List of top Questions asked in VITEEE

The derivative of  \(\sin^2\)\(( \cot^{-1} {\sqrt {( \frac{1 + x}{1 - x}} })\) with respect to \( x \) is equal to: (a) 0
 
A bob of mass \( m \) is suspended by a light string of length \( L \). It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half a circle, reaching the topmost position B. The ratio of kinetic energies \(\left(\frac{K.E.}{K.E.}\right)_A \), \(\text{to}\), \(\left(\frac{K.E.}{K.E.}\right)_B\) is:
Which of the following compounds does not show Lassaigne’s test for nitrogen? (A) Urea
(B) Hydrazine
(C) Phenylhydrazine
(D) Azobenzene
If \( f(x) = \cos^{-1 } \left( \frac{\sqrt{2x^2 + 1}}{x^2 + 1} \right) \), then the range of \( f(x) \) is:
In meter bridge or Wheatstone bridge for measurement of resistance, the known and the unknown resistance are interchanged. The error so removed is:
A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0°C will be:
The resistivity (\( \rho \)) of a semiconductor varies with temperature. Which of the following curves represents the correct behavior? resistivity ( ρ ρ) of a semiconductor varies with temperature
How many electrons are involved in the following redox reaction? \[ \text{Cr}_2\text{O}_7^{2-} + \text{Fe}^{2+} + \text{C}_2\text{O}_4^{2-} \rightarrow \text{Cr}^{3+} + \text{Fe}^{3+} + \text{CO}_2 \quad (\text{Unbalanced}) \] 
 
Intermolecular forces in nylon-6, 6 are:
Product of the following reaction is:
Product of the following reaction is:
When unpolarized light is incident at an angle of 60° on a transparent medium from air, the reflected ray is completely polarized. The angle of refraction in the medium is:
The IUPAC name for
1-chloro-4-methyl-2-nitrobenzene
Mass numbers of two nuclei are in the ratio of 4:3. Their nuclear densities will be in the ratio of:
The range of \( 2 \left| \sin x + \cos x \right| - \sqrt{2} \) is:
At 25°C and 1 atm pressure, the enthalpy of combustion of benzene (l) and acetylene (g) are \(3268 \, \text{kJ mol}^{-1}\) and \(1300 \, \text{kJ mol}^{-1}\), respectively. The change in enthalpy for the reaction 
the enthalpyis
Two light beams of intensities in the ratio of 9:4 are allowed to interfere. The ratio of the intensity of maxima and minima will be:
Oxidation number of H in NaH, CaH$_2$, and LiH, respectively is:
A parallel plate capacitor has 1 \(\mu\)F capacitance. One of its two plates is given \(+2 \mu C\) charge and the other plate, \(+4 \mu C\) charge. The potential difference developed across the capacitor is:

In the given circuit, the rms value of current (\( I_{\text{rms}} \)) through the resistor \( R \) is: 

If the roots of the quadratic equation $$ (a^2 + b^2) \, x^2 - 2 \, (bc + ad) \, x + (c^2 + d^2) = 0 $$ are equal, then: 
Five charges \( +q, +5q, -2q, +3q \) and \( -4q \) are situated as shown in the figure. The electric flux due to this configuration through the surface S is: 
Five charges +q, +5q, −2q, +3q and
A small ball of mass \( M \) and density \( \rho \) is dropped in a viscous liquid of density \( \rho_0 \). After some time, the ball falls with a constant velocity. What is the viscous force on the ball?
A first order reaction is half completed in 45 minutes. How long does it need for 99.9% of the reaction to be completed?
Let \( n(A) = m \) and \( n(B) = n \), if the number of subsets of \( A \) is 56 more than that of subsets of \( B \), then \( m + n \) is equal to:
Let \( f(x) \) be a polynomial function satisfying \[ f(x) \cdot f\left(\frac{1}{x}\right) = f(x) + f\left(\frac{1}{x}\right). \] If \( f(4) = 65 \) and \( I_1, I_2, I_3 \) are in GP, then \( f'(I_1), f'(I_2), f'(I_3) \) are in: