List of practice Questions

A $12.5\, eV$ electron beam is used to bombard gaseous hydrogen at room temperature. It will emit :

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$. The piston and the cylinder have equal cross-sectional area $A$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency

Find the variance of the data given below \[ \text{Size of item:} \quad 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5 \\ \text{Frequency:} \quad 3, 7, 22, 60, 85, 32, 8 \]

The determinant \[ \left| \begin{matrix} 1 & x & x^2 \\ 1 & x^3 & x^4 \\ 1 & x^5 & x^6 \end{matrix} \right| \] vanishes for

If \( f(x) = \begin{cases} \frac{x^2 + 3x - 10}{x^2 + 2x - 15}, & x \neq -5 \\ a, & x = -5 \end{cases} \) is continuous at \( x = -5 \), then the value of \( a \) will be

Sushma walks 20m towards north. Then she turns right and walks 30m. Now, she turns right and walks 35m. Now turning left, she walks 15m. Again, she turns left and moves 15m. Finally, she turns left and walks 15m. In which direction and how far is she from her original position?

In a classroom, there are 5 rows and 5 children A, B, C, D and E are seated one behind the other in 5 separate rows as follows. - A is sitting behind C but in front of B. - C is sitting behind E and D is sitting in front of E. The order in which they are sitting from the first row to the last is

Which of the following will fill the series? \[ 2, 9, 28, 2, 126 \]

Two signs in the equations have been interchanged, find out the two signs to make the equation correct. \[ 3 \, - \, 5 \, + \, 8 \, + \, 2 \, - \, 10 = 13 \]

Assertion: [A] India is a democratic country. Reason: [R] India has a constitution of its own. Choose the correct alternative from the given options.

You should not laugh ..... the poor.

1. He is a famous doctor. 2. Once I had to consult with him. 3. I never believed him. 4. He suggested me a proper remedy. 5. I become completely fine. 6. Now I also admit this fact.

We don’t know the plan of Ram. He cares for his friends. He is a complete person. We want some help and advice. As we are in trouble. We hope he will do his best for us.

It is not my problem. All residents of this society are careless. I am unable to convince anyone. They don’t want to do some good. Every one seems to be unwise here. We all have to suffer one day.

In a certain code language "DOME" is written as "8943" and "MEAL" is written as "4321". What group of letters can be formed for the code "38249"?

Choose the word opposite in meaning to the given word "PROGENY".

It was not possible to drag any conclusion so he left the case.

I am looking after my pen which is missing.

“Mind your language!” he shouted.