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)
Start Passage
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) |
1^{st} | 79 | 26.4 | HD Rutherford (37) | PG Fulton (41) |
2^{nd} | 181 | 68 | KS Williamson (91) | PG Fulton (83) |
3^{rd} | 29 | 11.2 | LRPL Taylor (19) | PG Fulton (9) |
4^{th} | 8 | 6.3 | PG Fulton (3) | DG Brownlie(5) |
5^{th} | 68 | 20.1 | BB Mc Cullum(38) | DG Brownlie(30) |
6^{th} | 8 | 5 | DG Brownlie (1) | BJ Watling (7) |
7^{TH} | 51 | 10.4 | TG Southee(44) | BJ Watling (7) |
8^{th} | 12 | 2.2 | BP Martin(10) | BJ Watling(2) |
9^{th} | 7 | 1.4 | BJ Watling (5) | N Wagner(2) |
10^{th} | 0 | 0.1 | TA Boult(0) | N Wagner(0) |
Q: 21. What was the run rate of the New Zealand innings when the 5^{th} 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) 8^{th}
(C) 9^{th}
(D) 5^{th}
Ans: B
Sol:
From the table we can say 8^{th} 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)
End Passage