Surds and Indices - Aptitude Questions and Answers | Online Surds and Indices MCQ Aptitude Test

Surds and Indices - Aptitude Questions and Answers | Online Surds and Indices MCQ Aptitude Test

Quiz Name	Surds and Indices
Category	Online Aptitude Test
Number of Questions	15
Time	30 Minutes
Exam Type	MCQ (Multiple Choice Questions)

1. (17.5) x (17.5) = 178
a. 2.29
b. 2.75
c. 4.25
d. 4.5

Answer: D

Explanation:
Let (17)3.5 x (17)x = 178 be the answer.As a result, (17)3.5 + x = 178.8 = 3.5 + x= x (8 - 3.5)=4.5 = x’

2. If an x - 1 Equals b x - 3, then the value of x is: b a.
a. 1/2
b. 1
c. 2
d. 7/2

Answer: C

Explanation:
Given (a/b )x - 1 = (b/a )x - 3 (a/b )x - 1= (a/b)-(x - 3) = (a/b )x - 1= (a/b)-(x - 3) = (a/b )x - 1= (a/b)-(x - 3) = (a/b )x - 1= (a/b ) (3 - x),3 - x 2x = 4 x - 1 = 3 - x 2x = 4,2 = x.

3. If 100.48 = x, 100.70 = y, and xz = y2, the value of z is approximately:
a. 1.45
b. 1.88
c. 2.9
d. 3.7

Answer: C

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

4. If 5a = 3125, the value of 5(a - 3) is as follows:
a. 25
b. 125
c. 625
d. 1625

Answer: A

Explanation:
3125 = 5a 55 + 5a,a = five.5(a - 3) = 5(5 - 3) = 52 = 25 is the answer.

5. If 3(x - y) = 27 and 3(x + y) = 243, then the value of x is:
a. 0
b. 2
c. 4
d. 6

Answer: C

Explanation:
3x - y = 27 = 33 x - y = 3 x - y = 3 x - y = 3 x - y = 3 x - (i),3x + y = 243 = 35 x + y = 5 x + y = 5 (ii),We get x = 4 after solving I and (ii).

6. What is the product of (256)0.16 and (256)0.09?
a. 4
b. 16
c. 64
d. 256.5

Answer: A

Explanation:
(256)0.16 multiplied by (256)0.09 equals (256)(0.16 + 0.09)= 0.25 (256)= (256)(25/100)= (1/4)(256)= (1/4)(44)= 4 to the fourth power= 4.

7. [(10)150 (10)146] is the value.
a. 1000
b. 10000
c. 100000
d. 10 to the power 6

Answer: B

Explanation:
(10 to the power 150/10 to the power 146 = 10to the power,150/10 to the power 146,150 - 146 = 10

8. What is the sum of 1 + 1 + 1? 1 + x(b - a) + x(b - a) + x(b - a) + x( (c - a) 1 + x(a - b) + x(a - b) + x(a - b) + x( (c - b) 1 + x(b - c) + x(a - b) + x(a - b) + x( (a - c)
a. 0
b. 1
c. xa - b - c
d. None of these

Answer: B

Explanation:
Given Exp. = 1/1 +xb/xa +xc/xa + 1/1 +xb/xa +xc/xa + 1/1 +xb/xa +xc/xa + 1/1 +xb/xa +xc/xa + 1/1 +xb/xa +xc/xa + 1/1 +xb/xa +xc/xa + 1/1 +xb/xa +xc= xa/(xa + xb + xc) + xb/(xa + xb + xc) + xc/(xa + xb + xc) + xc/(xa + xb + xc)= (xa + xb + xc)/(xa + xb + xc)/(xa + xb + xc)=equals 1.

9. (125)1.5 x (25)7.5 = 5?
a. 8.5
b. 13
c. 16
d. 17.5

Answer: B

Explanation:
Let (25)7.5 x (5)2.5 (125)1.5 = 5x be the answer.As a result, (52)7.5 x (5)2.5/(53)1.5 = 5x.5x = 5(2 x 7.5) x 52.5/5(3 x 1.5),5x = 515 x 52.5/54.5,5(15 + 2.5 - 4.5) = 5x,513 = 5x,x equals 13.

10. (0.04) + 1.5 =?
a. 25
b. 125
c. 620
d. 625

Answer: B

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

11. 9n x 3n - 1 = 11. (243)n/5 x 32n + 1 =?
a. 1
b. 2
c. 9
d. 3n

Answer: C

Explanation:
(243)(n/5) x 32n + 1/9n x 3n - 1 is the given expression.1/(32)n x 3n - 1 = (35)(n/5) x 32n + 1/(32)n x 3n,35 x (n/5) x 32n + 1 = 35 x (n/5) x 32n + 1 = 35 x (n/5) x 32n (32n x 3n - 1),3(n + 2n + 1)/3(2n + n - 1) = 3(n + 2n + 1)= 33n + 1 = 33n - 1 = 33n - 1= 3(3n - 1 - 3n - 1) = 32 = 9.

12. 1 + a =? 12. 1 + 1 =? (n - m) 1 plus a (m - n)
a. 0
b. 1/2
c. 1
d. am + n

Answer: C

Explanation:
1+1+=1 + 1,1 plus an am,am a plus one,1 plus a (n - m),1 + a(m - n) = am + a (am + an) (am + an) = 1

13. If m and n are both whole numbers, and mn = 121, (m - 1)n + 1 equals:
a. 1
b. 10
c. 121
d. 1000

Answer: D

Explanation:
We know that 112 + 121 equals 121.When m = 11 and n = 2 are combined, we get:(11 - 1)(2 + 1) = 103 = 1000.

14. xb/xc(b + c - a) is a 14. (c + a - b) xc/xa xc (a + b - c) = xa/xb(a + b - c) = xa/xb(a + b - c) =?
a. xabc
b. 1
c. xab + bc + ca
d. xa + b + c

Answer: B

Explanation:
Exp. = x(b - c)(b + c - a) is given. (c + a - b) x(c - a) x(c - a) x(c - a) x(c + a - b) = x(b - c)(b + c)(a + b - c)(a + b - c)(a + b - c)(a + b - c)(a + b - c)(a + b - c)( - (a)(b)(c)(d)( x(c - a)(c + a)(c + a)(c + a)(c + a)(c + - (c - a) b(c - a) b(c - a) b(c - x(a - b)(a + b) - c(a - b) = x(b2 - c2 + c2 - a2 + a2 - b2) + x(b2 - c2 + c2 - a2 + a2 - b2) (x0 x x0) = (1 x 1) = 1. x-a(b - c) - b(c - a) - c(a - b) = (x0 x x0).

15. If x = 3 + 22 and root x -1/x is equal to:
a. 1
b. 2
c. 22
d. 33

Answer: B

Explanation:
(3 + ROOT 2) = x+1- 2 3 + ROOT 2) + +1- 2 = (3 + ROOT 2) 3 - ROOT2) = (3 + 22) + +1x(3 - ROOT2)- 2,(3 + ROOT2) (3 - ROOT2) (3 - 22) -2 equals four.ROOT x -1/ROOT X= 2

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