List of top Mathematics Questions

The principal value of \( \cot^{-1} \left( -\frac{1}{\sqrt{3}} \right) \) is:
If \[ A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & -2 \end{bmatrix}, \] then \( |A| \) is:
If \[ A = \begin{bmatrix} 1 & 2 & 3 \\ -4 & 3 & 7 \end{bmatrix}, \quad B = \begin{bmatrix} 4 & 3 \\ -1 & 2 \\ 0 & 5 \end{bmatrix}, \] then the correct statement is:

If \( P(A \cup B) = 0.9 \) and} \( P(A \cap B) = 0.4 \), then \( P(A) + P(B) \) is:

If \[ A = \begin{bmatrix} 5 & 0 \\ 0 & 5 \end{bmatrix}, \] then \( A^3 \) is:
Domain of the function \( f(x) = \frac{1{(x-2)(x-5)} \) is:}
Consider the following statements:
Statement-I: The set of all solutions of the linear inequalities 3x + 8 < 17 and 2x + 8 ≥ 12 are x < 3 and x ≥ 2 respectively.
Statement-II: The common set of solutions of the linear inequalities 3x + 8 < 17 and 2x + 8 ≥ 12 is (2,3).
Which of the following is true?
If \( B = \begin{bmatrix} 1 & 3 \\ 2 & \alpha \end{bmatrix} \) is the adjoint of a matrix \( A \) and \( |A| = 2 \), then the value of \( \alpha \) is:
If \[ y = \frac{\cos x}{1 + \sin x} \] then:

Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \). 

 Choose the correct answer from the options given below:

The function f(x) is given by:

For x < 0:
f(x) = ex + ax

For x ≥ 0:
f(x) = b(x - 1)2


The function is differentiable at x = 0. Then,
If 'a' and 'b' are the order and degree respectively of the differentiable equation \[ \frac{d^2 y}{dx^2} + \left(\frac{dy}{dx}\right)^3 + x^4 = 0, \quad \text{then} \, a - b = \, \_ \_ \]
The value of \[ \lim_{x \to 1} \frac{x^4 - \sqrt{x}}{\sqrt{x} - 1} \] is:
If \( A \) is a square matrix of order \( 3 \times 3 \), \( \det A = 3 \), then the value of \( \det(3A^{-1}) \) is:
If \(A\) is a square matrix such that \(A^2 = A\), then \((I - A)^3\) is:

The equation \[ 2 \cos^{-1} x = \sin^{-1} \left( 2 \sqrt{1 - x^2} \right) \] is valid for all values of \(x\) satisfying:

If \( \cos x + \cos^2 x = 1 \), then the value of \( \sin^2 x + \sin^4 x \) is:
Find \[ \sec^2 \left( \tan^{-1} 2 \right) + \csc^2 \left( \cot^{-1} 3 \right) = ? \]
If A and B are two matrices such that AB is an identity matrix and the order of matrix B is \(3 \times 4\), then the order of matrix A is:
A line passes through \( (-1, -3) \) and is perpendicular to \( x + 6y = 5 \). Its x-intercept is:
The number of diagonals that can be drawn in an octagon is:
The equation of the line through the point \( (0, 1, 2) \) and perpendicular to the line \[ \frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{-2} \] is:
If \( f(x) = \sin[\lfloor x^2 \rfloor] - \sin[\lfloor -x^2 \rfloor] \), where \( \lfloor x \rfloor \) denotes the greatest integer less than or equal to \( x \), then which of the following is not true?
If \( y = a \sin^3 t \), \( x = a \cos^3 t \), then \( \frac{dy}{dx} \) at \( t = \frac{3\pi}{4} \) is:
The derivative of \( \sin x \) with respect to \( \log x \) is: