List of top Mathematics Questions

The value of the determinant of the inverse of the matrix \(\begin{bmatrix} -4 & -5\\ 2 & 2 \end{bmatrix}\) is

If \(A=\begin{bmatrix}1 & 1\\ 0 & i\end{bmatrix}\) and \(A^{42}=\begin{bmatrix}a & b\\ c & d\end{bmatrix}\) then \(a+d\) is equal to

Let \(f(x) = \begin{vmatrix} x & 1\\ \sin(2\pi x) & 2x^2 \end{vmatrix}\). If \(f(x)\) is an odd function, \(f(-x)=g(x)\) and \(\lambda f(1)g(1)=4\), then the value of \(\lambda\) is equal to

If \(A=\begin{bmatrix}3 & \lambda-3\\ -1 & 1\end{bmatrix}\) and \(B=\begin{bmatrix}3 & 2\\ 2 & 1\end{bmatrix}\) and \(AB=\begin{bmatrix}7 & 1\\ -1 & -1\end{bmatrix}\), then \(\lambda\) is equal to

If $a,b,c$ are three unequal numbers such that $a,b,c$ are in arithmetic progression and $b-a, c-b, a-b$ are in geometric progression, then $a:b:c$ is

If \(\frac{1}{8!} + \frac{1}{9!} = \frac{x}{12!}\), then the value of \(x\) is equal to

If three geometric means are inserted between 2 and 32, then the three numbers are

If \(\frac{{}^nP_{r-1}}{a} = \frac{{}^nP_r}{b} = \frac{{}^nP_{r+1}}{c}\), then

The number of ways in which we can choose a committee from 3 men and 6 women so that the committee includes at least two men and exactly twice as many women as men is

A geometric progression has an even number of terms. If the sum of all terms is five times the sum of all odd terms, then the common ratio is equal to

The imaginary part of \(\frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}\) is

If $|z + 4| = 2|z + 1|$, where $z$ is a complex number then $|z|$ is equal to

In a geometric progression of positive terms, if any term is equal to the sum of the next two terms, then the common ratio of the geometric progression is equal to

The sum of $i^2 + i^4 + \cdots$ upto 25 terms is equal to

If $z(3 - i) = 2 + i$, then $z^2 =$

The number of elements in the set \(\{(x,y): 2x^2 + 3y^2 = 35, x,y \in \mathbb{Z}\}\), where \(\mathbb{Z}\) is the set of all integers, is

Let $A$ and $B$ be two sets of having 3 and 2 elements respectively. Then the number of subsets of $A \times B$ having at least three elements is

The domain of \(f(x) = \frac{x^2 + 1}{x^2 + x + 1}\) is

Let \(R\) be a relation in \(\mathbb{N}\) defined by \(\{(x,y): x + 3y = 10, x,y \in \mathbb{N}\}\). Then the range of \(R\) is

If the set of all solutions of \(|x^2 + x - 9| = |x| + |x^2 - 9|\) is \([\alpha, \beta] \cup [\gamma, \infty)\), then \((\alpha^2 + \beta^2 + \gamma^2)\) is equal to:

Find the distance between the planes \(2x + 3y + 4z = 4\) and \(4x + 6y + 8z = 12\).

$$ \int \frac{dx}{x(x^{10}+1)} = $$

$$ \int \frac{1}{(x-3)(x-7)} \, dx = ? $$

$$ \int_{0}^{\pi/4} (\tan^8 x + \tan^6 x) \, dx = ? $$

$$ \int e^x \left( \log x + \frac{1}{x^2} \right) dx = ? $$