Number System (Part-2)

11. A length of a violin string varies inversely with respect to the frequency of Its vibrations. The frequency of a 14-inch-long violin string is 450 cycles per second. Find the frequency of a 12-inch violin string. [SSC MTS 17/10/2024 (Evening)]

(a) 515 cycles per second
(b) 525 cycles per second
(c) 520 cycles per second
(d) 510 cycles per second

Correct Answer: (b) 525 cycles per second

Solution:

According to questions

12. b is the sum of two quantities, one of which varies inversely as the square of a², and the other of which varies directly as a. Identify the relationship between a and b if b = 49 when a = 3 or 5. [SSC MTS 21/10/2024 (Morning)]

(a) a = 3b
(b) a = 3b² - 7/a
(c) b = 8a + 225/a²
(d) b = 2a

Correct Answer: (c) b = 8a + 225/a²

Solution:

13. If p is directly proportional to q and is p = 7 when q = 6 then what is the value of p when q = 21 ? [SSC MTS 21/10/2024 (Evening)]

(a) 24.0
(b) 24.5
(c) 23.5
(d) 25.0

Correct Answer: (b) 24.5

Solution:

14. If P (P > 0) is the least possible number that must be subtracted from 7, 9, and 12 so that the resulting numbers are in continued proportion, then find the value of P²+ 1. [SSC MTS 29/10/2024 (Evening)]

(a) 10
(b) 12
(c) 3
(d) 8

Correct Answer: (a) 10

Solution:

15. Which of the following can be the value of 'k' so that the number 217924k is divisible by 6? [SSC CGL 09/09/2024 (1st Shift)]

(a) 4
(b) 6
(c) 2
(d) 0

Correct Answer: (c) 2

Solution:

16. Without doing the actual division, find the remainder when 28735429 is divided by 9. [SSC CGL 09/09/2024 (2nd Shift)]

(a) 4
(b) 2
(c) 8
(d) 9

Correct Answer: (a) 4

Solution:

17. If 7845K854 is divisible by 11, then what is the value of K? [SSC CGL 09/09/2024 (3rd Shift)]

(a) 6
(b) 9
(c) 7
(d) 8

Correct Answer: (b) 9

Solution:

18. Which of the following is the largest 5-digit number divisible by 47 ? [SSC CGL 10/09/2024 (1st Shift)]

(a) 99999
(b) 98888
(c) 99969
(d) 10000

Correct Answer: (c) 99969

Solution:

19. Akshay purchased pens and notebooks from a shop for a total sum of 180. From the following data, what is the value of "X" [SSC CGL 10/09/2024 (2nd Shift)]

Items	Price per unit (in) ₹	Quantity
Pens	10	X
Notebooks	20	6

(a) 4
(b) 6
(c) 5
(d) 7

Correct Answer: (b) 6

Solution:

20. If (77⁷⁷ +77) is divided by 78, then the remainder will be: [SSC CGL 10/09/2024 (2nd Shift)]

(a) 76
(b) 77
(c) 78
(d) 1

Correct Answer: (a) 76

Solution:

Number System (Part-2)

11. A length of a violin string varies inversely with respect to the frequency of Its vibrations. The frequency of a 14-inch-long violin string is 450 cycles per second. Find the frequency of a 12-inch violin string. [SSC MTS 17/10/2024 (Evening)]

12. b is the sum of two quantities, one of which varies inversely as the square of a², and the other of which varies directly as a. Identify the relationship between a and b if b = 49 when a = 3 or 5. [SSC MTS 21/10/2024 (Morning)]

13. If p is directly proportional to q and is p = 7 when q = 6 then what is the value of p when q = 21 ? [SSC MTS 21/10/2024 (Evening)]

14. If P (P > 0) is the least possible number that must be subtracted from 7, 9, and 12 so that the resulting numbers are in continued proportion, then find the value of P²+ 1. [SSC MTS 29/10/2024 (Evening)]

15. Which of the following can be the value of 'k' so that the number 217924k is divisible by 6? [SSC CGL 09/09/2024 (1st Shift)]

16. Without doing the actual division, find the remainder when 28735429 is divided by 9. [SSC CGL 09/09/2024 (2nd Shift)]

17. If 7845K854 is divisible by 11, then what is the value of K? [SSC CGL 09/09/2024 (3rd Shift)]

18. Which of the following is the largest 5-digit number divisible by 47 ? [SSC CGL 10/09/2024 (1st Shift)]

19. Akshay purchased pens and notebooks from a shop for a total sum of 180. From the following data, what is the value of "X" [SSC CGL 10/09/2024 (2nd Shift)]

20. If (77⁷⁷ +77) is divided by 78, then the remainder will be: [SSC CGL 10/09/2024 (2nd Shift)]

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