List of top Mathematics Questions

Let $A$ be the square of natural numbers and $x$, $y$ are any two elements of $A$. Then

If $2\,sin\,x=\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}$, then

Let $0(0, 0), P(3, 4)$ and $Q(6, 0)$ be the vertices of a $\Delta$ OP The point R inside the $\Delta OPQ$ is such th at the triangles $OPR, PQR$ and $OQR $ are of equal area. The coordinates of R are

One Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that Indian m an is seated adjacent to his wife given that each American man is seated adjacent to his wife, is

A man walks a distance of 3 units from the origin towards the North-East (N 45$^{\circ}$ E) direction. From there, he walks a distance of 4 units towards the North-West (N 45$^\circ$ W) direction to reach a point P. Then, the position of P in the Arg and plane is

Let $E^c$ denotes the complement of an event $E$. If $E, F, G$ are pairwise independent events with $P (G) > 0$ and $P(E \cap F \cap G)=0$ then , $P(E^c \cap F^c|G) equals$

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be unit vectors such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}.$ Which one of the following is correct?

The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2\widehat{i}+\widehat{j}+\widehat{k}, \widehat{i}-\lambda^2\widehat{j}+\widehat{k}$ and $\widehat{i}+\widehat{j}-\lambda^2\widehat{k}$ are coplanar, is

Let $ABCD$ be a quadrilateral with area 18, with side AB parallel to the side $CD$ and $AB = 2 CD$. Let $AD$ be perpendicular to $AB$ and $CD$. If a circle is drawn inside the quadrilateral $ABCD$ touching all the sides, then its radius is

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN, is

The angle between the lines with direction ratios $ (4,-3,5) $ and $ (3,4,5) $ is

$\int\limits_{0}^{8}| x -5| d x$ is equal to

If the normal to the curve $y = f(x)$ at $(3,4)$ makes an angle $\frac{3 \pi}{4}$ with the positive x-axis, then $f'(3)$ is equal to

The equation of a directrix of the ellipse $\frac{x^2}{16} + \frac{y^2}{25} = 1 $ is

f(x) is cubic polynomial with f(2) = 18 and f(1) = -1. Also f(x) has local maxima at x = -1 and f '(x) has local minima at x = 0, then

If \( x = -9 \) is a root of \( \begin{pmatrix} 2 & 3 \\ 7 & 6 \end{pmatrix} \times \begin{pmatrix} x \end{pmatrix} = 0 \), then other two roots are:

Let \( A = \begin{pmatrix} 1 & 3 & 2 \\ 4 & 2 & 5 \\ 7 & -t & -6 \end{pmatrix} \), then the values of \( t \) for which inverse of \( A \) does not exist are:

If \( f'(x) = \frac{x}{\sqrt{1 + x^2}} \) and \( f(0) = 0 \), then \( f(x) = \):

The probability density \( f(x) \) of a continuous random variable is given by \( f(x) = K e^{-|x| \) for \( -\infty<x<\infty \). Then the value of \( K \) is:}

In rolling two fair dice, what is the probability of obtaining a sum greater than 3 but not exceeding 6?

Team A has probability \( \frac{2}{3} \) of winning whenever it plays. Suppose A plays four games. What is the probability that A wins more than half of its games?

An unprepared student takes five questions of true-false type quiz and guesses every answer. What is the probability that the student will pass the quiz if at least four correct answers is the passing grade?

Consider the set \( Q \) of rational numbers. Let \( * \) be the operation \( a * b = a + b - ab \). The identity element under \( * \) is:

The statement \( p \to q \) is equivalent to: