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Test: Surds And Indices- 1 - UPSC MCQ


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10 Questions MCQ Test CSAT Preparation - Test: Surds And Indices- 1

Test: Surds And Indices- 1 for UPSC 2024 is part of CSAT Preparation preparation. The Test: Surds And Indices- 1 questions and answers have been prepared according to the UPSC exam syllabus.The Test: Surds And Indices- 1 MCQs are made for UPSC 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Surds And Indices- 1 below.
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Test: Surds And Indices- 1 - Question 1

(17)3.5 x (17)? = 178

Detailed Solution for Test: Surds And Indices- 1 - Question 1

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

Test: Surds And Indices- 1 - Question 2

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

Detailed Solution for Test: Surds And Indices- 1 - Question 2

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

Test: Surds And Indices- 1 - Question 3

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

Detailed Solution for Test: Surds And Indices- 1 - Question 3

 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.)

Test: Surds And Indices- 1 - Question 4

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

Detailed Solution for Test: Surds And Indices- 1 - Question 4

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

Test: Surds And Indices- 1 - Question 5

The simplest value of the expression is

Detailed Solution for Test: Surds And Indices- 1 - Question 5




 

Hence, option (c).

Test: Surds And Indices- 1 - Question 6

(256)0.16 x (256)0.09 = ?

Detailed Solution for Test: Surds And Indices- 1 - Question 6

 (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

Test: Surds And Indices- 1 - Question 7

The value of [(10)150 ÷ (10)146]

Detailed Solution for Test: Surds And Indices- 1 - Question 7

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

Test: Surds And Indices- 1 - Question 8

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

Detailed Solution for Test: Surds And Indices- 1 - Question 8

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 ) + xc/(xa + xb + xc )
= (xa + xb + xc ) / (xa + xb + xc )
= 1.

Test: Surds And Indices- 1 - Question 9

(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?

Detailed Solution for Test: Surds And Indices- 1 - Question 9

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.

Test: Surds And Indices- 1 - Question 10

(0.04)-1.5 = ?

Detailed Solution for Test: Surds And Indices- 1 - Question 10

⇒ (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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