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CMAT Mock Test - 1 (New Pattern) - CAT MCQ


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30 Questions MCQ Test - CMAT Mock Test - 1 (New Pattern)

CMAT Mock Test - 1 (New Pattern) for CAT 2024 is part of CAT preparation. The CMAT Mock Test - 1 (New Pattern) questions and answers have been prepared according to the CAT exam syllabus.The CMAT Mock Test - 1 (New Pattern) MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CMAT Mock Test - 1 (New Pattern) below.
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CMAT Mock Test - 1 (New Pattern) - Question 1

Directions: In the following question, out of the given four alternatives, select the one which is opposite in meaning of the given word.

Aggrandize

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 1
'Aggrandize' means 'to make someone more powerful or important' whereas 'belittle' means 'to make a person seem as if he or she is not important.'

So, option 4 is the antonym of the given word.

CMAT Mock Test - 1 (New Pattern) - Question 2

Directions: In the following question, some part of the sentence may have errors. Find out which part of the sentence has an error and select the appropriate option. If a sentence is free from error, select 'No Error'.

The Delhi Police organize a mega (1)/ function at the Thayagaraj Stadium (2)/ to promote 'self defence training' for women and girls. (3)/ No error (4)

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 2
A past event is being described. So, past tense should be used. Replace 'organize' with 'organized'.
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CMAT Mock Test - 1 (New Pattern) - Question 3

Directions: The question below consists of a set of labelled sentences. These sentences, when properly sequenced form a coherent paragraph. Select the most logical order of sentences from among the options.

P: The leaders I admire most are the ones who give selflessly of themselves and make personal development a priority.

Q: Both are important and one without the other does not work as I have observed some of the great leaders, I find they all have some things in common.

R: Great leaders balance personal development and organizational development.

S: I can not give of myself as a leader if I do not first take care of myself.

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 3
In P, the author says that he admires the leaders 'who give selflessly of themselves' and in S it is mentioned that 'I can not give of myself as a leader ...', so we can draw the inference that P is followed by S, because the idea in sentence P continues in sentence S. The only option which has P and S together (in this order) is 3. So, it is the correct answer.
CMAT Mock Test - 1 (New Pattern) - Question 4

Directions: Read the passage given below and answer the question that follows by selecting the most appropriate option.

Adversity provides us with an opportunity to develop our character in a natural, recurring and powerful way that only the challenges of adversity offer. According to Solomon, adversity refines and reveals the gold and silver of our character.

A lot of times adversity comes our way as a direct or indirect result of our own actions. We make a bad choice or a bad decision, or we simply fail to do something we should have done. When I made bad investment decisions, I had to accept responsibility for my greed and naive choices. Yes, several men had misrepresented the opportunities to me but the fact is, I am the one who made the decisions. And I experienced the very consequences that Solomon had cautioned us about. Any time you make a contribution to your own adversity, you need to accept responsibility for it. Don't simply blame someone or something else.

Nonetheless, throughout our lives we will experience a great deal of adversity that is not a result of our own actions. It is critically important that we do not assign fault to ourselves or to those who had nothing to do with it. When a friend of mine lost his daughter to leukemia, he confided in me that he felt God was punishing him for his past sins. In other words, he was blaming himself. It is believed that adversity sometimes has a purpose that we cannot know or understand. As tempting as it may be to try to figure out such a mystery is not only an exercise in futility, it is foolish also.

Q. The author quotes Solomon to

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 4
The line 'According to Solomon, adversity refines and reveals the gold and silver of our character' indicates that the author is quoting Solomon as an authority. This indicates the author is quoting Solomon to add force to his statement.
CMAT Mock Test - 1 (New Pattern) - Question 5

Directions: In the following question, some part of the sentence may have errors. Find out which part of the sentence has an error and select the appropriate option. If a sentence is free from error, select 'No Error'.

With God's blessings and hard work, (1)/ I cleared many hurdles in life and did (2)/ reasonable with both professional and personally well. (3)/ No error (4)

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 5
The adverb form 'reasonably' should be used as it modifies the verb 'did'. 'With' is redundant. To maintain parallelism with 'personally' correct form will be 'professionally'. So, correct phrase will be 'did reasonably well both professionally and personally'.
CMAT Mock Test - 1 (New Pattern) - Question 6

Directions: Choose the phrase from the phrases (1), (2) and (3) that should replace the phrase given in bold in the following sentence to make the sentence grammatically meaningful and correct. If the sentence is correct as it is and no correction is required, mark (4) as the answer.

This necessitated regular keep-up and maintenance of the aircraft.

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 6
The context of the sentence suggests the necessity for keeping the aircraft in good condition. So, up-keep which means 'the process of keeping something in good condition', makes the sentence grammatically correct.

Therefore, option 3 is the correct answer.

CMAT Mock Test - 1 (New Pattern) - Question 7

Directions: In the following question, out of the given four alternatives, select the one which best expresses the meaning of the given word.

Bereft

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 7
'Bereft' means 'deprived of or lacking something.'

'Deprived' also means 'lacking something which is necessary.'

So, option 2 is the correct answer.

CMAT Mock Test - 1 (New Pattern) - Question 8

Directions: Read the given passage and answer the question that follows.

"Vibrant salads, wholesome bites, vegan baking, all vegetarian!" Thus proclaimed a billboard on a stand placed just outside The Lighthouse Cafe. Well, well, well, I thought to myself, another one of those places designed to attract tourists; can't be genuine, can it? I couldn't have been more wrong. I'd embarked on a walking tour of Galway, a city facing the Atlantic, in the Republic of Ireland, and my guide was Billy Murray who told me at the outset that I would be the solitary walker – others had stayed away because of the dismal weather. The weather had indeed been unfriendly, with beating rain, thunder, poor visibility and of course, gray and cold, especially on the Wild Atlantic Way where I had braved the weather and carried on with a coach tour I'd booked earlier, after having spent the previous day driving down to Galway from Dublin.

But today the rains had stopped and the sky was clear but still gray and yet, I found the ambience rather romantic and full of promise.

"Of course, we'll go on that walking tour," I said to a surprised Billy who led me out of the Tourist Centre in downtown Galway and onto the rain-washed street. At the end of the rather comprehensive tour I asked Billy for advice – where should I eat my lunch? And he'd recommended the Lighthouse Cafe near Lynch's Castle (now a bank) when I specified that I was vegetarian.

It seems there are quite a few local residents who are vegetarian and more are exploring this choice, mainly because of health and environmental reasons. But the decor inside the restaurant suggested that the owner turned to this choice due to compassion. I remembered then that Billy did mention that Kerry Legh and her spouse, who run the place, practise Sahaj Marga meditation. The lotus flower was a dominant feature of the restaurant's interior. Be that as it may, my lunch turned out to be one of the best vegetarian ones I've ever had anywhere in the world. When I'd entered the restaurant, a large dog that answers to the name of 'Chieftain' was seated beside his owner, intently watching him eat, without begging even once. Maybe they too practise some kind of meditation, I figured.

Q. Why was the author considered as solitary walker in Galway by the guide Billy Murray?

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 8
The following sentences, '... my guide was Billy Murray who told me at the outset that I would be the solitary walker – others had stayed away because of the dismal weather. The weather had indeed been unfriendly, with beating rain, thunder, poor visibility and of course, gray and cold ...' indicate the correct answer.

Hence, option 1 is the correct choice.

CMAT Mock Test - 1 (New Pattern) - Question 9

Directions: Read the given passage and answer the question that follows.

"Vibrant salads, wholesome bites, vegan baking, all vegetarian!" Thus proclaimed a billboard on a stand placed just outside The Lighthouse Cafe. Well, well, well, I thought to myself, another one of those places designed to attract tourists; can't be genuine, can it? I couldn't have been more wrong. I'd embarked on a walking tour of Galway, a city facing the Atlantic, in the Republic of Ireland, and my guide was Billy Murray who told me at the outset that I would be the solitary walker – others had stayed away because of the dismal weather. The weather had indeed been unfriendly, with beating rain, thunder, poor visibility and of course, gray and cold, especially on the Wild Atlantic Way where I had braved the weather and carried on with a coach tour I'd booked earlier, after having spent the previous day driving down to Galway from Dublin.

But today the rains had stopped and the sky was clear but still gray and yet, I found the ambience rather romantic and full of promise.

"Of course, we'll go on that walking tour," I said to a surprised Billy who led me out of the Tourist Centre in downtown Galway and on to the rain-washed street. At the end of the rather comprehensive tour I asked Billy for advice – where should I eat my lunch? And he'd recommended the Lighthouse Cafe near Lynch's Castle (now a bank) when I specified that I was vegetarian.

It seems there are quite a few local residents who are vegetarian and more are exploring this choice, mainly because of health and environmental reasons. But the decor inside the restaurant suggested that the owner turned to this choice due to compassion. I remembered then that Billy did mention that Kerry Legh and her spouse, who run the place, practise Sahaj Marga meditation. The lotus flower was a dominant feature of the restaurant's interior. Be that as it may, my lunch turned out to be one of the best vegetarian ones I've ever had anywhere in the world. When I'd entered the restaurant, a large dog that answers to the name of 'Chieftain' was seated beside his owner, intently watching him eat, without begging even once. Maybe they too practise some kind of meditation, I figured.

Q. Why was just Lighthouse Cafe recommended to the author to have lunch at?

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 9
Only the Lighthouse Cafe was recommended to the author since it served vegetarian food and the author was also a vegetarian.

The passage states, 'Vibrant salads, wholesome bites, vegan baking, all vegetarian!' Thus proclaimed a billboard' and '... he'd recommended the Lighthouse Cafe near Lynch's Castle (now a bank) when I specified that I was vegetarian'.

Hence, option 4 is the correct answer.

CMAT Mock Test - 1 (New Pattern) - Question 10

Directions: Choose the phrase from the phrases (1), (2) and (3) that should replace the phrase given in bold in the following sentence to make the sentence grammatically meaningful and correct. If the sentence is correct as it is and no correction is required, mark (4) as the answer.

Implementing it wisely, the national education policy will benefit all the sections of the society.

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 10
The clause preceding the comma ought to be complete in itself, even if it is conditional. Only (2) does it. Therefore, option 2 is the correct answer.
CMAT Mock Test - 1 (New Pattern) - Question 11

Directions: The sentence below has two blanks, each blank indicating that something has been omitted. The sentence is followed by four sets of words. Choose the set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.

The ground reality demanded _______ administrative measures which were being ______ due to variety of reasons.

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 11
The context of the sentence suggests that the ground reality demanded tough measures which were opposed due to variety of reasons. So, accordingly option 2 is best suited. Rest of the options do not fit the given sentence.
CMAT Mock Test - 1 (New Pattern) - Question 12

Directions: The sentence has two blanks, each blank indicating that something has been omitted. Choose the set of words for the blanks which best fits the meaning of the sentence as a whole.

As night _____ and fog covered the land, Ramesh could not ______ anything.

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 12
The use of 'night' and 'fog' indicate nothing could be seen. With 'night', the verb 'fell' is the correct usage. So, option 1 is correct.
CMAT Mock Test - 1 (New Pattern) - Question 13

Directions: Read the passage given below and answer the question that follows by selecting the most appropriate option.

Adversity provides us with an opportunity to develop our character in a natural, recurring and powerful way that only the challenges of adversity offer. According to Solomon, adversity refines and reveals the gold and silver of our character.

A lot of times adversity comes our way as a direct or indirect result of our own actions. We make a bad choice or a bad decision, or we simply fail to do something we should have done. When I made bad investment decisions, I had to accept responsibility for my greed and naive choices. Yes, several men had misrepresented the opportunities to me but the fact is, I am the one who made the decisions. And I experienced the very consequences that Solomon had cautioned us about. Any time you make a contribution to your own adversity, you need to accept responsibility for it. Don't simply blame someone or something else.

Nonetheless, throughout our lives we will experience a great deal of adversity that is not a result of our own actions. It is critically important that we do not assign fault to ourselves or to those who had nothing to do with it. When a friend of mine lost his daughter to leukemia, he confided in me that he felt God was punishing him for his past sins. In other words, he was blaming himself. It is believed that adversity sometimes has a purpose that we cannot know or understand. As tempting as it may be to try to figure out such a mystery is not only an exercise in futility, it is foolish also.

Q. Adversity provides us with an opportunity to

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 13
The passage states, 'Adversity provides us with an opportunity to develop our character in a natural, recurring and powerful way that only the challenges of adversity offer.'
CMAT Mock Test - 1 (New Pattern) - Question 14

Directions: Read the passage given below and answer the question that follows by selecting the most appropriate option.

Adversity provides us with an opportunity to develop our character in a natural, recurring and powerful way that only the challenges of adversity offer. According to Solomon, adversity refines and reveals the gold and silver of our character.

A lot of times adversity comes our way as a direct or indirect result of our own actions. We make a bad choice or a bad decision, or we simply fail to do something we should have done. When I made bad investment decisions, I had to accept responsibility for my greed and naive choices. Yes, several men had misrepresented the opportunities to me but the fact is, I am the one who made the decisions. And I experienced the very consequences that Solomon had cautioned us about. Any time you make a contribution to your own adversity, you need to accept responsibility for it. Don't simply blame someone or something else.

Nonetheless, throughout our lives we will experience a great deal of adversity that is not a result of our own actions. It is critically important that we do not assign fault to ourselves or to those who had nothing to do with it. When a friend of mine lost his daughter to leukemia, he confided in me that he felt God was punishing him for his past sins. In other words, he was blaming himself. It is believed that adversity sometimes has a purpose that we cannot know or understand. As tempting as it may be to try to figure out such a mystery is not only an exercise in futility, it is foolish also.

Q. Most often our misfortunes are the result of our own

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 14
The first sentence of the second paragraph states, 'A lot of times adversity comes our way as a direct or indirect result of our own actions.'
CMAT Mock Test - 1 (New Pattern) - Question 15

Directions: The sentence below has two blanks, each blank indicating that something has been omitted. The sentence is followed by four sets of words. Choose the set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.

He absorbed the communist _________ of an ideal society where the lowliest peasants would enjoy ______ prosperity.

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 15
The thought of 'lowliest peasant enjoying prosperity' is 'utopian'. So, the answer is (2). Rest of the options do not fit the sentence.
CMAT Mock Test - 1 (New Pattern) - Question 16

Directions: The sentence below has two blanks, each blank indicating that something has been omitted. Beneath the sentence are four sets of words labelled (1) to (4). Choose the set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.

The government adopted a ________ attitude towards telecom operators who were ______ to clear all their dues before the year end.

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 16
This option fits the best in the context of the sentence. Servile/Obsequious does not fit as government would not be servile to operators who are opposed to paying their dues. Strict does not fit with 'willing'. 'Lenient' would fit as government could show some relaxation till year end. The context indicates the operators were unwilling to pay before the year end. This means they would pay later. So, leniency can fit.
CMAT Mock Test - 1 (New Pattern) - Question 17

Directions: In the following question, some part of the sentence may have errors. Find out which part of the sentence has an error and select the appropriate option. If a sentence is free from error, select 'No Error'.

All they need to do is feed their contact (1)/ details, feed the IMEI number to receiving (2)/ an OTP on their mobile. (3)/ No error (4)

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 17
After 'to' base form of verb is generally used. So, correct phrase will be 'to receive'.
CMAT Mock Test - 1 (New Pattern) - Question 18

Directions: Read the given passage and answer the question that follows.

"Vibrant salads, wholesome bites, vegan baking, all vegetarian!" Thus proclaimed a billboard on a stand placed just outside The Lighthouse Cafe. Well, well, well, I thought to myself, another one of those places designed to attract tourists; can't be genuine, can it? I couldn't have been more wrong. I'd embarked on a walking tour of Galway, a city facing the Atlantic, in the Republic of Ireland, and my guide was Billy Murray who told me at the outset that I would be the solitary walker – others had stayed away because of the dismal weather. The weather had indeed been unfriendly, with beating rain, thunder, poor visibility and of course, gray and cold, especially on the Wild Atlantic Way where I had braved the weather and carried on with a coach tour I'd booked earlier, after having spent the previous day driving down to Galway from Dublin.

But today the rains had stopped and the sky was clear but still gray and yet, I found the ambience rather romantic and full of promise.

"Of course, we'll go on that walking tour," I said to a surprised Billy who led me out of the Tourist Centre in downtown Galway and on to the rain-washed street. At the end of the rather comprehensive tour I asked Billy for advice – where should I eat my lunch? And he'd recommended the Lighthouse Cafe near Lynch's Castle (now a bank) when I specified that I was vegetarian.

It seems there are quite a few local residents who are vegetarian and more are exploring this choice, mainly because of health and environmental reasons. But the decor inside the restaurant suggested that the owner turned to this choice due to compassion. I remembered then that Billy did mention that Kerry Legh and her spouse, who run the place, practise Sahaj Marga meditation. The lotus flower was a dominant feature of the restaurant's interior. Be that as it may, my lunch turned out to be one of the best vegetarian ones I've ever had anywhere in the world. When I'd entered the restaurant, a large dog that answers to the name of 'Chieftain' was seated beside his owner, intently watching him eat, without begging even once. Maybe they too practise some kind of meditation, I figured.

Q. What kind of nature is reflected of the author from the first line of the second para of the passage?

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 18
Even though the sky was gray, the author found the atmosphere (ambience) 'romantic and full of promise.' This suggests that option 1 is the correct answer.

Options 2 and 3 do not fit with the rest of the passage. Option 4 uses 'always' which is too extreme.

CMAT Mock Test - 1 (New Pattern) - Question 19

Directions: Four alternatives are given for the idiom/phrase underlined in the sentence. Choose the alternative which best expresses the meaning of the idiom/phrase.

They have latched on to tourism as a way of boosting the local economy.

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 19
'To latch on to something' means 'to become involved in something; indulged'.

Thus, option (1) is the correct answer.

CMAT Mock Test - 1 (New Pattern) - Question 20

Directions: In the following question, some part of the sentence may have errors. Find out which part of the sentence has an error and select the appropriate option. If a sentence is free from error, select 'No Error'.

So, the next time you are eating sushi, (1)/ you exactly know what to do with (2)/ that extra wasabi that have come along. (3)/ No error (4)

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 20
'That' refers to 'wasabi' which is singular. So, 'has' will be used instead of 'have'.
CMAT Mock Test - 1 (New Pattern) - Question 21

The number of ways in which 5 beads of different colours form a necklace is

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 21
If we have n beads of different colours and we have to make a necklace, then the beads can be arranged in (n - 1)! ways. In case of a necklace there is no difference between clockwise and anticlockwise arrangement, so the number of necklaces that can be formed from n beads of different colours is

Hence, the number of necklaces that can be formed = = 12

CMAT Mock Test - 1 (New Pattern) - Question 22

Given below are two statements.

Statement 1: Rahul threw two dice simultaneously. The total on two dice is 6. The probability of this is ⅙.

Statement 2: Rohan threw two dice simultaneously. The probability of getting at least one 6 is 11/36.

Which of the following options is correct?

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 22
Statement 1

Total possible number of outcomes of 2 dice = 36

Outcomes which have a total of 6 are:

(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)

Total number of outcomes which have a total of 6 = 5

Probability of outcomes which have sum 6 = Total number of outcomes which have ∑6/Total possible number of outcomes of 2 dice = 5/36

So, statement 1 is false.

Statement 2

Total possible number of outcomes of 2 dice = 36

Outcomes which have at least one 6 are:

(1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)

Total number of outcomes which have at least one 6 = 11Probability of outcomes which have sum 6 = Total number of outcomes which have at least one 6/Total possible number of outcomes of 2 dice

= 11/36

So, statement 2 is true.

CMAT Mock Test - 1 (New Pattern) - Question 23

If a : b = 3 : 2, then (5a + 2b) : (3a + 4b) is equal to:

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 23
a : b = 3 : 2

Then, (5a + 2b) : (3a + 4b)

a/b = 3/2

So, a = 3 and b = 2

(5 × 3 + 2 × 2) : (3 × 3 + 4 × 2)

= 19 : 17

CMAT Mock Test - 1 (New Pattern) - Question 24

The difference between the compound interest and simple interest on Rs. x at 9% per annum for 2 years is Rs. 20.25. What is the value of x?

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 24
Let x be P (principal amount).

Compound interest =

Compound interest =

Simple interest =

Compound interest - Simple interest = 20.25

0.1881P - 0.18P = 20.25

0.0081P = 20.25

P = 20.25/0.0081 = 2500

The value of x is 2500.

CMAT Mock Test - 1 (New Pattern) - Question 25

Mahesh invested an amount of Rs. 25,000 and started a business. Rocky joined him after six month with an amount of Rs. 40,000. After two years from starting the business, they earned the profit of Rs. 55,000. What will be Mahesh share in the profit?

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 25
Mahesh investment in the business = 25,000 x 24 = Rs. 6,00,000

Rocky investment in the business = 40,000 x 18 = Rs. 7,20,000

Ratio of share of Mahesh and Rocky in the business = 6,00,000 : 7,20,000 = 5 : 6

Hence, share of profit of Mahesh in the business = (5/11) x 55,000 = Rs. 25,000

CMAT Mock Test - 1 (New Pattern) - Question 26

In an isosceles triangle ABC, AB = AC. The exterior angle made at vertex A is 140°. Find the angle opposite to the unequal side of the triangle.

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 26

From the figure above, it is clear that sum of B and C is 140°.

Hence, A = 180° - 140° = 40°

CMAT Mock Test - 1 (New Pattern) - Question 27

An article is sold for Rs. 680 after two successive discounts of 20% and x% on its marked price. The marked price of the article is Rs. 1000. What is the value of x?

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 27
Marked price of the article = Rs. 1000

Selling price of article = Rs. 680

Discounts = 20% and x%

After allowing 20% discount on Rs. 1000, we get

(20/100) × 1000 = 200

New price = 1000 - 200 = 800

Now, 800 - 680 = 120

⇒ (120/800) × 100 = 15%

CMAT Mock Test - 1 (New Pattern) - Question 28

The dimensions of a rectangular block are in the ratio 4 : 2 : 1. Its volume is 27,000 dm3. Find the cost of polishing the entire surface, at the rate of 3 cents per dm2.

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 28
Let the dimensions be 4x, 2x and x, respectively.

Volume = 27,000

⇒ 4x 2x x = 27,000

⇒ 8x3 = 27,000

⇒ x3 = 27,000/8

⇒ x = 15 dm

So, the dimensions are 60 dm, 30 dm and 15 dm.

Surface area = 2(60 30 + 30 15 + 15 60) dm2 = 2(1800 + 450 + 900) = 2 3150 = 6300 dm2

Cost of polishing = $(3/100) x 6300 = $189

CMAT Mock Test - 1 (New Pattern) - Question 29

The table shows the production of different types of cars (in thousands).

What is the ratio of the total production of type C and type D cars in 2012 to the total production of type A cars in 2014 and type E cars in 2015?

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 29
Total production of type C and type D cars in 2012 = 43 + 47 = 90 thousand

Total production of type A cars in 2014 = 56 thousand

Total production of type E cars in 2015 = 64 thousand

Total production of type A and type E cars in 2014 and 2015, respectively = 56 + 64 = 120 thousand

Required ratio = 90 thousand : 120 thousand = 3 : 4

CMAT Mock Test - 1 (New Pattern) - Question 30

If a2 + b2 + c2 = 21 and a + b + c = 7, then (ab + bc + ca) is equal to

Detailed Solution for CMAT Mock Test - 1 (New Pattern) - Question 30
According to the question,

Equation 1:

a2 + b2 + c2 = 21

Equation 2:

a + b + c = 7

To find (ab + bc + ca), square equation 2 from both sides.

(a + b + c)2 = 72

a2 + b2 + c2 + 2ab + 2bc + 2ca = 49

Equation 3:

a2 + b2 + c2 + 2ab + 2bc + 2ca = 49

Putting the value of equation 1 in equation 3,

21 + 2ab + 2bc + 2ca = 49

⇒ 2ab + 2bc + 2ca = 49 - 21

⇒ 2(ab + bc + ca) = 28

⇒ ab + bc + ca = 28 ÷ 2

⇒ ab + bc + ca = 14

So, the answer is 14.

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