List of practice Questions

How is PROCESS written in that code language?
I. In a certain code language, QUEUE is written as RVFVF.
II. In a certain code language, CRWTH is written as BQVSG.
Is the integer number \( n \) divisible by 15?
I. 9 divides \( n \).
II. 20 divides \( n \).
5 books in Math and 3 books in Physics are placed on a shelf so that the books on the same subject always remain together. The possible arrangements are
A long straight wire carrying a current 3 A produces a magnetic field \( B \) at a certain distance. The current that flows through the same wire will produce a magnetic field \( \frac{B}{3} \) at the same distance is:
If the length, breadth and height of a cuboid are 8 cm, 3 cm and 4 cm respectively, then the total surface area of the cuboid is
An increase in magnetic flux through a coil of 100 turns in 0.1 s is 0.001 Wb. The maximum induced EMF generated in the coil is
A tennis ball of mass 50g thrown vertically up at a speed of 25 m s\(^{-1}\) reaches a maximum height of 25 m. The work done by the resistance forces on the ball is:
A body of mass \( M \) is at equilibrium under the action of four forces \( F_1, F_2, F_3 \), and \( F_4 \). If \( F_1 \) is removed from the body, then the body moves with an acceleration of:
Evaluate the integral: \[ \int \frac{x^2 - 1}{x^4 + 3x^2 + 1} \, dx \]
The process by which the electrons can come out of the metal in a spark plug is:
If \( \tan \left( \frac{\pi}{12} + 2x \right) = \cot 3x \), where \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
In moving a body of mass \( m \) down a smooth incline of inclination \( \theta \) with velocity \( v \), the power required is (g = acceleration due to gravity):
If the number of electron-hole pairs per cm\(^3\) of an intrinsic Si wafer at temperature 300 K is \(1.1 \times 10^{10}\) and the mobilities of electrons and holes at 300 K are 1500 and 500 cm\(^2\) per volt, second, respectively, then the conductivity of the Si wafer at this temperature (in \(\mu\)mho cm\(^{-1}\)) is nearly:

Let \( I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{\tan^2 x}{1+5^x} \, dx \). Then:

Which of the following statement is correct?
In \( \triangle ABC \), if \( (r_2 - r_1)(r_3 - r_1) = 2r_2r_3 \), then \( 2(r + R) = \):
If 35 is removed from the data 30, 34, 35, 36, 37, 38, 39, 40, then the median increases by
If R is the resistance of a conductor of length l, then
The power of a lens of focal length 20 cm is
The common ratio of a G.P. is \( \frac{1}{2} \). If the product of the first three terms is 64, then the sum of the first 10 terms is:

The focus of the parabola \(y^2 + 4y - 8x + 20 = 0\) is at the point:

Compound ‘X’ (C\(_6\)H\(_6\)O) reacts with aqueous NaOH to give compound ‘Y’. ‘Y’ reacts with CO\(_2\) followed by acidification to give compound ‘Z’. The compounds X, Y and Z are respectively
An ink mark is made on a piece of paper and a glass slab of thickness $t$ and refractive index $\mu$ is placed on it. If the image of the ink mark appears to be at a distance of $x$ from the top surface of the slab, then the value of $x$ is
The symmetric equation of the straight line passing through the points \( (-1, 4, 2) \) and \( (-3, 0, 5) \) is
A rectangular tank of depth 4 m is full of water of refractive index \(\frac 43\). When viewed from the top, the bottom of the tank is seen at a depth of