List of top Mathematics Questions

If $a + b = 5$ and $ab = 6$, find $a^2 + b^2$:

If a function is increasing, then its derivative is:

Evaluate: $\int x \, dx$

The derivative of $\sin x$ is:

The interval in which \( y = x^2 e^x \) is decreasing is _____

The maximum value of the function \( f(x) = -|x+1| + 3, \; x \in \mathbb{R} \) is _____

The total revenue in Rupees received from the sale of \( x \) units of a product is given by \( R(x) = 3x^2 + 36x + 5 \). The marginal revenue, when \( x = 15 \), is _____

If \( y = \log_{2026}(\log_{2025} x) \), then \( \frac{dy}{dx} \)= _____

If \( x = a t^2, \; y = 2at \), then \( \frac{d^2 y}{dx^2} =\) _____

If function \( f \) is continuous at point \( x = \pi \) and \[ f(x) = \begin{cases} kx + 1, & x \le \pi \\ \cos x, & x>\pi \end{cases} \] then the value of \( k \) is ______

If inverse matrix of \( A = \begin{bmatrix} 2 & 3 \\ 1 & -4 \end{bmatrix} \) is \( A^{-1} = \begin{bmatrix} a & \frac{3}{11} \\ \frac{1}{11} & b \end{bmatrix} \), then a + b = _____

If \[ A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -3 \end{bmatrix} \] then \( A^2 + B^2 = \underline{\hspace{2cm}} \)

If area of triangle is 35 sq. units with vertices \( (2,-6), (5,4) \) and \( (k,4) \), then \( k \) is _____

If \( A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix} \), then \( A^2 + I = \) _____

If \( A \) and \( B \) are skew-symmetric matrices of same order, then \( AB - BA \) is a _____

If \( A = \begin{bmatrix} a & b \\ c & -a \end{bmatrix} \) is such that \( A^2 = I \), then _____

\( \tan^{-1} \left[ 2\cos \left( 2\sin^{-1} \frac{1}{2} \right) \right] = \)_____

\( \sin^{-1} \left(\sin \frac{3\pi}{5}\right) =\) _____

If \( \cos^{-1} x = y \), then _____

Let \( f : \mathbb{N} \rightarrow \mathbb{N} \) be defined by \[ f(n) = \begin{cases} \frac{n+1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases} \] for all \( n \in \mathbb{N} \). Then \( f \) is _____

Let \( R \) be the relation in the set \( \mathbb{N} \) given by \( R = \{(a,b) : a = b - 2, \; b<6\} \), then _____

Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. The probability that first two cards are kings and the third card drawn is an ace is _____

If \(A\) and \(B\) are any two events such that \( P(A) + P(B) - P(A and B) = P(A) \), then _____