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Home ‣ Aptitude ‣ Surds and Indices Comments
- Question
- Evaluate ( 0.00032)2/5
Options- A. 1/625
- B. 1/225
- C. 1/125
- D. 1/25
- Correct Answer
- 1/25
ExplanationGiven that
(0.00032)2/5 = (32/100000)2/5
Solve the equation by algebra Law
= (25/105)2/5
= {(2/10)5}2/5
= (2/10)5x2/5
= (1/5)2 = 1/25 - 1. If {(24)1/2}? = 256, find the value of '?'.
Options- A. 1
- B. 2
- C. 4
- D. 8 Discuss
- 2. If ?10 + ? x = 4, then what is the value of x?
Options- A. 150
- B. 216
- C. 316
- D. 450 Discuss
- 3. Value of ? in expression
78.9 ÷ (343)1.7 x (49)4.8 = 7? is
Options- A. 13.4
- B. 12.8
- C. 11.4
- D. 9.6 Discuss
- 4. If a2x + 2 = 1,where a is a positive real number other than 1, then x =?
Options- A. - 2
- B. - 1
- C. 0
- D. 1 Discuss
- 5. If 3x - 3x-1 = 18, then xx is equal to
Options- A. 3
- B. 8
- C. 27
- D. 216 Discuss
- 6. If 2x - 1 + 2x + 1 = 2560, find the value of x.
Options- A. 10
- B. 12
- C. 9
- D. 8 Discuss
- 7. Find the value of (10)200 ÷ (10)196 .
Options- A. 10000
- B. 1000
- C. 100
- D. 100000 Discuss
- 8. Value of ?5 + 2?6 - 1/?5 - 2?6 is
Options- A. 2?2
- B. 0
- C. 2?3
- D. ?5 - 1 Discuss
- 9. If 2 x - 1 + 2 x + 1 = 320, then find the value of x?
Options- A. 6
- B. 8
- C. 7
- D. 5 Discuss
- 10. if ax = b, by= c and xyz = 1, then what is the value of cz?
Options- A. a
- B. b
- C. ab
- D. a / b Discuss
Surds and Indices problems
Search Results
Correct Answer: 4
Explanation:
Given that, (24x 1/2)? = 256
Apply the law of Fractional Exponents and Laws of Exponents
? (22)? = 28
? 22 x ? = 28
? 2 x ? = 8
? ? = 8/2 = 4
Correct Answer: 216
Explanation:
Given, ?10 + ? x = 4
On squaring both sides, we get
10 + ?x = 16
? ?x = 6
Now, cubic on both sides, we get
x = (6)3 = 216
Correct Answer: 13.4
Explanation:
78.9 ÷ (343)1.7 x (49)4.8 = 7?
Apply the law of Fractional Exponents and Laws of Exponents
(am)(an) = am+n
am÷an=am?n
am/an=am?n
(am)n = amn
78.9 ÷ (343)1.7 x (49)4.8 = 7?
? 78.9 ÷ (73)1.7 x (72)4.8 = 7?
? 78.9 ÷ 75.1 x 79.6 = 7?
? 78.9 - 5.1 + 9.6 = 7?
? 718.5 - 5.1 = 7?
? ? = 13.4
Correct Answer: - 1
Explanation:
Given that, a2x + 2 = 1
Apply the algebra Law,
p0 = 1
? a2x + 2 = a0
Apply the algebra law
pX = pY then X will be equal to Y. means X = Y;
? 2x + 2 = 0
? x = -2/2 = -1
Correct Answer: 27
Explanation:
? 3x - 3x - 1 = 18
? 3x - 1(3 - 1) = 18
? 3x - 1(2) = 18
? 3x - 1 = 18/2
? 3x - 1 = 9
? 3x - 1 = 32
Apply the Algebra law,
If aX = aY then X will be equal to Y.
means X = Y;
? x - 1 = 2
? x = 3
Then xx = (3)3 = 27
Correct Answer: 10
Explanation:
2x - 1 + 2x + 1 = 2560
2x - 1 + 2x - 1 + 2 = 2560
Apply the Law of Algebra
2x - 1 + 2x - 1 x 2 2 = 2560
? 2x - 1 ( 1 + 22 ) = 2560
? 2x - 1 = 2560/5 = 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
? 2x - 1 = 29
? x - 1 = 9
? x = 9 + 1 = 10
Correct Answer: 10000
Explanation:
Given equation is
(10)200 ÷ (10)196
Apply the law of Algebra
am ÷ an = am ? n
= (10)200 - 196
= 104
= 10000
Correct Answer: 0
Explanation:
?5 + 2?6 - 1/?5 - 2?6
= ((?5 + 2?6 x ?5 - 2?6 ) - 1)/?5 - 2?6
Apply the formula of Algebra.
( a + b ) x (a - b ) = a2 - b2
= (?(5)2 - (2?6 )2 - 1)/?5 - 2?6
= (?25 - 4 x 6 - 1) /?5 - 2?6
= (?25 - 24 - 1) /?5 - 2?6
= (? 1 - 1 )/?5 - 2?6
= (1 - 1 )/?5 - 2?6
= 0/?5 - 2?6
= 0
Correct Answer: 7
Explanation:
? 2x - 1 + 2x + 1 = 320
Apply the law of Algebra
? 2x - 1(1 + 2 2 ) = 320
? 2x - 1(1 + 4 ) = 320
? 2x - 1 x 5 = 320
? 2x - 1 = 64 = 2 x 2 x 2 x 2 x 2 x 2
? 2x - 1 = 26
if pX = pY then X will be equal to Y. means X = Y;
? x - 1 = 6
? x = 7
Correct Answer: a
Explanation:
Given, xyz = 1, ax = b, by = c
Now, b = ax
Apply the law of algebra .
Take the power y of both side equation.
? by= axy
Take the power z of both side equation.
? byz = axyz
? ( by )z = axyz
Replace the by with c and xyz with 1 as per given equation,
? cz = a
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