List of top Mathematics Questions asked in VITEEE

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

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

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

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

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

Find \(x\): \(4(x - 2) = 3(x + 5)\).

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

Probability of getting at least one head in two coin tosses: ____.

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

Find \(x\): \(2x + 3 = 7x - 8\).

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

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

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

Find the area bounded by the curve \( y^2 = 4x \) and its latus rectum.

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.

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

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

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

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 determinant of a matrix is zero, then matrix is: ____.

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

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