List of practice Questions

Evaluate the integral: \[ \int \frac{1 + x^8}{x^3} \, dx \] The correct answer is:

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

If \[ A = \begin{bmatrix} 2 & -3 \\ 4 & 6 \end{bmatrix} \] then \[ A^{-1} = \] The correct answer is:

If \[ A = \begin{bmatrix} 3 & 6 \\ -5 & 4 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} 7 & 8 \\ 5 & 6 \end{bmatrix}, \] then \[ 6A - 5B = \] The correct answer is:

If \[ A = \begin{bmatrix} 2 & \sqrt{2} & 0 \\ 3 & -2 & \frac{2}{5} \end{bmatrix} \] then \[ A^t = \] The correct answer is:

If \[ 2A + B + X = 0 \] where \[ A = \begin{bmatrix} -1 & 2 \\ 3 & 4 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} 3 & 1 \\ 5 & -2 \end{bmatrix}, \] then \[ X = \]

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

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

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

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

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

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

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

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

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

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