100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS Page 147 InterviewSolution

7301.	निम्नलिखित शब्दों को शब्दकोश में आने वाले क्रम के अनुसार लिखें \| 1. Home 2. House 3. Houston 4. Honor 5. HorrorA. 15432B. 14523C. 14532D. 15423
Answer» Correct Answer - B शब्दकोश के अनुसार शब्दों का क्रम : `{:("1. Home"),(" " darr),("4. Honor"),(" " darr),("5. Horror"),(" "darr),("2. House"),(" "darr),("3. Houston"):}`

Discussion

7302.	निम्नलिखित शब्दों को शब्दकोश में आने वाले क्रम के अनुसार लिखें \| 1. Soften 2. Sterlize 3. Stick 4. Sterile 5. StatusA. 15423B. 25134C. 54213D. 32154
Answer» Correct Answer - A शब्दकोश के अनुसार शब्दों का क्रम : `{:("1. Soften"),(" " darr),("2. Status"),(" " darr),("4. Stertile"),(" "darr),("2. Sterilize"),(" "darr),("3. Stick"):}`

Discussion

7303.	निम्नलिखित शब्दों को शब्दकोश में आने वाले क्रम के अनुसार लिखें : 1. Dillydallying 2. Dillydallied 3. Dillydally 4. Dilled 5. DillydalliesA. 42351B. 42531C. 45312D. 45321
Answer» Correct Answer - B शब्दकोश के अनुसार शब्दों का क्रम : `{:("4. Dilled"),(" " darr),("2. Dillydallied"),(" " darr),("5. Dillydallies"),(" "darr),("3. Dillydally"),(" "darr),("1. Dillydallying"):}`

Discussion

7304.	निम्नलिखित शब्दों को शब्दकोश में आने वाले क्रम के अनुसार लिखें : 1. Storm 2. Strap 3. Strangle 4. Stamped 5. SatireA. 51432B. 51342C. 54132D. 53412
Answer» Correct Answer - C शब्दकोश के अनुसार शब्दों का क्रम : `{:("5. Satire"),(" " darr),("4. Stamped"),(" " darr),("1. Storm"),(" "darr),("3. Strangle"),(" "darr),("2. Strap"):}`

Discussion

7305.	Find the antonym of wordAlly A) adversary B) partner C) friend D) associate
Answer» Correct option is A) adversary

Discussion

7306.	Down there at the back of the room old Hauser had put on his spectacles and, holding his primer in both hands, spelled the letters with them. You could see that he, too, was crying; his voice trembled with emotion, and it was so funny to hear him that we all wanted to laugh and cry. Ah, how well I remember it, that last lesson! All at once the church-clock struck twelve. Then the Angelus. At the same moment the trumpets of the Prussians, returning from drill, sounded under our windows. i. What was the Hauser crying for? a) Because he had not taken his mother tongue seriously b) Because M. Hamel was going to leave forever c) Because he was neither able to speak nor write French d) All of the above ii. Choose the version which best matches the term “Angelus” a. A Catholic devotion commemorating the incarnation by Romans b. A Catholic devotion commemorating the incarnation by Anglican c. A Catholic devotion commemorating the incarnation by Baptist d. A Catholic devotion commemorating the incarnation by Lutheran iii. Choose the term which best matches the statement “his voice trembled with emotions”. a) Shudder or move due to shame b) Palpitating with excitement c) Quavering with vehemence d) Trembling with rage iv. What do the marching soldiers under the windows represent? a) The Dawn of Prussia in the defeat of French people b) The defeat of Prussia c) The victory of French d) None of these
Answer» i. a) Because he had not taken his mother tongue seriously ii. d) A Catholic devotion commemorating the incarnation by Lutheran iii. c) Quavering with vehemence iv. a) The Dawn of Prussia in the defeat of French people

7306.

Down there at the back of the room old Hauser had put on his spectacles and, holding his primer in both hands, spelled the letters with them. You could see that he, too, was crying; his voice trembled with emotion, and it was so funny to hear him that we all wanted to laugh and cry. Ah, how well I remember it, that last lesson! All at once the church-clock struck twelve. Then the Angelus. At the same moment the trumpets of the Prussians, returning from drill, sounded under our windows. i. What was the Hauser crying for? a) Because he had not taken his mother tongue seriously b) Because M. Hamel was going to leave forever c) Because he was neither able to speak nor write French d) All of the above ii. Choose the version which best matches the term “Angelus” a. A Catholic devotion commemorating the incarnation by Romans b. A Catholic devotion commemorating the incarnation by Anglican c. A Catholic devotion commemorating the incarnation by Baptist d. A Catholic devotion commemorating the incarnation by Lutheran iii. Choose the term which best matches the statement “his voice trembled with emotions”. a) Shudder or move due to shame b) Palpitating with excitement c) Quavering with vehemence d) Trembling with rage iv. What do the marching soldiers under the windows represent? a) The Dawn of Prussia in the defeat of French people b) The defeat of Prussia c) The victory of French d) None of these

Answer»

i. a) Because he had not taken his mother tongue seriously

ii. d) A Catholic devotion commemorating the incarnation by Lutheran

iii. c) Quavering with vehemence

iv. a) The Dawn of Prussia in the defeat of French people

Discussion

7307.	“I will learn to drive a car,” he answers, looking straight into my eyes. His dream like a mirage amidst the dust of streets that fill his town Firozabad, famous for its bangles. Every other family in Firozabad is engaged in making bangles. It is the centre of India’s glass-blowing industry where families have spent generations working around furnaces, welding glass, making bangles for all the women in the land it seems. i. How Mukesh is different from the other bangle makers?a) He wants to open his own bangle making company b) He wants to become a pilot c) He wants to open his own garage d) He wants to be his own master ii. The phrase “dreams looms like a mirage amidst the dust of streets” indicates that Mukesh dream was a) A reality, yet seemed distant b) Lost in the sea of dust c) Illusory and indistinct d) Hanging in the dusty air iii. Every other family in Firozabad is engaged in bangle making indicates that a) Bangle making is the only industry that flourishes in Firozabad b) The entire population of Firozabad is involved in making bangles c) Majority of population in Firozabad is involved in bangle making d) Bangle making is most loved occupation in Firozabad iv. Why is the writer calling it as his 'dream'? a) He cannot become a driver b) He will not be allowed to go as per his wish and work else were c) His parent will not allow him to work elsewhere d) He is lazy and dreaming
Answer» i. a) He wants to open his own bangle making company ii. c) Illusory and indistinct iii. c) Majority of population in Firozabad is involved in bangle making iv. b) He will not be allowed to go as per his wish and work else were

7307.

“I will learn to drive a car,” he answers, looking straight into my eyes. His dream like a mirage amidst the dust of streets that fill his town Firozabad, famous for its bangles. Every other family in Firozabad is engaged in making bangles. It is the centre of India’s glass-blowing industry where families have spent generations working around furnaces, welding glass, making bangles for all the women in the land it seems. i. How Mukesh is different from the other bangle makers?a) He wants to open his own bangle making company b) He wants to become a pilot c) He wants to open his own garage d) He wants to be his own master ii. The phrase “dreams looms like a mirage amidst the dust of streets” indicates that Mukesh dream was a) A reality, yet seemed distant b) Lost in the sea of dust c) Illusory and indistinct d) Hanging in the dusty air iii. Every other family in Firozabad is engaged in bangle making indicates that a) Bangle making is the only industry that flourishes in Firozabad b) The entire population of Firozabad is involved in making bangles c) Majority of population in Firozabad is involved in bangle making d) Bangle making is most loved occupation in Firozabad iv. Why is the writer calling it as his 'dream'? a) He cannot become a driver b) He will not be allowed to go as per his wish and work else were c) His parent will not allow him to work elsewhere d) He is lazy and dreaming

Answer»

i. a) He wants to open his own bangle making company

ii. c) Illusory and indistinct

iii. c) Majority of population in Firozabad is involved in bangle making

iv. b) He will not be allowed to go as per his wish and work else were

Discussion

7308.	निम्नलिखित शब्दों को शब्दकोश में आने वाले क्रम के अनुसार लिखें : 1. Bright 2. Bingo 3. Better 4. Bleak 5. BeakA. 52341B. 53241C. 34251D. 32514
Answer» Correct Answer - B शब्दकोश के अनुसार शब्दों का क्रम : `{:("5. Beak"),(" " darr),("3. Better"),(" " darr),("2. Bingo"),(" "darr),("4. Bleak"),(" "darr),("1. Bright"):}`

Discussion

7309.	i ‘But promises like mine abound in every corner of his bleak world’. This suggests that a) there is no dearth of promises which remain unfulfilled. b) there is a scarcity of people promising things for betterment. c) people make a lot of promises which are often fulfilled. d) promises made, live up to the expectations of people. ii From this chapter, it is evident that the author has an attitude of a) sympathy.b) apathy. c) empathy. d) bewilderment. iii ‘That’s why they left, looking for gold in the big city.’ Here ‘gold’ indicates a) misfortune of circumstances. b) ample wealth. c) means of survival. d) a sign of luxury. iv Choose the statement that is NOT TRUE about ragpickers in Seemapuri. a) Children are equally involved in rag picking as their parents. b) The ragpickers settle down in a place permanently. c) Rag picking has accomplished itself as a skill and form of art. d) Ragpickers live in unsteady shanties on the outskirts of Delhi.
Answer» i – a); ii – a); iii – c); iv – c); v – b)

7309.

i ‘But promises like mine abound in every corner of his bleak world’. This suggests that a) there is no dearth of promises which remain unfulfilled. b) there is a scarcity of people promising things for betterment. c) people make a lot of promises which are often fulfilled. d) promises made, live up to the expectations of people. ii From this chapter, it is evident that the author has an attitude of a) sympathy.b) apathy. c) empathy. d) bewilderment. iii ‘That’s why they left, looking for gold in the big city.’ Here ‘gold’ indicates a) misfortune of circumstances. b) ample wealth. c) means of survival. d) a sign of luxury. iv Choose the statement that is NOT TRUE about ragpickers in Seemapuri. a) Children are equally involved in rag picking as their parents. b) The ragpickers settle down in a place permanently. c) Rag picking has accomplished itself as a skill and form of art. d) Ragpickers live in unsteady shanties on the outskirts of Delhi.

Answer»

i – a);

ii – a);

iii – c);

iv – c);

v – b)

Discussion

7310.	Find the antonym of wordStingy A) rude B) generous C) gaunt D) ignorant
Answer» Correct option is B) generous

Discussion

7311.	Find the antonym of wordFlat A) icy B) even C) bumpy D) slippery
Answer» Correct option is C) bumpy

Discussion

7312.	“I have nothing else to do,” he mutters, looking away. “Go to school,” I say glibly, realising immediately how hollow the advice must sound. “There is no school in my neighbourhood. When they build one, I will go.” “If I start a school, will you come?” I ask, half-joking. “Yes,” he says, smiling broadly. A few days later I see him running up to me. “Is your school ready? “It takes longer to build a school,” I say, embarrassed at having made a promise that was not meant. But promises like mine abound in every corner of his bleak world.i. ‘But promise like mine abound in every corner of his bleak world'. This suggest thata) There is no dearth of promises which remain unfulfilled b) There is scarcity of people promising for betterment c) People make a lot of promises which are often fulfilled d) Promises made, live up to the expectations of people ii. What does “how hollow the advice must sound” refers?a) The narrator has realised that his advice is very valuable b) The narrator has realised that his advice is meaningless c) The narrator has realised that the listener has not accepted his advice d) The narrator has realised that his advice is feasible iii. Choose the term which best matches the statement- 'When they built one, I will go?’ a) Optimistic b) Courageous c) Confidence d) Determination iv. What does 'scrounging for Gold' in the garbage mean? a) Searching forsome valuable thing that may make money for him b) Searching for gold in the g a ra g e c) Searching for gold ornaments in the garbage d) Searching for gold in the garbage
Answer» i. a) There is no dearth of promises which remain unfulfilled ii. b) The narrator has realised that his advice is meaningless iii. d) Determination iv. a) Searching forsome valuable thing that may make money for him

7312.

“I have nothing else to do,” he mutters, looking away. “Go to school,” I say glibly, realising immediately how hollow the advice must sound. “There is no school in my neighbourhood. When they build one, I will go.” “If I start a school, will you come?” I ask, half-joking. “Yes,” he says, smiling broadly. A few days later I see him running up to me. “Is your school ready? “It takes longer to build a school,” I say, embarrassed at having made a promise that was not meant. But promises like mine abound in every corner of his bleak world.i. ‘But promise like mine abound in every corner of his bleak world'. This suggest thata) There is no dearth of promises which remain unfulfilled b) There is scarcity of people promising for betterment c) People make a lot of promises which are often fulfilled d) Promises made, live up to the expectations of people ii. What does “how hollow the advice must sound” refers?a) The narrator has realised that his advice is very valuable b) The narrator has realised that his advice is meaningless c) The narrator has realised that the listener has not accepted his advice d) The narrator has realised that his advice is feasible iii. Choose the term which best matches the statement- 'When they built one, I will go?’ a) Optimistic b) Courageous c) Confidence d) Determination iv. What does 'scrounging for Gold' in the garbage mean? a) Searching forsome valuable thing that may make money for him b) Searching for gold in the g a ra g e c) Searching for gold ornaments in the garbage d) Searching for gold in the garbage

Answer»

i. a) There is no dearth of promises which remain unfulfilled

ii. b) The narrator has realised that his advice is meaningless

iii. d) Determination

iv. a) Searching forsome valuable thing that may make money for him

Discussion

7313.	Find the antonym of wordAdjacent A) apart B) void C) bleak D) blank
Answer» Correct option is A) apart

Discussion

7314.	Term of independent of x (x - 1/x2)15.
Answer» (x - \(\frac1{x^2}\))¹⁵ (Term of independent of x in (x - \(\frac1{x^2}\))¹⁵) General term in the expansion of (x - \(\frac1{x^2}\))¹⁵ is T_r+1 = ¹⁵C_r x^15-r (\(-\frac1{x^2}\))^r = (-1)^r ¹⁵C_r x^15-r^{- 2r} = (-1)^r15C_r x^15-3r For independent term of x, we have 15 - 3r = 0 ⇒ r = 15/3 = 5 \(\therefore\) Independent term of x in (x - \(\frac1{x^2}\))¹⁵ is T₆ = (-1)⁵ ¹⁵C₅ = -¹⁵C₅

7314.

Term of independent of x (x - 1/x2)15.

Answer»

(x - \(\frac1{x^2}\))¹⁵ (Term of independent of x in (x - \(\frac1{x^2}\))¹⁵)

General term in the expansion of

(x - \(\frac1{x^2}\))¹⁵ is T_r+1 = ¹⁵C_r x^15-r (\(-\frac1{x^2}\))^r

= (-1)^r ¹⁵C_r x^15-r^{- 2r}

= (-1)^r15C_r x^15-3r

For independent term of x, we have

15 - 3r = 0

⇒ r = 15/3 = 5

\(\therefore\) Independent term of x in (x - \(\frac1{x^2}\))¹⁵ is

T₆ = (-1)⁵ ¹⁵C₅ = -¹⁵C₅

Discussion

7315.	A soloist is auditioning for a musical play. If she is required to sing any three of the 7 prepared songs, in how many ways can she make her choice?
Answer» C(m, n) = \(\frac{n!}{m!(n-m)!}\) C(3, 7) = \(\frac{7!}{3!(7-5)!}\) = \(\frac{7\times6\times5\times4!}{3!\times4!}\) = \(\frac{7\times6\times5}{3\times2\times1}\) = 35 So, she make her choice in 35 ways.

7315.

A soloist is auditioning for a musical play. If she is required to sing any three of the 7 prepared songs, in how many ways can she make her choice?

Answer»

C(m, n) = \(\frac{n!}{m!(n-m)!}\)

C(3, 7) = \(\frac{7!}{3!(7-5)!}\)

= \(\frac{7\times6\times5\times4!}{3!\times4!}\)

= \(\frac{7\times6\times5}{3\times2\times1}\)

= 35

So, she make her choice in 35 ways.

Discussion

7316.	Find the synonymEnterprise A) hospitality B) immunity C) imagination D) undertaking
Answer» Correct option is D) undertaking

Discussion

7317.	Enlist any eight roles and functions of the Ministry of Tourism?
Answer» 1) All Policy Matters, including 2) Investment Facilitation 3) Planning 4) Co-ordination with other Ministries, Departments, State/UT Government 5) Regulation 6) Infrastructure & Product Development 7) Human Resource Development 8) Publicity & Marketing 9) Research, Analysis, Monitoring and Evaluation 10) International Co-operation and External Assistance 11) Legislation and Parliamentary Work 12) Establishment matters 13) Vigilance matters 14) Implementation of official language policy 15) Budget co-ordination and related matters 16) Plan-coordination and monitoring

7317.

Enlist any eight roles and functions of the Ministry of Tourism?

Answer»

1) All Policy Matters, including

2) Investment Facilitation

3) Planning

4) Co-ordination with other Ministries, Departments, State/UT Government

5) Regulation

6) Infrastructure & Product Development

7) Human Resource Development

8) Publicity & Marketing

9) Research, Analysis, Monitoring and Evaluation

10) International Co-operation and External Assistance

11) Legislation and Parliamentary Work

12) Establishment matters

13) Vigilance matters

14) Implementation of official language policy

15) Budget co-ordination and related matters

16) Plan-coordination and monitoring

Discussion

7318.	Write any six attributes required by hospitality professional?
Answer» Attributes of hospitality professional: Be conscious of their image- they dress smartly and carry themselves confidently. Be knowledgeable and have the required specialized skills and experience. Be visionary leaders who can motivate their subordinates. Be honest and trustworthy. Willing to learn from mistakes. Respond to a crisis and effectively resolve problems.

7318.

Write any six attributes required by hospitality professional?

Answer»

Attributes of hospitality professional:

Be conscious of their image- they dress smartly and carry themselves confidently.
Be knowledgeable and have the required specialized skills and experience.
Be visionary leaders who can motivate their subordinates.
Be honest and trustworthy.
Willing to learn from mistakes.
Respond to a crisis and effectively resolve problems.

Discussion

7319.	Enlist any four attributes of a hospitality professional.
Answer» Be conscious of their image-they dress smartly and carry themselves confidently. Be knowledgeable and have the required specialized skills and experience. Be hard working, self-disciplines individuals who are accountable for their words and actions. Be visionary leaders who can motivate their subordinates.

Discussion

7320.	Enlist two cultural benefits of tourism impacts ?
Answer» Two cultural benefits of tourism impacts: 1. Tourism can enhance local cultural awareness. 2. Tourism can generate revenue to help pay for the preservation of monuments, historical buildings etc

7320.

Enlist two cultural benefits of tourism impacts ?

Answer»

Two cultural benefits of tourism impacts:

1. Tourism can enhance local cultural awareness.

2. Tourism can generate revenue to help pay for the preservation of monuments, historical buildings etc

Discussion

7321.	Good grooming influences the hospitality professional in a positive manner. Discuss any four points to support the above statement?
Answer» 1. Image Building/Enhances Organizations Image: Working at a hotel means you are the face of the hotel, whether you are greeting a guest on arrival or cleaning their rooms. So, it is of utmost importance to have high personal grooming standards and be well maintained. 2.Delivers Good Quality Service: Employees feel good if they look good and provide services as per guests’ expectations. 3. Boosts Self-Confidence: In hotel industry looks make a lot of difference. It boosts self-confidence and self-esteem. One feels very reassured when other people admire them and prefer to associate with them as they find them good. 4. Guest Comfort: A pleasing face is nice to look at. Guests like to relax in the presence of beautiful things. A pleasant face can relax the mind. Those with an aesthetic sense like to admire beautiful people and things.

7321.

Good grooming influences the hospitality professional in a positive manner. Discuss any four points to support the above statement?

Answer»

1. Image Building/Enhances Organizations Image: Working at a hotel means you are the face of the hotel, whether you are greeting a guest on arrival or cleaning their rooms. So, it is of utmost importance to have high personal grooming standards and be well maintained.

2.Delivers Good Quality Service: Employees feel good if they look good and provide services as per guests’ expectations.

3. Boosts Self-Confidence: In hotel industry looks make a lot of difference. It boosts self-confidence and self-esteem. One feels very reassured when other people admire them and prefer to associate with them as they find them good.

4. Guest Comfort: A pleasing face is nice to look at. Guests like to relax in the presence of beautiful things. A pleasant face can relax the mind. Those with an aesthetic sense like to admire beautiful people and things.

Discussion

7322.	Write about the importance of grooming in tourism industry?
Answer» Grooming refers to have neat and tidy appearance. Grooming means to take care of overall appearance which includes neatness and cleanliness of body and hair, also the way we manage accessories, belt, shoes, purse, watch, jewellery .

Discussion

7323.	Briefly explain any six positive effects of good grooming in the hospitality industry?
Answer» Image Building: Working at a hotel means employees are the face of the hotel,So it is of utmost importance to have high personal grooming standards and be well maintained. Reveals Positive Guest Service Attitude: If the employees of the organization are well groomed, project a positive guest service attitude there are more chance they will be noticed because of employees’ empathetic qualities, attitude and disposition. Fulfils guest expectations: Guests expect a high level of personal grooming and hygiene from all employees which complement the facilities of the hotel. Delivers good quality service: Employees feel good if they look good and provide services as per guest’s expectations. Boosts self confidence: In hotel industry looks make a lot of differences. It boosts self-confidence and self-esteem. One feels very reassured when other people admire them and prefer to associate with them. Guest Comfort: A pleasing face is nice to look at. Guests like to relax in the presence of beautiful things.

7323.

Briefly explain any six positive effects of good grooming in the hospitality industry?

Answer»

Image Building: Working at a hotel means employees are the face of the hotel,So it is of utmost importance to have high personal grooming standards and be well maintained.

Reveals Positive Guest Service Attitude: If the employees of the organization are well groomed, project a positive guest service attitude there are more chance they will be noticed because of employees’ empathetic qualities, attitude and disposition.

Fulfils guest expectations: Guests expect a high level of personal grooming and hygiene from all employees which complement the facilities of the hotel.

Delivers good quality service: Employees feel good if they look good and provide services as per guest’s expectations.

Boosts self confidence: In hotel industry looks make a lot of differences. It boosts self-confidence and self-esteem. One feels very reassured when other people admire them and prefer to associate with them.

Guest Comfort: A pleasing face is nice to look at. Guests like to relax in the presence of beautiful things.

Discussion

7324.	This is the third group of direct dyes that is further identified as naphthol and rapidogen types. Identify the dye. a. Azoic dyes b. Direct dyes c. Vat dyes d. Basic dyes
Answer» Correct option: a. Azoic dyes

Discussion

7325.	Sulpher dyes are used to dye _____ fabrics A] Cotton & Linen B] Silk C] Synthetic D] Acrylic
Answer» [A] Cotton & Linen Sulpher dyes are used to dye Cotton & Linen fabrics.

7325.

Sulpher dyes are used to dye _____ fabrics A] Cotton & Linen B] Silk C] Synthetic D] Acrylic

Answer»

[A] Cotton & Linen

Sulpher dyes are used to dye Cotton & Linen fabrics.

Discussion

7326.	Find the centre and radius of the circle x2 + y2 + 8x + 10y – 8 = 0
Answer» x² + y² + 8x + 10y – 8 = 0 ⇒ (x² + 2.x.4 + 16) - 16 + (y² + 2.y.5 + 25) – 25 – 8 = 0 ⇒ (x + 4)² + (y + 5)² = 49 ⇒ centre = (-4, -5), radius = 7

7326.

Find the centre and radius of the circle x2 + y2 + 8x + 10y – 8 = 0

Answer»

x² + y² + 8x + 10y – 8 = 0 ⇒ (x² + 2.x.4 + 16) - 16 + (y² + 2.y.5 + 25) – 25 – 8 = 0

⇒ (x + 4)² + (y + 5)² = 49

⇒ centre = (-4, -5), radius = 7

Discussion

7327.	Find the sum of the sequence 8, 88, 888, 8888, … to n terms.
Answer» S_n = 8 + 88 + 888 + ……………… = 8[1 + 11 + 111 + ………….. ] = 8/9(9 + 99 + 999 + ……n^th term) = 8/9[(10 – 1)+(10² – 1]+ ………] = 8/9[10(10² – 1) ] [(10 + 10² + 10³ + ……. n^th term) – (1 + 1 + 1 + …..)]

7327.

Find the sum of the sequence 8, 88, 888, 8888, … to n terms.

Answer»

S_n = 8 + 88 + 888 + ………………

= 8[1 + 11 + 111 + ………….. ]

= 8/9(9 + 99 + 999 + ……n^th term)

= 8/9[(10 – 1)+(10² – 1]+ ………]

= 8/9[10(10² – 1) ] [(10 + 10² + 10³ + ……. n^th term) – (1 + 1 + 1 + …..)]

Discussion

7328.	Let \(\left<x_n\right>\) and \(\left<y_n\right>\) be real sequences and let for some k ϵ N, 0 ≤ xn ≤ yn for n ≥ k.Then, which of the following statements is true?1. Divergence of ∑ yn ⇒ Divergence of ∑ xn2. ∑ xn and ∑ yn are always divergent3. Convergence of ∑ xn ⇒ Convergence of ∑ yn4. Convergence of ∑ yn ⇒ Convergence of ∑ xn
Answer» Correct Answer - Option 4 : Convergence of ∑ y_n ⇒ Convergence of ∑ x_n Concept: The convergence or divergence of sequences is tested by various methods. One is Comparison test. Comparison test: Suppose that we have two series ∑a_n and ∑b_n with a_n, b_n ≥ 0 for all n and a_n ≤ b_n for all n. Then, 1. If ∑b_n is convergent then so is ∑a_n 2. If ∑a_n is divergent then so is ∑b_n The statement 1 is given in the 4th option.

7328.

Let \(\left<x_n\right>\) and \(\left<y_n\right>\) be real sequences and let for some k ϵ N, 0 ≤ xn ≤ yn for n ≥ k.Then, which of the following statements is true?1. Divergence of ∑ yn ⇒ Divergence of ∑ xn2. ∑ xn and ∑ yn are always divergent3. Convergence of ∑ xn ⇒ Convergence of ∑ yn4. Convergence of ∑ yn ⇒ Convergence of ∑ xn

Answer» Correct Answer - Option 4 : Convergence of ∑ y_n ⇒ Convergence of ∑ x_n

Concept:

The convergence or divergence of sequences is tested by various methods. One is Comparison test.

Comparison test:

Suppose that we have two series ∑a_n and ∑b_n with a_n, b_n ≥ 0 for all n and a_n ≤ b_n for all n. Then,

1. If ∑b_n is convergent then so is ∑a_n

2. If ∑a_n is divergent then so is ∑b_n

The statement 1 is given in the 4th option.

Discussion

7329.	For what value of μ do the simultaneous equations 5x + 7y = 2, 15x + 21y = μ have no solution?1. μ = 02. μ ≠ 63. μ ≠ 04. μ = 6
Answer» Correct Answer - Option 2 : μ ≠ 6 Concept: System of equations a₁x + b₁y = c₁ a₂x + b₂y = c₂ For unique solution \(\frac {a_1}{a_2}≠ \frac {b_1}{b_2}\) For Infinite solution \(\frac {a_1}{a_2}= \frac {b_1}{b_2}= \frac {c_1}{c_2}\) For no solution \(\frac {a_1}{a_2}=\frac {b_1}{b_2}≠ \frac {c_1}{c_2}\) Calculation: Given: 5x + 7y = 2, 15x + 21y = μ Here For no solution \(\frac 5{15}=\frac 7{21}≠ \frac 2{μ}\) Hence for no solution μ ≠ 6

7329.

For what value of μ do the simultaneous equations 5x + 7y = 2, 15x + 21y = μ have no solution?1. μ = 02. μ ≠ 63. μ ≠ 04. μ = 6

Answer» Correct Answer - Option 2 : μ ≠ 6

Concept:

System of equations

a₁x + b₁y = c₁

a₂x + b₂y = c₂

For unique solution

\(\frac {a_1}{a_2}≠ \frac {b_1}{b_2}\)

For Infinite solution

\(\frac {a_1}{a_2}= \frac {b_1}{b_2}= \frac {c_1}{c_2}\)

For no solution

\(\frac {a_1}{a_2}=\frac {b_1}{b_2}≠ \frac {c_1}{c_2}\)

Calculation:

Given:

5x + 7y = 2, 15x + 21y = μ

Here For no solution

\(\frac 5{15}=\frac 7{21}≠ \frac 2{μ}\)

Hence for no solution μ ≠ 6

Discussion

7330.	∇ × ∇ × P, where P is a vector, is equal to (a) × ∇ × − ∇2 (b)∇2 + ∇(∇ ∙ P) (c) ∇2 + ∇ × P (d)∇(∇ ∙ P) − ∇2P
Answer» Correct option (d) Explanation: ∇ × ∇ × = ∇(∇.P) − ∇²P

7330.

∇ × ∇ × P, where P is a vector, is equal to (a) × ∇ × − ∇2 (b)∇2 + ∇(∇ ∙ P) (c) ∇2 + ∇ × P (d)∇(∇ ∙ P) − ∇2P

Answer»

Correct option (d)

Explanation:

∇ × ∇ × = ∇(∇.P) − ∇²P

Discussion

7331.	Can you tell what model each of ________ ? A) them to beB) them are C) they are D) them is
Answer» Correct option is D) them is

Discussion

7332.	Directions: In the following question, two statements are numbered as I and II. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option.Quantity I: When 5 is subtracted from one-third of one-fifth of a number, the result is 1/30 of the same number. Find the number.Quantity II: A bag contains an equal number of ₹ 50, ₹ 100, and ₹ 200 notes. If total amount in the bag is ₹ 10500. Find the number of notes of each kind.1.Quantity I ≤ Quantity II2.Quantity I ≥ Quantity II3.Quantity I > Quantity II4.Quantity I < Quantity II5.Quantity I = Quantity II or no relation
Answer» Correct Answer - Option 3 : Quantity I > Quantity II Quantity I: Given: [(1/3) of (1/5) of a number] – 5 = (1/30) of the same number Calculation: Let the number be x [(1/3) × (1/5) × x] – 5 = (1/30) × x ⇒ [(1/15) × x] – 5 = (1/30) × x ⇒ (x – 75)/15 = (1/30) × x ⇒ (x – 75) = (1/2) × x ⇒ 2x – 150 = x ⇒ x = 150 The number is 150. Quantity II: Given: Denomination of notes in the bag are ₹ 50, ₹ 100 and ₹ 200 Calculation: Let x be the number of notes in each bag 50x + 100x + 200x = 10500 ⇒ 350x = 10500 ⇒ x = 30 The number of notes in each bag are 30. ∴ We can deduce that Quantity I > Quantity II.

7332.

Directions: In the following question, two statements are numbered as I and II. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option.Quantity I: When 5 is subtracted from one-third of one-fifth of a number, the result is 1/30 of the same number. Find the number.Quantity II: A bag contains an equal number of ₹ 50, ₹ 100, and ₹ 200 notes. If total amount in the bag is ₹ 10500. Find the number of notes of each kind.1.Quantity I ≤ Quantity II2.Quantity I ≥ Quantity II3.Quantity I > Quantity II4.Quantity I < Quantity II5.Quantity I = Quantity II or no relation

Answer» Correct Answer - Option 3 :

Quantity I > Quantity II

Quantity I:

Given:

[(1/3) of (1/5) of a number] – 5 = (1/30) of the same number

Calculation:

Let the number be x

[(1/3) × (1/5) × x] – 5 = (1/30) × x

⇒ [(1/15) × x] – 5 = (1/30) × x

⇒ (x – 75)/15 = (1/30) × x

⇒ (x – 75) = (1/2) × x

⇒ 2x – 150 = x

⇒ x = 150

The number is 150.

Quantity II:

Given:

Denomination of notes in the bag are ₹ 50, ₹ 100 and ₹ 200

Calculation:

Let x be the number of notes in each bag

50x + 100x + 200x = 10500

⇒ 350x = 10500

⇒ x = 30

The number of notes in each bag are 30.

∴ We can deduce that Quantity I > Quantity II.

Discussion

7333.	In a pouch there are 5 orange, 3 brown, and 4 red balls. 3 balls are picked at random?Quantity I: The probability that 2 balls are brown in color and 1 ball is red in color.Quantity II: The probability that all balls are orange in color.1. Quantity I < Quantity II2. Quantity I = Quantity II3. Quantity I > Quantity II4. Quantity I ≥ Quantity II5. Quantity I ≤ Quantity II
Answer» Correct Answer - Option 3 : Quantity I > Quantity II Calculation: Quantity I: Favorable outcomes: 2 brown + 1 red ball = ³C₂ × ⁴C₁ ⇒ 12 Total outcomes = ¹²C₃ ⇒ 220 ∴ Probability = 12/220 ⇒ 3/55 Quantity II: 3 Orange balls = ⁵C₃ ⇒ 10 Total outcomes = ¹²C₃ ⇒ 220 ∴ Probability = 10/220 ⇒ 1/22 Quantity I > Quantity II

7333.

In a pouch there are 5 orange, 3 brown, and 4 red balls. 3 balls are picked at random?Quantity I: The probability that 2 balls are brown in color and 1 ball is red in color.Quantity II: The probability that all balls are orange in color.1. Quantity I < Quantity II2. Quantity I = Quantity II3. Quantity I > Quantity II4. Quantity I ≥ Quantity II5. Quantity I ≤ Quantity II

Answer» Correct Answer - Option 3 : Quantity I > Quantity II

Calculation:

Quantity I:

Favorable outcomes:

2 brown + 1 red ball = ³C₂ × ⁴C₁

⇒ 12

Total outcomes = ¹²C₃

⇒ 220

∴ Probability = 12/220

⇒ 3/55

Quantity II:

3 Orange balls = ⁵C₃

⇒ 10

Total outcomes = ¹²C₃

⇒ 220

∴ Probability = 10/220

⇒ 1/22

Quantity I > Quantity II

Discussion

7334.	Quantity I: An envelope has 3 green, 2 yellow, and 3 purple tablets. Two tablets are drawn randomly. What is the probability of no tablet is purple?Quantity II: (14x - 5) (7x - 8) = 01. Quantity I < Quantity II2. Quantity I = Quantity II3. Quantity I > Quantity II4. Quantity I ≥ Quantity II5. Quantity I ≤ Quantity II
Answer» Correct Answer - Option 5 : Quantity I ≤ Quantity II Calculation: Quantity I: Favorable Outcomes = ⁵C₂ ⇒ 10 Total Outcomes = ⁸C₂ ⇒ 28 ∴ Probability = 10/28 ⇒ 5/14 Quantity II: (14x - 5) (7x - 8) = 0 ⇒14x – 5 = 0 or 7x – 8 = 0 ∴ x = 5/14 or 8/7 Quantity I ≤ Quantity II

7334.

Quantity I: An envelope has 3 green, 2 yellow, and 3 purple tablets. Two tablets are drawn randomly. What is the probability of no tablet is purple?Quantity II: (14x - 5) (7x - 8) = 01. Quantity I < Quantity II2. Quantity I = Quantity II3. Quantity I > Quantity II4. Quantity I ≥ Quantity II5. Quantity I ≤ Quantity II

Answer» Correct Answer - Option 5 : Quantity I ≤ Quantity II

Calculation:

Quantity I:

Favorable Outcomes = ⁵C₂

⇒ 10

Total Outcomes = ⁸C₂

⇒ 28

∴ Probability = 10/28

⇒ 5/14

Quantity II:

(14x - 5) (7x - 8) = 0

⇒14x – 5 = 0 or 7x – 8 = 0

∴ x = 5/14 or 8/7

Quantity I ≤ Quantity II

Discussion

7335.	The diplomats haven’t been able to arrive ______ an agreement yet. A) by B) at C) on D) to
Answer» Correct option is B) at

Discussion

7336.	_______ a drop of rain fell for months, and all the crops died. A) No B) None C) Not D) Not any
Answer» Correct option is C) Not

Discussion

7337.	A box contains 50 balls, in which 5 are red balls, 6 are green balls, 9 are blue balls, and the remaining are yellow balls.Quantity I: Probability of picking 2 balls such that one is green and the other one is blueQuantity II: Probability of picking 3 balls such that at least one of them is redQuantity III: Probability of picking 3 balls such that at least one of them is blue1. Quantity III > Quantity I > Quantity II2. Quantity II > Quantity III > Quantity I3. Quantity III > Quantity II > Quantity I4. Quantity I = Quantity II > Quantity III5. Quantity I > Quantity III < Quantity II
Answer» Correct Answer - Option 3 : Quantity III > Quantity II > Quantity I Quantity I: Probability of picking 2 tiles such that one is green and the other one is blue ⇒ (6 × 9)/⁵⁰C₂ ⇒ 54/(50 × 49/2) ⇒ 54/1225 ⇒ 0.044 Quantity II: Probability of picking 3 balls such that at least one of them is red ⇒ 1 – ⁴⁵C₃/⁵⁰C₃ ⇒ 1 – (45 × 44 × 43/3)/(50 × 49 × 48/3) ⇒ 1 – (14190/19600) ⇒ 541/1960 ⇒ 0.276 Quantity III: Probability of picking 3 balls such that at least one of them is blue ⇒ 1 – ⁴¹C₃/⁵⁰C₃ ⇒ 1 – (41 × 40 × 39/3)/(50 × 49 × 48/3) ⇒ 1 – (10660/19600) ⇒ 894/1960 ⇒ 0.456 Quantity III > Quantity II > Quantity I

7337.

A box contains 50 balls, in which 5 are red balls, 6 are green balls, 9 are blue balls, and the remaining are yellow balls.Quantity I: Probability of picking 2 balls such that one is green and the other one is blueQuantity II: Probability of picking 3 balls such that at least one of them is redQuantity III: Probability of picking 3 balls such that at least one of them is blue1. Quantity III > Quantity I > Quantity II2. Quantity II > Quantity III > Quantity I3. Quantity III > Quantity II > Quantity I4. Quantity I = Quantity II > Quantity III5. Quantity I > Quantity III < Quantity II

Answer» Correct Answer - Option 3 : Quantity III > Quantity II > Quantity I

Quantity I:

Probability of picking 2 tiles such that one is green and the other one is blue

⇒ (6 × 9)/⁵⁰C₂

⇒ 54/(50 × 49/2)

⇒ 54/1225

⇒ 0.044

Quantity II:

Probability of picking 3 balls such that at least one of them is red

⇒ 1 – ⁴⁵C₃/⁵⁰C₃

⇒ 1 – (45 × 44 × 43/3)/(50 × 49 × 48/3)

⇒ 1 – (14190/19600)

⇒ 541/1960

⇒ 0.276

Quantity III:

Probability of picking 3 balls such that at least one of them is blue

⇒ 1 – ⁴¹C₃/⁵⁰C₃

⇒ 1 – (41 × 40 × 39/3)/(50 × 49 × 48/3)

⇒ 1 – (10660/19600)

⇒ 894/1960

⇒ 0.456

Quantity III > Quantity II > Quantity I

Discussion

7338.	All athletes who have taken drugs will be disqualified ______ the race. A) out B) to C) against D) from
Answer» Correct option is D) from

Discussion

7339.	Fill in the blanks to make the statements true.We get additive inverse of an integer a when we multiply it by _________.
Answer» We get additive inverse of an integer a when we multiply it by (-1)

Discussion

7340.	Present age of Ankit is thrice the present age of his son. If 4 years ago the ratio of their age is 13 : 3. What is present age of Ankit?1. 30 years2. 25 years3. 60 years4. 45 years5. 65 years
Answer» Correct Answer - Option 1 : 30 years Given: Present age of Ankit is thrice the present age of his son 4 years ago the ratio of Ankit’s son and Ankit = 3 : 13 Calculation: According to question, Ratio of age of Ankit’s son and Ankit = 1 : 3 Let the age of Ankit’s son and Ankit be x and 3x So, (x - 4)/(3x - 4) = 3/13 13x – 52 = 9x – 12 4x = 40 X = 10 ⇒ Present age of Ankit = 3 × 10 = 30 years

7340.

Present age of Ankit is thrice the present age of his son. If 4 years ago the ratio of their age is 13 : 3. What is present age of Ankit?1. 30 years2. 25 years3. 60 years4. 45 years5. 65 years

Answer» Correct Answer - Option 1 : 30 years

Given:

Present age of Ankit is thrice the present age of his son

4 years ago the ratio of Ankit’s son and Ankit = 3 : 13

Calculation:

According to question,

Ratio of age of Ankit’s son and Ankit = 1 : 3

Let the age of Ankit’s son and Ankit be x and 3x

So, (x - 4)/(3x - 4) = 3/13

13x – 52 = 9x – 12

4x = 40

X = 10

⇒ Present age of Ankit = 3 × 10 = 30 years

Discussion

7341.	Quantity I: In a party, 75% of the total number of female is equal to 50% of the total number of male then the number of female is what percentage of the total number of person in the party? Quantity II: In a school, 66.66% of the total number of girls is equal to 40% of the total number of boys then the total number of girls is what percentage of the total number of students of the school? 1. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2
Answer» Correct Answer - Option 1 : Quantity 1 > Quantity 2 Given: 75% of female = 50% of male 66.66% of girls = 40% of boys Calculation: Quantity I: Let the number of female = x and the number of male = y ⇒ 75% of x = 50% of y ⇒ 3x = 2y ⇒ x : y = 2 : 3 So, if x = number of female = 2a and y = number of boys = 3a ⇒ required % = (2a × 100) / 5a ⇒ required % = 40% Quantity II: Let the number of girls = x and the number of boys = y ⇒ 66.66% of x = 40% of y ⇒ 5x = 3y ⇒ x : y = 3 : 5 So, if x = number of girls = 3a then y = number of boys = 5a ⇒ required, % = 3a × 100 / 8a ⇒ required % ≈ 37% ∴ Quantity I > Quantity II

7341.

Quantity I: In a party, 75% of the total number of female is equal to 50% of the total number of male then the number of female is what percentage of the total number of person in the party? Quantity II: In a school, 66.66% of the total number of girls is equal to 40% of the total number of boys then the total number of girls is what percentage of the total number of students of the school? 1. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2

Answer» Correct Answer - Option 1 : Quantity 1 > Quantity 2

Given:

75% of female = 50% of male

66.66% of girls = 40% of boys

Calculation:

Quantity I:

Let the number of female = x and the number of male = y

⇒ 75% of x = 50% of y

⇒ 3x = 2y

⇒ x : y = 2 : 3

So, if x = number of female = 2a and y = number of boys = 3a

⇒ required % = (2a × 100) / 5a

⇒ required % = 40%

Quantity II:

Let the number of girls = x and the number of boys = y

⇒ 66.66% of x = 40% of y

⇒ 5x = 3y

⇒ x : y = 3 : 5

So, if x = number of girls = 3a then y = number of boys = 5a

⇒ required, % = 3a × 100 / 8a

⇒ required % ≈ 37%

∴ Quantity I > Quantity II

Discussion

7342.	Directions: In the following question, two statements are numbered as Quantity I and Quantity II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.In a mixture of milk and water, the quantity of water is 25% less than the quantity of milk. When 10 liters of pure milk were added then the quantity of milk becomes 60% more than the quantity of water. Quantity I: What is the quantity of water in the mixture?Quantity II: 40 litres1. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2
Answer» Correct Answer - Option 3 : Quantity 1 < Quantity 2 Given: Q water = 25% less than Q milk Calculation: Let the quantity of milk = 100x litres ⇒ Quantity of water = (100 – 25)% of 100x ⇒ 75% of 100x = 75x litres When 10 litres of milk was added then the quantity of milk = 100x + 10 litres and the quantity of water = 75x litres According to the question, ⇒ 160% of 75x = (100x + 10) ⇒ 120x = 100x + 10 ⇒ 20x = 10 ⇒ x = 0.5 litres Quantity I: The quantity of water = 75x ⇒ 75 × 0.5 = 37.5 litres Quantity II = 40 litres ∴ Quantity I < Quantity II

7342.

Directions: In the following question, two statements are numbered as Quantity I and Quantity II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.In a mixture of milk and water, the quantity of water is 25% less than the quantity of milk. When 10 liters of pure milk were added then the quantity of milk becomes 60% more than the quantity of water. Quantity I: What is the quantity of water in the mixture?Quantity II: 40 litres1. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2

Answer» Correct Answer - Option 3 : Quantity 1 < Quantity 2

Given:

Q water = 25% less than Q milk

Calculation:

Let the quantity of milk = 100x litres

⇒ Quantity of water = (100 – 25)% of 100x

⇒ 75% of 100x = 75x litres

When 10 litres of milk was added then the quantity of milk = 100x + 10 litres and the quantity of water = 75x litres

According to the question,

⇒ 160% of 75x = (100x + 10)

⇒ 120x = 100x + 10

⇒ 20x = 10

⇒ x = 0.5 litres

Quantity I:

The quantity of water = 75x

⇒ 75 × 0.5 = 37.5 litres

Quantity II = 40 litres

∴ Quantity I < Quantity II

Discussion

7343.	Directions: In the following question, two statements are numbered as Quantity I and Quantity II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.Quantity I: Amar gave (2/5) of the amount he had to Balram. Balram then gave half of money what he received from Amar to Chandan. If the difference between the remaining amount with Amar and the amount received by Chandan is Rs. 600, how much money did Balram receive from Amar?Quantity II: Rs. 2501. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2
Answer» Correct Answer - Option 1 : Quantity 1 > Quantity 2 Given: Balram = 2/5 amount less than amar Chandan = 1/2 amount less than balram Chandan = Rs. 600 Calculation: Quantity I: Let initially Amar had Rs. x ⇒ Amount received by Balram = Rs. (2x/5) ⇒ Amount remaining with Amar = x – (2x / 5) ⇒ Amount remaining with Amar = Rs. 3x / 5 ⇒ Amount received by chandan = (1 / 2) × (2x / 5) ⇒ Amount received by chandan = Rs. x / 5 ⇒ (3x / 5) – (x / 5) = 600 ⇒ x = 1500 ⇒ Amount received by balram = (2× 1500/5) = Rs. 600 Quantity II : Rs. 250 ∴ Quantity I > Quantity II

7343.

Directions: In the following question, two statements are numbered as Quantity I and Quantity II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.Quantity I: Amar gave (2/5) of the amount he had to Balram. Balram then gave half of money what he received from Amar to Chandan. If the difference between the remaining amount with Amar and the amount received by Chandan is Rs. 600, how much money did Balram receive from Amar?Quantity II: Rs. 2501. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2

Answer» Correct Answer - Option 1 : Quantity 1 > Quantity 2

Given:

Balram = 2/5 amount less than amar

Chandan = 1/2 amount less than balram

Chandan = Rs. 600

Calculation:

Quantity I:

Let initially Amar had Rs. x

⇒ Amount received by Balram = Rs. (2x/5)

⇒ Amount remaining with Amar = x – (2x / 5)

⇒ Amount remaining with Amar = Rs. 3x / 5

⇒ Amount received by chandan = (1 / 2) × (2x / 5)

⇒ Amount received by chandan = Rs. x / 5

⇒ (3x / 5) – (x / 5) = 600

⇒ x = 1500

⇒ Amount received by balram = (2× 1500/5) = Rs. 600

Quantity II : Rs. 250

∴ Quantity I > Quantity II

Discussion

7344.	The efficiency of radha is 50% more than that of shyam. Total work is 240 units.Quantity I: Find the number of days radha alone will take to complete 200% of the work?Quantity II: Find the number of days radha and shyam together will take to complete 50% of the work?1. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2
Answer» Correct Answer - Option 1 : Quantity 1 > Quantity 2 Given: Radha = 50% more efficient then shyam Calculations: The ratio of the efficiency of radha and shyam = 3 : 2 ⇒ The total units of work = 240 units ⇒ the number of days, radha will take = 240 / 3 ⇒ Number of days radha will take = 80 days ⇒ the number of days, shyam will take = 120 (∵ 240/2 = 120) Quantity I: 200% of the work = 200% of 240 ⇒ 480 units The number of days, radha alone will take = 160 days (∵ 480/3 = 160) Quantity II: 50% of the work = 120 units ⇒ The number of days, radha and shyam together will take to complete ⇒ 120 / 5 ⇒ 24 days ∴ Quantity I > Quantity II

7344.

The efficiency of radha is 50% more than that of shyam. Total work is 240 units.Quantity I: Find the number of days radha alone will take to complete 200% of the work?Quantity II: Find the number of days radha and shyam together will take to complete 50% of the work?1. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2

Answer» Correct Answer - Option 1 : Quantity 1 > Quantity 2

Given:

Radha = 50% more efficient then shyam

Calculations:

The ratio of the efficiency of radha and shyam = 3 : 2

⇒ The total units of work = 240 units

⇒ the number of days, radha will take = 240 / 3

⇒ Number of days radha will take = 80 days

⇒ the number of days, shyam will take = 120 (∵ 240/2 = 120)

Quantity I:

200% of the work = 200% of 240

⇒ 480 units

The number of days, radha alone will take = 160 days (∵ 480/3 = 160)

Quantity II:

50% of the work = 120 units

⇒ The number of days, radha and shyam together will take to complete

⇒ 120 / 5

⇒ 24 days

∴ Quantity I > Quantity II

Discussion

7345.	Directions: In the following question, two statements are numbered as Quantity I and Quantity II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.Quantity I: Find the missing term in the series 2, 11, 38, X, 362……Quantity II: Find the value of X, 125% of X = 2501. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2
Answer» Correct Answer - Option 3 : Quantity 1 < Quantity 2 Given: Series = 2, 11, 38, X, 362…… 125% of X = 250 Calculation: Quantity I: 2, 11, 38, X, 362 ⇒ series key = (3 × x) + 5, where x is preceding term ⇒ X = (3 × 38) + 5 ⇒ X = 119 Quantity II: 125% of X = 250 ⇒ (125 / 100) × X = 250 ⇒ 250 × 100 / 125 = X ⇒ X = 200 ∴ Quantity I < Quantity II

7345.

Directions: In the following question, two statements are numbered as Quantity I and Quantity II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.Quantity I: Find the missing term in the series 2, 11, 38, X, 362……Quantity II: Find the value of X, 125% of X = 2501. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2

Answer» Correct Answer - Option 3 : Quantity 1 < Quantity 2

Given:

Series = 2, 11, 38, X, 362……

125% of X = 250

Calculation:

Quantity I:

2, 11, 38, X, 362

⇒ series key = (3 × x) + 5, where x is preceding term

⇒ X = (3 × 38) + 5

⇒ X = 119

Quantity II:

125% of X = 250

⇒ (125 / 100) × X = 250

⇒ 250 × 100 / 125 = X

⇒ X = 200

∴ Quantity I < Quantity II

Discussion

7346.

Pipe P alone can fill a tank in 5 minutes and pipe Q alone can fill it in 4 minutes. Pipe R alone can empty the same tank in 2 minutes. Pipe P and Q are opened together to fill the tank. After 2 minutes, pipe R is also opened. How much time pipe R will take to empty this tank? 1. 18 Minutes2. 15 Minutes3. 12 Minutes4. 20 Minutes

Answer» Correct Answer - Option 1 : 18 Minutes

Given:

Pipe P can fill a tank in 5 minutes

Pipe Q can fill a tank in 4 minutes

Pipe R can empty a tank in 2 minutes

Calculation:

Pipe	Time	Total Work = LCM (5, 4 and 2)	Efficiency(No. of units worked in a day)
P	5		20 ÷ 5 = 4
Q	4	20	20 ÷ 4 = 5
R	(2)		20 ÷ 2 = (10)
P+ Q + (-R)			4 + 5 -10 = (1) Work done by all three pipes in a minute

⇒ Work done by (P + Q) in first 2 minutes = (4 + 5) × 2 = 18 units

⇒ Work done by (P+ Q – R) = 18/(1)

∴ R will take 18 minutes to empty the tank.

The Correct option is 1 i.e. 18 minutes.

Discussion

7347.	A train 300 m long passes a pole in 15 seconds and crosses another train of the same length traveling in the opposite direction in 8 seconds. Calculate the speed of the other train in km/h.1. 200 km/h2. 198 km/h3. 190 km/h4. 222 km/h5. None of the above
Answer» Correct Answer - Option 2 : 198 km/h Length of train = 300 m Time is taken by train to pass a pole = 15 seconds Time taken to cross another train of the same length = 8 seconds Calculations: Speed of the 1^st train = 300/15 = 20 m/s Let the speed of 2^nd train be x Relative speed = (20 + x) m/s Length of 1^st train + length of 2^nd train = 300 + 300 = 600 m In the second scenario the equation is ⇒ 600/(20 + x) = 8 ⇒ 600 = 160 + 8x ⇒ 600 – 160 = 8x ⇒ 440 = 8x ⇒ x = 55 m/s ∴ Speed of the train = 55 × 18/5 = 198 km/h. The speed of the train is 198 km/h.

7347.

A train 300 m long passes a pole in 15 seconds and crosses another train of the same length traveling in the opposite direction in 8 seconds. Calculate the speed of the other train in km/h.1. 200 km/h2. 198 km/h3. 190 km/h4. 222 km/h5. None of the above

Answer» Correct Answer - Option 2 : 198 km/h

Length of train = 300 m

Time is taken by train to pass a pole = 15 seconds

Time taken to cross another train of the same length = 8 seconds

Calculations:

Speed of the 1^st train = 300/15 = 20 m/s

Let the speed of 2^nd train be x

Relative speed = (20 + x) m/s

Length of 1^st train + length of 2^nd train = 300 + 300 = 600 m

In the second scenario the equation is

⇒ 600/(20 + x) = 8

⇒ 600 = 160 + 8x

⇒ 600 – 160 = 8x

⇒ 440 = 8x

⇒ x = 55 m/s

∴ Speed of the train = 55 × 18/5 = 198 km/h.

The speed of the train is 198 km/h.

Discussion

7348.	A train of 210 m length passes a pole in 15 seconds. Find the difference in time for the train to cross the driver and the guard of another train of length 100 m going in the same direction with a speed of 36 km/hr.1. 20 seconds2. 25 seconds3. 30 seconds4. 40 seconds5. 35 seconds
Answer» Correct Answer - Option 2 : 25 seconds Given: The train passes a pole in 15 seconds Length of the train = 210 m Length of second train = 100 m Speed of the second train = 36 km/hr = 10 m/sec Concept: This is a question related to relative velocity. Formula used: Relative speed in same direction = Difference in speeds between the two trains. Calculation: Speed of the first train = 210/15 = 14 m/sec Relative speed between two trains = 14 – 10 = 4 m/sec Time taken for the first train to cross the guard of the second train = 210/4 = 52.5 sec Time taken for the first train to cross the driver of the second train = (210 + 100)/4 = 77.5 sec [In order to cross the driver, the first train has to travel the combined length of both the trains] Difference in time = (77.5 – 52.5) = 25 seconds

7348.

A train of 210 m length passes a pole in 15 seconds. Find the difference in time for the train to cross the driver and the guard of another train of length 100 m going in the same direction with a speed of 36 km/hr.1. 20 seconds2. 25 seconds3. 30 seconds4. 40 seconds5. 35 seconds

Answer» Correct Answer - Option 2 : 25 seconds

Given:

The train passes a pole in 15 seconds

Length of the train = 210 m

Length of second train = 100 m

Speed of the second train = 36 km/hr = 10 m/sec

Concept:

This is a question related to relative velocity.

Formula used:

Relative speed in same direction = Difference in speeds between the two trains.

Calculation:

Speed of the first train = 210/15 = 14 m/sec

Relative speed between two trains = 14 – 10 = 4 m/sec

Time taken for the first train to cross the guard of the second train = 210/4 = 52.5 sec

Time taken for the first train to cross the driver of the second train = (210 + 100)/4 = 77.5 sec

[In order to cross the driver, the first train has to travel the combined length of both the trains]

Difference in time = (77.5 – 52.5) = 25 seconds

Discussion

7349.	Pipe 1 and 2 can fill up the tank in 15 minutes and pipe 3 can drain the tank in 30 minutes.Quantity I: What is the time taken by pipe 1 alone to fill the tank if pipe 2 takes 100% more time than pipe 1?Quantity II: What is time taken to fill the tank when all 3 pipes are open?1. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2
Answer» Correct Answer - Option 3 : Quantity 1 < Quantity 2 Given: Pipe 1 + Pipe 2 = 15 minutes Pipe 3 = 30 minutes Pipe 1 = 2 × pipe 2 Formula used: If t1 and t2 fill up the tank then time taken to fill the tank ⇒ (1/ t) = (1/ t1) + (1/ t2) Calculation: Quantity I: Let time taken by Pipe 1 = X ⇒ Time taken by Pipe 2 = 2X ⇒ (1/ 15) = (1/ X) + (1/ 2X) ⇒ (1/ 15) = (3/ 2X) ⇒ X = 22.5 minutes Quantity II: Total time taken = (1/ 15) – (1/ 30) ⇒ (1/ T) = (1/ 30) ⇒ T = 30 minutes ∴ Quantity I < Quantity II

7349.

Pipe 1 and 2 can fill up the tank in 15 minutes and pipe 3 can drain the tank in 30 minutes.Quantity I: What is the time taken by pipe 1 alone to fill the tank if pipe 2 takes 100% more time than pipe 1?Quantity II: What is time taken to fill the tank when all 3 pipes are open?1. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2

Answer» Correct Answer - Option 3 : Quantity 1 < Quantity 2

Given:

Pipe 1 + Pipe 2 = 15 minutes

Pipe 3 = 30 minutes

Pipe 1 = 2 × pipe 2

Formula used:

If t1 and t2 fill up the tank then time taken to fill the tank ⇒ (1/ t) = (1/ t1) + (1/ t2)

Calculation:

Quantity I:

Let time taken by Pipe 1 = X

⇒ Time taken by Pipe 2 = 2X

⇒ (1/ 15) = (1/ X) + (1/ 2X)

⇒ (1/ 15) = (3/ 2X)

⇒ X = 22.5 minutes

Quantity II:

Total time taken = (1/ 15) – (1/ 30)

⇒ (1/ T) = (1/ 30)

⇒ T = 30 minutes

∴ Quantity I < Quantity II

Discussion

7350.

A train, 150 m long, passes a pole in 15 seconds and another train of the same length travelling in the opposite direction in 10 seconds. The speed of the second train is1. 18 m/s2. 20 km/h3. 10 m/s4. 20 m/s

Answer» Correct Answer - Option 4 : 20 m/s

Given:

Length of train = 150 m

Time taken by train to pass a pole = 15 seconds

Time taken by train to pass the same length of train which are running in the opposite direction = 10 seconds

Formula used:

Distance = speed × time

Concept used:

If the speed of A is x km/h and that of B is y km/h.

then Relative speed of A and B moving in opposite direction = (x + y) km/h.

Calculations:

Let the speed of the second train be x m/s

Speed of the first train = 150/15 = 10 m/s

Relative speed of trains = (x + 10) m/s

Total distance covered = 150 + 150 = 300 metres

so time taken = 300/(x + 10)

According to the question

⇒ 10 = 300/(x + 10)

⇒ 10x + 100 = 300

⇒ 10x = 200

⇒ x = 20

∴ The speed of second train is 20 m/s

Discussion

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