51)

If, \(\frac{r}{13} + \frac{13}{r} = 1\) then the value of r³ is:

SSC CGL 2022

A)

2157

B)

2197

C)

-2157

D)

-2197

52)

If \(\frac{a}{b} + \frac{b}{a}\) = -1 and a - b = 2, then the value of a³ - b³ is:

SSC CGL 2022

A)

1

B)

\(\frac{1}{2}\)

C)

zero

D)

- 1

53)

Which of the following statement is correct?
I. The value of 100² - 99² + 98² -97²+96²-95²+94²-93²+.......+22²-21² is 4840.
II. The value of \((k^{2}+ \frac{1}{k^{2}})(k - \frac{1}{k})(k^{4} + \frac{1}{k^{4}})(k + \frac{1}{k})(k^{4} - \frac{1}{k^{4}})\) is \(k^{16}- \frac{1}{k^{16}}\).

SSC CGL 2022

A)

Only II

B)

Both I and II

C)

Neither I nor II

D)

Only I

54)

If a - b = 8 and ab = 9, then the value of a + b is ________.

SSC CGL 2022

A)

±8

B)

±7

C)

±9

D)

±10

55)

If 2p + q = 19 and 8p³ + q³ = 361, then find the value of pq.

SSC CGL 2022

A)

58

B)

59

C)

56

D)

57

56)

Which of the following statement is correct?
I. If x = 12, y = -2 and z = -10, then x³ + y³ + z³ = 720
II. If x + y = 48 and 4xy = 128, then s the value of 4x² + 4y² is 8960

SSC CGL 2022

A)

Both I and II

B)

Only I

C)

Neither I nor II

D)

Only II

57)

A four-digit pin, say abcd, of a lock has different non-zero digits. The digits satisfy b = 2a, c = 2b, d = 2c. The pin is divisible by ________.

SSC CGL 2022

A)

2, 3, 13

B)

2, 3, 7

C)

2, 3, 5

D)

2, 3, 11

58)

Which of the following statement is correct?
I. If x = 12, y = -2 and z = -10, then x + y + z = 360.
II. If x + y = 48 and 4xy = 128, then 4x + 4y = 4480.

SSC CGL 2022

A)

Both I and II

B)

Only I

C)

Neither I nor II

D)

Only II

59)

If K +\( \frac{1}{K}\) + 2 = 0 and K < 0, then what is the value of K¹¹ +\( \frac{1}{K^4}\) ?

SSC CGL 2022

A)

-1

B)

-2

C)

0

D)

-17

60)

If \(x + \frac{{1}}{{x}}\) = 6, then find the value of\( \frac{{3x}}{{2{x^2} - 5x + 2}}\) .

SSC CGL 2022

A)

\(\frac{2}{3}\)

B)

\(\frac{3}{7}\)

C)

1

D)

0