List of top Mathematics Questions

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?
The mean deviation about the mean for the data \( 4, 7, 8, 9, 10, 12, 13, 17 \) is:
If \( \cos x + \cos^2 x = 1 \), then the value of \( \sin^2 x + \sin^4 x \) 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 '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 the integral \[ \int_0^1 \log(1 - x) \, dx \] is:
The area of the region bounded by the curve \[ y = x^2 \quad \text{and the line} \quad y = 16 \quad \text{is:} \]
The distance of the point \( P(-3,4,5) \) from the yz-plane is:
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:
The function \( f(x) = \tan x - x \)
The integral \[ \int \frac{dx}{x^2 \left( x^4 + 1 \right)^{3/4}} \] equals:
The value of \( \int \frac{dx}{(x+1)(x+2)} \) is:
The value of \( \int_0^{\frac{2\pi}{0}} \left( 1 + \sin \left( \frac{x}{2} \right) \right) \, dx \) is:
The value of \( \int_{-1}^1 \sin^5 x \cos^4 x \, dx \) is:
If \( y = a \sin^3 t \), \( x = a \cos^3 t \), then \( \frac{dy}{dx} \) at \( t = \frac{3\pi}{4} \) is:
The minimum value of \( 1 - \sin x \) 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 a line makes angles \( 90^\circ, 60^\circ \) and \( \theta \) with \( x, y \) and \( z \) axes respectively, where \( \theta \) is acute, then the value of \( \theta \) is:
The length of the latus rectum of \( x^2 + 3y^2 = 12 \) is:
A line passes through \( (-1, -3) \) and is perpendicular to \( x + 6y = 5 \). Its x-intercept 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?
If \( |\vec{a}| = 10, |\vec{b}| = 2 \) and \( \vec{a} \cdot \vec{b} = 12 \), then the value of \( |\vec{a} \times \vec{b}| \) 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 \( \vec{a} = \hat{i} + 2\hat{j} + \hat{k} \), \( \vec{b} = \hat{i} - \hat{j} + 4\hat{k} \), 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:
The system of equations \( 4x + 6y = 5 \) and \( 8x + 12y = 10 \) has: