CAT Model Paper 2 Questions and Answers with Explanation Part 4
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Q: 18. In how many ways can five distinct natural numbers be selected from the first 100 natural numbers such that all five numbers are in geometric progression?
(A) 14
(B) 16
(C) 18
(D) 20
Ans: A
Sol:
The numbers can be chosen as each of them in 2 ways- ways or or or or ways Total of 14 ways. Hence option A
The correct choice is (A)
Q: 19. Which of the following numbers is a prime number?
(A)
(B)
(C)
(D) None of the above
Ans: D
Sol:
Consider the option
When is divided by 61, the remainder is or (-1) .
When is divided by 61, the remainder is 1 (Fermat՚s theorem: The remainder when is
divided by ‘x’ is 1 if ‘x’ is a prime number and ‘a’ is not a multiple of ‘x’ ) .
Hence remainder when is divided by 61 is zero. is not prime.
Consider the option
The unit՚s digit of is 1. (Any power of a number whose unit՚s digit is 1 ends in 1) .
The unit՚s digit of is 9. ( will always end in 9 provided the units digit of ‘a’ is 9 and
where ‘k’ is any whole number) .
Hence, will end in a zero. Therefore, it is a multiple of 10.
Consider the option
Since 97 is common to all the terms, the number is a multiple of 97. Hence correct answer is ‘none of the above’ .
The correct choice is (D)
Q: 20. The ratio of the sum of the first four terms of an AP to that of the first five terms of the same AP is . The common difference of this AP is 8. Find the sum of the first terms of the AP
(A)
(B)
(C)
(D) 800
Ans: A
Sol:
Simplifying the above expression,
Since
Sum of the first 20 terms of the AP
The correct choice is (A)
Directions for questions 21 to 23:
The following table gives the partnerships and the runs scored by New Zealand batsman in that partnership in one innings of a test match. Extras are included in the partnership score but not in terms of Individual scores. In the Overs column means Overs and 4 balls where each over is of 6 balls. Answer the following questions based on the data given
| Wicket | Runs | Overs | Player (Runs Scored) | Player (Runs Scored) |
| 1st | 79 | 26.4 | HD Rutherford (37) | PG Fulton (41) |
| 2nd | 181 | 68 | KS Williamson (91) | PG Fulton (83) |
| 3rd | 29 | 11.2 | LRPL Taylor (19) | PG Fulton (9) |
| 4th | 8 | 6.3 | PG Fulton (3) | DG Brownlie (5) |
| 5th | 68 | 20.1 | BB Mc Cullum (38) | DG Brownlie (30) |
| 6th | 8 | 5 | DG Brownlie (1) | BJ Watling (7) |
| 7TH | 51 | 10.4 | TG Southee (44) | BJ Watling (7) |
| 8th | 12 | 2.2 | BP Martin (10) | BJ Watling (2) |
| 9th | 7 | 1.4 | BJ Watling (5) | N Wagner (2) |
| 10th | 0 | 0.1 | TA Boult (0) | N Wagner (0) |
Q: 21. What was the run rate of the New Zealand innings when the 5th wicket fell? (Run rate is defined as the number of runs scored per over)
(A) 2.60
(B) 2.97
(C) 2.97
(D) 3.05
Ans: B
Sol:
The fifth wicket fell at 132.4 overs and the score then was Run rate .
The correct choice is (B)
Q: 22. For which wicket՚s partnership did the team score at the maximum run rate?
(A)
(B) 8th
(C) 9th
(D) 5th
Ans: B
Sol:
From the table we can say 8th wicket is the only partnership which was scored at over 5runs per over. All the other wickets partnerships were scored at
The correct choice is (B)
Q: 23. What is the total number of extras in the innings?
(A) 9
(B) 10
(C) 13
(D) 11
Ans: A
Sol:
Extras for wicket wicket wicket = 1 and 0 for rest all wickets. Total = 9 extras.
The correct choice is (A)