fifth of total area of whole circle 
Question 291 :
Lengthof an arc of a circle with radius $r$ and central angle $\theta$is(angle in radians):
Question 292 :
If the area of a circle is $346.5 \displaystyle cm^{2}$. Its circumference is
Question 293 :
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 294 :
The perimeter of a sector of a circle is $56$ cms and the area of the circle is $64\pi$ sq. cms  Find the area of sector.
Question 296 :
If the radius of a circle is tripled, the ares becomes.
Question 297 :
Circular dome is a 3D example of which kind of sector of the circle?
Question 298 :
If one side of a square is 2.4 m. Then what will be the area of the circle inscribed in the square?
Question 300 :
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 301 :
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 302 :
The area of a sector formed by two mutually perpendicular radii in $\odot \left( 0,5cm \right) $ is ............... ${cm}^{2}$.
Question 303 :
The circumference of a circular field is $528\ m$. Then its area  is
Question 304 :
A wire of length $36$ cm is bent in the form of a semicircle. What is the radius of the semicircle?
Question 305 :
If the area of the circle be $ \displaystyle 154 cm^{2},$ then its radius is equal to:
Question 306 :
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 307 :
A circular disc of radius 10 cm is divided into sectors with angles $ \displaystyle 120^{\circ}   $ and  $ \displaystyle 150^{\circ}   $ then  the ratio of the areas of two sectors is
Question 308 :
The perimeter of a sector of a circle is 37cm. If its radius is 7cm, then its arc length is
Question 309 :
The sum of the circumference and diameter of a circle is $116 cm$. Find its radius.
Question 310 :
Find the area of equilateral  triangle inscribed in a circle of unit radius.
Question 311 :
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 312 :
The radius of a wheel is $0.25 m$. How many rounds will it take to complete the distance of $11 km$?
Question 313 :
If the radius of a circle be r cm then its area will be equal to-
Question 314 :
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 315 :
If 'c' be the circumference and 'd' be the diameter then the value of$ \displaystyle \pi $ is equal to-<br>
Question 316 :
What is the minimum radius $(>1)$ of a circle whose circumference is an integer?
Question 317 :
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 318 :
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 319 :
If a circle is divided into two equal parts, then equal part of the circle is called ________.
Question 320 :
The diameter of a circle is $1$. Calculate the area of the circle.
Question 321 :
If the difference between the circumference and radius of a circle is 37 cm then its diameter is
Question 322 :
If the circumference of a circle be 8.8 m then its radius is equal to -
Question 324 :
If the diameter of a circle is increased by 200% then its area is increased by<br>
Question 325 :
The length of minor arc $\widehat {AB}$ of a circle with radius $7$ units  is $14$. Find the length of major arc $\widehat {AB}$.
Question 326 :
If the circumference of a circle is reduced by 50 % then the area will be reduced by
Question 327 :
Say true or false:A sector is a region between the chord and its corresponding arc.
Question 328 :
A sector of a circle with sectorial angle of$\displaystyle 36^{\circ} $ has an area of 15.4 sq cm The length of the arc of the sector is
Question 331 :
According to Euclid's division algorithm, HCF of any two positive integers a and b with a > b is obtained by applying Euclid's division lemma to a and b to find q and r such that $a = bq + r$, where r must satisfy<br/>
Question 334 :
$2\times 2\times 2\times 3\times 3\times 13 = 2^{3} \times 3^{2} \times 13$ is equal to
Question 336 :
The LCM of 54 90 and a third number is 1890 and their HCF is 18 The third number is
Question 337 :
............. states that for any two positive integers $a$ and $b$ we can find two whole numbers $q$ and $r$ such that $a = b \times q + r$ where $0 \leq r < b .$
Question 338 :
Euclid's division lemma states that for two positive integers a and b, there exist unique integers q and r such that $a = bq + r$, where r must satisfy<br>
Question 341 :
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 342 :
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 343 :
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 344 :
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 345 :
State whether the following statement is true or not:$\left( 3+\sqrt { 5 }  \right) $ is an irrational number. 
Question 349 :
Use Euclid's division lemma to find the HCF of the following<br/>16 and 176
Question 350 :
The greatest number that will divided $398, 436$ and $542$ leaving $7,11$ and $14$ remainders, respectively, is
Question 352 :
What is the HCF of $4x^{3} + 3x^{2}y - 9xy^{2} + 2y^{3}$ and $x^{2} + xy - 2y^{2}$?
Question 353 :
State whether the following statement is true or false.The following number is irrational<br/>$6+\sqrt {2}$
Question 354 :
Without actually dividing find which of the following are terminating decimals.
Question 356 :
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 357 :
................. states the possibility of the prime factorization of any natural number is unique. The numbers can be multiplied in any order.
Question 358 :
If $a=\sqrt{11}+\sqrt{3}, b =\sqrt{12}+\sqrt{2}, c=\sqrt{6}+\sqrt{4}$, then which of the following holds true ?<br/>
Question 360 :
Assertion: $\displaystyle \frac{13}{3125}$ is a terminating decimal fraction.
Reason: If $q=2^n \cdot 5^m$ where $n, m$ are non-negative integers, then $\displaystyle \frac{p}{q}$ is a terminating decimal fraction.
Question 362 :
Determine the HCF of $a^2 - 25, a^2 -2a -35$ and $a^2+12a+35$
Question 363 :
Fundamental theorem of arithmetic is also called as ______ Factorization Theorem.
Question 364 :
Which of the following irrational number lies between $\dfrac{3}{5}$ and $\dfrac{9}{10}$
Question 365 :
State whether the following statement is true or false.The following number is irrational<br/>$7\sqrt {5}$
Question 367 :
State the following statement is True or False<br>35.251252253...is an irrational number<br>
Question 372 :
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 375 :
For three irrational numbers $p,q$ and $r$ then $p.(q+r)$ can be
Question 376 :
Euclids division lemma can be used to find the $...........$ of any two positive integers and to show the common properties of numbers.
Question 377 :
We need blocks to build a building. In the same way _______ are basic blocks to form all natural numbers .
Question 378 :
Using fundamental theorem of Arithmetic find L.C.M. and H.C.F of $816$ and $170$.
Question 379 :
H.C.F. of $x^3 -1$ and $x^4 + x^2 + 1$ is
