List of top Mathematics Questions

In a shelf there are three mathematics and two physics books. A student takes a book randomly. If he randomly takes, successively for three time by replacing the book already taken every time, then the mean of the number of mathematics books which is treated as random variable is

The sum of order and degree of the differential equation \[ y=x\frac{dy}{dx}+2\sqrt{1+\left(\frac{dy}{dx}\right)^2} \] is:

Let $\alpha, \beta$ be the roots of the quadratic equation \[ 12x^2 - 20x + 3\lambda = 0,\ \lambda \in \mathbb{Z}. \] If \[ \frac{1}{2} \le |\beta-\alpha| \le \frac{3}{2}, \] then the sum of all possible values of $\lambda$ is

Find the area of the region bounded by the curve \( y^2 = x \) and the line \( x = 4 \):

Find the interval in which the function \( f(x) = 2x^3 - 3x^2 - 36x + 7 \) is strictly increasing:

A bag contains \( 5 \) red and \( 4 \) black balls. Two balls are drawn at random one after the other without replacement. What is the conditional probability that the second ball drawn is red, given that the first ball drawn was black?

Find the general solution of the differential equation: \( \frac{dy}{dx} + \frac{y}{x} = x^2 \)

Find the value of the composite inverse trigonometric expression: \( \cot^{-1}\left[2\cos\left(2\sin^{-1}\frac{1}{2}\right)\right] \)

If \( A \) is a square matrix of order \( 3 \) such that \( |2(\text{adj}\,A)| = 288 \), then the possible value of the determinant \( |A| \) is:

Evaluate the indefinite integral: \( \int \frac{x^2+1}{x^4+1}\,dx \)

Let \( A \) be a non-singular \( 3 \times 3 \) matrix satisfying the equation \( A^3 - 6A^2 + 11A - 6I = O \). If \( B = A^2 - 5A + 7I \) and \( \det(A) = 6 \), then the value of \( \det(B) \) is equal to:

Let \(X\) denote the number of heads in a simultaneous toss of three coins, then \[ P(0<X<3) \] is:

The area of region bounded by the curve \[ y^2=4ax \] and the straight line \[ x=2a,\qquad a>0 \] in the first quadrant is:

The function \[ f:\mathbb R\to\mathbb R,\qquad f(x)=|x| \] (\(\mathbb R\) is the set of real numbers) is:

The relation \(R\) on the set of real numbers defined by \[ R=\{(a,b):a\leq b^2\} \] is:
• [(A)] Reflexive
• [(B)] Not symmetric
• [(C)] Neither reflexive nor transitive
• [(D)] Transitive Choose the correct answer from the options given below:

For the L.P.P. Maximize \[ z=10x+6y \] subjected to: \[ 3x+y\leq12 \] \[ 2x+5y\leq34 \] \[ x,y\geq0 \] Then the feasible region represented by system of inequalities is:

If \[ \begin{bmatrix} 2x+1 & 5x \\ 0 & y^2+1 \end{bmatrix} = \begin{bmatrix} x+3 & 10 \\ 0 & 26 \end{bmatrix} \] then the possible values of \(x+y\) are:

If \[ y= \left( x^{\sin x} \right)^{\tan x}, \] then find \[ \dfrac{dy}{dx}. \]

If \[ \left| \begin{matrix} x+a & y & z \\ x & y+b & z \\ x & y & z+c \end{matrix} \right| = 2abc, \] where \(a,b,c\neq0\), then find the value of \[ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}. \]

If \[ f(x)=\left(\frac{1+\sin x}{1-\sin x}\right)^{\tan x}, \] then find \[ \lim_{x\to0}\frac{\ln f(x)}{x^2}. \]

Find the equation of the plane which passes through the point \[ (1,-2,3), \] contains the line of intersection of the planes \[ x+y+z=1 \] and \[ 2x-y+3z=4, \] and is perpendicular to the plane \[ x-2y+2z+5=0. \]

Evaluate: \[ \int \dfrac{x^2+1}{x^4+1}\,dx \]

If \[ y = \left(\dfrac{x+1}{x-1}\right)^x, \] then find \(\dfrac{dy}{dx}\).

If \[ \left| \begin{matrix} x+a & y & z \\ x & y+b & z \\ x & y & z+c \end{matrix} \right| = abc, \] where \(a,b,c\neq0\), then find the value of \[ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}. \]

If \( A \) is a square matrix of order \(3\) and \( |A|=-3 \), then the value of \( |2AA^T| \) is: