100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS

1.	During the reign of which Parthian (Pahlava) ruler did St Thomas come to India to preach Christianity?
Answer» Correct Answer is Gondphernes

Discussion

2.	The life of Genghis Khan was full of misery and backlashes. Comment.
Answer» The real name of Genghis khan is Temujin. He was born in 1162, in a region of the bank of River On on in the Northern side of the present Mongolia. When he was 12, his father was killed. Then it was his mother Hoelun who brought him and brothers up taking a lot of trouble. Temujin faced a lot of problems during the next 12 years. He was caught and was made a slave. Soon after his marriage his wife Borte was kidnapped by some people. Temujin had to fight hard to get his wife back. By 1209 Genghis Khan defeated the Xi Xia people, in 1213 he crossed the Great Wall and defeated the Chin dynasty. He looted Peking. His fights with the Chin dynasty continued until 1234, Genghis Khan also attacked places like Amu Darya, Transoxiana, and Khwaresmia.

2.

The life of Genghis Khan was full of misery and backlashes. Comment.

Answer»

The real name of Genghis khan is Temujin. He was born in 1162, in a region of the bank of River On on in the Northern side of the present Mongolia. When he was 12, his father was killed. Then it was his mother Hoelun who brought him and brothers up taking a lot of trouble. Temujin faced a lot of problems during the next 12 years. He was caught and was made a slave. Soon after his marriage his wife Borte was kidnapped by some people. Temujin had to fight hard to get his wife back.

By 1209 Genghis Khan defeated the Xi Xia people, in 1213 he crossed the Great Wall and defeated the Chin dynasty. He looted Peking. His fights with the Chin dynasty continued until 1234, Genghis Khan also attacked places like Amu Darya, Transoxiana, and Khwaresmia.

Discussion

3.	Sagi: Genghis Khan was an uncivilized attacker. Usha: He was a great leader.With whose opinion do you agree? Why?
Answer» When we think of Genghis khan now, in our imagination, we imagine him to be a violent destroyer of cities and a brute who caused the death of thousands of people. In the 13th century, the city dwellers of China, Iran, and Eastern Europe looked at the Mongols with anger and hatred. But for the Mongols Genghis Khan was their greatest leader. He unified them. He liberated them from the constant Tribal wars and the exploitation of the Chinese. To the Mongols, he was a great man who brought them prosperity, who formed an intercontinental empire, who recovered the trade routes and markets and who attracted travelers like Marco Polo.

3.

Sagi: Genghis Khan was an uncivilized attacker. Usha: He was a great leader.With whose opinion do you agree? Why?

Answer»

When we think of Genghis khan now, in our imagination, we imagine him to be a violent destroyer of cities and a brute who caused the death of thousands of people. In the 13th century, the city dwellers of China, Iran, and Eastern Europe looked at the Mongols with anger and hatred. But for the Mongols Genghis Khan was their greatest leader.

He unified them. He liberated them from the constant Tribal wars and the exploitation of the Chinese. To the Mongols, he was a great man who brought them prosperity, who formed an intercontinental empire, who recovered the trade routes and markets and who attracted travelers like Marco Polo.

Discussion

4.	Last week I ___ go to town on business trip as the Ministry of Education had asked me to come. A) had to B) might C) should D) could E) was able to
Answer» Correct option is A) had to

Discussion

5.	The Great Wall of China was built to protect the agricultural communities of North China from the attacks of the nomads, Based on this statement, describe the relations between the Mongolian nomads and the Chinese agricultural communities.
Answer» China experienced a lot of problems because of the constant attacks by the nomads and therefore China built fortresses to protect her citizens from these attacks. Connecting these fortresses, China made defensive wall-chain. This is the famous Great Wall of China. This is one of the wonders of the world.

Discussion

6.	An ___ is a programme of the items of the business to be discussed at a meeting in the order in which they are to be taken.
Answer» An Agenda is a programme of the items of the business to be discussed at a meeting in the order in which they are to be taken.

Discussion

7.	Who ___ to see me last week? A) comes B) will come C) came D) has come E) have come
Answer» Correct option is C) came

Discussion

8.	The plan ___ for two hours when he ___ .A) had been discussed / cameB) is discussed / comesC) will be discussed / comeD) has been discussed / comesE) was discussed / would come
Answer» Correct option is A) had been discussed / came

Discussion

9.	Mention any two theories of origin and evolution of earth.
Answer» 1. The Pulsating theory 2. The Big Bang theory

9.

Mention any two theories of origin and evolution of earth.

Answer»

1. The Pulsating theory

2. The Big Bang theory

Discussion

10.	Christopher Columbus didn’t know where he ___. When he landed he didn’t know where he ___ when he got back to Spain he didn’t know where he ___. A) was sailing / was / had been B) had sailed / was / was C) is sailing / had been / has been D) will be sailing / will be / will have been E) would sail / hadn’t been / haven’t been
Answer» Correct option is A) was sailing / was / had been

Discussion

11.	That day after Mr. Brown ___ the letter he ___ me to clarify some details. A) has studied / phoned B) studied / phoned C) had studied / phoned D) had studied / had phoned E) studied / is phoning
Answer» Correct option is C) had studied / phoned

Discussion

12.	Who is the author of ‘Divine Comedy’?
Answer» Dante is the author of ‘Divine Comedy’.

Discussion

13.	When Christopher Columbus ___ 14 he ___ a sailor. A) is / became B) was / became C) was / becomes D) are / become E) were / became
Answer» Correct option is B) was / became

Discussion

14.	What is Glasnost?
Answer» The policy of openness in external relations which was introduced by Mikhail Gorbachev is called Glasnost.

Discussion

15.	Who was the king of France at the time of French Revolution?
Answer» Louis XIV was the King of France at the time of French Revolution.

Discussion

16.	Who was called as the Navigator?
Answer» Prince Henry of Portugal was called as ‘Navigator’.

Discussion

17.	Who popularized Buddhism in China?
Answer» Buddhism spread to China from India during Kanishka’s period in 1^st century. The Buddhist monks and traders from India popularized Buddhism in China.

Discussion

18.	What is ‘Fief’?
Answer» In the European Feudal system, Kings / Greater Lords granted lands to Vassals who had to swear fidelity and loyalty of service to the Lords. These lands were called as fiefs.

Discussion

19.	Whose famous words are Vini. Vidi. Vici?
Answer» Julius Caesar.

Discussion

20.	Fill in the blanks with suitable form of the verbs given in brackets:It was quite a big city. I ...... (stay) in a small room in that city. I ........ (carry) on a profession of teaching English. ..... (teach) them to write addresses In English. People ...... (pay) one anna to four annas for writing an address.
Answer» stayed, carried, taught, paid.

Discussion

21.	Fill in the blanks with suitable form of the verbs given in brackets:By tradition, the people of the city ..... (be) soldiers. But, some of them ..... (go) to distant places. Many others ..... (serve) as watchmen. Money was highly valued by them. For money, they ........ (will + do) anything, even commit murder.
Answer» were, went, served, would do.

Discussion

22.	Fill in the blanks with suitable form of the verbs given in brackets:I got up at 4 p.m. and ..... (finish) my daily chores. Then I ....... (step) out for a meal, I ...... (have) 14 Rs. In the wallet which was In my coat pocket. I ...... (enter) a restaurant and ordered a meal.
Answer» finished, stepped, had, entered.

Discussion

23.	Fill in the blanks with suitable form of the verbs given in brackets:The narrator put his hand in his coat pocket to pay the bill. But he ..... (begin) to sweat and almost ..... (digest) in an instant all that he ....... (have + eat). The reason ...... (be) that his wallet was not there.
Answer» began, digested, had eaten, was.

Discussion

24.	Frame ‘Wh’ questions so as to get the understand word/s as the answer:1. The narrator took off his coat2. The narrator had fourteen rupees in his wallet.3. The people looked at the narrator like hungry wolves.4. We must have some money.5. Money the root of all evil.6. The boys help their families by working as mechanics.7. Tulu Rani Hazra has recruited 80 students. 8. The speaker wanted to be purified by burning in the holy fire.9. Tree are more humane than humans. 10. Mara sprang off like a buck.
Answer» 1. What did the narrator take off? 2. How much money did the narrator have in his wallet? 3. How did the people look at the narrator? 4. What must we have? 5. What is the root of all evil? 6. How do the boys help their families? 7. How many students has Tulu Rani Hazra recruited? 8. How did the speaker want to be purified? 9. What are more humane than humans? 10. How did Mata spring off?

24.

Frame ‘Wh’ questions so as to get the understand word/s as the answer:1. The narrator took off his coat2. The narrator had fourteen rupees in his wallet.3. The people looked at the narrator like hungry wolves.4. We must have some money.5. Money the root of all evil.6. The boys help their families by working as mechanics.7. Tulu Rani Hazra has recruited 80 students. 8. The speaker wanted to be purified by burning in the holy fire.9. Tree are more humane than humans. 10. Mara sprang off like a buck.

Answer»

1. What did the narrator take off?

2. How much money did the narrator have in his wallet?

3. How did the people look at the narrator?

4. What must we have?

5. What is the root of all evil?

6. How do the boys help their families?

7. How many students has Tulu Rani Hazra recruited?

8. How did the speaker want to be purified?

9. What are more humane than humans?

10. How did Mata spring off?

Discussion

25.	Correct the following sentences and rewrite them : Why did the narrator took this?
Answer» Why did the narrator take this?

Discussion

26.	The pie chart given below represents the results of a survey conducted by a non – profit NGO to understand how a rural family spends its income on various items. Based on the information, write a report in about 200 words.
Answer» Spending Pattern of Rural Families The pie chart above throws light on the spending pattern of rural families. The chart indicates that a typical rural family spends the least, that is, 10% each of its income on savings and education. Entertainment and health consume 15 % each. Next stands repayment of loan at 20%. the highest percentage, that is 30%, is spent on food and clothing. It is clear from the chart that the people concerned need to be educated about profitable saving plans and for this their educational level should also improve. Thus, it is surmised that a campaign to improve the educational levels of the people of the rural areas might bring about progress.

Discussion

27.	A survey was conducted on software job locations in India and the results are shown in the following pie chart. Using the data, write a report in about 120 words.
Answer» The given pie chart represents the results of the survey conducted on software job locations in India. The chart shows that 30% of the software jobs are located in Bengaluru, 17% in Delhi, 11% in Mumbai, 12% in Ahmedabad, 11% in Chennai and 19% in Hyderabad. The study reveals that the highest number of software professionals in India are employed in Bengaluru (with 30%) and the least in Mumbai and Chennai (with 11%). The reasons for Bengaluru to be considered the best location in India for software companies to set up their business are the weather, access to apt talent pool and the cultural diversity.

Discussion

28.	Consider a equation `x^(3)-3x=sqrt(x+2)` such that `x` is a real number then sum of its positive roots is `lamda` where `[(lamda)/2]` is______
Answer» Correct Answer - 1 If `xgt2` then `x^(3)-3xge4x-x=xge sqrt(x+2)` `implies\|x\|le2` take `x=2costheta` for some `theta epsilon[0,pi]` `implies2cos3theta=sqrt(2(1+costheta))` `implies2"sin"(7theta)/4."sin"(5theta)/4=0` `impliestheta=0, (4pi)7, (4pi)/5` `:. X-2, 2"cos"(4pi)/7, -1.2(1+sqrt(5))`

Discussion

29.	Which of the following is equal to cot 80° × cot 70° × cot 60° × ....× cot10° ? (A) 0 (B) 1 (C) 2 (D) 3
Answer» The correct option is (B) 1 Explanation: cot80° × cot70° × cot60° ...× cot10° cot80° × cot(90 – 80) × cot(70) cot (90 – 70) cot80° × tan80° × cot70°tan70° × cot60°tan60° × cot50° × tan50° ∵ cotθ × tanθ = 1 = 1

29.

Which of the following is equal to cot 80° × cot 70° × cot 60° × ....× cot10° ? (A) 0 (B) 1 (C) 2 (D) 3

Answer»

The correct option is (B) 1

Explanation:

cot80° × cot70° × cot60° ...× cot10°

cot80° × cot(90 – 80) × cot(70) cot (90 – 70)

cot80° × tan80° × cot70°tan70° × cot60°tan60° × cot50° × tan50°

∵ cotθ × tanθ = 1

= 1

Discussion

30.	Find the value of k if (x – 1) is a factor of the polynomial P(x) = x2 + kx + 2.
Answer» Given polynomial P(x) = x² + kx + 2 given factor = (x – 1) By remainder theorem x – 1 = 0 x = 1 remainder P(1) = 0 ⇒ (1)² + k(1) + 2 = 0 k + 3 = 0 k = – 3

30.

Find the value of k if (x – 1) is a factor of the polynomial P(x) = x2 + kx + 2.

Answer»

Given polynomial P(x) = x² + kx + 2

given factor = (x – 1)

By remainder theorem x – 1 = 0

x = 1

remainder P(1) = 0

⇒ (1)² + k(1) + 2 = 0

k + 3 = 0

k = – 3

Discussion

31.	For continuous function `f: [0, 1]-> R ; A =int_0^1 (x^2* f(x))dx ; B=int_0^1 x * (f(x))^2 dx` then, maximumvalue of `A-B `is `lambda` where `[1/(4lambda)]` is
Answer» Correct Answer - 4 `x((x))^(2)-x^(2)f(x)=(sqrt(x)f(x))^(2)-2.sqrt(2)xxf(x).(x^(3//2))/2+(x^(3))/4-(x^(3))/4` `(sqrt(x)f(x)-(x^(3//2))/2)^(2)-(x^(3))/4` `:. B-A=int_(0)^(1)(sqrt(x)f(x)-(x^(3//2))/2)(2)dx=-int_(0)^(1) (x^(3))/4 dx` `:.A-Ble 1/16`

Discussion

32.	Solve the quadratic equation : x2 – 9x = 0.
Answer» Given equation x² – 9x = 0 ⇒ x(x – 9) = 0 ⇒ x = 0 , x = 9

32.

Solve the quadratic equation : x2 – 9x = 0.

Answer»

Given equation x² – 9x = 0

⇒ x(x – 9) = 0

⇒ x = 0 , x = 9

Discussion

33.	In DLMN, sin (L + M) = 1. What is m∠N equal to ? (A) 60° (B) 90°(C) 120° (D) 135°
Answer» The correct option is (B) 90° Explanation: sin(L + M) = 1 sin(L + M) = sin90° ⇒ L + M = 90° by angle sum property ∠ N = 180– 90° = 90°

33.

In DLMN, sin (L + M) = 1. What is m∠N equal to ? (A) 60° (B) 90°(C) 120° (D) 135°

Answer»

The correct option is (B) 90°

Explanation:

sin(L + M) = 1

sin(L + M) = sin90°

⇒ L + M = 90° by angle sum property ∠ N = 180– 90° = 90°

Discussion

34.	Let `A_0,A_1,.......,A_(n-1)` be a n-sided polygon with vertices as `1,omega,omega^2,.......,omega^(n-1)` Let `B_1, B_1,..... B_(n -1)` be another polygon with vertices `1 , 1 + omega, 1 +omega^2,........,1+omega^(n-1)[omega=cos((2pi)/n)+i sin n((2pi)/n)] ` for `n=4,(A rdot(A_0, A_1, A_2, A_3))/(A r*(B_0, B_1, , B_3))` is `lambda` thenA. less than 1B. an irrational numberC. lies in `(0,pi)`D. less than `(pi)/2`
Answer» Correct Answer - C `Ar.(B_(0),B_(1),………B_(n-1))=n/4 cot ((pi)/n)` `Ar(A_(0)A_(1).A_(n-1))=n/s "sin" (2pi)/n` `:.(Ar.(A_(0)A_(1).A_(n)))/(Ar.(B_(0)B_(1)………B_(n)))=(n"sin" (pi)/n "cos" (pi)/n)/(n/4"cot" (pi)/n)=4"sin"^(2) (pi)/n`

Discussion

35.	Prove that 6n + 13 is an odd integer, where n is an integer.
Answer» To prove : 6n + 13 is odd integer , n ∈ I. Case I : When n is an odd integer n = 2m + 1 ⇒ 6n + 13 = 6 (2m + 1) + 13 = 12 m + 6 + 13 Which is odd. Case II : When n = Even = 2m 6n + 13 = 6 (2m) + 13 = 12m + 13 Which is again odd.

35.

Prove that 6n + 13 is an odd integer, where n is an integer.

Answer»

To prove : 6n + 13 is odd integer , n ∈ I.

Case I : When n is an odd integer n = 2m + 1

⇒ 6n + 13 = 6 (2m + 1) + 13 = 12 m + 6 + 13

Which is odd.

Case II : When n = Even = 2m

6n + 13 = 6 (2m) + 13 = 12m + 13

Which is again odd.

Discussion

36.	Consider `a,b,c,d,e,f,g,h` to be eight distinct alphabets then the number of ways in which they can be dividied in 4- parts isA. `1260` if exactly 2-parts are equalB. `1701`in totalC. `280` if its divided intotwo paritions of 3 and two of 1D. `210` if all parts are equal
Answer» Correct Answer - A::B::C Total Ways `=.^(8)C_(3)+.^(8)C_(4)xx.^(4)C_(2)+.^(8)C_(2)xx(.^(6)C_(3))/2+.^(8)C_(3)xx.^(5)C_(1)xx(.^(4)C_(2))/2+(\|__8)/((2)^(4)\|__4)`

Discussion

37.	Let `A_0,A_1,.......,A_(n-1)` be a n-sided polygon with vertices as `1,omega,omega^2,.......,omega^(n-1)` Let `B_1, B_1,..... B_(n -1)` be another polygon with vertices `1 , 1 + omega, 1 +omega^2,........,1+omega^(n-1)[omega=cos((2pi)/n)+i sin n((2pi)/n)] ` for `n=4,(A rdot(A_0, A_1, A_2, A_3))/(A r*(B_0, B_1, , B_3))` is `lambda` thenA. `[lamda]gt3`B. `(3lamda)/2 epsilon I^(+)`C. `([lamda])/3 epsilon I^(+)`D. `lamda` is irrational
Answer» Correct Answer - B `Ar.(B_(0),B_(1),………B_(n-1))=n/4 cot ((pi)/n)` `Ar(A_(0)A_(1).A_(n-1))=n/s "sin" (2pi)/n` `:.(Ar.(A_(0)A_(1).A_(n)))/(Ar.(B_(0)B_(1)………B_(n)))=(n"sin" (pi)/n "cos" (pi)/n)/(n/4"cot" (pi)/n)=4"sin"^(2) (pi)/n`

Discussion

38.	if n is an odd integer i=√-1 then (1+i)6n + (1-i)6n is equal to
Answer» (1+i)⁶ⁿ+(1−i)⁶ⁿ =((1+i)²)³ⁿ+((1−i)²)³ⁿ =(2i)³ⁿ+(−2i)³ⁿ =(2i)³ⁿ(1+(−1)³ⁿ) Since, n is odd, 3n is also odd. We know that the odd powers of -1 are equal to -1 =(2i)³ⁿ(1+(−1)) =0 Thus, (1+i)⁶ⁿ+(1−i)⁶ⁿ=0, where n is an odd integer.

38.

if n is an odd integer i=√-1 then (1+i)6n + (1-i)6n is equal to

Answer»

(1+i)⁶ⁿ+(1−i)⁶ⁿ

=((1+i)²)³ⁿ+((1−i)²)³ⁿ

=(2i)³ⁿ+(−2i)³ⁿ

=(2i)³ⁿ(1+(−1)³ⁿ)

Since, n is odd, 3n is also odd. We know that the odd powers of -1 are equal to -1

=(2i)³ⁿ(1+(−1))

=0

Thus,

(1+i)⁶ⁿ+(1−i)⁶ⁿ=0,

where n is an odd integer.

Discussion

39.	Consider a function `f : R -> R; f(x^2 +yf(z)) = xf(x) + zf(y), AA x,y,z in R`If `f(x) = 0,AA x in R` is not considered a part of solution set, thenA. `g(x)` is not continuous `AA xepsilonR`B. `g(x)` is differentiable except at two points `AA x epsilonR`C. `g(x)` is differentiable at `x=sinalpha(alpha!+npi, n epsilonI)`D. `g(x)` is non differentiable at integers
Answer» Correct Answer - C `f(x^(2)+yf(z))=x.f(x)+zf(y)` `x=y=z=0` `f(0)=0` `x=0` `f(y.f(z))=zf(y)` `y=z=t` `f(t.f(f))=t.f(t)` Using this and susbtitution, we get `f(x)=x` and `f(x)=0`

Discussion

40.	Consider a function `f : R -> R; f(x^2 +yf(z)) = xf(x) + zf(y), AA x,y,z in R`If `f(x) = 0,AA x in R` is not considered a part of solution set, thenA. `f(alpha) lt alpha^(4)AA alpha epsilon(0,1)`B. `f(alpha) lt alpha^(2)AA alpha epsilon(0,1)`C. `f(alpha)=alpha^(3)` for some `alpha epsilon R^(+)`D. `lim_(alphato 0^(+)) (f(alpha))/(alpha) lt lim_(alpha to 0^(+)) (sinalpha)/(alpha)`
Answer» Correct Answer - C `f(x^(2)+yf(z))=x.f(x)+zf(y)` `x=y=z=0` `f(0)=0` `x=0` `f(y.f(z))=zf(y)` `y=z=t` `f(t.f(f))=t.f(t)` Using this and susbtitution, we get `f(x)=x` and `f(x)=0`

Discussion

41.	The income of P and Q are in the ratio 8 ∶ 9 and their expenses are in the ratio 7 ∶ 6. If both saves Rs. 500 and Rs. 1500, then find their income?1. Rs. 8000, Rs. 90002. Rs. 5000, Rs. 60003. Rs. 4000, Rs. 45004. Rs. 6000, Rs. 7000
Answer» Correct Answer - Option 3 : Rs. 4000, Rs. 4500 Given: The income of P and Q ratio = 8 ∶ 9 And expenditure ratio = 7 ∶ 6 P saves = Rs. 500 Q saves = Rs. 1500 Formula used: Income = Expenditure + saving Calculations: Let incomes 8x and 9x According to the question, ⇒ (8x – 500)/(9x – 1500) = 7/6 ⇒ 48x – 3000 = 63x – 10500 ⇒ 15x = 7500 ⇒ x = 500 P’s income = 8 × 500 = Rs. 4000 Q’s income = 9 × 500 = Rs. 4500 ∴ P and Q’s income is Rs. 4000 and Rs. 4500 respectively.

41.

The income of P and Q are in the ratio 8 ∶ 9 and their expenses are in the ratio 7 ∶ 6. If both saves Rs. 500 and Rs. 1500, then find their income?1. Rs. 8000, Rs. 90002. Rs. 5000, Rs. 60003. Rs. 4000, Rs. 45004. Rs. 6000, Rs. 7000

Answer» Correct Answer - Option 3 : Rs. 4000, Rs. 4500

Given:

The income of P and Q ratio = 8 ∶ 9

And expenditure ratio = 7 ∶ 6

P saves = Rs. 500

Q saves = Rs. 1500

Formula used:

Income = Expenditure + saving

Calculations:

Let incomes 8x and 9x

According to the question,

⇒ (8x – 500)/(9x – 1500) = 7/6

⇒ 48x – 3000 = 63x – 10500

⇒ 15x = 7500

⇒ x = 500

P’s income = 8 × 500 = Rs. 4000

Q’s income = 9 × 500 = Rs. 4500

∴ P and Q’s income is Rs. 4000 and Rs. 4500 respectively.

Discussion

42.	If 61×52 is a multiple of 9 where x is a digit, find x
Answer» If a number is multiple of 9 then the the sum of the digits in the number should also be a multiple of 9. For example if we have 8991 it is multiple of 9.Now sum of digits of number is 8+9+9+1=27 which is also multiple of 9. In the same way now we have 61X52. Now sum of digits is 6+1+X+5+2=14+X Now 14+X should be multiple of 9.The nearest multiple of 9 to the number 14 is 18. So 14+X=18 X=18-14 X=4 So now after replacing X in 16X52 we will have 16452 which is multiple of 9.

Discussion

43.	Maximum wide scope is of -(A) Brand (B) Labelling (C) Packaging (D) Trade Mark
Answer» Correct option is: (C) Packaging

Discussion

44.	Consumer rights under Consumer Protection Act are - (A) 6 (B) 7 (C) 8 (D) 9
Answer» Correct option is: (A) 6

Discussion

45.	A researcher studying the properties of ions in the upper atmosphere wishes to construct an apparatus with the following charateristics: Using an electric field, a beam of ions, each having charge q, mass m , and initial velocity `vhati`, is turned through an angle of `90^@` as each ion undergoes displacement `Rhati + Rhatj`. The ions enter a chamber as shown in figure and leave through the exit port with the same speed they had when they entered the chamber. The electric field acting on the ions is to have constant magnitude. If the field is produced by two flat plates and is uniform in direction, what value should the field have in this case?A. `(mv^2)/(2qR) (hati+hatj)`B. `(mv^2)/(2qR) (-hati+hatj)`C. `(2mv^2)/(qR) (hati+hatj)`D. `(2mv^2)/(qR) (-hati+hatj)`
Answer» Correct Answer - B Concentric cylindrical electrodes will produce radial electric field. As ion is entering at O and leaving at B, hence the path followed by ion should be circular and centrered at A. Required centripetal force should be provided by force on the ion due to electric field. Hence `qE=(mv^(2))/(R)` or `E=(mv^(2))/(qR)` As final velocity along x-axis becomes zero and finally the ions starts moving towards y direction the electric field should have component towards x-and y-directions, respectively. for x-component of electric field (using `v_(x)^(2)=u_(x)^(2)+2a_(x)trianglex)` `0=v^(2)-2((qE_(x))/(m))R` or `E_(x)=(mv^(2))/(2qR)` for y-component of electric field (again using `v_(y)^(2)=u_(y)^(2)+2atriangley)` `v^(2)=0+2((qE_(y))/(m))R` or `E_(y)=(mv^(2))/(2qR)` ltbr. Hence net electric field is `vecE=-(mv^(2))/(2qR)hati+(mv^(2))/(2qR)hatj=(mv^(2))/(2qR)(-hati+hatj)`

Discussion

46.	A researcher studying the properties of ions in the upper atmosphere wishes to construct an apparatus with the following charateristics: Using an electric field, a beam of ions, each having charge q, mass m , and initial velocity `vhati`, is turned through an angle of `90^@` as each ion undergoes displacement `Rhati + Rhatj`. The ions enter a chamber as shown in figure and leave through the exit port with the same speed they had when they entered the chamber. The electric field acting on the ions is to have constant magnitude. Suppose the electric field is produced by two concentric cylindrical electrodes not shown in the diagram, and hence is radial. What magnitude should the field have?A. `(mv)^2/(2qR)` centered at AB. `(mv^2)/(2qR)` centered at OC. `(mv^2)/(qR)` centered at AD. `(mv)^2/(qR) `centered at O
Answer» Correct Answer - C Concentric cylindrical electrodes will produce radial electric field. As ion is entering at O and leaving at B, hence the path followed by ion should be circular and centrered at A. Required centripetal force should be provided by force on the ion due to electric field. Hence `qE=(mv^(2))/(R)` or `E=(mv^(2))/(qR)` As final velocity along x-axis becomes zero and finally the ions starts moving towards y direction the electric field should have component towards x-and y-directions, respectively. for x-component of electric field (using `v_(x)^(2)=u_(x)^(2)+2a_(x)trianglex)` `0=v^(2)-2((qE_(x))/(m))R` or `E_(x)=(mv^(2))/(2qR)` for y-component of electric field (again using `v_(y)^(2)=u_(y)^(2)+2atriangley)` `v^(2)=0+2((qE_(y))/(m))R` or `E_(y)=(mv^(2))/(2qR)` ltbr. Hence net electric field is `vecE=-(mv^(2))/(2qR)hati+(mv^(2))/(2qR)hatj=(mv^(2))/(2qR)(-hati+hatj)`

Discussion

47.	If y = 9x then d2y/dx2 = (A) 9xlog9 (B) 9x(log9)^2 (C) (9x)2 log9 (D) None of these
Answer» Correct option: (B) 9^{x(log9)^2}

47.

If y = 9x then d2y/dx2 = (A) 9xlog9 (B) 9x(log9)^2 (C) (9x)2 log9 (D) None of these

Answer»

Correct option:

(B) 9^{x(log9)^2}

Discussion

48.	Find the mean proportional between 0.08 and 0.18.
Answer» Mean proportional between 0.08 and 0.18 √0.08 x 0.18 = √8/100 x 18/100= √144/(100 x 100) = 12/100 = 0.12

48.

Find the mean proportional between 0.08 and 0.18.

Answer»

Mean proportional between 0.08 and 0.18

√0.08 x 0.18 = √8/100 x 18/100= √144/(100 x 100) = 12/100 = 0.12

Discussion

49.	If x : y = 3 : 4, find (4x + 5y) : (5x - 2y).
Answer» x/y=3/4 (4x+5y)/(5x+2y) = (4( x/y)+5)/(5 (x/y)-2) = (4(3/4)+5)/(5(3/4)-2) =(3+5)/(7/4) = 32/7

49.

If x : y = 3 : 4, find (4x + 5y) : (5x - 2y).

Answer»

x/y=3/4

(4x+5y)/(5x+2y) = (4( x/y)+5)/(5 (x/y)-2) = (4(3/4)+5)/(5(3/4)-2)

=(3+5)/(7/4)

= 32/7

Discussion

50.	What is the labelled price of the article? I. Cost price of the article is Rs.500/. II. Selling price after offering `5%` discount on the labelled price is Rs. 608/. III. Profit earned would have been `28%` in no discount was offered.A. Only IB. Only IIC. Only II & IIID. Only I and II
Answer» Correct Answer - D Let the marked price of the article be Rs. X. From statement II. `(95xx x)/(100)=608" "impliesx=(608xx100)/(95)=Rs.640` From statements I and III, Marked price `=(128xx500)/(100)=Rs.640` So statemetn II is sufficient to give the answer.

Discussion

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