List of top Mathematics Questions

If \( x \) and \( y \) are acute angles, such that \[ \cos x + \cos y = \frac{3}{2} \quad \text{and} \quad \sin x + \sin y = \frac{3}{4}, \quad \text{then} \quad \sin(x + y) \text{ equals:} \]
The expression \( \frac{\tan A + \cot A}{1 - \cot A} \) can be written as:
If \( \sin 2x = 4 \cos x \), then \( x \) is equal to:
The integral \( \int \frac{2^x}{\sqrt{1 - 4^x}} \, dx \) is equal to:
The integral \( \int_{\pi/2}^{-\pi/2} \sin x \, dx \) is:
The equation of a plane passing through the line of intersection of the planes \( x + 2y + 3z = 2 \) and \( x - y + z = 3 \) and at a distance \( \frac{2}{\sqrt{3}} \) from the point \( (3, 1, -1) \) is:
The point of intersection of the lines \( \frac{x - 1}{3} = \frac{y - 2}{-3} = \frac{z - 3}{4} \) and \( \frac{x - 4}{5} = \frac{y - 1}{2} = \frac{z - 1}{-2} \) is:
The angle between the lines \( 2x = 3y - z \) and \( 6x = -y - 4z \) is:
The integral of \( \int \frac{dx}{x^2[1 + x^4]^{3/4}} \) is:
The approximate value of \( f(5.001) \), where \( f(x) = x^3 - 7x^2 + 15 \), is:
The value of \( \lim_{x \to 0} \frac{ax^3 + bx^2 + cx}{3x^2} \), where \( a, b, c > 0 \), is:
Find the center and radius of the circle given by the equation \( 2x^2 + 2y^2 + 3x + 4y + 9 = 0 \).
The line \( \frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5} \) is parallel to the plane:
What will be the equation of the circle whose center is \( (1, 2) \) and which passes through the point \( (4, 6) \)?
The coefficients \( a, b, c \) of the quadratic equation \( ax^2 + bx + c = 0 \) are obtained by throwing a die three times. The probability that this equation has equal roots is:
If \( L = \lim_{x \to 0} \frac{a - \sqrt{a^2 - x^2}}{x^4} \), \( a > 0 \), then:
What will be the equation of the circle whose center is \( (1, 2) \) and touches the X-axis?
Evaluate: \( 8^{\log_5 5} \)
The vector that must be added to \[ \mathbf{i} - 3\mathbf{j} + 2\mathbf{k} \quad \text{and} \quad 3\mathbf{i} + 6\mathbf{j} - 7\mathbf{k} \] so resultant vector is a unit vector along the X-axis is:
If \( |\mathbf{a}| = 8 \), \( |\mathbf{b}| = 3 \) and \( |\mathbf{a} \times \mathbf{b}| = 12 \), then find the angle between \( \mathbf{a} \) and \( \mathbf{b} \).
If for \(\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}\), \(\vec{b} = \hat{i} - 2\hat{j} + \hat{k}\), and \(\vec{c} = -3\hat{i} + \hat{j} + 2\hat{k}\), then find \([\vec{a} \, \vec{b} \, \vec{c}]\).
The maximum value of \( x + y \) subject to \[ 2x + 3y \leq 6, \quad x \geq 0, \quad y \geq 0 \] is:
Write the solution of the following LPP \[ \text{Maximize } Z = x + y \] Subject to \[ 3x + 4y \leq 12, \quad x \geq 0, \quad y \geq 0 \] Which point the value of \( Z \) is maximum?
If a straight line is used to connect V 3, what will be the angle formed between the lines V3 and V1?
straight line
The perimeter of a rhombus is 52 cm, if its one diagonal is 24 cm then the length of its other diagonal is