List of top Questions asked in VITEEE- 2016

If \( e^x = y + \sqrt{1 + y^2} \), then the value of \( y \) is

What is the area of a loop of the curve \( y = \sin 30^\circ \)?

Convert the hexadecimal numeral ABCD into binary numeral

The normal at the point \( (t_1, t_2) \) on the parabola, cuts the parabola again at the point whose parameter is

The distance moved by the particle in time \( t \) is given by \[ s = t^3 - 12t^2 + 6t + 8 \] At the instant, when its acceleration is zero, its velocity is

If \( |a| = 3, |b| = 2, |c| = 1 \) then the value of \[ |a \cdot b + b \cdot c + c \cdot c| \text{ is} \]

If \( A \) and \( B \) are matrices and \( AB = BA = A^{-1} \) then the value of \( (A + B)(A - B) \) is

The value of \( (1 + \omega)^3 \), where \( \omega = e^{i 2\pi/3} \) is

The moment about the point \( 2i + 3j + k \) of a force represented by \( i + j + k \) acting through the point \( 2i + 3j + k \) is

The equation of one of the common tangents to the parabola \( y^2 = 8x \) and \( x^2 = 4y - 4 \) is

The distance moved by the particle in time \( t \) is given by \[ s = t^3 - 12t^2 + 6t + 8 \] At the instant, when its acceleration is zero, its velocity is

The equation of one of the common tangents to the parabola \( y^2 = 8x \) and \( x^2 = 4y - 4 \) is

If the tangent to the function \( y = f(x) \) at \( (3, 4) \) makes an angle of \( \frac{3\pi}{4} \) with the positive direction of the x-axis in anticlockwise direction, then \( f'(3) \) is

The probability of India winning a test match against Australia is \( \frac{1}{2} \), assuming independence from match to match. The probability that in a match series India’s second win occurs at third test match is

The following data were obtained for a given reaction at 300 K. \[ \begin{array}{|c|c|} \hline \text{Reaction} & \text{Energy of activation (kJ mol}^{-1}\text{)} \\ \hline \text{(i) Uncatalysed} & 76 \\ \text{(ii) Catalysed} & 57 \\ \hline \end{array} \] The factor by which the rate of catalysed reaction is increased is

The foci of the ellipse \( \frac{x^2}{144} + \frac{y^2}{81} = 1 \) and the hyperbola \( \frac{x^2}{144} - \frac{y^2}{81} = 1 \) coincide then value of \( b^2 \) is

Which of the following reactions of xenon compounds is not feasible?

Anisole is treated with HI under two different conditions. \[ C_6H_5OCH_3 + D \xrightarrow{\text{conc. HI}} A + B \] The nature of A and B will be

Phenol undergoes electrophilic substitution more easily than benzene because

Which of the following name reaction is not used for introducing a \( \text{-COOH} \) group?

Esterification of acid chloride with ethanol is usually carried out in the presence of pyridine. The function of pyridine is

The solution of the differential equation \[ (1 + y^2) + (x - e^{\tan^{-1}y}) \frac{dy}{dx} = 0 \] is

A tetrahedron has vertices at \( O(0,0,0), A(1,2,1), B(2,1,3) \) and \( C(-1,1,2) \). Then the angle between the faces \( OAB \) and \( ABC \) will be

The enthalpy change for a given reaction at 298 K is \( -x \, \text{J mol}^{-1} \). For the reaction to be spontaneous at 298 K, the entropy change at that temperature

\( a \) moles of \( \text{PCl}_5 \) is heated in a closed container to equilibrate \[ \text{PCl}_5 (g) \rightleftharpoons \text{PCl}_3 (g) + \text{Cl}_2 (g) \] at a pressure of \( P \) atm. If \( x \) moles of \( \text{PCl}_5 \) dissociate at equilibrium, then the correct expression for the equilibrium constant is