List of top Mathematics Questions

The area bounded by the curve \[ y = \sin\left(\frac{x}{3}\right), \quad x \text{ axis}, \quad \text{the lines } x = 0 \text{ and } x = 3\pi \] is:

If \(A\) is a square matrix such that \(A^2 = A\), then \((I - A)^3\) is:

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:

Which of the following statements is not correct?

If a matrix \( A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix} \) satisfies \( A^6 = kA' \), then the value of \( k \) is:

If \( A = \begin{bmatrix} k & 2 \\ 2 & k \end{bmatrix} \) and \( |A^3| = 125 \), then the value of \( k \) is:

If \( A \) is a square matrix satisfying the equation \( A^2 - 5A + 7I = 0 \), where \( I \) is the identity matrix and \( 0 \) is the null matrix of the same order, then \( A^{-1} \) is:

If \( A \) is a square matrix of order \( 3 \times 3 \), \( \det A = 3 \), then the value of \( \det(3A^{-1}) \) is:

If \( B = \begin{bmatrix} 1 & 3 \\ 2 & \alpha \end{bmatrix} \) is the adjoint of a matrix \( A \) and \( |A| = 2 \), then the value of \( \alpha \) is:

A and B are two sets having 3 and 6 elements respectively. Consider the following statements: - Statement (I): Minimum number of elements in \( A \cup B \) is 3 - Statement (II): Maximum number of elements in \( A \cap B \) is 3 Which of the following is correct?

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 \( \vec{a} = \hat{i} + 2\hat{j} + \hat{k} \), \( \vec{b} = \hat{i} - \hat{j} + 4\hat{k} \), and \( \vec{c} = \hat{i} + \hat{j} + \hat{k} \) are such that \( \vec{a} + \lambda \vec{b} \) is perpendicular to \( \vec{c} \), then the value of \( \lambda \) is:

Consider the following statements: Statement (I): In a LPP, the objective function is always linear. Statement (II): In a LPP, the linear inequalities on variables are called constraints. Which of the following is correct?

If the 4th, 10th, and 16th terms of a G.P. are \(x\), \(y\), and \(z\) respectively, then

The integral \[ \int \frac{dx}{x^2 \left( x^4 + 1 \right)^{3/4}} \] equals:

The value of the integral \[ \int_0^1 \log(1 - x) \, dx \] is:

If the number of terms in the binomial expansion of \((2x + 3)^n\) is 22, then the value of \(n\) is:

Consider the following statements:
% Statement Statement (I): If either \( |\vec{a}| = 0 \) or \( |\vec{b}| = 0 \), then \( \vec{a} \cdot \vec{b} = 0 \).
% Statement Statement (II): If \( \vec{a} \times \vec{b} = 0 \), then \( \vec{a} \) is perpendicular to \( \vec{b} \).
Which of the following is correct?

The value of \( \int_{-1}^1 \sin^5 x \cos^4 x \, dx \) is:

General solution of the differential equation \[ \frac{dy}{dx} + y \tan x = \sec x \quad \text{is:} \]

The system of equations \( 4x + 6y = 5 \) and \( 8x + 12y = 10 \) has:

Domain of the function \( f(x) = \frac{1{(x-2)(x-5)} \) is:}