List of top Mathematics Questions asked in VITEEE

Evaluate \[ \int \frac{x^2 + 4}{x^4 + 16} \, dx \]

Find the value of the limit \[ \lim_{x \to 0} \frac{\sqrt{1 - \cos x}}{x} \]

If D is the set of all real x such that \( 1 - e^{(1/x)} \) is positive, then D is equal to:

The number of ways of painting the faces of a cube of six different colours is:

If \( R \) be a relation from \( A = \{1, 2, 3, 4\} \) to \( B = \{1, 3, 5\} \) such that \( (a, b) \in R \) if \( a<b \), then ROR is:

To the lines \( ax^2 + 2hxy + by^2 = 0 \), the line \( ax^2 + 2h(a+b)xy + b^2y^2 = 0 \) are:

For a GP, \( a_n = 3(2^n) \), \( n \in \mathbb{N} \), Find the common ratio.

If \( x^2 + 2x + 7<6 \), \( x \in \mathbb{R} \), then:

If \( a, b, c \) are in HP, then \( \frac{a}{b+c} = \frac{b}{c+a} = \frac{c}{a+b} \) will be in:

If \( x + y = (1 + i \sqrt{3})^{100} \), then find \( (x, y) \):

If $\frac{x^{2}+2x+7}{2x+3} < 6, x\,\in\,R, $ then

A dice is rolled twice and the sum of the numbers appearing on them is observed to be $7$. What is the conditional probability that the number $2$ has appeared at least once ?

If $X$ is a poisson variate such that $P(X = 1) = P(X = 2)$, then $P(X=4)$ is equal to

Evaluate $\int \frac{x^{2}+4}{x^{4}+16}dx.$

In an equilateral triangle, the inradius, circumradius and one of the exradii are in the ratio

Evaluate $\int\limits^{3\pi/4}_{\pi/4} \frac{1}{1+cos\,x}dx$

Find the value of $(7.995)^{1/3}$ correct to four decimal places.

The sum of the coefficients of $(6\,a-5\,b)^n$, where $n$ is a positive integer, is

In how many ways 6 letters be posted in 5 different letter boxes?

If $D$ is the set of all real $x$ such that $1-e^{\left(1/ x\right)-1}$ is positive, then $D$ is equal to

The number of ways of painting the faces of a cube of six different colours is

If one $AM 'A'$ and two $GM$ $p$ and $q$ are inserted between two given numbers, then find the value of $\frac{p^{2}}{q}+\frac{q^{2}}{p}$

If the roots of the equation $x^2 + ax + b = 0$ are $c$ and $d$, then one of the roots of the equation $x^{2}+\left(2c+a\right)x+c^{2}+ac+b=0$ is

The numerically greatest term in the expansion of \((3-5x)^{11}\) when \(x=\dfrac{1}{5}\), is

If \(f(x)=\sqrt{\log_{10}(x^2)}\), the set of all values of \(x\) for which \(f(x)\) is real, is