List of top Mathematics Questions asked in VITEEE

Find the value of \(k\) if the lines \( \frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4} \) and \( \frac{x-4}{k} = \frac{y-1}{2} = \frac{z}{1} \) are perpendicular.

A bag contains 5 red and 7 blue balls. Find the probability of drawing 2 red balls without replacement.

If \( z = \frac{3i}{2} \), what is the value of \( \arg(z) \)?

Find the value of \(k\) if the lines \[ \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4} \] and \[ \frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{k} \] are coplanar.

Find the area of the region bounded by the curve \( y^2 = 4x \) and the line \( x = 3 \).

Evaluate \( \displaystyle \int_{0}^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \).

If \(A\) is a \(3 \times 3\) matrix such that \( |A| = 5 \), find the value of \( |adj(A)| \).

A bag contains 4 red and 6 black balls. A ball is drawn at random, its colour is noted and it is returned to the bag. Moreover, 2 additional balls of the colour drawn are put in the bag and then a ball is drawn at random. What is the probability that the second ball is red?

If \( S_n = 3n^2 + 5n \) represents the sum of \( n \) terms of an A.P., find the \(10^{th}\) term \( (a_{10}) \).

If \( \omega \) is an imaginary cube root of unity, find the value of \( (1 + \omega - \omega^2)^7 \).

Find the integrating factor (I.F.) for the differential equation \[ \frac{dy}{dx} + y\sec x = \tan x . \]

Evaluate the integral \( \displaystyle \int \frac{1}{x\log x}\,dx \).

Find the distance of the point \( (1,-2,3) \) from the \(yz\)-plane.

Find the area of the region bounded by the curve \(y^2=4x\) and the line \(x=3\).

If \(A\) is a square matrix of order \(3\) such that \( |adj\,A| = 64 \), then find the value of \( |A| \).

The sum of the first \(10\) terms of an A.P. is \(150\). If the first term is \(10\), what is the common difference?

What is the distance of the point \((1,2,3)\) from the \(yz\)-plane?

Find the distance between the planes \(2x + 3y + 4z = 4\) and \(4x + 6y + 8z = 12\).

If the sum of the first \(n\) terms of an A.P. is \(S_n = 3n^2 + 5n\), find the \(10^{th}\) term.

Find the missing number in the series: \(2,\,6,\,12,\,20,\,30,\,?\)

Find the value of \( \displaystyle \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x}\,dx \).

If \( \tan^{-1}x + \tan^{-1}y = \frac{\pi}{4} \), then what is the value of \(x + y + xy\)?

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

If \(A\) is a square matrix of order \(3\) and \(|A| = 5\), find \(|adj(A)|\).

Evaluate the integral \[ \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x}\,dx. \]