List of top Questions asked in VITEEE

Four independent waves are represented by equations : (1) $X_{1}=a_{1} \sin \omega t$ (2) $X_{2}=a_{1} \sin 2 \omega t$ (3) $X_{3}=a_{1} \sin \omega_{1} t$ (4) $X_{4}=a_{1} \sin (\omega t+\delta)$ Interference is possible between waves represented by equations :

Radar waves are sent towards a moving airplane and the reflected waves are received. When the airplane is moving towards the radar, the wavelength of the wave

Indicate which one of the following statements is not correct?
(a) Intensities of reflections from different crystallographic planes are equal
(b) According to Bragg's law higher order of reflections have high $\theta$ values for a given wavelength of radiation
(c) For a given wavelength of radiation, there is a smallest distance between the crystallographic planes which can be determined
(d) Bragg's law may predict a reflection from a crystallographic plane to be present but it may be absent due to the crystal symmetry

If (x +y )sin u = $x^2y^2$, then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} = $

The product of all values of $(\cos \alpha + i \sin \alpha)^{3/5}$ is equal to

If the normal at $(ap^2, 2ap)$ on the parabola $y^2 = 4ax,$ meets the parabola again at $(aq^2, 2aq)$, then

A box contains $9$ tickets numbered $1$ to $9$ inclusive. If $3$ tickets are drawn from the box one at a time, the probability that they are alternatively either {odd, even, odd} or {even, odd, even} is

The sum of the series $ \frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+... $ upto $ n $ term is

If the rank of the matrix $\begin{bmatrix}-1 &2&5\\ 2&-4&a-4\\ 1&-2&a+1\end{bmatrix}$ is 1, then the value of $a$ is

The length of the straight line $x - 3y = 1$ intercepted by the hyperbola $x^2 - 4y^2 = 1$ is

The curve described parametrically by $x = t^2 + 2t - 1, y = 3t + 5$ represents

If $\sin^{-1} x + \sin^{-1} y = \frac{\pi}{2}$ , then $\cos^{-1} x + \cos^{-1} y$ is equal to

$\frac{1+\tan ^{2} x}{1-\tan ^{2} x} d x$ is equal to

The function $f(x) = x^2 \; e^{-2} x, x > 0$. Then the maximum value of $f(x)$ is

If b$^2 \ge 4 ac$ for the equation $ax^4 + bx^2 + c = 0$, then all the roots of the equation will be real if

Let $A = \{1,2,3,....., n\}$ and $B = \{a,b,c\}$, then the number of functions from $A$ to $B$ that are onto is

The differential equation of the system of all circles of radius $r$ in the $xy$ plane is

If $x > 0$ and $\log_{3} x+\log_{3}\left(\sqrt{x}\right)+\log_{3}\left(\sqrt[4]{x}\right)+\log_{3}\sqrt[8]{x}+\log_{3}\left(\sqrt[16]{x}\right)+....=4,$ then x equals

If the normal to the curve $y = f(x)$ at $(3,4)$ makes an angle $\frac{3 \pi}{4}$ with the positive x-axis, then $f'(3)$ is equal to

The equation of a directrix of the ellipse $\frac{x^2}{16} + \frac{y^2}{25} = 1 $ is

Name the complex Ni(\(PF_6\))\(_2\):

If \( x = -9 \) is a root of \( \begin{pmatrix} 2 & 3 \\ 7 & 6 \end{pmatrix} \times \begin{pmatrix} x \end{pmatrix} = 0 \), then other two roots are:

Let \( A = \begin{pmatrix} 1 & 3 & 2 \\ 4 & 2 & 5 \\ 7 & -t & -6 \end{pmatrix} \), then the values of \( t \) for which inverse of \( A \) does not exist are:

If \( f'(x) = \frac{x}{\sqrt{1 + x^2}} \) and \( f(0) = 0 \), then \( f(x) = \):

The probability density \( f(x) \) of a continuous random variable is given by \( f(x) = K e^{-|x| \) for \( -\infty<x<\infty \). Then the value of \( K \) is:}