List of top Mathematics Questions

If the statement \( (p \land q) \rightarrow (r \lor \neg s) \) is False, find the truth values of \(p, q, r,\) and \(s\).

If \( y = \sin^{-1}\!\left(\dfrac{5x + 12\sqrt{1-x^2}}{13}\right) \), then \( \dfrac{dy}{dx} \) is equal to:

Evaluate the definite integral: \( \displaystyle \int_{3}^{5} |x-4|\,dx \).

The equation of a plane passing through three non-collinear points is determined using:

Let \( A = \begin{bmatrix} 1 & 0 & 0 0 & 1 & 0 3 & 2 & 1 \end{bmatrix} \). Find \( A^{100} \).

Find the value of \( k \) if the function \( f(x) = \dfrac{k\cos x}{\pi - 2x} \) is continuous at \( x = \dfrac{\pi}{2} \).

Find the angle between non-zero vectors \( \mathbf{a} \) and \( \mathbf{b} \) if their dot product \( \mathbf{a}\cdot\mathbf{b} = 0 \).

If \( y = \sin^{-1}(3x - 4x^3) \), find the derivative \( \dfrac{dy}{dx} \) in its standard form.

Let the foot of perpendicular from a point \( P(1,2,-1) \) to the straight line \( L: \frac{x}{1} = \frac{y}{0} = \frac{z}{-1} \) be \( N \). Let a line be drawn from \( P \) parallel to the plane \( x + y + 2z = 0 \) which meets \( L \) at point \( Q \). If \( \alpha \) is the acute angle between the lines PN and PQ, then \( \cos \alpha \) is equal to

The magnitude of projection of line joining (3, 4, 5) and (4, 6, 3) on the line joining (−1, 2, 4) and (1, 0, 5) is

If \( \vec{a} = 2\hat{i} + \hat{j} + 2\hat{k} \), then the value of \( |\hat{i} \times (\vec{a} \times \hat{i})|^2 + |\hat{j} \times (\vec{a} \times \hat{j})|^2 + |\hat{k} \times (\vec{a} \times \hat{k})|^2 \) is equal to

The value of \( \int e^{\tan \theta} (\sec \theta - \sin \theta) \, d\theta \) is

The area of the region bounded by the curves \( x = y^2 - 2 \) and \( x = y \) is

Find the equation of the normal to a parabola which is perpendicular to a given line. This involves:

The angle between two lines in 3D space can be found using:

In a Linear Programming Problem (LPP), the objective function Z is minimized subject to constraints. Where does the minimum value occur?

Find the term independent of \( x \) in the expansion of \( (1 + x)^{n} (1 + \frac{1}{x})^{n} \).

Evaluate: \( \cot^{-1}(2) - \cot^{-1}(8) - \cot^{-1}(18) - \dots \)

Evaluate: \( \int e^{x} \sin x \cos x \, dx \)

Let \( f : \mathbb{R} \to \mathbb{R} \) and \( g : \mathbb{R} \to \mathbb{R} \) such that \( g(x) \neq 0 \) for all \( x \in \mathbb{R} \), and \( f = f^{-1} \). Which of the following is correct?

A person travels from Hyderabad to Goa and returns, but does not use the same bus for both journeys. If there are 25 buses available for each direction, how many ways can the round trip be made?

If \(\log_8 x = \frac{1}{3}\), find the value of \(x\).

Find the mean deviation about the mean for the data set: 1, 3, 5, 7, \dots, 101

Evaluate the integral: \[ \int \frac{2x}{x^2 - 5x + 4}\, dx \]

Two players A and B play a series of games of badminton. The player who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways in which player A wins the series is _________.