List of top Mathematics Questions

The value of the integral \(\int\limits_2^4 \frac{x}{x^2+1} dx\) is:

The sum of order and degree of the differential equation\[\frac{\{1+(\frac{dy}{dx})^2\}^\frac{5}{2}}{\frac{d^2y}{dx^2}}=p\]is:

The solution of the differential equation\(\frac{dy}{dx}= \frac{6}{x^2}; y(1) = 3\) is:

The mean of the number of heads in a simultaneous toss of three coins is :

For the LPP
Maximise z=x+y
subject to x-y≤-1, x+y≤2, x, y≥0, z has:

Choose the wrong statement from the following:

Let f: R→R defined by f(x)=2x³-7 for x∈R. Then:
(A) f is one-one function
(B) f is many to one function
(C) f is bijective function
(D) f is into function
Choose the correct answer from the options given below:

Match List I with List II

Choose the correct answer from the options given below:

Let \(tan^{-1}y=tan^{-1}x+tan^{-1}(\frac{2x}{1-x^2})\). Then y is:

The value of 2y-3x, if
\(2\begin {bmatrix}x &5\\ 7&y-3\end{bmatrix}+\begin{bmatrix}3&-4\\ 1&2\end{bmatrix}=\begin{bmatrix}7&6 \\15&14\end{bmatrix}\) is:

Match List - I with List II. If \(A = \begin{vmatrix}3&-2&3 \\2 &1 &-1 \\4 &-3 &2\end{vmatrix}\)

Choose the correct answer from the options given below:

The number of square matrices of order 2 using numbers 1 and -1 exactly once and the number 0 twice is:

Let \(\begin{vmatrix}3x&-7\\1&4\end{vmatrix}=\begin{vmatrix}3&2\\ 4&x\end{vmatrix}\), then value of x is:

The value of the determinant \(\begin{vmatrix}acosθ&bsinθ&0 \\-bsinθ&acosθ&0\\ 0&0&c\end{vmatrix}\) is:

The points of discontinuity of the function \(f\) defined by \(f(x) = \begin{cases} x+2 & x≤1 \\ x-2 &1<x<2\\ 0& x≥2\end{cases}\) are:

If \( f(x) = \begin{cases} \sqrt{\pi - \cos^{-1} x}, & x = -1 \\ \frac{\sqrt{2(1 + x)}}{\pi + \cos^{-1} x}, & x \neq -1 \end{cases} \) is right continuous at \( x = -1 \), then \( \lambda = \)

If \( y = y(x) \) is the solution of \( \frac{dy}{dx} = \frac{x - y \cos x}{1 + \sin x} \), \( y\left(\frac{\pi}{2}\right) = \frac{\pi^2}{8} \), then \( y(\pi) = \)

Given that \( \frac{d}{dx} \left[ \int_0^{\phi(x)} f(t) dt \right] = \phi'(x) f(\phi(x)) \). If \( \int_0^{x^3} f(t) dt = x^2 \sin 2\pi x \), then the value of \( f(8) \) is

\( \lim_{n \to \infty} \frac{1}{n} \left( \frac{1}{e^{1/n}} + \frac{1}{e^{2/n}} + \frac{1}{e^{3/n}} + \dots + \frac{1}{e^{n/n}} \right) = \)

\( \int_0^{1/2} \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} dx = \)

\( \int \frac{x^2 - 1}{x^3 \sqrt{2x^4 - 2x^2 + 1}} dx = \)

Let \( f(x) = \max\{\cos x, \sin x, 0\} \). If the number of points at which \( f(x) \) is not differentiable in \( (0, 2024\pi) \) is \( 1012k \), then \( k = \)

If the tangent drawn at \( A(2, 1) \) to the curve \( x = 1 + \frac{1}{y^2} \) meets the curve again at \( B \), then

The points on the curve \( y^2 = x + \sin x \) at which the normal is parallel to the Y-axis lie on

Let \( f(x) = |x - 3| + |x + 5| \) and \( A = \left\{ a \in \mathbb{R} / \lim_{x \to a} \frac{f(x) - f(a)}{x - a} \text{ exists} \right\} \). Then the number of real numbers which are in \( [-8, 3] \cup [5, \infty) \) but not in \( A \) is