List of top Mathematics Questions

If $f(x)= x^5 + 2x^3 + 3x + 1$ and $g(f(x)) = x,$ then $\frac{g(1)}{g’(1)}$ is equal to
Consider the equation ax2 + bx + c = 0 . Find probability if a, b, c ∈ A where A = {1,2,3, ... , 8} that the equation has equal roots.
If matrices \( A \) and \( B \) are of order \( 1 \times 3 \) and \( 3 \times 1 \) respectively, then the order of \( A'B' \) is:
If a matrix has 36 elements, the number of possible orders it can have, is:
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 the sum of all the elements of a \( 3 \times 3 \) scalar matrix is 9, then the product of all its elements is:
If \( A = [a_{ij}] \) 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 \( P' = -P \).
The number of all scalar matrices of order 3, with each entry \( -1, 0, 1 \), is:
If the sum of all the elements of a \( 3 \times 3 \) scalar matrix is 9, then the product of all its elements 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 \( P' = -P \).
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?

The integrating factor of the differential equation \(x\frac{dy}{dx}-y=2x^{2}\) is

The integrating factor of the differential equation.
\((1-y^{2})\frac{dx}{dy}+yx=ay\)\((-1<y<1)\)\(is\)
The general solution of the differential equation \(\frac{ydx-xdy}{y}=0 \) is

The general solution of a differential equation of the type \(\frac{dx}{dy}+p_{1}x=Q1\) is

The general solution of the differential equation \(e^{x}dy+(ye^{x}+2x)dx=0\) is

The solution of the differential equation \( \frac{dy}{dx} = \frac{1}{\log y} \) is:
The integrating factor of the differential equation \[ (1 - x^2) \frac{dy}{dx} + xy = ax, \quad -1 < x < 1, \] is:
The differential equation \( \frac{dy}{dx} = F(x, y) \) will not be a homogeneous differential equation, if \( F(x, y) \) is: