List of top Questions asked in CBSE Class XI

In which of the following examples of motion, can the body be considered approximately a point object:
The position-time (x-t) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in Fig. 2.9. Choose the correct entries in the brackets below ; 
  1. (A/B) lives closer to the school than (B/A) 
  2. (A/B) starts from the school earlier than (B/A) 
  3. (A/B) walks faster than (B/A) 
  4. A and B reach home at the (same/different) time 
  5. (A/B) overtakes (B/A) on the road (once/twice).
     
position-time (x-t) graph
A woman starts from her home at 9.00 am, walks with a speed of 5 km \(\text{h}^{-1}\)on a straight road up to her office 2.5 km away, stays at the office up to 5.00 pm, and returns home by an auto with a speed of 25 \(\text {km}\) \(\text{h}^{-1}\). Choose suitable scales and plot the x-t graph of her motion.
A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the x-t graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.
A car moving along a straight highway with speed of 126 \(\text{km}\;\text h^{-1}\) is brought to a stop within a distance of 200 \(\text m\). What is the retardation of the car (assumed uniform), and how long does it take for the car to stop ?
A player throws a ball upwards with an initial speed of 29.4 m \(\text s^{-1}\). 
  1. What is the direction of acceleration during the upward motion of the ball ?
  2. What are the velocity and acceleration of the ball at the highest point of its motion ?
  3. Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion.
  4. To what height does the ball rise and after how long does the ball return to the player’s hands ? (Take g = 9.8 \(\text m \;\)\(\text s^{-2}\) and neglect air resistance).
Find the union of each of the following pairs of sets:
(i) X = {1, 3, 5} Y = {1, 2, 3}
(ii) A = {a, e, i, o, u} B = {a, b, c}
(iii) A = {x: x is a natural number and multiple of 3}
B = {x: x is a natural number less than 6}
(iv) A = {x: x is a natural number and \(1 <x ≤ 6\)}
B = {x: x is a natural number and \(6 <x< 10\)}
(v) A = {1, 2, 3}, B = \(\phi\)
Read each statement below carefully and state with reasons and examples, if it is true or false ; 
A particle in one-dimensional motion 
  1. with zero speed at an instant may have non-zero acceleration at that instant 
  2. with zero speed may have non-zero velocity, 
  3. with constant speed must have zero acceleration, 
  4. with positive value of acceleration must be speeding up.
Let A = {a, b}, B = {a, b, c}. Is \(\subset\) B? What is \(A ∪ B\)?
A rocket is fired vertically with a speed of 5 km s-1 from the earth’s surface. How far from the earth does the rocket go before returning to the earth ? Mass of the earth = 6.0 × 1024 kg; mean radius of the earth = 6.4 × 106 m; G = 6.67 × 10–11 N m2 kg–2
If A and B are two sets such that \(A \subset B\), then what is \(A \cup B\)?
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find
(i) \(A∪ B\)
(ii) \(A ∪ C\)
(iii) \(B ∪ C\)
(iv) \(B ∪ D\)
(v) \(A ∪ B ∪ C\)
(vi) \(A∪ B ∪ D\)
(vii) \(B ∪ C ∪ D\)
A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is 4.0 × 104 J/g ?
Find the intersection of each pair of sets:
(i) X = {1, 3, 5} Y = {1, 2, 3}
(ii) A = {a, e, i, o, u} B = {a, b, c}
(iii) A = {x: x is a natural number and multiple of 3}
B = {x: x is a natural number less than 6}
(iv) A = {x: x is a natural number and \(1 < x ≤ 6\)}
B = {x: x is a natural number and \(6 < x < 10\)}
(v) A = {1, 2, 3}, B = \(\phi\)
What amount of heat must be supplied to \(2.0 × 10^–2\) kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure ? (Molecular mass of \(N_2\) = 28; R = 8.3 J \(mol^{–1} K^{–1}\).)

Explain why

 (a) Two bodies at different temperatures T1 and T2 if brought in thermal contact do not necessarily settle to the mean temperature \(\frac{(T1 + T2 )}{2}\). 

(b) The coolant in a chemical or a nuclear plant (i.e., the liquid used to prevent the different parts of a plant from getting too hot) should have high specific heat. 

(c) Air pressure in a car tyre increases during driving. 

(d) The climate of a harbour town is more temperate than that of a town in a desert at the same latitude.

A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following : 

(a) What is the final pressure of the gas in A and B ? 

(b) What is the change in internal energy of the gas ? 

(c) What is the change in the temperature of the gas ? 

Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following 1) What is the final pressure of the gas in A and B? 2) What is the change in internal energy of the gas? 3) What is the change in the temperature of the gas? 

Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following : 

(a) What is the final pressure of the gas in A and B ? 

(b) What is the change in internal energy of the gas ? 

(c) What is the change in the temperature of the gas ? 

Explain clearly, with examples, the distinction between : 
  1. magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval; 
  2. magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the equality sign true ? [For simplicity, consider one-dimensional motion only].
An electric heater supplies heat to a system at a rate of 100W. If system performs work at a rate of 75 joules per second. At what rate is the internal energy increasing?

A thermodynamic system is taken from an original state to an intermediate state by the linear process shown in Fig. (11.13). 

A thermodynamic system

Its volume is then reduced to the original value from E to F by an isobaric process. Calculate the total work done by the gas from D to E to F

A man walks on a straight road from his home to a market 2.5 \(\text {km}\) away with a speed of 5 \(\text {km}\) \(\text h^{-1}\). Finding the market closed, he instantly turns and walks back home with a speed of 7.5 \(\text {km}\) \(\text h^{-1}\) What is the 
  1. magnitude of average velocity, and 
  2. average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to 50 min, (iii) 0 to 40 min ? [Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as magnitude of average velocity. You would not like to tell the tired man on his return home that his average speed was zero !].
Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be 3 Å.