List of top Questions asked in VITEEE

If \(\vec{a}=\hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=2\hat{i}+4\hat{j}+3\hat{k}\) are one of the sides and medians respectively, through the same vertex, then area of the triangle is

The system of equations
\[ x+y+z=0 \] \[ 2x+3y+z=0 \] \[ x+2y=0 \] has

If \(\begin{vmatrix} 0 & a^4 \\ b & 0 \end{vmatrix}=1\), then

If \(D=\text{diag}(d_1,d_2,\ldots,d_n)\), where \(d_i\neq 0\), for \(i=1,2,\ldots,n\), then \(D^{-1}\) is equal to

In how many number of ways can 10 students be divided into three teams, one containing four students and the other three?

If \(R\) be a relation defined as \(aRb\) iff \(|a-b|>0\), then the relation is

Let \(S\) be a finite set containing \(n\) elements. Then the total number of commutative binary operation on \(S\) is

A manufacturer of cotter pins knows that 5% of his product is defective. He sells pins in boxes of 100 and guarantees that not more than one pin will be defective in a box. In order to find the probability that a box will fail to meet the guaranteed quality, the probability distribution he should use is

The probability that a certain kind of component will survive a given shock test is \(\frac{3}{4}\). The probability that exactly 2 of the next 4 components tested survive is

Mean and standard deviation of marks obtained in some particular subject by four classes are given below. Report the class with the best performance

A random variable \(X\) follows binomial distribution with mean \(\alpha\) and variance \(\beta\). Then

Area enclosed by the curve \(\pi\left[4(x-\sqrt{2})^2+y^2\right]=8\) is

The value of \(\int_{0}^{a}\sqrt{\frac{a-x}{x}}\,dx\) is

Let \(y\) be the number of people in a village at time \(t\). Assume that the rate of change of the population is proportional to the number of people in the village at any time and further assume that the population never increases in time. Then the population of the village at any fixed time \(t\) is given by

The differential equation of all straight lines touching the circle \(x^2+y^2=a^2\) is

The differential equation \(\left|\frac{dy}{dx}\right|+|y|+3=0\) admits

Solution of the differential equation \(xdy-ydx-\sqrt{x^2+y^2}\,dx=0\) is

Let P, Q, R and S be statements and suppose that \(P\to Q \to R \to P\); if \(\sim S \to R\), then

The directrix of the parabola \(y^2 + 4x + 3 = 0\) is

If \(g(x)\) is a polynomial satisfying \(g(x)g(y)=g(x)+g(y)+g(xy)-2\) for all real \(x\) and \(y\) and \(g(2)=5\), then \(\lim_{x\to 3} g(x)\) is

The value of \(f(0)\) so that \(\frac{-e^x+2^x}{x}\) may be continuous at \(x=0\) is

Let \([\,]\) denote the greatest integer function and \(f(x)=[\tan^2 x]\). Then

A spherical balloon is expanding. If the radius is increasing at the rate of 2 centimeters per minute, the rate at which the volume increases (in cubic centimeters per minute) when the radius is 5 centimeters is

The length of the parabola \(y^2=12x\) cut off by the latus-rectum is

If \(I=\int \frac{x^5}{\sqrt{1+x^3}}\,dx\), then \(I\) is equal to