List of top Mathematics Questions

If we insert two numbers between $\sqrt{2}$ and $4$ so that the resulting sequence is in G.P., then the inserted numbers in the order are

Match List-I with List-II
List-I
a) A matrix which is not a square matrix
b) A square matrix $A' = A$
c) The diagonal elements of a diagonal matrix are same
d) A matrix which is both symmetric and skew symmetric
List-II
i) Symmetric matrix
ii) Null matrix
iii) Rectangular matrix
iv) Scalar matrix
Codes:

Consider the following statements:
Statement I : If $A$ is a non-singular matrix, then $A^{-1}$ exists.
Statement II : If $A$ and $B$ are symmetric matrices of same order, then $(AB - BA)$ is a skew symmetric matrix.
Choose the correct option.

A row matrix has only

Let $X$ be a matrix of order $2 \times n$ and $Z$ be a matrix of order $2 \times p$. If $n = p$, then the order of the matrix $7X - 5Z$ is:

Which of the following is correct?

If $A$ and $B$ are invertible matrices of same order, then which of the following is not correct?

If $A$ and $B$ are invertible square matrices of order $n$, then which of the following isnot correct?

The area of the triangle with vertices $(3, 8), (-4, 2)$ and $(5, 1)$ is $\frac{P}{4}$, then the value of $P$ is

The system of equations $x + 2y = 3$ and $2x + 3y = 3$ has

If $\vec{a} = 2\hat{i} + 2\hat{j} - \hat{k}$, $\vec{b} = \alpha\hat{i} + \beta\hat{j} + 2\hat{k}$ and $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|$, then $\alpha + \beta$ is equal to

If $\vec{a} = \hat{i} + \hat{j} + \hat{k}$, $\vec{b} = \hat{j} - \hat{k}$ and $\vec{a} \times \vec{c} = \vec{b}$, $\vec{a} \cdot \vec{c} = 3$, then $\vec{c}$ is

The value of $\lambda$ for which the vectors $\vec{a} = 2\hat{i} + \lambda\hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} + 3\hat{k}$ are orthogonal is

The angle between the lines whose direction ratios are $a, b, c$ and $b - c, c - a, a - b$ is

The measure of the angle between the lines $x = k - 1, y = 2k + 1, z = 2k + 3, k \in \mathbb{R}$ and $\frac{x+1}{2} = \frac{y-2}{1} = \frac{z-1}{2}$ is

The line $L_{1}$ joining the two points $(-1, 2)$ and $(3, 6)$ divides the line $L_{2}$ which passes through $(3, -1)$ in the ratio $1 : 3$ internally, then the equation of $L_{2}$ is

In the figure
Statement I : When $\alpha>\beta \ge 0$, the section is hyperbola
Statement II : When $\beta = 90^\circ$, the section is ellipse
Which of the following is correct?

The three points $A(2, 4, 3)$, $B(4, a, 9)$ and $C(10, -1, 7)$ form a right-angled triangle with $\angle B = 90^\circ$, then the value of 'a' is

If $\lim_{x \to 3} \left( \frac{x^2 - ax - 3a}{x - 3} \right) = 5$, then $a + b =$

If $f(x) = \begin{cases} x^2 - 1 & \text{if } x \ge 2 \\ x + 1 & \text{if } x<2 \end{cases}$, then $\lim_{x \to 2^+} f(x) + \lim_{x \to 2^-} f(x) = $

If $y = \sqrt{\tan x + y}$, then $\frac{dy}{dx} = $

If $f(x) = \begin{cases} ax + 7 & \text{if } x<1 \\ 2x - 3 & \text{if } x = 1 \\ \frac{x+b}{b} & \text{if } x>1 \end{cases}$ is continuous at $x = 1$, then

The second order derivative of $\sec^{-1}\left(\frac{1}{2x^2 - 1}\right)$ with respect to $\cos^{-1}(2x^2 - 1)$, where $0<x<\frac{1}{\sqrt{2}}$ is

If $f(x) = \sin^{-1}\left(\frac{2x}{1 + x^2}\right)$, then $f'\left(\frac{1}{2}\right) =$

If $\sqrt{x} \sqrt[3]{y} = (x + y)^n$ and $x\frac{dy}{dx} - y = 0$, then $n =$