List of top Questions asked in VITEEE

A planet in a distant solar system is 10 times more massive than Earth and its radius is 10 times smaller. Given that the escape velocity from Earth's surface is 11 km/s, the escape velocity from the planet’s surface would be:
A Carnot engine takes \( 3 \times 10^6 \) cal of heat from a reservoir at \( 627^\circ C \), and gives it to a sink at \( 27^\circ C \). The work done by the engine is:
Water falls from a \( 40 \) m high dam at the rate of \( 9 \times 10^4 \) kg per hour. Fifty percent of gravitational potential energy can be converted into electrical energy. The number of \( 100W \) lamps that can be lit is:

Consider an electric field \( \mathbf{E} = E_0 \hat{x} \), where \( E_0 \) is a constant. The flux through the shaded area (as shown in the figure) due to this field is: 
 

In YDSE, how many maximas can be obtained on a screen, including central maxima, on both sides of the central fringe if \( \lambda = 3000\) Å, \( d = 5000\) Å?
A sinusoidal voltage of amplitude \( 25 \) V and frequency \( 50 \) Hz is applied to a half-wave rectifier using a P-N junction diode. No filter is used, and the load resistor is \( 1000\Omega \). The forward resistance \( R_f \) of the ideal diode is \( 10\Omega \). The percentage rectifier efficiency is:
A sinusoidal voltage of amplitude 25 V and frequency 50 Hz is applied to a half-wave rectifier using a P-N junction diode. No filter is used, and the load resistor is \( 1000\Omega \). The forward resistance \( R_f \) of the ideal diode is \( 10\Omega \). The percentage rectifier efficiency is:
A flask contains a monoatomic and a diatomic gas in the ratio of \( 4:1 \) by mass at a temperature of \( 300K \). The ratio of average kinetic energy per molecule of the two gases is:
The equation of a wave on a string of linear mass density \( 0.04 \) kg/m is given by:
\[ y = 0.02 \sin 2\pi \left( \frac{t}{0.04} - \frac{x}{0.50} \right) \] The tension in the string is:

If 

and \[ (A + B)^2 = A^2 + B^2 \] then \( x + y \) is:

If \( n(A) = 4 \) and \( n(B) = 7 \), then the difference between the maximum and minimum value of \( n(A \cup B) \) is:
The lines \[ p(p^2 + 1)x - y + q = 0 \quad {and} \quad (p^2 + 1)^2 x + (p^2 + 1)y + 2q = 0 \] are perpendicular to a common line for:
The argument of the complex number \[ \left( \frac{i}{2} - \frac{2}{i} \right) \] is equal to:

If \[ \sin x + \cos x = \frac{1}{5} \] then \( \tan 2x \) is: 

The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
The domain of the function \[ f(x) = \frac{1}{\sqrt{9 - x^2}} \] is:
Evaluate: \[ \cos^{-1} \frac{1}{2} + \sin^{-1} (1) + \tan^{-1} \frac{1}{\sqrt{3}} \]
For the binary operation defined on \( \mathbb{R} - \{1\} \) such that: \[ a b = \frac{a}{b + 1} \] which of the following is true?
If \[ R = \{ (x, y) : x \text{ is exactly } 7\text{cm taller than } y \} \] then \( R \) is:
Negation of the Boolean expression \[ p \Leftrightarrow (q \Rightarrow p) \] is:
If the function \[ f(x) = \begin{cases} 1, & x \leq 2 \\ ax + b, & 2 < x < 4 \\ 7, & x \geq 4 \end{cases} \] is continuous at \( x = 2 \) and \( x = 4 \), then the values of \( a \) and \( b \) are:
Evaluate: \[ \tan (\cos^{-1} \frac{4}{5}) + \tan^{-1} \frac{2}{3} \]

The integral \[ \int x^n (1 + \log x) \, dx \] is equal to: 

Bag P contains 6 red and 4 blue balls, and Bag Q contains 5 red and 6 blue balls. A ball is transferred from Bag P to Bag Q, and then a ball is drawn from Bag Q. What is the probability that the ball drawn is blue?
The area of the region bounded by the ellipse \[ \frac{x^2}{16} + \frac{y^2}{9} = 1 \] is: