CAT Practice Test: September 29 - CAT MCQ

Number of squares in a board having m rows and n columns (m ≥ n) = m × n + (m - 1) × (n - 1) + (m - 2) × (n - 2) ... (m - n + 1) × 1
Here, m = 10 and n = 9
Number of squares = 10 × 9 + 9 × 8 + 8 × 7 + 7 × 6 + 6 × 5 + 5 × 4 + 4 × 3 + 3 × 2 + 2 × 1
= 90 + 72 + 56 + 42 + 30 + 20 + 12 + 6 + 2 = 330

26 cards can be chosen out of 52 cards in ⁵²C₂₆ ways. There are two ways in which each card can be dealt, either from the first pack or from the second.
Total number of ways = ⁵²C₂₆ . 2²⁶

We require that the particular person is found in every group of 6 people out of a total of 10. As this person is common to all groups of 6, we will have to consider the number of ways of choosing the remaining 5 persons out of the other 9. This can be done in ⁹C₅ ways = 126 ways.

Odd digits: 1, 3, 5, 7, and 9
Even digits: 2, 4, 6, and 8
Number of ways to fill an odd place = 5
Number of ways to fill an even place = 4

Therefore,
Total number of cases = (5)⁴ × (4)³

For every box, we have three different possibilities of colours.
Therefore, total number of possibilities = 3 × 3 × 3 × 3 × 3

¹⁰P₅ × ⁴P₃ = ⁶P₅ × X × 2
10 × 9 × 8 × 7 × 6 × 4 × 3 × 2 = 6 × 5 × 4 × 3 × 2 × X × 2
9 × 8 × 7 = X then X = ⁹P₃

Let 7 occur in the units place. So, the units digit can be placed in 1 way. The tens digit can be placed by the rest of 9 numbers. The hundreds digit can be placed by 6 only, i.e. one way.
As the numbers are between 600 and 700, number of ways = 1 × 9 × 1 = 9
Now, let 7 occur in the tens place. The units place can be filled by any of the numbers from 0-9 except 7.
The hundreds place can be filled in one way (by only 6). So, total 9 ways. 7 can't occur in the hundreds place.
∴ Total number of ways in which numbers can be formed = 9 + 9 = 18

First all the numbers are arranged in ascending order, one by one, then once this is done, all the words are arranged in reverse alphabetical order one by one.

Input: jack 88 sell 70 his 87 apple 90 tree
Step 1: 70 jack 88 sell his 87 apple 90 tree
Step 2: 70 87 jack 88 sell his apple 90 tree
Step 3: 70 87 88 jack sell his apple 90 tree
Step 4: 70 87 88 90 jack sell his apple tree

First all the numbers are arranged in ascending order, one by one, then once this is done, all the words are arranged in reverse alphabetical order one by one.

Input: jack 88 sell 70 his 87 apple 90 tree
Step 1: 70 jack 88 sell his 87 apple 90 tree
Step 2: 70 87 jack 88 sell his apple 90 tree
Step 3: 70 87 88 jack sell his apple 90 tree
Step 4: 70 87 88 90 jack sell his apple tree
Step 4 gives this output.

First all the numbers are arranged in ascending order, one by one, then once this is done, all the words are arranged in reverse alphabetical order one by one.

Input: jack 88 sell 70 his 87 apple 90 tree
Step 1: 70 jack 88 sell his 87 apple 90 tree
Step 2: 70 87 jack 88 sell his apple 90 tree
Step 3: 70 87 88 jack sell his apple 90 tree
Step 4: 70 87 88 90 jack sell his apple tree
Step 5: 70 87 88 90 tree jack sell his apple
Step 5 gives this output.

On studying the input and steps, it is found that the numbers are written in ascending order while the words are written in reverse order of the English alphabet, alternately.

Input: 83 42 bench lower 13 upper floor 37
Step I: 13 83 42 bench lower upper floor 37
Step II: 13 upper 83 42 bench lower floor 37
Step III: 13 upper 37 83 42 bench lower floor

On studying the input and steps, it is found that the numbers are written in ascending order while the words are written in reverse order of the English alphabet in alternate order.

Input: case over 12 36 49 long ago 42
Step I: 12 case over 36 49 long ago 42
Step II: 12 over case 36 49 long ago 42
Step III: 12 over 36 case 49 long ago 42
Step IV: 12 over 36 long case 49 ago 42
Step V: 12 over 36 long 42 case 49 ago

Thus, step V is the last step and the second-last step is step IV.

The statement implies that capsuled Vitamin E does not function so effectively as natural Vitamin E. Since no negative effect of capsuled Vitamin E is mentioned, so I does not follow. Hence, only course II follows.

The disease occurs at the end of monsoons every year. So, precautionary measures every four years shall not help. The second course of action shall be a preventive measure. So, only course II follows

The word "although" tells us that the sentence contains a contrast in its ideas, so the two parts of the sentence should contain opposite ideas. Reticent and convivial are opposites. 
Reticent: Quiet, reserved, not inclined to speak much.
Convivial: Sociable, friendly, enjoys socializing and being around others.

• From the given statement, it refers the meaning that the food provided in this hotel is not good and it didn't match with the food which we were eating in the Kohinoor hotel at the late hours.
• So, the correct meaning of the given is "Hotel Kohinoor served us good quality food than what we get here".

The weather outside was extremely pleasant and hence we decided to enjoy a morning ride in the open.

The word 'glean' means 'to collect information in small amounts and often with difficulty.' 'To gather' also means 'to collect several things, often from different places or people.' So, option A is the correct answer.

The word 'homage' means 'special honour or respect shown publicly.'
'Show respect' also means 'to show admiration for someone or something that you believe has good ideas or qualities.'
So, option B is the correct answer.

The word 'irk' means 'to irritate or annoy.'
'To annoy' also means 'to make someone a little angry; irritate.'
So, option D is the correct answer.

The word 'goad' means 'to provoke or annoy someone so as to stimulate an action or reaction.'
Whereas 'curb' means 'to restrain or keep in check.'
So, option D is the antonym of the given word.

The word 'incite' means 'urge or persuade someone to do something'. 'Stimulate' means 'to encourage or arouse interest or enthusiasm in'. Thus, they are synonyms of each other.
'Dissuade' means 'to discourage'. Thus, it is an antonym. 'Bother' means 'to worry, disturb, or upset (someone)'. Thus, they are not synonyms of the given word.

The word 'fallow' means 'a piece of land plowed and left uncultivated for a season or more.'
Whereas 'in use' means 'something which is being utilised or used for some purpose.'
So, option D is the antonym of the given word.

The word 'ingenuous' means 'showing innocent or childlike simplicity and candidness.'
'Honest' also means 'free from fraud or deception.'
So, option B is the correct answer.

'Flagrant' means '(of an action considered wrong or immoral) obviously offensive', e.g. a flagrant violation of the law. 'Blatant' means '(of bad behaviour) done openly and unashamedly'. Thus, 'blatant' is closest in meaning to 'flagrant'.
So, option C is the correct answer.

The word 'fracas' means 'a noisy argument or fight.'
Whereas 'ennui' means 'a feeling of being bored and mentally tired caused by having nothing interesting or exciting to do.'
So, option D is the antonym of the given word.