List of top Mathematics Questions

If \( P(A) = \frac{1}{2}, P(B) = \frac{3}{8} \) and \( P(A \cap B) = \frac{1}{5} \), then \( P(A \cup B) \) is equal to:

Prove that \[ 2 \tan^{-1} \left( \frac{1}{3} \right) + \tan^{-1} \left( \frac{1}{7} \right) = \frac{\pi}{4} \]

A wire of length 28m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and circle is minimized?

Evaluating \( \int \frac{dx}{x^3 + 1} \):

Differentiate \( x \sin x + (\sin x)^x \) with respect to \( x \).

Solve the L.P.P graphically
Maximize \( Z = 7x + 8y \) subject to constraints \[ x + y \geq 50, \quad x + 2y \leq 100, \quad x - y \geq 10, \quad x \geq 0, \quad y \geq 0 \]

If \( y = (\tan^{-1} x)^2 \), prove that \( (x^2 + 1)^2 y_2 + 2x (x^2 + 1) y_1 = 2 \).

Evaluate \[ \int \frac{dx}{x^2 - 8x + 17} \]

Find the intervals in which the function \( f(x) = 2x^3 - 15x^2 + 36x + 1 \) is strictly increasing or decreasing?

\( \tan^{-1} \sqrt{3} - \sec^{-1}(-2) \) is equal to \( \frac{\pi}{3} \).

Evaluate \( \int_{-1}^{1} \log \left( \frac{2 + x}{2 - x} \right) \, dx \)

Evaluate \( \int e^x \left( \cot x + \log \sin x \right) \, dx \)

Objective function of a L.P.P is a function to be optimized.

\( \int_1^1 (x^{19} + x^{21}) \, dx = 0 \)

\( \int dx = x^2 + C \)

The function \( y = \sin x \) is increasing in \( \left[ 0, \frac{\pi}{2} \right] \).

\( \frac{d}{dx} \left( \cos^{-1}x \right) \) is:

\( \int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \) equals:

The rate of change of the area of a circle with respect to its radius \( r \) at \( r = 6 \, \text{cm} \) is:

If \( AB = C \) where \( B \) and \( C \) are of order \( 3 \times 5 \), then the order of \( A \) is:

Maximum value of \( Z = 3x + y \) for the constraints \( x + y \leq 4, x \geq 0, y \geq 0 \) is:

\( \int e^x(f(x) + f'(x)) \, dx \) equals:

The value of \( \cos^{-1} \left( \cos \frac{2\pi}{3} \right) \) is equal to: