Surds And indices Test

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Surds And indices Test - 1

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Weekly Quiz Competition

Question 1
3 / -1

(17)^3.5 x (17)^? = 17⁸

A
2.29

B
2.75

C
4.25

D
4.5

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
3 / -1

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

A
1 / 2

B
1

C
2

D
7 / 2

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
3 / -1

Given that 10^0.48 = x, 10^0.70 = y and x^z = y², then the value of z is close to:

A
1.45

B
1.88

C
2.9

D
3.7

Solution

⇒ x^z = y² ⇔ 10^{(0.48 z)} = 10^{(2 x 0.70)} = 10^1.40
⇒ 0.48 z = 1.40
⇒ z = 140 / 48 = 35 / 12 = 2.9(approx.)
Question 4
3 / -1

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

A
25

B
125

C
625

D
1625

Solution

⇒ 5^a = 3125 ⇔ 5^a = 5⁵
⇒ a = 5.
∴ 5^{(a - 3)} = 5^{(5 - 3)}= 5² = 25.
Question 5
3 / -1

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

A
0

B
2

C
4

D
6

Solution

⇒ 3^x - y = 27 = 3³ ⇔ x - y = 3 ....(i)
⇒ 3^x + y = 243 = 3⁵ ⇔ x + y = 5 ....(ii)
On solving (i) and (ii), we get x = 4.
Question 6
3 / -1

(256)^0.16 x (256)^0.09 = ?

A
4

B
16

C
64

D
256.25

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
3 / -1

The value of [(10)¹⁵⁰ ÷ (10)¹⁴⁶]

A
1000

B
10000

C
100000

D
10⁶

Solution

⇒ (10)¹⁵⁰ ÷ (10)¹⁴⁶ = 10¹⁵⁰ / 10¹⁴⁶
= (10)¹⁵⁰ ^-146
= 10⁴
= 10000.
Question 8
3 / -1

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

A
0

B
1

C
x^{a - b - c}

D
None of these

Solution

Given Exp:
1/(1 + x^b / x^a + x^c / x^a) + 1/(1 + x^a / x^b + x^c / x^b) + 1/(1 + x^b / x^c +x^a / x^c)
= x^a/(x^a + x^b + x^c ) + x^b/(x^a + x^b + x^c ) + x^c/(x^a + x^b + x^c )
= (x^a + x^b + x^c ) / (x^a + x^b + x^c )
= 1.
Question 9
3 / -1

(25)^7.5 x (5)^2.5 ÷ (125)^1.5 = 5^?

A
8.5

B
13

C
16

D
17.5

Solution

Let (25)^7.5 x (5)^2.5 ÷ (125)^1.5 = 5^x.
Then, (5²)^7.5 x 5^2.5 / (5³) ^1.5 = 5^x
⇒ (5²)^7.5 x 5^2.5 / (5)^3 x ^1.5 = 5x
⇒ 5¹⁵ x 5^2.5 / 5^4.5 = 5^x
⇒ 5^x = 5^{(15 + 2.5 - 4.5)}
⇒ 5^x = 5¹³
∴ x = 13.
Question 10
3 / -1

(0.04)^-1.5 = ?

A
25

B
125

C
250

D
625

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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Re-Attempt Weekly Quiz Competition

Surds And indices Test - 1

Result

Surds And indices Test - 1

Score

-

Rank

-

SHARING IS CARING

Question 1

2.29

2.75

4.25

4.5

Solution

Question 2

1 / 2

1

2

7 / 2

Solution

Question 3

1.45

1.88

2.9

3.7

Solution

Question 4

25

125

625

1625

Solution

Question 5

0

2

4

6

Solution

Question 6

4

16

64

256.25

Solution

Question 7

1000

10000

100000

106

Solution

Question 8

0

1

xa - b - c

None of these

Solution

Question 9

8.5

13

16

17.5

Solution

Question 10

25

125

250

625

Solution

User

Question Analysis

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Rank

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10⁶

x^{a - b - c}