List of top Mathematics Questions

If \( (2 - x)^9 = a_0 + a_1x + \dots + a_9x^9 \), find \( a_1 + a_2 + \dots + a_8 \)

Maximum of \( f(x) = \alpha - 4x - x^2 \), find \(\alpha = ?\)

Given that \( \vec{a} = 2\hat{i} - \lambda \hat{j} + 5\hat{k} \), \( \vec{b} = \mu \hat{i} + 7\hat{j} + 3\hat{k} \), and the midpoint of \( \overrightarrow{AB} = 3\hat{i} + 2\hat{j} + 4\hat{k} \), find \( \lambda + \mu \).

If the area of the circle \( x^2 + y^2 + 8x - 6y + c = 0 \).

Find \( \alpha \) if \[ \lim_{x \to 0} \frac{1 - \sec^2(\alpha x)}{\alpha x^2} = -3 \]

Find \(\int_{0}^{\frac{\pi}{2}} \sqrt{\cos x \sin 2x} \, dx\)

The distance of the point (10, 10, 10) from the Z-axis.

Find minimum value of \( \sin x \sin \left( x + \frac{\pi}{3} \right) \)

Solve \( 6(2x+3) + x>53 - 2x \).

Find the integral \( \int 2 \, dy = (y + \cos x) \, dx \)

Find unit vector parallel to \(- (s + 4s) \hat{i} + (7 - 2s) \hat{j} + (3 + 4s) \hat{k}\)

If \( y = \log_e (x^3 + 24) \), find \( \frac{dy}{dx} \) at \( y = \log_e 2 \).

Compute \( \int (\cot 2x + \cos 2x) \, dx \)

Find \(\int_{-1}^{1} \frac{\log(1 + |x|)}{1 + |x|} \, dx\)

If \( \alpha = \frac{\pi}{4} \), find \( (\sin \alpha + \sin \beta)^2 + (\cos \alpha + \cos \beta)^2 \).

Compute \( \int \frac{\sqrt{x + 1}}{\sqrt{x}} \, dx \)

If \( y = \frac{1 + \tan^2 x}{1 - \tan^2 x} \), find \( y' \left( \frac{\pi}{8} \right) \), where \( 0<x<\frac{\pi}{4} \).

If \(y = 4\sqrt{x}\) then \(\frac{d^2y}{dx^2} =\)

Number of ways 3 boys and 4 girls can be arranged such that there is one girl between any 2 boys and one boy between any 2 girls.

Number of words that can be formed starting and ending with the same letter from the word BANANA.

Find the value of \( \tan(105^\circ) \) using compound angle identities.

The converse of the statement \( ((\sim p) \land q) \rightarrow r \) is:

If \(A\) is a \(3\times3\) matrix such that \(|A| = 4\) and \(B = \text{adj}\,A\), find the value of \(|B|\).

Consider two matrices \(A=\begin{bmatrix}3 & -4 1 & -1\end{bmatrix}\) and \(B=\begin{bmatrix}6 & -13 5 & -10\end{bmatrix}\). If the following matrix equation holds true: \[ \left((A^{-1})^2 + B\right)\begin{bmatrix}x y\end{bmatrix} = \begin{bmatrix}0 0\end{bmatrix} \] Find the values of \(x\) and \(y\).

Evaluate the following indefinite integral: \[ \int \sin(\log x)\,dx \]