List of top Questions asked in VITEEE

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
A metallic sphere is placed in a uniform electric field. The line of force follow the path (s) shown in the figure as
What is the length of the projection of $3\hat{i}+4\hat{j}+5\hat{k}$ on the xy-plane ?
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 solution of \[ \frac{dv}{dt} + \frac{k}{m} v = -g \] 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 mean and variance of a random variable \( X \) having binomial distribution are 4 and 2 respectively, then \( P(X = 1) \) is:
If \( \mathbf{a} = ( \hat{i} + \hat{j} + \hat{k} ) \), \( \mathbf{a} \times \mathbf{b} = \hat{i} - \hat{j} \), then \( \mathbf{b} \) is:
A unit vector perpendicular to the plane formed by the points \( (1, 0, 1) \), \( (0, 2, 2) \), and \( (3, 3, 0) \) is:
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 radius of the sphere \[ x^2 + y^2 + z^2 = 49, \quad 2x + 3y - z - 5\sqrt{14} = 0 \] is:
If at \( x = 1 \), the function \( x^4 - 62x^2 + ax + 9 \) attains its maximum value on the interval \( [0, 2] \), then the value of \( a \) is:
The two curves \( x^3 - 3x^2 + 2 = 0 \) and \( 3x y - y^3 - 2 = 0 \) intersect at an angle of:
One of the values of \[ \left( \frac{1 + i}{\sqrt{2}} \right)^{2/3} \] is:
The combined equation of the asymptotes of the hyperbola \[ 2x^2 + 5xy + 2y^2 + 4x + 5y = 0 \] is:
The value of \( \lambda \) does the line \( y = x + \lambda \) touches the ellipse \( 9x^2 + 16y^2 = 144 \) is:
The value of the determinant \( \Delta = \begin{vmatrix} 1 & 4 & 3 \\ 0 & 12 & 9 \\ 1 & 2 & 2 \end{vmatrix} \) is:
The area of the region bounded by the curve \( x = 2y + 3 \) and lines \( y = 1 \) and \( y = -1 \) is:
What is the length of the projection of \( 3\hat{i} + 4\hat{j} + 5\hat{k} \) on the xy-plane?
If the I.F. of the differential equation \[ \frac{dy}{dx} + 5y = \cos x \sin x e^{Adx}, \text{ then } A = \]