Question 1 :
We need blocks to build a building. In the same way _______ are basic blocks to form all natural numbers .
Question 5 :
Use Euclid's division lemma to find the HCF of the following<br/>16 and 176
Question 6 :
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 9 :
Use Euclid's division algorithm to find the HCF of :$196$ and $38220$
Question 10 :
If $a=107,b=13$ using Euclid's division algorithm find the values of $q$ and $r$ such that $a=bq+r$
Question 12 :
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 13 :
Fundamental theorem of arithmetic is also called as ______ Factorization Theorem.
Question 15 :
Determine the HCF of $a^2 - 25, a^2 -2a -35$ and $a^2+12a+35$
Question 18 :
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 20 :
Euclids division lemma, the general equation can be represented as .......
Question 21 :
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 22 :
State the following statement is True or False<br>35.251252253...is an irrational number<br>
Question 23 :
............. 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 26 :
Which of the following irrational number lies between $\dfrac{3}{5}$ and $\dfrac{9}{10}$
Question 27 :
State whether the following statement is true or not:$\left( 3+\sqrt { 5 }  \right) $ is an irrational number. 
Question 28 :
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 29 :
State whether the following statement is True or False.<br/>3.54672 is an irrational number.
Question 30 :
Using fundamental theorem of Arithmetic find L.C.M. and H.C.F of $816$ and $170$.
Question 33 :
State True or False:$4\, - \,5\sqrt 2 $ is irrational if $\sqrt 2 $ is irrational.
Question 34 :
Without actually dividing find which of the following are terminating decimals.
Question 35 :
The ........... when multiplied always give a new unique natural number.
Question 36 :
The statement dividend $=$ divisor $\times$ quotient $+$ remainder is called 
Question 38 :
State whether the following statement is true or false.The following number is irrational<br/>$6+\sqrt {2}$
Question 39 :
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 41 :
Euclids division lemma can be used to find the $...........$ of any two positive integers and to show the common properties of numbers.
Question 43 :
What is the HCF of $4x^{3} + 3x^{2}y - 9xy^{2} + 2y^{3}$ and $x^{2} + xy - 2y^{2}$?
Question 45 :
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is<br>
Question 46 :
The greatest number that will divided $398, 436$ and $542$ leaving $7,11$ and $14$ remainders, respectively, is
Question 48 :
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 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 51 :
Use Euclid's division lemma to find the HCF of $40$ and $248$.
Question 52 :
The simplified form of the expression $\sqrt { \sqrt [ 3 ]{ 729{ x }^{ 12 } }  } -\dfrac { { x }^{ -2 }-{ x }^{ -3 } }{ { x }^{ -4 }-{ x }^{ -5 } } $ is
Question 53 :
 One and only one out of  $n, n + 4, n + 8, n + 12\  and \ n + 16 $ is ......(where n is any positive integer)<br/>
Question 55 :
The given pair of number $ 231, 396$ are __________ .<br/>
Question 56 :
Which of the following irrational number lies between 20 and 21
Question 60 :
If HCF of numbers $408$ and $1032$ can be expressed in the form of $1032x -408 \times 5$, then find the value of $x$.
Question 61 :
$n$  is a whole number which when divided by  $4$  gives  $3 $ as remainder. What will be the remainder when  $2n$  is divided by $4$ ?<br/>
Question 62 :
The H. C. F. of $252$, $324$ and $594$ is ____________.
Question 63 :
Write whether every positive integer can be of the form $4q + 2$, where $q$ is an integer.<br/>
Question 64 :
The value of $\sqrt { 1+2\sqrt { 1+2\sqrt { 1+2+.... } } }$ is
Question 65 :
If $x=6+2\sqrt {6}$, then what is the value of $\sqrt { x-1 } +\cfrac { 1 }{ \sqrt { x-1 } } $?
Question 67 :
The divisor when the quotient, dividend and the remainder are respectively $547, 171282$ and $71$ is equal to 
Question 68 :
State true or false of the following.<br>If a and b are natural numbers and $a < b$, than there is a natural number c such that $a < c < b$.<br>
Question 69 :
We know that any odd positive integer is of the form $4q + 1 $ or $4q + 3$ for some integer $q.$<br/>Thus, we have the following two cases.<br/>
Question 70 :
State whether the given statement is True or False :<br/>$5-2\sqrt { 3 } $ is an irrational number.
Question 71 :
State true or false. $\sqrt { 3 } + \sqrt { 4 }$ is an rational number.
Question 72 :
If $a$ is an irrational number then which of the following describe the additive inverse of $a$.
Question 75 :
There are five odd numbers $1, 3, 5, 7, 9$. What is the HCF of these odd numbers?
Question 76 :
State whether True or False :<br/>All the following numbers are irrationals.<br/>(i) $\dfrac { 2 }{ \sqrt { 7 }  } $ (ii) $\dfrac { 3 }{ 2\sqrt { 5 }  }$ (iii) $4+\sqrt { 2 } $ (iv) $5\sqrt { 2 } $
Question 78 :
State whether the given statement is True or False :<br/>$2-3\sqrt { 5 }$ is an irrational number.
Question 79 :
When the HCF of $468$ and $222$ is written in the form of  $ 468 x + 222y$ then the value of $ x$ and $y$ is 
Question 80 :
Find HCF of $70$ and $245$ using Fundamental Theorem of Arithmetic. 
Question 81 :
 The square of any positive odd integer for some integer $ m$ is of the form <br/>
Question 82 :
If $d$ is the $HCF$ of 45 and 27, then $x, y$ satisfying $d=27x+45y$ are :
Question 84 :
State whether the given statement is true/false:$\sqrt{p} + \sqrt{q}$, is irrational, where <i>p,q</i> are primes.
Question 86 :
Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.<br/>$\dfrac { 13 }{ 3125 } $
Question 87 :
State whether the given statement is True or False :If $p,  q $ are prime positive integers, then $\sqrt { p } +\sqrt { q } $ is an irrational number.<br/>
Question 88 :
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.<br/>$\dfrac {29}{343}$<br/>
Question 89 :
If the H.C.F. of $A$ and $B$ is $24$ and that of $C$ and $D$ is $56,$ then the H.C.F. of $A, B, C$ and $D$ is
Question 90 :
Using the theory that any positive odd integers are of the form $4 q + 1$ or $4 q + 3$ where $q$ is a positive integer. If quotient is $4$, dividend is $19$ what will be the remainder?
Question 92 :
If any positive' even integer is of the form 4q or 4q + 2, then q belongs to:<br/>
Question 93 :
Sum of digits of the smallest number by which $1440$ should be multiplied so that it becomes a perfect cube is
Question 94 :
If the square of an odd positive integer can be of the form $6q + 1 $ or  $6q + 3$ for some $ q$ then q belongs to:<br/>
Question 95 :
Find the dividend which when a number is divided by $45$ and the quotient was $21$ and remainder is $14.$
Question 99 :
A number when divided by $114$ leaves the remainder $21.$ If the same number is divided by $19$ the remainder will be
Question 102 :
Find the expression which is equivalent to : $\displaystyle \frac { { x }^{ 3 }+{ x }^{ 2 } }{ { x }^{ 4 }+{ x }^{ 3 } } $?
Question 105 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$a^2-b^2 ; a-b$
Question 106 :
Factorise the expressions and divide them as directed.$4yz(z^2 + 6z-  16)\div  2y(z + 8)$<br/>
Question 108 :
If $\alpha , \beta $ are the roots of the equation $ax^{2}+bx+c=0$, find the value of $\alpha ^{2}+\beta ^{2}$.
Question 110 :
If $\alpha , \beta$ are the zeros of the polynomials $f(x) = x^2+x+1 $ then $\dfrac{1}{\alpha}+\dfrac{1}{\beta}=$________.
Question 111 :
What must be added to $x^3-3x^2-12x + 19$, so that the result is exactly divisible by $x^2 + x-6$?
Question 112 :
The product of the roots of the quadratic equation $2x^{2}-8x+3=0$ is
Question 113 :
Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.$49x^2-81$<br/>
Question 114 :
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 115 :
$\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 116 :
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 117 :
If the roots of ${ x }^{ 2 }-2mx+{ m }^{ 2 }-1=0$ lie between $-2$ and $4$, then
Question 118 :
Factorise the expressions and divide them as directed.$12xy(9x^2-  16y^2)\div  4xy(3x + 4y)$
Question 121 :
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 122 :
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 124 :
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 125 :
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 126 :
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 127 :
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 129 :
State whether True or False.Divide : $a^2 +7a + 12 $ by $  a + 4 $, then the answer is $a+3$.<br/>
Question 130 :
If $x\ne -5$ , then the expression $\cfrac{3x}{x+5}\div \cfrac {6}{4x+20}$ can be simplified to
Question 132 :
Work out the following divisions.$10y(6y + 21) \div 5(2y + 7)$<br/>
Question 133 :
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 135 :
Simplify:$20(y + 4) (y^2 + 5y + 3) \div 5(y + 4)$<br/>
Question 136 :
If a polynomial $p(x)$ is divided by $x - a$ then remainder is<br/>
Question 139 :
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 140 :
Is $(3x^{2} + 5xy + 4y^{2})$ a factor of $ 9x^{4} + 3x^{3}y + 16x^{2} y^{2} + 24xy^{3}  + 32y^{4}$?<br/>
Question 144 :
State whether True or False.Divide: $x^2 + 3x -54 $ by $ x-6 $, then the answer is $x+9$.<br/>
Question 148 :
Work out the following divisions.<br/>$96abc(3a -12) (5b +30)\div  144(a-  4) (b+  6)$<br/>
Question 150 :
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 151 :
$\left[2x\right]-2\left[x\right]=\lambda$ where $\left[.\right]$ represents greatest integer function and $\left\{.\right\}$ represents fractional part of a real number then 
Question 152 :
If $\alpha$ and $\beta$ be two zeros of the quadratic polynomial $ax^2+bx+c$, then evaluate:$\alpha^3+\beta^3$<br/>
Question 153 :
If equation $\displaystyle { x }^{ 2 }+8x+p=0$ has real and distinct roots then
Question 154 :
If $\alpha, \beta$ are real and $\alpha^2, -\beta^2$ are the roots of $a^2 x^2 + x+1-a^2=0;\ (a  >  1)$, then $\beta^2=$
Question 156 :
Value(s) of k for which the quadratic equation$2x^{2} - kx + k = 0$. has equal roots is
Question 157 :
If $\alpha$ and $\beta$ are the roots of $x^2 - ax + b^2 = 0$, then $\alpha^2 + \beta^2$ is equal to
Question 158 :
Divide $\displaystyle 8\left( 3x+4 \right) \left( 8x+9 \right) $ by $\displaystyle \left( 3x+4 \right) $
Question 159 :
Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing $f(x) =10x^4 +17x^3-62x^2+30x -3$ by $g(x) =2x^2-x+1$
Question 160 :
If a and b are the roots of the quadratic equation$\displaystyle { 2x }^{ 2 }-6x+3=0$, find the value of<br>$\displaystyle { a }^{ 3 }+{ b }^{ 3 }-3ab\left( { a }^{ 2 }+{ b }^{ 2 } \right) -3ab\left( a+b \right)$.<br>
Question 161 :
If the equation$\displaystyle{ px }^{ 2 }+2x+p=0$ hastwo distinct roots if.
Question 162 :
Find the zeros of the quadratic polynomial $f(x) = x^2-3x -28$ and verify the relationships between the zeros and the coefficients.
Question 163 :
The remainder obtained by dividing$ \displaystyle x^{n}-\frac{a}{b} $ by ax-b is
Question 165 :
The product of the roots of the equation $(x -2)^2 -3(x -2) + 2 = 0$ is
Question 167 :
Divide $\displaystyle 4{ x }^{ 2 }{ y }^{ 2 }\left( 6x-24 \right) \div 4xy\left( x-4 \right) $
Question 169 :
Divide the following and write your answer in lowest terms: $\dfrac{x^2-4x-5}{x^2-25}\div \dfrac{x^2-3x-10}{x^2+7x+10}$
Question 170 :
The sum of the reciprocals of the roots of the equation$\displaystyle \frac{2009}{2010}x+1+\frac{1}{x}=0$ is
Question 171 :
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 172 :
Find the Quotient and the Remainder when the first polynomial is divided by the second.<br/>$(x^3+1) $ by $(x+1)$
Question 173 :
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 174 :
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 175 :
Divide the following and write your answer in lowest terms: $\dfrac{x}{x+1}\div \dfrac{x^2}{x^2-1}$
Question 176 :
If one of the zeros of a quadratic polynomial of the form $x^2 + ax + b$ is the negative of the other, then it<br>
Question 177 :
When $(x^{3} - x^{2} - 5x - 3)$ is divided by $(x - 3)$, the remainder is
Question 178 :
Consider the equation ${x^2} + 2x - n = 0$, where $n \in N$ and $n \in \left[ {5,100} \right]$. Total number of different values of 'n' so that the given equation has integral roots, is
Question 179 :
Divide :$\displaystyle \left[ { x }^{ 4 }-{ \left( y+z \right)  }^{ 4 }\right] \ by \left[{ x }^{ 2 }+{ \left( y+z \right)  }^{ 2 }\right]$
Question 180 :
Divide the following and write your answer in lowest terms: $\dfrac{3x^2-x-4}{9x^2-16}\div \dfrac {4x^2-4}{3x^2-2x-1}$
Question 181 :
If the polynomial $(x + 1)^{2015} - x^{2015} - 1$ is divided by $(x + x^2 + x^3)$, then the remainder is
Question 183 :
If $x^4 \, + \, 2x^3 \, - \, 3x^2 \, + \, x \, - \, 1$ is divided by $x - 2$. then the remainder is
Question 185 :
Evaluate: $96 abc (3a -12)(5b -30) \div 144 (a -4) (b -6)$
Question 186 :
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 187 :
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 188 :
$mx^2+(m-1)x +2=0$ has roots on either side of x=1 the m $\in$
Question 191 :
The sum of all real roots of the equation ${|x-2|}^2+|x-2|-2=0$ is
Question 192 :
If$\displaystyle \alpha ,\beta$ are the roots of the equation$\displaystyle { x }^{ 2 }-x-4=0$, find the value of$\displaystyle \frac { 1 }{ \alpha } +\frac { 1 }{ \beta } -\alpha \beta$.
Question 193 :
The possible values of p for which the equation$\displaystyle { x }^{ 2 }+px+64=0$ and$\displaystyle { x }^{ 2 }-8x+p=0$ will both have real roots is
Question 195 :
Workout the following divisions<br/>$36(x + 4) (x^2 + 7x + 10) \div 9(x + 4)$
Question 197 :
Simplify: $\cfrac { { x }^{ 2 }-4x-21 }{ { x }^{ 2 }-9x+14 } $
Question 200 :
The condition that one root is twice the other root of the quadratic equation$\displaystyle x^{2}+px+q=0$ is
Question 201 :
Find the value of p for which the given equation has real roots.<br>$\displaystyle8p{ x }^{ 2 }-9x+3=0$<br>
Question 202 :
Divide $\displaystyle 10{ a }^{ 2 }{ b }^{ 2 }\left( 5x-25 \right)$ by $15ab\left( x-5 \right) $
Question 203 :
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 204 :
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 205 :
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 206 :
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 208 :
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 210 :
The difference of the roots of$\displaystyle 2y^{2}-ky+16=0$ is 1/3 Find k
Question 211 :
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 212 :
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 213 :
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 214 :
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 215 :
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 216 :
Simplify: $\displaystyle \frac { 45\left( { a }^{ 4 }-3{ a }^{ 3 }-28{ a }^{ 2 } \right)  }{ 9a\left( a+4 \right)  } $
Question 217 :
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 218 :
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 219 :
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 220 :
$x_1$ 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 221 :
The number of integers $n$ for which $3x^3-25x+n=0$ has three real roots is$?$<br/>
Question 222 :
Simplify: $\displaystyle \frac { 49\left( { x }^{ 4 }-2{ x }^{ 3 }-15{ x }^{ 2 } \right)  }{ 14x\left( x-5 \right)  } $
Question 223 :
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 224 :
Evaluate: $\displaystyle \frac { 35\left( x-3 \right) \left( { x }^{ 2 }+2x+4 \right)  }{ 7\left( x-3 \right)  } $
Question 225 :
$\displaystyle \frac{x^{-1}}{x^{-1} + y^{-1}} + \frac{x^{-1}}{x^{-1} - y^{-1}}$ is equal to
Question 226 :
If (a, 4) lies on the graph of $3x + y = 10$, then the value of a is
Question 227 :
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 228 :
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 229 :
The solution of the simultaneous equations $\displaystyle \frac{x}{2}+\frac{y}{3}=4\: \: and\: \: x+y=10 $ is given by
Question 231 :
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 232 :
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 233 :
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 234 :
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 236 :
The sum of two numbers is $2$ and their difference is $1$. Find the numbers.
Question 237 :
If $p+q=1$ andthe ordered pair (p, q) satisfies $3x+2y=1$,then it also satisfies
Question 239 :
If $x + y = 25$ and $\dfrac{100}{x + y} + \dfrac{30}{x - y} = 6$, then the value of $x - y$ is
Question 240 :
The value of $k$ for which the system of equations $3x + 5y= 0$ and $kx + 10y = 0$ has a non-zero solution, is ________.
Question 242 :
Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$
Question 243 :
The linear equation $y = 2x + 3$ cuts the $y$-axis at 
Question 244 :
What is the equationof Y-axis? Hence, find the point of intersection of Y-axis and the line $y\,=\, 3x\, +\, 2$.
Question 245 :
Five tables and eight chairs cost Rs. $7350$; three tables and five chairs cost Rs. $4475$. The price of a table is
Question 246 :
If $(a, 3)$ is the point lying on the graph of the equation $5x\, +\, 2y\, =\, -4$, then find $a$.
Question 247 :
If $2x + y = 5$, then $4x + 2y$ is equal to _________.
Question 249 :
The values of x and y satisfying the two equation 32x+33y=31, 33x+32y=34 respectively will be
Question 251 :
Solve the following equations:<br/>$x + \dfrac {4}{y} = 1$,<br/>$y + \dfrac {4}{x} = 25$.Then $(x,y)=$
Question 253 :
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 254 :
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 255 :
If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is
Question 256 :
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 258 :
The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point
Question 260 :
Examine whether the point $(2, 5)$ lies on the graph of the equation $3x\, -\, y\, =\, 1$.
Question 261 :
For what value of k does the system of equations$\displaystyle 2x+ky=11\:and\:5x-7y=5$ has no solution?
Question 262 :
What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes ?
Question 263 :
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 264 :
What is the nature of the graphs of a system of linear equations with exactly one solution?
Question 265 :
The graph of the line $5x + 3y = 4$ cuts the $y$-axis at the point
Question 266 :
A member of these family with positive gradient making an angle of$\frac{\pi }{4}$ with the line3x-4y=2, is
Question 267 :
$\dfrac{1}{3}x - \dfrac{1}{6}y = 4$<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 268 :
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 269 :
A line which passes through (5, 6) and (-3. -4) has an equation of
Question 270 :
The unit digit of a number is $x$ and its tenth digit is $y$ then the number will be 
Question 272 :
The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is
Question 273 :
The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is
Question 274 :
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 276 :
Solve: $4x\, +\, \displaystyle \frac{6}{y}\, =\, 15$ and $6x\, -\,  \displaystyle \frac{8}{y}\, =\, 14$<br/>Hence, find 'a' if $y\, =\, ax\, -\, 2$
Question 277 :
The solution of $64^{2x - 5} = 4 \times 8^{x - 5}$ is<br>
Question 278 :
Solve the equations using elimination method:<br>$2x + 3y =15$ and $3x + 3y = 12$
Question 279 :
Solve the following pair of simultaneous equations:$\displaystyle\, 4x\, +\, \frac{3}{y}\, =\, 1\,; 3x\, -\, \frac{2}{y}\, =\, 5$
Question 280 :
Solve the equations using elimination method:<br>$3x + 2y = 7$ and $4x - 3y = -2$
Question 281 :
If $bx+ay=a^2+b^2$ and $ax-by=0$, then the value of $(x-y) $ is<br/>
Question 284 :
What is the value of $a$ for the following equation: $3a + 4b = 13$ and $a + 3b = 1$? (Use cross multiplication method).<br/>
Question 286 :
Solve : $\displaystyle \frac{9}{x}\, -\, \displaystyle \frac{4}{y}\, =\, 8$ and $\displaystyle \frac{13}{x}\, +\, \displaystyle \frac{7}{y}\, =\, 101$
Question 287 :
Solution of the equations $\cfrac{x + 3}{4} + \cfrac{2y + 9}{3} = 3$ and $\cfrac{2x - 1}{2} - \cfrac{y + 3}{4} = 4 \cfrac{1}{2}$ is<br/>
Question 288 :
Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution: $8x + 5y = 9$, $3x + 2y = 4$
Question 289 :
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 290 :
Solve: $4x+\displaystyle \frac{6}{y}= 15$ and $6x-\displaystyle \frac{8}{y}= 14$. Hence, find $a$ if $y= ax-2$
Question 291 :
If $(3)^{x + y} = 81$ and $(81)^{x - y} = 3$, then the values of $x$ and $y$ are<br>
Question 292 :
If $6$ kg of sugar and $5$ kg of tea together cost Rs. $209$ and $4$ kg of sugar and $3$ kg of tea together cost Rs. $131$, then the cost of $1$ kg sugar and $1$ kg tea are respectively<br/>
Question 293 :
Solve the following simultaneous equations by the method of equating coefficients.$x-2y=-10; \, \, 3x-5y=-12$
Question 294 :
A particular work can be completed by $6$ men and $6$ women in $24$ days; whereas the same work can be completed by $8$ men and $12$ women in $15$ days, according to the amount of work done , one man is equivalent to how many women?
Question 295 :
Solve the following pair of simultaneous equations:$\displaystyle \frac{1}{x}\, +\, \frac{1}{y}\, =\, 5\,;\, \frac{1}{x}\, -\, \frac{1}{y}\, =\, 1$
Question 297 :
For what value of $\alpha$, the system of equations<br>$\alpha x+3y=\alpha-3$<br>$12x+\alpha y=\alpha$<br>will have no solution
Question 298 :
Solve the following pair of simultaneous equations:$\displaystyle \frac{6}{x}\, -\, \frac{2}{y}\, =\, 1\,;\, \frac{9}{x}\, -\, \frac{6}{y}\,=\, 0$
Question 299 :
Solve the equations using elimination method:<br>$2x - y = 20$ and $4x + 3y = 0$
Question 300 :
If 10y = 7x - 4 and 12x + 18y = 1; find the values of 4x + 6y and 8y - x.
Question 301 :
The number of solutions for the system of equations $2x + y = 4, 3x + 2y = 2$ and $x + y = - 2$ is
Question 302 :
The expression ax + b is equal to 13 when x is 5and ax + b is equal to 29 when x is 13. The valueof expression when x is 0.5
Question 303 :
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 304 :
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 305 :
Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$\dfrac {1}{(x-1)}+\dfrac {1}{(y-2)}=2, \ \dfrac {6}{(x-1)}-\dfrac {2}{(y-2)}=1$<br/>
Question 306 :
Find the value of x and y using cross multiplication method: <br>$3x - 5y = -1$ and $x + 2y = -4$
Question 308 :
Solve: $4x+\displaystyle \frac{6}{y}= 15$ and $6x-\displaystyle \frac{8}{y}= 14$. Hence find the value of $k$, if $y= kx-2$.
Question 309 :
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 310 :
a, b, c (a > c) are the three digits, from left to right of a three digit number. If the number with these digits reversed is subtracted from the original number, the resulting number has the digit 4 in its unit's place. The other two digits from left to right are -
Question 311 :
Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution:$1.5x + 0.1y = 6.2$, $3x - 0.4y = 11.2$
Question 312 :
Solve the set of equations: $3\left ( 2u+v \right )= 7uv$ and $3\left ( u+3v \right )= 11uv$
Question 313 :
Find the value of x and y using cross multiplication method: <br>$x - 6y = 2$ and $x + y = 4$
Question 315 :
Solve the following pair of linear (simultaneous) equations by the method of elimination:<br/>$2x+7y= 39$<br/>$3x+5y= 31$
Question 317 :
Find the value of x and y using cross multiplication method: <br>$x + y = 15$ and $x - y = 3$
Question 318 :
Solve the following pair of equations :$x\, -\, y\, =\, 0.9$<br/>$\displaystyle \frac{11}{2\, (x\, +\, y)}\, =\, 1$
Question 319 :
Solve: $4x\, +\, \displaystyle \frac{6}{y}\, =\, 15$ and $6x\, -\, \displaystyle \frac{8}{y}\, =\, 14$
Question 320 :
Solve the following pairs of equations by reducing them to a pair of linear equations.<br/>$\displaystyle \frac{3}{x+1}-\frac{1}{y+1}=2$ and $\dfrac{6}{x+1}-\dfrac{1}{y+1}=5$
Question 321 :
If $2p + 3q = 18$ and $4p^{2} + 4pq - 3q^{2} - 36 = 0$ then what is $(2p + q)$ equal to?
Question 322 :
Find the value of x and y using cross multiplication method: <br>$3x + 4y = 43$ and $-2x + 3y = 11$
Question 323 :
Solve the following pair of equations by reducing them to a pair of linear equations:$6x + 3y = 6xy, 2x + 4y = 5xy$<br/>
Question 324 :
From the following figure, we can say: $\displaystyle \frac{2x}{3}+\frac{3y}{2}=8\frac{1}{3}; \, \, \frac{3x}{2}+\frac{2y}{3}=13\frac{1}{3}$
Question 325 :
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 326 :
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 327 :
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 328 :
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 329 :
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 330 :
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 331 :
If the equations $y = mx + c$ and $x  \cos  \alpha + y \sin  \alpha = p$ represent the same straight line, then
Question 332 :
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 333 :
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 334 :
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 335 :
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 336 :
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 337 :
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 338 :
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 339 :
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 341 :
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 342 :
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 343 :
Equation of straight line $ax + by + c= 0$, where $3a + 4b + c = 0$, which is at maximum distance from $(1, -2)$,is
Question 344 :
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 345 :
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 346 :
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 347 :
A pair of dice is thrown once The probability that the sum of the outcomes is less than 11 is
Question 348 :
What is the maximum value of the probability of an event?
Question 349 :
If $P(A) = \dfrac{5}{9}$, then the odds against the event $A$ is
Question 350 :
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 351 :
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 352 :
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 353 : 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 354 :
The probability of an event $A$ lies between $0$ and $1$, both inclusive. Which mathematical expression best describes this statement?<br/>
Question 355 :
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 359 :
If the odd in favour of an event are $4$ to $7$, find the probability of its no occurence.
Question 360 :
The probability expressed as a percentage of a particular occurrence can never be
Question 361 :
According to the property of probability, $P(\phi) = 0$ is used for <br>
Question 362 :
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 363 :
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 364 :
The probability of an event happening and the probability of the same event not happening (or the complement) must be a <br/>
Question 365 :
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 367 :
If the probability of the occurrence of an event is P then what is the probability that the event doesn't occur.
Question 368 :
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 369 :
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 370 :
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 371 :
If I calculate the probability of an event and it turns out to be $7$, then I surely know that<br/>
Question 372 :
Two dice are thrown. Find the odds in favour of getting the sum $4$.<br/>
Question 373 :
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 374 :
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 375 :
A die is thrown .The probability that the number comes up even is ______ .
Question 376 :
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 377 :
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 378 :
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 379 :
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 380 :
$A, B$ 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 381 :
Two dice are tossed. What is the probability that neither die is a $4$?
Question 382 :
If a person throw $3$ dice the probability of getting sum of digit exactly $15$ is
Question 383 :
If $\dfrac {1 + 3p}{3}, \dfrac {1 - 2p}{2}$ are probabilities of two mutually exclusive events, then p lies the interval
Question 384 :
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 385 :
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 386 :
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 387 :
A die is rolled. If the outcome is an odd number, what is the probability that it is prime?
Question 388 :
If E and $\bar{E}$ denote the happening and not happeningof an event and$P\left ( \bar{E} \right )=\frac{1}{5}, P\left ( E \right )=$
Question 389 :
In a ODI cricket match, probability of loosing the game is $\dfrac{1}{4}$. What is the probability of winning the game ?
Question 390 :
$A$ and $B$ each throw a dice. The probability that "$B$" throw is not smaller than "$A$" throw, is
Question 391 :
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 392 :
A card is drawn from an ordinary pack of $52$ cards and a gambler bets that it is a spade or an ace. What are the odds against his winning the bet?<br/>
Question 393 :
The probability of getting head or tail in a throw ofa coin is ______.
Question 394 :
$P(A\cap B) = \dfrac{1}{2}, P(\overline{A} \cap \overline{B})=\dfrac{1}{2}$ and $2P(A)=P(B)=p$, then the value of $p$ is equal to
Question 395 :
What are the odds in favour of throwing at least $8$ in a single throw with two dice?<br>
Question 396 :
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 397 :
The odds in favour of getting atleast one time an even prime when a fair die is tossed three times is
Question 398 :
The probability of students not attending class is $0.24$. What is the probability of students attending class ?
Question 399 :
The sum of the probabilities of the distinct outcomes within a sample space is
Question 400 :
If two fair dice are rolled, what is the probability that the sum of the dice is at most $5$?
Question 401 :
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 402 :
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 403 :
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 404 :
If the odds in favour of winning a race by three horses are $1 : 4, 1 : 5$ and $1 : 6$, find the probability that exactly one of these horses will win.
Question 405 :
A card is drawn randomly from a well shuffled pack of 52 playing cards and following events are defined:<br>A : The drawn card is a face card.<br>Find odds in favor of A<br>
Question 406 :
Two cards are drawn at random from a pack of $52$ cards. The probability of these two being "Aces" is
Question 407 :
$(a)$ The probability that it will rain tomorrow is $0.85$. What is the probability that it will not rain tomorrow?<br><br>$(b)$ If the probability of winning a game is $0.6$, what is the probability of losing it?
Question 408 :
If the odd in favour of an event are $4$ to $7$, find the probability of its occurrence.
Question 409 :
A pair of dice is thrown seven times . Getting a total of numbers on the two dice to be seven is considered as a success . Find the probability of getting $7$ in exactly $2$ trials out of $7$.<br/>
Question 410 :
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 411 : Results on the bar exam of Law School Graduates<br/><table class="wysiwyg-table"><tbody><tr><td></td><td>Passed bar exam</td><td>Did not pass bar exam</td></tr><tr><td>Took review course</td><td>18</td><td>82</td></tr><tr><td>Did not take review course</td><td>7</td><td>93</td></tr></tbody></table>The table above summarizes the results of $200$ law school graduates who took the bar exam. If one of the surveyed graduates who passed the bar exam is chosen at random for an interview, what is the probability that the person chosen did not take the review course?<br/>
Question 412 :
In a single cast with two dice, the odds against drawing $7$ is
Question 413 :
The odds against a certain events are $5:2$ and the odds in favour of another events are $6:5$. The probability that at least one of the events will happens is:
Question 414 :
The chance of one event happening is the square of the chance of a $2^{nd}$ event, but odds against the first are the cubes of the odds against the 2nd. Find the chances of first event. (Assume that both events are neither sure nor impossible)<br/>
Question 415 :
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 416 :
The probability of atleast one double six being thrown in $n$ thrown with two ordinary dice is greater than $99$%.<br>Then, the least numerical value of $n$ is
Question 417 :
The probability that a person will hit a target in shooting practice is $0.3$. If he shoots $10$ times, then the probability of his shooting the target is
Question 418 :
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 419 :
A coin is tossed $100$ times with following frequency:<br/>Head: $25$, Tail: $75$<br/>Find the probability of not getting a head.
Question 420 :
In a box, there are $8$ red, $7$ blue and $6$ green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
Question 421 :
Two dices are thrown simultaneously. What is the probability of getting two numbers whose product is even?
Question 422 :
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 423 :
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 424 :
If $E$ and $F$ are event with $P\left( E \right) \le P\left( F \right) $ and $P\left( E\cap F \right) >0$, then
Question 425 :
One of the two events, A and B must occur. If $P\left ( A \right )=\dfrac{2}{3}P\left ( B \right ),$ the odds in favour of $B$ are
Question 426 :
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 427 :
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 428 :
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 429 :
In throwing $3$ dice, the probability that atleast $2$ of the three numbers obtained are same is
Question 430 :
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 431 :
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 432 :
A fair coin is flipped $5$ times.<br/> The probability of getting more heads than tails is $\dfrac{1}{2}$<br/><br/>
Question 433 :
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 434 :
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 435 :
If $2$ cards are drawn from a pack of $52$, then the probability that they are from the same suit is___
Question 436 :
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 437 :
A party of $23$ persons take their seats at a round table. The odds against two specified persons sitting together is
Question 438 :
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 439 :
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 440 :
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 441 :
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 ?
Question 442 :
There are four letters and four addressed envelopes. The probability that all letters are not dispatched in the right envelope is:<br/>
Question 443 :
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 444 :
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 445 :
A fair coin is tossed five times. Calculate the probability that it lands head-up at least twice.
Question 446 :
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 448 :
An isosceles triangle has vertices at (4,0), (-4,0), and (0,8) The length of the equal sides is
Question 449 :
$A=\left(2,-1\right), B=\left(4,3\right)$. If $AB$ is extended to $C$ such that $AB=BC$, then $C=$
Question 450 :
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 451 :
Find the value of $x$ if the distance between the points $(2, -11)$ and $(x, -3)$ is $10$ units.
Question 452 :
The point which lies in the perpendicular bisector of the line segment joining the points A (-2, -5) and B (2,5) is
Question 453 :
The points which trisect the line segment joining the points $(0,0)$ and $(9,12)$ are
Question 454 :
The distance between the points (sin x, cos x) and (cos x -sin x) is
Question 455 :
The coordinates of the midpointof a line segment joining$P ( 5,7 )$ and Q $( - 3,3 )$ are
Question 456 :
A Cartesian plane consists of two mutually _____ lines intersecting at their zeros.  
Question 457 :
$P$ 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 458 :
Find the distance from the point (2, 3) to the line 3x + 4y + 9 = 0
Question 459 :
Find the co-ordinates of the mid point of a point that divides AB in the ratio 3 : 2.
Question 460 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?
Question 461 : <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 462 :
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 463 :
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 464 :
The line $x+y=4$ divides the line joining the points $(-1,1)$ and $(5,7)$ in the ratio
Question 465 :
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 466 :
$M(2, 6)$ is the midpoint of $\overline {AB}$. If $A$ has coordinates $(10, 12)$, the coordinates of $B$ are
Question 467 :
The centroid of the triangle with vertices (2,6), (-5,6) and (9,3) is
Question 468 :
If A(x,0), B(-4,6), and C(14, -2) form an isosceles triangle with AB=AC, then x=
Question 469 :
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 470 :
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 471 :
How far is the line 3x - 4y + 15 = 0 from the origin?
Question 472 :
A point R (2,-5) divides the line segment joining the point A (-3,5) and B (4,-9) , then the ratio is
Question 473 :
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 474 :
If the distance between the points $(4, p)$ and $(1, 0)$ is $5$, then the value of $p$ is:<br/>
Question 475 :
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 476 :
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 478 :
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 479 :
Find the distance from the point (5, -3) to the line 7x - 4y - 28 = 0
Question 481 :
Distance between the points $(2,-3)$ and $(5,a)$ is $5$. Hence the value of $a=$............
Question 482 :
The vertices of a triangle are $(-2,0) ,(2,3)$ and  $(1, -3)$ , then the type of the triangle is 
Question 483 :
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 486 :
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 487 :
The distance between the points $(3,5)$ and $(x,8)$ is $5$ units. Then the value of $x$ 
Question 488 :
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 489 :
The coordinates of the point of intersection of X-axis and Y-axis is( 0,0)<br/>State true or false.<br/>
Question 490 :
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 493 :
If the points (1,1) (2,3) and (5,-1) form a right triangle, then the hypotenuse is of length
Question 494 :
Which of the following points is not 10 units from the origin ?
Question 495 :
Given the points $A(-1,3)$ and $B(4,9)$.Find the co-ordinates of the mid-point of $AB$
Question 496 :
The ratio in which the line segment joining (3,4) and (-2,1) is divided by the y-axis is
Question 497 :
The point which lies on the perpendicular bisector of the line segment joining the points $P(-2,0)$ and $Q(2,5)$ is:
Question 498 :
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 499 :
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 500 :
The point which divides the line segmentjoining the points (3, 5) and (8, 10) internallyin the ratio 2 :3 is:
Question 501 :
The ratio in which X-axis divides the line segment joining $(3,6)$ and $(12,-3)$ is
Question 502 :
The ratio in which the joint of (-3, 10), (6, -8)is divided by (-1, 6),
Question 503 :
In what ratio does the point P(-2, 3) divide theline segment joining the points A(-3, 5) andB(4, -9) internally?
Question 504 :
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 505 :
The mid-point of line segment joining thepoints (3, 0) and (-1, 4) is :
Question 506 :
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 507 :
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 508 :
The ratio in which the line $3x+y-9=0$ divides the line segment joining points (1, 3) and (2, 7) is:
Question 509 :
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 510 :
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 511 :
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 512 :
Find the ratio in which the line segment joining the points $(3,5)$ and $(-4,2)$ is divided by y-axis.<br/>
Question 513 :
What is the ratio in which $P(2, 5)$ divides the line joining the points $(8, 2)$ and $(-6, 9)$?
Question 514 :
What is the approximate slope of a line perpendicular to the line $\sqrt{11}x+\sqrt{5}y=2$?
Question 515 : <p>x-axis divides line segment joining points (2, -3) and (5,6) in the ratio</p>
Question 516 :
The ratio by which the line $2x + 5y - 7 = 0$ divides the straight line joining the points $(-4, 7) $ and $(6, -5)$ is
Question 517 :
The straight line $3x+y=9$ divides the line segment joining the points $(1,\,3)$ and $(2,\,7)$ in the ratio
Question 518 :
If the line joining A(2, 3) and B(-5, 7) is cut by X - axis at P, then find AP : PB.
Question 519 :
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 520 :
If the point P (2, 1) lies on the segment joining Points A (4, 2) and B (8, 4) then
Question 521 :
Length of the median from B on AC where A (-1, 3), B (1, -1), C (5, 1) is
Question 522 :
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 523 :
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 524 :
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 525 :
Find the coordinates of the point which divides the line segment joining $(-3,5)$ and $(4,-9)$ in the ratio $1:6$ internally.
Question 526 :
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 527 :
Find the midpoint of the segment joining the points $(4, -2)$ and $(-8,6)$.
Question 528 :
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 529 :
In what ratio is the line segment joining the points $(4, 6)$ and $(-7, -1)$ Is divided by $X$-axis ?
Question 530 :
<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 531 :
Find the distance between the points $(-1,-3)$ and the midpoint of the line segment joining $(2,4)$ and $(4,6)$.
Question 532 :
$A(5,1)$, $B(1,5)$ and $C(-3, -1)$ are the vertices of $\Delta ABC$. The length of its median AD is:
Question 533 :
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 534 :
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 535 :
The point which is equi-distant from the points $(0,0),(0,8) and (4,6)$ is 
Question 536 :
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 537 :
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 538 :
In how many maximum equal parts, a rectangular cake can be divided using three straight cuts?
Question 539 :
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 540 :
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 541 :
The coordinates of the third vertex of an equilateral triangle whose two vertices are at $(3, 4), (-2 3)$ are ______.
Question 543 :
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 544 :
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 545 :
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 546 :
Number of points with integral co-ordinates that lie inside a triangle whose co-ordinate are (0,0), (0, 21) and (21, 0)
Question 547 :
The mid point of the segment joining $(2a, 4)$ and $(-2, 2b)$ is $(1, 2a+1)$, then value of b is
Question 548 :
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 549 :
$\mathrm{P}_{1},\ \mathrm{P}_{2},\ldots\ldots.,\ \mathrm{P}_{\mathrm{n}}$ 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 550 :
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 551 :
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 552 :
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 553 :
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 554 :
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 555 :
The point whose abscissa is equal to its ordinate and which is equidistant from $A(5,0)$ and $B(0,3)$ is
Question 556 :
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 557 :
If $(-6, -4), (3, 5), (-2, 1)$ are the vertices of a parallelogram, then remaining vertex can be
Question 558 :
The points given are $(1, 1)$, $(-2, 7)$ and $(3, 3)$.Find distance between the points.
Question 559 :
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 560 :
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 561 :
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 562 :
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 563 :
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 564 :
The points $(-2,2)$, $(8, -2)$ and $(-4, -3)$ are the vertices of a:
Question 566 :
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 567 :
$ABC$ is an isosceles triangle. If the coordinates of the base are $B(1,3)$ and $C(-2,7)$. The vertex $A$ can be
Question 568 :
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 569 :
$ABC$ 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 570 :
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 571 :
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 572 :
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 573 :
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 574 :
A cord in the form of square encloses the area 'S'$ \displaystyle cm^{2} $ If the same cord is bent into the form of a circle then the area of the circle is
Question 575 :
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 576 :
If the circumference of a circle be 8.8 m then its radius is equal to -
Question 577 :
The sum of the circumference and diameter of a circle is $116 cm$. Find its radius.
Question 578 :
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 579 :
If one side of a square is 2.4 m. Then what will be the area of the circle inscribed in the square?
Question 580 :
A square is inscribed in a circle of radius $7\: cm$. Find area of the square.
Question 581 :
What is the minimum radius $(>1)$ of a circle whose circumference is an integer?
Question 583 :
The diameter of a wheel of a cycle is 21 cm How far will it go in 28 complete revolutions?
Question 584 :
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 585 :
If the radius of a circle increased by 20% then the corresponding increase in the area of circle is ................
Question 587 :
If the diameter of a circle is increased by 200% then its area is increased by<br>
Question 588 :
If the radius of a circle is $\dfrac{7}{\sqrt{\pi}}$, what is the area of the circle (in $cm^2$)?
Question 589 :
If radius of a circle is increased to twice its original length, how much will the area of the circle increase ?
Question 590 :
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 591 :
$r$ is the radius and $l$  is the length of an arc. The area of a sector is ______.
Question 592 :
If an arc of a circle subtends an angle of<b></b>$ \displaystyle x^{\circ} $ at the centre then the length of the arc will be equal to - (Given radius of the circle=r)
Question 593 :
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 594 :
What is the circumference of a circle whose radius is 8 cm?
Question 595 :
Find the area of equilateral  triangle inscribed in a circle of unit radius.
Question 596 :
The radius of a wheel is $0.25 m$. How many rounds will it take to complete the distance of $11 km$?
Question 597 :
The diameter of a circle is $1$. Calculate the area of the circle.
Question 598 :
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 599 :
The area of a circle is $24.64$. $\displaystyle m^{2}$ What is the circumference of the circle ?
Question 600 :
The circumference of a circular field is $528\ m$. Then its area  is
Question 602 :
State true or false.Sector is the region between the chord and its corresponding arc.
Question 603 :
Circular dome is a 3D example of which kind of sector of the circle?
Question 605 :
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 606 :
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 607 :
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 608 :
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 609 :
If the circumference of a circle is reduced by 50 % then the area will be reduced by
Question 610 :
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 612 :
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 613 :
Find the circumference of the circle with the following radius : 10 cm
Question 614 :
If the difference between the circumference and radius of a circle is 37 cm then its diameter is
Question 615 :
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 616 :
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 618 :
Lengthof an arc of a circle with radius $r$ and central angle $\theta$is(angle in radians):
Question 619 :
The region between an arc and two radii joining the centre to the end points of the arc is called
Question 620 :
Which of the following is not a sector of a circle?<br/>
Question 621 :
If 'c' be the circumference and 'd' be the diameter then the value of$ \displaystyle \pi $ is equal to-<br>
Question 622 :
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 623 :
If the area of the circle be $ \displaystyle 154 cm^{2},$ then its radius is equal to:
Question 624 :
Ratio of circumference of a circle to its radius is always $2 \pi : 1$
Question 625 :
The area of the sector of a circle, whose radius is $6$ m when the angle at the centre is $42^0$, is
Question 626 :
If the radius of a circle is increased by 50% then the area of the circle is increased by ?
Question 627 :
If the radii of two circles re $7\,cm$ and $24\,cm$, then the radius of the circle having area equal to the sum of the areas of the two circles, is
Question 628 :
The sides of a triangle are $5$, $12$ and$ 13$ units. A rectangle of width $10$ units is constructed equal in area to the area of the triangle. Then the perimeter of the rectangle is 
Question 629 :
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 630 :
A wire is bent to form a square of side $22\, cm$ If the wire is rebent to form a circle, its radius is.<br>
Question 631 :
The sum of the radii of two circle is $140\ cm$ and the difference of their circumference is 88 cm. Find the radii of the two circles.
Question 632 :
The diameter of a circle is $10$ cm, then find the length of the arc, when the corresponding central angle is $144^{\circ}$.$(\pi =3.14)$
Question 633 :
If the difference between the circumference and radius of a circle is $37$ cm, then the area of the circle is<br/>
Question 634 :
The length of minute hand of a clock is $14cm$. Find the area swept by the minute hand in one minute.<br/> [Use $\pi=\dfrac{22}{7}$]
Question 635 :
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 638 :
If the area of a sector of a circle is $\dfrac{5}{18}$th of the area of that circle, then the central angle of the sector is 100. Is it true or false?
Question 639 :
The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?<br><br>
Question 640 :
The area of a circle drawn with its diameter as the diagonal of a cube of side of length 1 cm each is :
Question 641 :
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 642 :
Let a and b be two positive real numbers such that a $a + 2b \leq 1$. Let $A_{1} \space and \space A_{2}$ be, respectively. the areas of circles with radii $ab^{3} \space and \space b^{2}$. Then the maximum possible value of $\dfrac{A_{1}}{A_{2}}$ is
Question 643 :
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 644 :
In $\bigodot (P, 6)$, the length of an arc is $\pi$. Then the arc subtends an angle of measure ___at the center.
Question 645 :
If the diameter of a circle is $14$ cm, then its circumference is
Question 646 :
State whether True or False:The radius of a circle is $7 cm$, then area of the sector of this circle if the corresponding angle is:<br/>$3$ rt. angles is $115.50 \,cm^2$<br/>
Question 647 :
If the circumference of a circle increases from $4\pi $to $8\pi $,then its area is :
Question 648 :
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 649 :
What is the area of a sector with a central angle of $100$ degrees and a radius of $5$? (Use $\pi = 3.14$)<br/>
Question 650 :
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 651 :
The ratio between the diameters of two circles is $3 : 5,$ then find the ratio between their areas.<br/>
Question 652 :
A square sheet of paper is converted into a cylinder by rolling it along its length. What is the ratio of the base radius to side of the square ?
Question 653 :
The cost of fencing a circular field at the rate of $Rs\:.240\: per\: metre$ is $Rs. \: 52,800$ . The field is to be ploughed at the rate of $Rs. 12.50 \: per \: m^{2}$. Find the cost of ploughing the field.
Question 654 :
If the sum of the areas of two circles with radii $R_1$ and $R_2$ is equal to the area of a circle of radius R, then <br><br>
Question 655 :
The radius of a circle is $7 cm$, then area of the sector of this circle if the corresponding angle is:$210^{\circ}$ is <br/><br/>
Question 656 :
The circumference of a circle exceeds its diameter by $15 cm$ then, the circumference of the circle is
Question 657 :
The ratio of the circumference of a circle to twice the diameter of the circle is 
Question 658 :
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 659 :
Find the area of a sector with an arc length of $20 cm$ and a radius of $6 cm$.<br/>
Question 660 :
Each wheel of a car is of diameter $80 cm$. How many complete revolutions does each wheel make in $10  min$ when the car is travelling at a speed of $66$ km per hour. 
Question 661 :
A circular disc of radius 10 cm is divided into sectors with angles $120^{\circ}$ and $150^{\circ}$ then the ratio of the area of two sectors is<br>
Question 662 :
If area of circular field is $6.16 \ sq. m$, then its diameter will be<br/>
Question 663 :
Tick the correct answer in the following:<br/>Area of a sector of angle $\theta$ (in degrees) of a circle with radius R is
Question 664 :
If the radius of a circle is doubled then its area is increased by
Question 665 :
A horse is tethered to a stoke by a rope $30\ m$ long. If the horse moves along the circumference of a circle always keeping the rope tight then how far it will have gone when the rope has traced an angle of $105^{\circ}$?
Question 666 :
The angle subtended at the centre of a circle of radius $3cm$ by an arc of length $1cm$ is:
Question 667 :
What is the area of the circle whose equation is $(x - 3)^{2} + (y + 5)^{2} = 18$?
Question 668 :
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 669 :
If the difference between the circumference and diameter of a circle is $30\ cm$, then the radius of the circle must be:
Question 670 :
Find the diameter of a wheel that makes $113$ revolutions to go $2 km 26dm$. $ \displaystyle \left ( \pi =\frac{22}{7} \right )$
Question 671 :
Which of the following shapes of equal perimeter the one having the largest areas is
Question 672 :
The diameter of two circles are $32 cm$ and $24 cm$. Find the radius of the circle having its area equal to sum of the area of the two given circle.
Question 673 :
The crescent shaded in the diagram, is like that found on many flags. $PSR$ is an arc of a circle, centre $O$ and radius $24.0$ cm. Angle POR $=$ $48.2^{\circ}$.<br/>$PQR$ is a semicircle on $PR$ as diameter, where $PR$ $=$ $19.6$ cm<br/>$[\pi = 3.14] [\cos 24.1 = 0.91]$The area of the crescent is<br/>
Question 674 :
The perimeter of a quadrant of a circle of radius $\dfrac{7}{2}$ cm is:<br/>
Question 675 :
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 676 :
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 677 :
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 678 :
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 679 :
If a bicycle wheel makes $5000$ revolution in moving $11$ km, then diameter of wheel is
