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SAMPLE PAPER FOR PLACEMENT IN ZENSAR
Section-A
| Read the sentence to find out whether there is any grammatical error in it. The error, if any will be in one part of the sentence. The letter of that part is the answer. If there is no error, the answer is ‘D’. (Ignore the errors of punctuation, if any). |
| 1. | (solve as per the direction given above) | | A. | We discussed about the problem so thoroughly | | B. | on the eve of the examination | | C. | that I found it very easy to work it out. | | D. | No error. |
Answer & Explanation Answer: Option A Explanation: We discussed the problem so thoroughly Pick out the most effective word(s) from the given words to fill in the blank to make the sentence meaningfully complete. | 2. The miser gazed …… at the pile of gold coins in front of him. | | A. | avidly | B. | admiringly | | C. | thoughtfully | D. | earnestly |
Answer & Explanation Answer: Option A In the question below, there is a sentence of which some parts have been jumbled up. Rearrange these parts which are labelled P, Q, R and S to produce the correct sentence. Choose the proper sequence. 3. It has been established that| P : | Einstein was | | Q : | although a great scientist | | R : | weak in arithmetic | | S : | right from his school days |
The Proper sequence should be: | Answer & Explanation Answer: Option B |
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4.Even if it rains I shall come means …… |
| A. | if I come it will not rain | | B. | if it rains I shall not come | | C. | I will certainly come whether it rains or not | | D. | whenever there is rain I shall come | | E. | I am less likely to come if it rains |
Answer & Explanation Answer: Option C |
5. Today most businessmen are very worried. To begin with, they are not used to competition.In the past they sold whatever …(1)… produced at whatever prices they chose. But …(2)… increasing competition, customers began to …(3)… and choose. Imports suddenly became …(4)… available and that too at cheaper …(5)…
Some proverbs/idioms are given below together with their meanings. Choose the correct meaning of proverb/idiom, If there is no correct meaning given, E (i.e.) ‘None of these’ will be the answer.
| 6. To make clean breast of |
| A. | To gain prominence | | B. | To praise oneself | | C. | To confess without of reserve | | D. | To destroy before it blooms | | E. | None of these |
Answer & Explanation Answer: Option C
7. To keeps one’s temper | | A. | To become hungry | B. | To be in good mood | | C. | To preserve ones energy | D. | To be aloof from | | E. | None of these | | |
Answer & Explanation Answer: Option B |
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question consist of two words which have a certain relationship to each other followed by four pairs of related words, Select the pair which has the same relationship.
10.I felt the wall of the tunnel shiver. The master alarm squealed through my earphones. Almost simultaneously, Jack yelled down to me that there was a warning light on. Fleeting but spectacular sights snapped into ans out of view, the snow, the shower of debris, the moon, looming close and big, the dazzling sunshine for once unfiltered by layers of air. The last twelve hours before re-entry were particular bone-chilling. During this period, I had to go up in to command module. Even after the fiery re-entry splashing down in 81o water in south pacific, we could still see our frosty breath inside the command module.
| 1. | The word ‘Command Module’ used twice in the given passage indicates perhaps that it deals with |
| A. | an alarming journey | B. | a commanding situation | | C. | a journey into outer space | D. | a frightful battle. |
Answer & Explanation Answer: Option C |
| 2. | Which one of the following reasons would one consider as more as possible for the warning lights to be on? |
| A. | There was a shower of debris. | | B. | Jack was yelling. | | C. | A catastrophe was imminent. | | D. | The moon was looming close and big. |
Answer & Explanation Answer: Option C |
| 3. | The statement that the dazzling sunshine was “for once unfiltered by layers of air” means |
| A. | that the sun was very hot | B. | that there was no strong wind | | C. | that the air was unpolluted | D. | none of above |
Answer & Explanation Answer: Option D |
SECTION B
| A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of: |
Answer & Explanation Answer: Option A Explanation: C.P. = Rs. 3000. S.P. = Rs. | | 3600 x 100 | | = Rs. 3000. | 100 + (10 x 2) |
Gain = 0%. |
| 2. | A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is: |
| A. | 5.15 kmph | B. | 4.14 kmph | | C. | 4.25 kmph | D. | 4.4 kmph |
Answer & Explanation Answer: Option B Explanation: A’s speed = | | 5 x | 5 | m/sec | = | 25 | m/sec. | 18 | 18 |
Time taken by A to cover 100 m = | | 100 x | 18 | sec | = 72 sec. | 25 |
Time taken by B to cover 92 m = (72 + 8) = 80 sec. B’s speed = | | 92 | x | 18 | kmph | = 4.14 kmph. | 80 | 5 | | 3. | A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively? | | A. | 2 : 1 | B. | 3 : 2 | | C. | 8 : 3 | D. | Cannot be determined | | E. | None of these | | |
Answer & Explanation Answer: Option C Explanation: Let the man’s rate upstream be x kmph and that downstream be y kmph. Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs. Required ratio = | | y + x | | : | | y – x | | 2 | 2 |
= 8 : 3. |
| 4. | Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats? | | A. | 2 : 3 : 4 | B. | 6 : 7 : 8 | | C. | 6 : 8 : 9 | D. | None of these |
Answer & Explanation Answer: Option A Explanation: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7xand 8x respectively. Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x). | | 140 | x 5x | | , | | 150 | x 7x | | and | | 175 | x 8x | | 100 | 100 | 100 |
The required ratio = 7x : | 21x | : 14x | 2 |
14x : 21x : 28x 2 : 3 : 4. |
| 5. | The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ? | | A. | Rs. 1200 | B. | Rs. 2400 | | C. | Rs. 4800 | D. | Cannot be determined | | E. | None of these | | |
Answer & Explanation Answer: Option B Explanation: Let the price of a saree and a shirt be Rs. x and Rs. y respectively. Then, 2x + 4y = 1600 …. (i) and x + 6y = 1600 …. (ii) Divide equation (i) by 2, we get the below equation. => x + 2y = 800. — (iii) Now subtract (iii) from (ii) x + 6y = 1600 (-) x + 2y = 800 —————- 4y = 800 —————- Therefore, y = 200. Now apply value of y in (iii) => x + 2 x 200 = 800 => x + 400 = 800 Therefore x = 400 Solving (i) and (ii) we get x = 400, y = 200. Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400. |
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| 6. | The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? |
Answer & Explanation Answer: Option D Explanation: Let the ten’s digit be x and unit’s digit be y. Then, x + y = 15 and x – y = 3 or y – x = 3. Solving x + y = 15 and x – y = 3, we get: x = 9, y = 6. Solving x + y = 15 and y – x = 3, we get: x = 6, y = 9. So, the number is either 96 or 69. Hence, the number cannot be determined. |
| 7. | 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be: |
Answer & Explanation Answer: Option B Explanation: Total volume of water displaced = (4 x 50) m3 = 200 m3. Rise in water level = | | 200 | m 0.25 m = 25 cm. | 40 x 20 |
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| 8. | The angle between the minute hand and the hour hand of a clock when the time is 4.20, is: |
Answer & Explanation Answer: Option B Explanation: Angle traced by hour hand in | 13 | hrs = | | 360 | x | 13 | | º | = 130º. | 3 | 12 | 3 |
Angle traced by min. hand in 20 min. = | | 360 | x 20 | | º | = 120º. | 60 |
Required angle = (130 – 120)º = 10º. |
9 . A student multiplied a number by | 3 | instead of | 5 | . | 5 | 3 |
What is the percentage error in the calculation? |
Answer & Explanation Answer: Option D Explanation: Let the number be x. Then, error = | 5 | x – | 3 | x = | 16 | x. | 3 | 5 | 15 |
Error% = | | 16x | x | 3 | x 100 | % = 64%. | 15 | 5x |
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| 10. | The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is: |
Answer & Explanation Answer: Option D Explanation: Amount of Rs. 100 for 1 year
when compounded half-yearly | | = Rs. | | 100 x | | 1 + | 3 | | 2 | | = Rs. 106.09 | 100 |
Effective rate = (106.09 – 100)% = 6.09% |
| Find the odd man out. |
| 11. | 331, 482, 551, 263, 383, 362, 284 | Answer & Explanation Answer: Option B Explanation: In each number except 383, the product of first and third digits is the middle one. | 12. | A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is: | Answer & Explanation Answer: Option C Explanation: Let S be the sample space. | Then, n(S) | = number of ways of drawing 3 balls out of 15 | | = 15C3 | | = | (15 x 14 x 13) | (3 x 2 x 1) |
| | = 455. |
Let E = event of getting all the 3 red balls. n(E) = 5C3 = 5C2 = | (5 x 4) | = 10. | (2 x 1) |
P(E) = | n(E) | = | 10 | = | 2 | . | n(S) | 455 | 91 |
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| 13. | Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is: | Answer & Explanation Answer: Option D Explanation: Let S be the sample space. Then, n(S) = 52C2 = | (52 x 51) | = 1326. | (2 x 1) |
Let E = event of getting 1 spade and 1 heart. | n(E) | = number of ways of choosing 1 spade out of 13 and 1 heart out of 13 | | = (13C1 x 13C1) | | = (13 x 13) | | = 169. |
P(E) = | n(E) | = | 169 | = | 13 | . | n(S) | 1326 | 102 |
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| 14. | Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in: | Answer & Explanation Answer: Option C Explanation: (A + B)’s 1 hour’s work = | | 1 | + | 1 | | = | 9 | = | 3 | . | 12 | 15 | 60 | 20 |
(A + C)’s hour’s work = | | 1 | + | 1 | | = | 8 | = | 2 | . | 12 | 20 | 60 | 15 |
Part filled in 2 hrs = | | 3 | + | 2 | | = | 17 | . | 20 | 15 | 60 |
Part filled in 6 hrs = | | 3 x | 17 | | = | 17 | . | 60 | 20 |
Remaining part = | | 1 – | 17 | | = | 3 | . | 20 | 20 |
Now, it is the turn of A and B and | 3 | part is filled by A and B in 1 hour. | 20 |
Total time taken to fill the tank = (6 + 1) hrs = 7 hrs. |
| 15. | 72519 x 9999 = ? | | A. | 725117481 | B. | 674217481 | | C. | 685126481 | D. | 696217481 | | E. | None of these | | |
Answer & Explanation Answer: Option A Explanation: | 72519 x 9999 | = 72519 x (10000 – 1) | | = 72519 x 10000 – 72519 x 1 | | = 725190000 – 72519 | | = 725117481. |
| | 16. | If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be: | Answer & Explanation Answer: Option C Explanation: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3. x = 2. | | 17. | Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran’s share in the profit? | | A. | Rs. 9,423 | B. | Rs. 10,250 | | C. | Rs. 12,500 | D. | Rs. 10,500 |
Answer & Explanation Answer: Option D Explanation: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4. Simran’s share = Rs. | | 24500 x | 3 | | = Rs. 10,500. | 7 |
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| 18. | | What is the rate of simple interest? | I. | The total interest earned was Rs. 4000. | II. | The sum was invested for 4 years. |
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| A. | I alone sufficient while II alone not sufficient to answer | | B. | II alone sufficient while I alone not sufficient to answer | | C. | Either I or II alone sufficient to answer | | D. | Both I and II are not sufficient to answer | | E. | Both I and II are necessary to answer |
Answer & Explanation Answer: Option D Explanation: We know that, R = | | 100 x S.I. | | P x T |
Now, I gives, S.I. = Rs. 4000. II gives, T = 4 years. But, P is unknown. So, we cannot find R. So, given data is insufficient to get R. Correct answer is (D). | 19. | How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed? | Answer & Explanation Answer: Option C Explanation: ‘LOGARITHMS’ contains 10 different letters. | Required number of words | = Number of arrangements of 10 letters, taking 4 at a time. | | = 10P4 | | = (10 x 9 x 8 x 7) | | = 5040. |
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| 20. | | What is the length of a running train P crossing another running train Q? | I. | These two trains take 18 seconds to cross each other. | II. | These trains are running in opposite directions. | III. | The length of the train Q is 180 metres. |
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| A. | I only | | B. | II only | | C. | III only | | D. | All I, II and III are required | | E. | Even with I, II and III, the answer cannot be obtained. |
Answer & Explanation Answer: Option E Explanation: Let the length of the train P be x metres. II. These trains are running in opposite directions. III. Length of the train Q is 180 m. I. Time taken by P to cross Q = | (180 + x) | 18 = | (180 + x) | Relative speed | Relative speed |
Thus, even with I, II and III, the answer cannot be obtained. Correct answer is (E). |
SAPLE PAPER FOR PLACEMENT IN ZENSAR
Section-A
| Read the sentence to find out whether there is any grammatical error in it. The error, if any will be in one part of the sentence. The letter of that part is the answer. If there is no error, the answer is ‘D’. (Ignore the errors of punctuation, if any). |
| 1. | (solve as per the direction given above) | | A. | We discussed about the problem so thoroughly | | B. | on the eve of the examination | | C. | that I found it very easy to work it out. | | D. | No error. |
Answer & Explanation Answer: Option A Explanation: We discussed the problem so thoroughly Pick out the most effective word(s) from the given words to fill in the blank to make the sentence meaningfully complete. | 2. The miser gazed …… at the pile of gold coins in front of him. | | A. | avidly | B. | admiringly | | C. | thoughtfully | D. | earnestly |
Answer & Explanation Answer: Option A In the question below, there is a sentence of which some parts have been jumbled up. Rearrange these parts which are labelled P, Q, R and S to produce the correct sentence. Choose the proper sequence. 3. It has been established that| P : | Einstein was | | Q : | although a great scientist | | R : | weak in arithmetic | | S : | right from his school days |
The Proper sequence should be: | Answer & Explanation Answer: Option B |
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4.Even if it rains I shall come means …… |
| A. | if I come it will not rain | | B. | if it rains I shall not come | | C. | I will certainly come whether it rains or not | | D. | whenever there is rain I shall come | | E. | I am less likely to come if it rains |
Answer & Explanation Answer: Option C |
5. Today most businessmen are very worried. To begin with, they are not used to competition.In the past they sold whatever …(1)… produced at whatever prices they chose. But …(2)… increasing competition, customers began to …(3)… and choose. Imports suddenly became …(4)… available and that too at cheaper …(5)…
Some proverbs/idioms are given below together with their meanings. Choose the correct meaning of proverb/idiom, If there is no correct meaning given, E (i.e.) ‘None of these’ will be the answer.
| 6. To make clean breast of |
| A. | To gain prominence | | B. | To praise oneself | | C. | To confess without of reserve | | D. | To destroy before it blooms | | E. | None of these |
Answer & Explanation Answer: Option C
7. To keeps one’s temper | | A. | To become hungry | B. | To be in good mood | | C. | To preserve ones energy | D. | To be aloof from | | E. | None of these | | |
Answer & Explanation Answer: Option B |
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question consist of two words which have a certain relationship to each other followed by four pairs of related words, Select the pair which has the same relationship.
10.I felt the wall of the tunnel shiver. The master alarm squealed through my earphones. Almost simultaneously, Jack yelled down to me that there was a warning light on. Fleeting but spectacular sights snapped into ans out of view, the snow, the shower of debris, the moon, looming close and big, the dazzling sunshine for once unfiltered by layers of air. The last twelve hours before re-entry were particular bone-chilling. During this period, I had to go up in to command module. Even after the fiery re-entry splashing down in 81o water in south pacific, we could still see our frosty breath inside the command module.
| 1. | The word ‘Command Module’ used twice in the given passage indicates perhaps that it deals with |
| A. | an alarming journey | B. | a commanding situation | | C. | a journey into outer space | D. | a frightful battle. |
Answer & Explanation Answer: Option C |
| 2. | Which one of the following reasons would one consider as more as possible for the warning lights to be on? |
| A. | There was a shower of debris. | | B. | Jack was yelling. | | C. | A catastrophe was imminent. | | D. | The moon was looming close and big. |
Answer & Explanation Answer: Option C |
| 3. | The statement that the dazzling sunshine was “for once unfiltered by layers of air” means |
| A. | that the sun was very hot | B. | that there was no strong wind | | C. | that the air was unpolluted | D. | none of above |
Answer & Explanation Answer: Option D |
SECTION B
| A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of: |
Answer & Explanation Answer: Option A Explanation: C.P. = Rs. 3000. S.P. = Rs. | | 3600 x 100 | | = Rs. 3000. | 100 + (10 x 2) |
Gain = 0%. |
| 2. | A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is: |
| A. | 5.15 kmph | B. | 4.14 kmph | | C. | 4.25 kmph | D. | 4.4 kmph |
Answer & Explanation Answer: Option B Explanation: A’s speed = | | 5 x | 5 | m/sec | = | 25 | m/sec. | 18 | 18 |
Time taken by A to cover 100 m = | | 100 x | 18 | sec | = 72 sec. | 25 |
Time taken by B to cover 92 m = (72 + 8) = 80 sec. B’s speed = | | 92 | x | 18 | kmph | = 4.14 kmph. | 80 | 5 | | 3. | A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively? | | A. | 2 : 1 | B. | 3 : 2 | | C. | 8 : 3 | D. | Cannot be determined | | E. | None of these | | |
Answer & Explanation Answer: Option C Explanation: Let the man’s rate upstream be x kmph and that downstream be y kmph. Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs. Required ratio = | | y + x | | : | | y – x | | 2 | 2 |
= 8 : 3. |
| 4. | Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats? | | A. | 2 : 3 : 4 | B. | 6 : 7 : 8 | | C. | 6 : 8 : 9 | D. | None of these |
Answer & Explanation Answer: Option A Explanation: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7xand 8x respectively. Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x). | | 140 | x 5x | | , | | 150 | x 7x | | and | | 175 | x 8x | | 100 | 100 | 100 |
The required ratio = 7x : | 21x | : 14x | 2 |
14x : 21x : 28x 2 : 3 : 4. |
| 5. | The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ? | | A. | Rs. 1200 | B. | Rs. 2400 | | C. | Rs. 4800 | D. | Cannot be determined | | E. | None of these | | |
Answer & Explanation Answer: Option B Explanation: Let the price of a saree and a shirt be Rs. x and Rs. y respectively. Then, 2x + 4y = 1600 …. (i) and x + 6y = 1600 …. (ii) Divide equation (i) by 2, we get the below equation. => x + 2y = 800. — (iii) Now subtract (iii) from (ii) x + 6y = 1600 (-) x + 2y = 800 —————- 4y = 800 —————- Therefore, y = 200. Now apply value of y in (iii) => x + 2 x 200 = 800 => x + 400 = 800 Therefore x = 400 Solving (i) and (ii) we get x = 400, y = 200. Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400. |
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| 6. | The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? |
Answer & Explanation Answer: Option D Explanation: Let the ten’s digit be x and unit’s digit be y. Then, x + y = 15 and x – y = 3 or y – x = 3. Solving x + y = 15 and x – y = 3, we get: x = 9, y = 6. Solving x + y = 15 and y – x = 3, we get: x = 6, y = 9. So, the number is either 96 or 69. Hence, the number cannot be determined. |
| 7. | 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be: |
Answer & Explanation Answer: Option B Explanation: Total volume of water displaced = (4 x 50) m3 = 200 m3. Rise in water level = | | 200 | m 0.25 m = 25 cm. | 40 x 20 |
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| 8. | The angle between the minute hand and the hour hand of a clock when the time is 4.20, is: |
Answer & Explanation Answer: Option B Explanation: Angle traced by hour hand in | 13 | hrs = | | 360 | x | 13 | | º | = 130º. | 3 | 12 | 3 |
Angle traced by min. hand in 20 min. = | | 360 | x 20 | | º | = 120º. | 60 |
Required angle = (130 – 120)º = 10º. |
9 . A student multiplied a number by | 3 | instead of | 5 | . | 5 | 3 |
What is the percentage error in the calculation? |
Answer & Explanation Answer: Option D Explanation: Let the number be x. Then, error = | 5 | x – | 3 | x = | 16 | x. | 3 | 5 | 15 |
Error% = | | 16x | x | 3 | x 100 | % = 64%. | 15 | 5x |
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| 10. | The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is: |
Answer & Explanation Answer: Option D Explanation: Amount of Rs. 100 for 1 year
when compounded half-yearly | | = Rs. | | 100 x | | 1 + | 3 | | 2 | | = Rs. 106.09 | 100 |
Effective rate = (106.09 – 100)% = 6.09% |
| Find the odd man out. |
| 11. | 331, 482, 551, 263, 383, 362, 284 | Answer & Explanation Answer: Option B Explanation: In each number except 383, the product of first and third digits is the middle one. | 12. | A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is: | Answer & Explanation Answer: Option C Explanation: Let S be the sample space. | Then, n(S) | = number of ways of drawing 3 balls out of 15 | | = 15C3 | | = | (15 x 14 x 13) | (3 x 2 x 1) |
| | = 455. |
Let E = event of getting all the 3 red balls. n(E) = 5C3 = 5C2 = | (5 x 4) | = 10. | (2 x 1) |
P(E) = | n(E) | = | 10 | = | 2 | . | n(S) | 455 | 91 |
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| 13. | Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is: | Answer & Explanation Answer: Option D Explanation: Let S be the sample space. Then, n(S) = 52C2 = | (52 x 51) | = 1326. | (2 x 1) |
Let E = event of getting 1 spade and 1 heart. | n(E) | = number of ways of choosing 1 spade out of 13 and 1 heart out of 13 | | = (13C1 x 13C1) | | = (13 x 13) | | = 169. |
P(E) = | n(E) | = | 169 | = | 13 | . | n(S) | 1326 | 102 |
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| 14. | Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in: | Answer & Explanation Answer: Option C Explanation: (A + B)’s 1 hour’s work = | | 1 | + | 1 | | = | 9 | = | 3 | . | 12 | 15 | 60 | 20 |
(A + C)’s hour’s work = | | 1 | + | 1 | | = | 8 | = | 2 | . | 12 | 20 | 60 | 15 |
Part filled in 2 hrs = | | 3 | + | 2 | | = | 17 | . | 20 | 15 | 60 |
Part filled in 6 hrs = | | 3 x | 17 | | = | 17 | . | 60 | 20 |
Remaining part = | | 1 – | 17 | | = | 3 | . | 20 | 20 |
Now, it is the turn of A and B and | 3 | part is filled by A and B in 1 hour. | 20 |
Total time taken to fill the tank = (6 + 1) hrs = 7 hrs. |
| 15. | 72519 x 9999 = ? | | A. | 725117481 | B. | 674217481 | | C. | 685126481 | D. | 696217481 | | E. | None of these | | |
Answer & Explanation Answer: Option A Explanation: | 72519 x 9999 | = 72519 x (10000 – 1) | | = 72519 x 10000 – 72519 x 1 | | = 725190000 – 72519 | | = 725117481. |
| | 16. | If the number 517 * 324 is completely divisible by 3, then the smallest whole number in the place of * will be: | Answer & Explanation Answer: Option C Explanation: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3. x = 2. | | 17. | Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran’s share in the profit? | | A. | Rs. 9,423 | B. | Rs. 10,250 | | C. | Rs. 12,500 | D. | Rs. 10,500 |
Answer & Explanation Answer: Option D Explanation: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4. Simran’s share = Rs. | | 24500 x | 3 | | = Rs. 10,500. | 7 |
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| 18. | | What is the rate of simple interest? | I. | The total interest earned was Rs. 4000. | II. | The sum was invested for 4 years. |
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| A. | I alone sufficient while II alone not sufficient to answer | | B. | II alone sufficient while I alone not sufficient to answer | | C. | Either I or II alone sufficient to answer | | D. | Both I and II are not sufficient to answer | | E. | Both I and II are necessary to answer |
Answer & Explanation Answer: Option D Explanation: We know that, R = | | 100 x S.I. | | P x T |
Now, I gives, S.I. = Rs. 4000. II gives, T = 4 years. But, P is unknown. So, we cannot find R. So, given data is insufficient to get R. Correct answer is (D). | 19. | How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed? | Answer & Explanation Answer: Option C Explanation: ‘LOGARITHMS’ contains 10 different letters. | Required number of words | = Number of arrangements of 10 letters, taking 4 at a time. | | = 10P4 | | = (10 x 9 x 8 x 7) | | = 5040. |
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| 20. | | What is the length of a running train P crossing another running train Q? | I. | These two trains take 18 seconds to cross each other. | II. | These trains are running in opposite directions. | III. | The length of the train Q is 180 metres. |
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| A. | I only | | B. | II only | | C. | III only | | D. | All I, II and III are required | | E. | Even with I, II and III, the answer cannot be obtained. |
Answer & Explanation Answer: Option E Explanation: Let the length of the train P be x metres. II. These trains are running in opposite directions. III. Length of the train Q is 180 m. I. Time taken by P to cross Q = | (180 + x) | 18 = | (180 + x) | Relative speed | Relative speed |
Thus, even with I, II and III, the answer cannot be obtained. Correct answer is (E). |
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