List of top Mathematics Questions

If $ p,q $ are positive real numbers such that $ pq = 1 $ , then the least value of $ (1 + p) (1 + q) $ is

Let $ f(x) = (x+2)^2 -2 , x \ge -2 $ . Then, $ f^{-1}(x) $ is equal to

Let $ Z $ be the set of integers. Then, the relation $R = \{ (a, b) :1 + ab > 0 \}$ on $z$ is

For $3 \times 3$ matrices $M$ and $N$ , which of the following statement(s) is/are not correct ?

The Boolean expression for the $XOR$ gate is

If $ 3^x = 4^{ x - 1} $ then x is equal to

Which one of the following is not true?

The general solution of sin $ 3x + sin\, x - 3 \,sin 2x $ = $ cos\, 3x + cos\, x - 3 cos \,2x $ is

If P is a point $ (x,y) $ and $ P_1 = (3,0),P_2 = (-3,0) $ and $ 16 x^2 + 25y^2 = 400 $ , then $ PP_1 + PP_2 $ is equal to

The line $ x = my + c $ is normal to $ x^2 = - 4ay $ , if c is equal to

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8 : 15$ is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is $100$, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are

Let $\omega$ be a complex cube root of unity with $\omega \ne 0$ and $P = [P_{ii}] $ be an $n \times \, n$ matrix with $p_{ij} = \omega^{i+j}$ Then, $P^2 \ne 0$ when $n$ =

A line $l$ passing through the origin is perpendicular to the lines $ L_1 : (3+t) \widehat {i} +(1-2t) \widehat {j}+(4+2t)\widehat {k}, - \infty < t < \infty$ $ L_2 : (3+2s) \widehat {i} +(3+2s) \widehat {j}+(2+s)\widehat {k}, - \infty < s < \infty$ Then, the coordinate(s) of the point(s) on $l_2$ at a distance of $\sqrt 17$ from the point of intersection of l and $l_1$ is (are)

Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2},\frac{3}{4},\frac{1}{4},\frac{1}{8}$ Then,the probability that the problem is solved correctly by at least one of them, is

Two lines $L_1:x = 5\, \frac{y}{3-\alpha} = \frac{z}{-2}$ and $L_1:x = \alpha \, \frac{y}{-1} =\frac{z}{2-\alpha}$ are coplaner. Then, $\alpha$ can take value(s)

A multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is

Circle(s) touching X-axis at a distance 3 from the origin and having an intercept of length $2 \sqrt7$ on Y-axis is/are

The inverse of the proposition $(p \wedge \sim q)\rightarrow r$ is

The equation of straight line through the intersection of the lines $x - 2y = 1 $ and $x + 3y = 2$ and parallel $3x + 4y = 0$ is

The length of the sub-tangent, ordinate and the sub-normal are in

The value of $a$ for which the volume of parallelepiped formed by the vectors $\hat {i}+a\hat{j} + \hat{k} \,\, \hat{j}+a\hat{k} $ and $ a\hat{i}+\hat{k} $ is minimum, is

If mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value atleast one is

A boy is throwing stones at a target. The probability of hitting the target at any trial is $\frac{1}{2}$ .The probability of hitting the target $5^{th}$ time at the $10^{th}$ throw is :

Two dice are thrown together $4$ times. The probability that both dice will show same numbers twice is -