List of top Mathematics Questions asked in Bihar Board Class XII

Evaluate the integral: \[ \int \sec x \, dx \] The correct answer is:

Evaluate the integral: \[ \int \sec^5 x \tan x \, dx \] The correct answer is:

Evaluate the integral: \[ \int \tan^2 x \, dx \] The correct answer is:

Evaluate the integral: \[ \int \cos^2 x \cdot \sin^2 x \, dx \] The correct answer is:

Evaluate the integral: \[ \int \frac{x^2 + 1}{x^4 + 1} \, dx \] The correct answer is:

Evaluate the integral: \[ \int \frac{1 + \cos(2x)}{1 - \cos(2x)} \, dx \] The correct answer is:

Evaluate the integral: \[ \int \frac{2}{2 - 3x} \, dx \] The correct answer is:

Evaluate: \(\tan^{-1} 3 - \sec^{-1} (-2)\)

Evaluate: \(\frac{3\pi}{2} - \sin^{-1} \left( -\frac{1}{2} \right)\)

Let \( R \) be the relation in the set \( \mathbb{N} \) given by: \[ R = \{ (a, b) : a = b - 2, b>6 \}. \] The correct answer in the following is:

Evaluate the integral: \[ \int \frac{dx}{a^2 + x^2} \] The correct answer is:

Evaluate: \(\sin \left( \cot^{-1} x \right)\)

Evaluate: \(\tan \left( \tan^{-1} \frac{3}{1} + \tan^{-1} \frac{2}{1} \right)\)

Evaluate: \(\cos^{-1} \left( \cos \frac{6\pi}{7} \right)\)

If \( x \in [-1,1] \), then \(\displaystyle \sin^{-1}(-x) = \)

If \( x \in [-1,1] \), then \(\displaystyle \cos^{-1} x = \)

Evaluate: \(\displaystyle \cos^{-1}\left(-\frac{1}{2}\right) = \)

Evaluate: \(\displaystyle \int_0^4 \sqrt{x} \, dx = \)

Evaluate: \(\displaystyle \int_{-\pi}^{\pi} \tan x \, dx = \)

Evaluate: \(\displaystyle \int_0^{\frac{\pi}{6}} \cos x \cdot \cos 2x \, dx = \)

Evaluate: \(\displaystyle \int (x + \cos 2x) \, dx = \)

Evaluate: \(\displaystyle \int e^x \left( \sin^{-1} x + \frac{1}{\sqrt{1 - x^2}} \right) dx = \)

Evaluate: \(\displaystyle \int \frac{dx}{x(x+2)} = \)

Evaluate: \(\displaystyle \int \sqrt{a^2 - x^2} \, dx = \)

Evaluate: \(\displaystyle \int_0^{\frac{\pi}{2}} \cos 2x \, dx = \)