List of top Mathematics Questions

The value of $\frac{1\times 2^2+2\times3^2+...+100\times (101)^2}{1^2 \times 2\times2^2 \times3+...+100^2 \times 101}$

if  $∫_{-1}^1 \frac{cos \, \alpha x}{1+3^x} dx = \frac2{\pi} $ then $\alpha$ is

If a, b, c are in increasing A.P. and a + 1, b, c + 3 are in G.P. If A.M. of a, b, c is 8. Find cube of G.M. of a, b, c.

Find the numbers of distinct real roots $|x||x + 2| - 5|x + 1| - 1$ =0

$ \lim_{t \rightarrow x} \frac{t^2f(x) - x^2 f(t)}{t-x} = 1$, then 2f(2) + 3f(3) equals to:

The value of $∫_0^{\frac{\pi}{4}} \frac{dx}{1+tanx} $

A rectangle ABCD with ABCD with AB = 2 and BC = 4 is inscribed in rectangle PQRS such that vertices of ABCD lie on sides of PQRS then maximum possible area(in sq. unit) of rectangle PQRS is :

When 4 dice are rolled, then the probability of 16 as a sum is:

Let f(x) = $x^2 - 5x$ and $g(x) = 7x - x^2$, then the area between the curves equals to:

If $f(x)= x^5 + 2x^3 + 3x + 1$ and $g(f(x)) = x,$ then $\frac{g(1)}{g’(1)}$ is equal to

If

\[ \begin{bmatrix} x + y & 2 \\ 5 & xy \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 5 & 8 \end{bmatrix}, \]

then the value of

\[ \left(\frac{24}{x} + \frac{24}{y}\right) \]

is:

If \( A = [a_{ij}] \) be a \( 3 \times 3 \) matrix, where \( a_{ij} = i - 3j \), then which of the following is \textbf{false?}

If \( F(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix} \) and \( [F(x)]^2 = F(kx) \), then the value of \( k \) is:

Assertion (A): For any symmetric matrix \( A \), \( B'A B \) is a skew-symmetric matrix.
Reason (R): A square matrix \( P \) is skew-symmetric if \( P' = -P \).

Assertion (A): For any symmetric matrix \( A \), \( B'A B \) is a skew-symmetric matrix.
Reason (R): A square matrix \( P \) is skew-symmetric if \( P' = -P \).

If the sum of all the elements of a \( 3 \times 3 \) scalar matrix is 9, then the product of all its elements is:

If \( A = [a_{ij}] \) is a \( 3 \times 3 \) matrix, where \( a_{ij} = i - 3j \), then which of the following is false?

Assertion (A): For any symmetric matrix \( A \), \( B'A B \) is a skew-symmetric matrix.
Reason (R): A square matrix \( P \) is skew-symmetric if \( P' = -P \).

If for the matrix \( A = \begin{bmatrix} \tan x & 1 \\ -1 & \tan x \end{bmatrix} \), \( A + A' = 2\sqrt{3}I \), then the value of \( x \in \left[ 0, \frac{\pi}{2} \right] \) is:

Which of the following is a homogenous differential equation?