Test: Surds And Indices- 1


10 Questions MCQ Test General Aptitude for GATE 2020 | Test: Surds And Indices- 1


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QUESTION: 1

(17)3.5 x (17)? = 178

Solution:

Let (17)3.5 x (17)x = 178
Then, (17)3.5 + x = 178
∴ 3.5 + x = 8
⇒ x = (8 - 3.5)
⇒ x = 4.5

QUESTION: 2

If (a / b)x - 1 = (b / a)x - 3 , then the value of x is:

Solution:

Given (a / b)x - 1 = (b / a)x - 3
⇒ (a / b) x - 1 = (b / a) -(x - 3) = (a / b)(3 - x)
⇒ x - 1 = 3 - x
⇒ 2x = 4
⇒ x = 2

QUESTION: 3

Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:

Solution:

xz = y2 ⇔ 10(0.48 z) = 10(2 x 0.70) = 101.40
⇒ 0.48 z = 1.40
⇒ z = 140 / 48 = 35 / 12 = 2.9(approx.)

QUESTION: 4

If 5a = 3125, then the value of 5(a - 3) is:

Solution:

5a = 3125 ⇔ 5a = 55
⇒ a = 5.
∴ 5(a - 3) = 5(5 - 3) = 52 = 25.

QUESTION: 5

If 3(x - y) = 27 and 3(x + y) = 243, then x is equal to:

Solution:

3x - y = 27 = 33    ⇔    x - y = 3 ....(i)

3x + y = 243 = 35    ⇔    x + y = 5 ....(ii)

On solving (i) and (ii), we get x = 4.

QUESTION: 6

(256)0.16 x (256)0.09 = ?

Solution:

(256)0.16 x (256)0.09 = (256)(0.16 + 0.09)
= (256)0.25
= (256)(25 / 100)
= (256)(1 / 4)
= (44)(1 / 4)
= 44(1 / 4)
= 41
= 4

QUESTION: 7

The value of [(10)150 ÷ (10)146]

Solution:

(10)150 ÷ (10)146 = 10150 / 10146
= (10)150 -146
= 104
= 10000.

QUESTION: 8

1/(1 + x(b - a) + x(c - a)) + 1/(1 + x(a - b) + x(c - d)) + 1/(1 + x(b - c) +x(a - c) ) = ?

Solution:

Given Exp. = 1 / (1 + xb / xa + xc / xa) + 1 / (1 + xa / xb + xc / xb) + 1 / (1 + xb / xc +xa / xc)
= xa / (xa + xb + xc ) + xb / (xa + xb + xc ) + x/ (xa + xb + xc )
= (xa + xb + xc ) / (xa + xb + xc )
= 1.

QUESTION: 9

(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?

Solution:

Let (25)7.5 x (5)2.5 ÷ (125)1.5 = 5x.
Then, (52)7.5 x 52.5 / (53) 1.5 = 5x
⇒ (52)7.5 x 52.5 / (5)3 x 1.5 = 5x
⇒ 515 x 52.5 / 54.5 = 5x
⇒ 5x = 5(15 + 2.5 - 4.5)
⇒ 5x = 513
∴ x = 13.

QUESTION: 10

(0.04)-1.5 = ?

Solution:

(0.04)-1.5 = (4 / 100)-1.5
= (1 / 25) -(3 / 2)
= (52)(3 / 2)
= (5)2 x (3 / 2)
= 53
= 125.

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