31)

If 5√3 + √75 = 17.32, then the value of 14√3 + √108 is:

SSC CGL 2022

A)

34.64

B)

33.86

C)

32.46

D)

35.64

32)

If (4a - 3b) = 1, ab = \(\frac{1}{2}\) , where a > 0 and b > 0, what is the value of (64a³ + 27b³)?

SSC CGL 2022

A)

35

B)

15

C)

25

D)

30

33)

If a + b + c = 6, a² + b² + c² = 32, and a³ + b³ + c³ = 189, then the value of 4abc is:

SSC CGL 2022

A)

9

B)

12

C)

8

D)

16

34)

If \(5x  - {1\over 4x}= 6\), x > 0, then find the value of \(25x^2-\frac{1}{16x^{2}}\).

SSC CGL 2022

A)

\(6 \sqrt{31}\)

B)

36

C)

\(\sqrt{246}\)

D)

\(6 \sqrt{41}\)

35)

If 4x - 3y = 12 and xy = 5, then find the value of \(\frac{{16{x^2} + 9{y^2}}}{8}\) .

SSC CGL 2022

A)

18

B)

3

C)

44

D)

33

36)

If \((a+\frac{1}{a}+3)^2 = 16\), where a is a non-zero real number, then find the value of \(a^2+{1\over a^2}\).

SSC CGL 2022

A)

47

B)

7

C)

3

D)

49

37)

If a² + b² = 65 and ab = 8, a > b > 0, then find the value of a² - b².

SSC CGL 2022

A)

65

B)

60

C)

63

D)

72

38)

If x⁴ - 79x² + 1 = 0, then a value of x + x^-1 can be:

SSC CGL 2022

A)

9

B)

8

C)

7

D)

5

39)

If \(x^{2} - 5x + 1 = 0\), then the value of \(\frac{x^{6}+x^{4}+x^{2}+1}{5x^{3}}=?\)

SSC CGL 2022

A)

23

B)

25

C)

30

D)

28

40)

k is a negative number, such that, k + k^-1 = -2, then what is the value of \(\frac{k^2+4 k-2}{k^2+k-5}\) ?

SSC CGL 2022

A)

-7

B)

1

C)

7

D)

-1