List of top Mathematics Questions

Evaluate the definite integral: \( \displaystyle \int_{0}^{\pi/2} \frac{\sin^n x}{\sin^n x + \cos^n x}\, dx \).

Find the value of \(k\) if the function \(f(x)=\dfrac{k\sin x}{x}\) for \(x\neq0\) and \(f(0)=3\) is continuous at \(x=0\).

If the vectors \(2i - j + k\), \(i + 2j - 3k\) and \(3i + aj + 5k\) are coplanar, find the value of \(a\).

Assertion (A) : \((\sqrt{3} + \sqrt{5})\) is an irrational number.
Reason (R) : Sum of the any two irrational numbers is always irrational.

Determine the distance of the point \( (1,2,3) \) from the plane \( 2x + 3y - z = 7 \).

Find the general solution of the differential equation \( \frac{dy}{dx} + y = e^{-x} \).

Find the truth value of the statement: "If 2 is even, then 5 is prime."

The value of \( \displaystyle \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x} \, dx \) is:

Assertion (A) : If probability of happening of an event is \(0.2p\), \(p>0\), then \(p\) can't be more than 5.
Reason (R) : \(P(\bar{E}) = 1 - P(E)\) for an event \(E\).

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:

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 \( (1 + x)^{n} (1 + \frac{1}{x})^{n} \).