# Olympiad Test: Surds And Indices

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## 20 Questions MCQ Test | Olympiad Test: Surds And Indices

Olympiad Test: Surds And Indices for Class 7 2023 is part of Class 7 preparation. The Olympiad Test: Surds And Indices questions and answers have been prepared according to the Class 7 exam syllabus.The Olympiad Test: Surds And Indices MCQs are made for Class 7 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: Surds And Indices below.
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Olympiad Test: Surds And Indices - Question 1

### ​If x = 3 + 2√2 , then the value of is:

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

Here, Olympiad Test: Surds And Indices - Question 2

### Detailed Solution for Olympiad Test: Surds And Indices - Question 2

Given Expression
= x(b – c)(b + c – a). x(c – a)(c + a – b)
. x(a – b)(a + b – c)
= x(b – c)(b + c) – a(b – c) . x(c - a)(c + a) – b(c – a)
. x(a - b)(a + b) - c(a - b) . x–a(b – c) – b(c – a) – c(a – b)
= (x0 × x0)
= (1 × 1) = 1

Olympiad Test: Surds And Indices - Question 3

### If m and n are whole numbers such that mn = 121, the value of (m – 1)n + 1 is:

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

We know that 112 = 121 = mn (given)
Hence, putting m = 11 and n = 2, in
(m – 1)n + 1 = (11 – 1)(2 + 1) = 103 = 1000

Olympiad Test: Surds And Indices - Question 4

(256)0.16 × (256)0.09 = ?

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

(256)0.16 × (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

Olympiad Test: Surds And Indices - Question 5

The value of [(10)150 ÷ (10)146] is

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

(10)150 ÷ (10)146 = 10150 – 146
= 104
= 10000

Olympiad Test: Surds And Indices - Question 6

If (25)7.5 × (5)2.5 ÷ (125)1.5 = 5x then x = ?

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

Given (25)7.5 × (5)2.5 ÷ (125)1.5 = 5x
Then, (52)7.5 × (5)2.5 ÷ (53)1.5 = 5x
⇒ 5(2 × 7.5) × 52.5 ÷ 5(3 × 1.5) = 5x
⇒ 515 × 52.5 ÷ 54.5 = 5x
⇒ 5x = 5(15 + 2.5 – 4.5)
⇒ 5x = 513
⇒ x = 13

Olympiad Test: Surds And Indices - Question 7

(0.04)–1.5 = ?

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

(0.04) – 1.5 = (4/100) –1.5 = (1/25) –3/2
= (25)(3/2)
= (52)(3/2)
= (5)2 × (3/2)
= 53
= 125

Olympiad Test: Surds And Indices - Question 8

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

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

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.

Olympiad Test: Surds And Indices - Question 9

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

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

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

Olympiad Test: Surds And Indices - Question 10

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

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

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

Olympiad Test: Surds And Indices - Question 11

(17)3.5 × (17)? = 178

Detailed Solution for Olympiad Test: Surds And Indices - Question 11

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

Olympiad Test: Surds And Indices - Question 12

Find the value of √300.

Detailed Solution for Olympiad Test: Surds And Indices - Question 12 = 10 × 1.732 = 17.32

Olympiad Test: Surds And Indices - Question 13

Evaluate: √75 + √147 =?

Detailed Solution for Olympiad Test: Surds And Indices - Question 13 Olympiad Test: Surds And Indices - Question 14

Find the value of: Detailed Solution for Olympiad Test: Surds And Indices - Question 14 Olympiad Test: Surds And Indices - Question 15

Find √242 ÷ √72 .

Detailed Solution for Olympiad Test: Surds And Indices - Question 15 Olympiad Test: Surds And Indices - Question 16

(18a8b6) ÷ (3a2b2) simplifies to

Detailed Solution for Olympiad Test: Surds And Indices - Question 16

(18a8b6) ÷ (3a2b2) = 18/3 × a8 – 2 × b6 – 2
= 6a6b4

Olympiad Test: Surds And Indices - Question 17

Replace question mark with the suitable answer:
56 - 45- √? = √36

Detailed Solution for Olympiad Test: Surds And Indices - Question 17

56 - 45 -√? = √36
⇒ 11 - √36 =√?
⇒ 11 - 6 =√?
∴ ? = 25

Olympiad Test: Surds And Indices - Question 18

Replace question mark with the suitable answer: Detailed Solution for Olympiad Test: Surds And Indices - Question 18 Olympiad Test: Surds And Indices - Question 19 Detailed Solution for Olympiad Test: Surds And Indices - Question 19 Olympiad Test: Surds And Indices - Question 20

What is the value of (0.003)3 ?

Detailed Solution for Olympiad Test: Surds And Indices - Question 20

(0.003)3 = 0.003 × 0.003 × 0.003
= 0.000000027 (Scan QR code)