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No effect on the rms speed of the molecules. 

Let P(n): 10^2n-1 +1, is divisible by 11. 

For n = 1, P(1):10^2-1 +1, is divisible by 11, which is true. 

P(1) is true. Let us assume P(k) is true for some k∈N. 

i.e., 10^2n-1+1 is divisible by 11. 

⇒10^2-1 +1 = 1 W, d∈N. 

Consider 10^2(k+1)-1+1 = 10^2k+1 +1 

= 10^2k-1 10² + 1 = (11d - 1)10²+1 

= 11d(10²) -100 + 1 = 11(100d) - 99 

= 11(100d - 9) 

∴ 10^{2(k + 1)-1} +1 is divisible by 11.

Thus, P(k) ⇒ P(k +1) 

Hence, by mathematical induction, P(n) is true for all n∈N

Let P(n): 3²ⁿ⁺² - 8n - 9 is divisible by 8. 

For n = 1, P(1): 3^{2 + 2} – 8(2) – 9 = 64 is divisible by 8, which is true. 

P( 1) is true. 

Let us assume P(k) is true for some k ∈ N 

i.e., 3^2k+2 - 8k - 9 is divisible by 8. 

Let 3^2k+2 - 8k - 9 = 8d, d ∈ N ………………(1) 

Consider 3^2(k+1)+2 – 8(k +1) – 9 = 3^2k+4 – 8k – 8 – 9 

= 3^2k+2 - 3² - 8(k - 1) = (8d + 8k + 9)9-8k-17 using (1) 

= (8d + 8k)9 + 81- 8k - 17 

= 8(d + k)9 + 64 - 8k = 8[9(d + k) + 8 - k] 

which is divisible by 8. 

Thus, P(k) ⇒ P(k +1) 

Hence, by mathematical induction, P(n) is true for all n∈N

The air comes out of balloon in one direction and the balloon moves on the opposite direction with the same speed.

1. Diwali rocket cracker takes flight, when it is fired. 

2. Motion of the actual rocket is similar to it.

Correct option is D) translatory

Correct option is B) Unequal

Correct option is A) Equal

Correct option is D) Bicycle

If no external force acts on a system, the momentum of the system remains constant.

The symbol mN stands for milli newton (10^-3 N) and nm stands for nanometer (10^-9 m)

A force which acts for a small time and also varies with time is called an impulsive force.

It is valid in an inertial frame of reference. In a non-inertial frame of reference (such as a car moving along a circular path). Newton's second law does not hold apparently.

2N means two nitrogen atoms. 

N₂ means one nitrogen molecule.

(a) N – one atom of nitrogen 

(b) 2N – two separate atoms of nitrogen 

(c) N₂ – one molecule of nitrogen 

(d) 2N₂ – two molecules of nitrogen

Correct option is A) 98 u

H₂ is the hydrogen molecule in which two hydrogen atoms are combined to form one hydrogen molecule. 

2H is the hydrogen atom. Here 2 hydrogen atoms are ready to participate in chemical reaction.

1) Yes, I agree with Mohan’s statement.

2) ‘O’ means single oxygen atom. ‘O₂ ‘ means single oxygen molecule.

There were mainly two problems before Sanku : 

(1) to meet the expenses of his family in his small income, and 

(2) to repay the loan which he owed to different people. Sanku had only one way to solve these problems, to pick up the gold watch from the office table of his officer and to get money by selling it.

Sanku’s urgent needs and pressure of the people to pay loan made him decide that he had no other choice but to steal.

Sanku thought that interval was the most suitable time for stealing the gold watch because at this time everyone went out for lunch. 

Sanku was much afraid before stealing the watch. He feared that someone might see him. He was nervous. His heart throbbed.

One day Sanku saw that his engineer had gone to lunch and his watch was lying on his table. So he went into the office, looked all around him and put the watch into his pocket with trembling hands.

One day Sanku saw that his engineer had gone to lunch and his watch was lying on his table. So he went into the office, looked all around him and put the watch into his pocket with trembling hands.

Sanku was afraid of being caught. So this thing stopped Sanku from stealing the watch.

Sanku’s urgent needs and pressure of the people to pay loan made him decide that he had no other choice but to steal.

Sanku worked in a factory. 

Sanku was much afraid before stealing the watch. He feared that someone might see him. He was nervous. His heart throbbed.

I fully agree with the statement that Sanku was essentially an honest man. He stole the watch under compulsion of his poverty. But he could not keep it with him and put back on the table of his officer. So it also shows that he was honest.

Sanku put the watch back on the table because he was afraid of being caught and punished.

After committing the theft Sanku feared that somebody had seen him stealing the watch. He would be caught as a thief. He would be dismissed. These thoughts troubled Sanku very much.

After committing the theft Sanku feared that somebody had seen him stealing the watch. He would be caught as a thief. He would be dismissed. These thoughts troubled Sanku very much.

(d) The Governor

After committing the theft Sanku feared that somebody had seen him stealing the watch. He would be caught as a thief. He would be dismissed. These thoughts troubled Sanku very much.

Rashtrakutas were initially subordinate to the Chalukyas of Karnataka. In the mideighteenth century, Dantidurga, a Rashtrakuta chief, overthrew his Chalukya overlord and established his right to rule by performminging the hiranyagarbha ritual.

Ben appreciates his father-in-law saying it’s a good thing he did’ when he comes to know from Mrs. Slater that the old man has gone out to pay his insurance premium on the day of his death. Later, he comes to know that he has not paid the premium and therefore calls him a drunken old beggar’. Ben has changed his opinion about his father-in-law when be realises that he hasn’t paid premium because, now after his death, they can t claim the insurance company.

Answer is (B) Madurai

Answer is (A) Cholas

1. B) Sri Krishnadevaraya

2. C) Pruthviraj

The Rasthtrakuta kings used the resources to finance the king’s establishment, as well as for the construction of temples and forts. They were also used to fight wars, which were in turn expected to lead to the acquisition of wealth in the form of plunder and access to land as well as trade routes. Close relatives of the king held higher positions. They often shared power with their ‘Samanthas’ as well as with associations of peasants, traders and brahmins. Thus they became powerful.

1. (ii) I' is Mrs. Pumphrey and 3he3 is Tricki, her pet dog.

2. (iv) These words tell us that her dog Tricki was a pampered tog who was overfed by his mistress.

3. (i) Mrs. Pumphrey cut down on giving Tricki sweet foods, but only for a bit of time.

4. (iii) Mrs. Pumphrey couldn’t bear to refuse her dog Tricki.

5. (ii) No, the surgeon had told Mrs. Pumphrey that he was not supposed to have so many sweet foods.

The advantages of S.I. are as under:

(i) S.I. has broader base. It has seven base units and two supplementary units.

(ii) S.I. is rational, i.e., it gives one unit for one physical quantity, e.g., for energy of any type, i.e., mechanical or heat or electrical. There is only one unit, Joule (J) but in M.K.S. system unit for mechanical energy is Joule.

(iii) S.I. is coherent.

(iv) S.I. is metric. 

(v) S.I. is the modernised and improved form of M.K.S. system so it is readily accepted in almost all the countries of the world. 

(vi) The symbols fixed by S.I. are not subject to change

whatever may be the language, e.g., unit of mass kilogram having symbol ‘kg’ has to be written like this only in French or German or Hindi or Punjabi etc.

Any phenomenon that repeats itself regularly at equal intervals of time can used to measure time.

The examples are:

(i) Rotation of earth – The time interval for one complete rotation is called a day.

(ii) Oscillations of a pendulum.

Force of attraction between molecules of the same substance is called cohesive force. Force of attraction between molecules of the different substances is called adhesive force.

1. Unlike oxygen and hydrogen, which exhibit various isotopes in higher proportions, carbon- 12 is the single most abundant (98% of available carbon) isotope of carbon.

2. it is also very stable.

Hence, it makes more accurate unit of measuring mass and is used to define atomic mass unit.

False. Valid only for static fluid.

In 0.8 s, the human heart make on beat.

∴ In 1 s the human heart makes

= \(\frac{1}{0.8}=\frac{10}{8}\) beats.

∴ In 10 years the human heart makes

= \(\frac{10}{8}\times10\times365\times24\times60\times60\) beats

= 3.942 x 10⁸ beats.

Terminal velocity × (rad. of ball)² Required ratio is 3²/1 = 9.

The angle through which the radius vector rotates is called angular displacement.

Since Pressure is transmitted undiminished throughout the fluid,

F₁ = A₁/A₂ F₂ = {π(8 x 5)}/{π(5 x 15)} x (1530 x 9.81) = 1.5 x 10³ N

The air pressure that will produce this force is

p = F₁/A₁ = {1.5 x 10³}/{π(5 x 10^-2)²} = 1.9 x 10³ Pa