List of top Mathematics & Statistics Questions

Evaluate: \( \int \frac{dx}{2 + \cos x - \sin x} \)
Two dice are thrown simultaneously. If \( X \) denotes the number of sixes, find the expectation of \( X \).
Find the distance between the parallel lines \( \frac{x}{2} = \frac{y}{-1} = \frac{z}{2} \) and \( \frac{x-1}{2} = \frac{y+1}{-1} = \frac{z-4}{2} \).
Show that function \( f(x) = \tan x \) is increasing in \( (0, \frac{\pi}{2}) \).
Using truth table verify that: \( (p \wedge q) \vee \sim q \equiv p \vee \sim q \)
Find the cartesian coordinates of the point whose polar coordinates are \( \left( \frac{1}{2}, \frac{\pi}{3} \right) \).
If \( \int \frac{dx}{4x - 1} = A \log |2x + 1| + c \), then \( A = \)
If \( f'(x) = x^{-1} \), then find \( f(x) \)
Find the principal value of \( \cot^{-1} \left( -\frac{1}{\sqrt{3}} \right) \)
Write the degree of differential equation \( (y''')^4 + 3(y'') + 3xy + 5y = 0 \)
If the p.m.f of a r.v. \( X \) is \( P(x) = \frac{c}{x^3} \), for \( x = 1, 2, 3 \), = 0 otherwise, then \( E(X) = \)
The value of \( \hat{i} \cdot (\hat{j} \times \hat{k}) + \hat{j} \cdot (\hat{k} \times \hat{i}) + \hat{k} \cdot (\hat{i} \times \hat{j}) \) is
The negation of \( p \wedge (q \to r) \) is