List of top Questions asked in VITEEE

A hollow sphere and a solid sphere, of equal mass and equal radii roll down without slipping on an inclined plane. If the torque experienced by the hollow sphere and solid sphere are $\tau_H$ and $\tau_S$ respectively, then
A circle has radius 3 and its centre lies on the line $y = x -1$ . The equation of the circle, if it passes through $(7, 3)$, is
If $\left(\vec{a}\times\vec{b}\right)^{2}+\left(\vec{a}.\vec{b}\right)^{2}=676$ and $\left|\vec{b}\right|=2,$ then $\left|\vec{a}\right|$ is equal to
The system of linear equations : $x + y + z = 0, 2x + y - z = 0, 3x + 2y = 0$ has :
The area under the curve $y = | cos\, x - sin \,x |, 0 \le x\le\frac{\pi}{2}$, and above x-axis is :
If vector equation of the line$\frac{x-2}{2}=\frac{2y-5}{-3}=z+1,$ is $\vec{r}=\left(2\hat{i}+\frac{5}{2} \hat{j}-\hat{k}\right)+\lambda\left(2\hat{i}-\frac{3}{2} \hat{j}+p\hat{k}\right)$ then $p$ is equal to
At how many points between the interval $ \left(-\infty, \infty\right)$ is the function $f (x) = sin\, x$ is not differentiable.
The position vector of $A$ and $B$ are $ 2\hat{i}+2\hat{j}+\hat{k}$ and $2\hat{i}+4\hat{j}+4\hat{k}$ The length of the internal bisector of $?BOA$ triangle $AOB$ is
Let $a, b, c, be$ in $A.P.$ with a common difference $d.$ Then $e^{1/e}, e^{b/bc}, e^{1/a}$ are in :
Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is
If sin y = x sin (a + y), then  dydxis
A metal ring is held horizontally and bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet
Judiciary has become the centre of controversy, in the recent past, on account of the sudden 'Me' in the level of judicial intervention. The area of judicial intervention has been steadily expanding through the device of public interest litigation. The judiciary has shed its pro-status-quo approach and taken upon itself the duty to enforce the basic rights of the poor and vulnerable sections of society, by progressive interpretation and positive action. The Supreme Court has developed new methods of dispensing justice to the masses through the public interest litigation. Former Chief Justice PN. Bhagwat, under whose leadership public interest litigation attained a new dimension comments that "the Supreme Court has developed several new commitments. It has carried forward participative justice".
\( f(x) = \left\{ \begin{array}{ll} \sin \frac{1}{x} , & \text{for} \, x \neq 0 \\ 0, & \text{for} \, x = 0 \end{array} \right. \) is:
In the questions below, a sentence is given, a part of which is printed in bold and underlined. This part may contain a grammatical error. Each sentence is followed by phrases a, b, c and d. Find out which phrase should replace the phrase given in bold/underline to correct the error, if there is any, to make the sentence grammatically meaningful and correct.
Recent incidents of tigers straying have brought to focus the lack of proper regulatory mechanism and powers with the forest department to take action against the resorts mushroom in forest fringes.
Choose the best pronunciation of the word 'Mischievous' from the following options:
The value of \[ \int_{-1}^{1} (x - \lfloor x \rfloor) dx \quad (\text{where} \, \lfloor \cdot \rfloor \, \text{denotes the greatest integer function}) \] is:
The correct evaluation of \[ \int_0^{\frac{\pi}{2}} \sin^4 x \, dx \] is:
The order and degree of the differential equation whose solution is \( y = cx + c^2 - 3c^3y^2 + 2 \), where \( c \) is a parameter, is:
The solution of \[ \frac{dv}{dt} + \frac{k}{m} v = -g \] is:
A unit vector perpendicular to the plane formed by the points \( (1, 0, 1) \), \( (0, 2, 2) \), and \( (3, 3, 0) \) is:
If \( \mathbf{a} = ( \hat{i} + \hat{j} + \hat{k} ) \), \( \mathbf{a} \times \mathbf{b} = \hat{i} - \hat{j} \), then \( \mathbf{b} \) is:
The mean and variance of a random variable \( X \) having binomial distribution are 4 and 2 respectively, then \( P(X = 1) \) is:
The radius of the sphere \[ x^2 + y^2 + z^2 = 49, \quad 2x + 3y - z - 5\sqrt{14} = 0 \] is:
One of the values of \[ \left( \frac{1 + i}{\sqrt{2}} \right)^{2/3} \] is: