Discussion
Home ‣ Aptitude ‣ Surds and Indices Comments
- Question
- The value of 6a3 b3 c2 ÷ 2ab2 c is :
Options- A. 3a 2 bc
- B. 3a b 2 c
- C. 3a 2 b 2 c 2
- D. 3a 3 b3 c3
- Correct Answer
- 3a b 2 c
Explanation
- 1. (100)0 is equivalent to :
Options- A. 0
- B. 10
- C. 1
- D. 100 Discuss
- 2. If ?2n = 64 , what will be the value of n?
Options- A. 8
- B. 4
- C. 12
- D. 16 Discuss
- 3. If m = 7 - 4?3, then (?m + 1/?m) =?
Options- A. 8
- B. 3
- C. 4
- D. 9 Discuss
- 4. If m and n are natural numbers, the m?n
Options- A. always irrational
- B. irrational unless n is the mth power of an integer
- C. irrational unless m is the nthpower of an integer
- D. irrational unless m and n are coprime Discuss
- 5. if a = 2 + ?3, then what is the value of (a2 + a -2)?
Options- A. 12
- B. 14
- C. 16
- D. 18 Discuss
- 6. (16)?3/4 + 2?3 + (8)?2/3 is equivalent to :
Options- A. 1 2
- B. 3 2
- C. 9 2
- D. 5 4 Discuss
- 7. [(2a2)3]3 [(3a3)2]2 ÷ [(6a6)2]2 is equivalent to :
Options- A. 36a6
- B. 32 a6
- C. 32 a4
- D. 34 a5 Discuss
- 8.
[(3 -2) -5] 1/5 + [ (4 -3) -6] 1/6 - 1 is equivalent to : [ ( 2-3 )-4 ]1/4
Options- A. 9
- B. 8
- C. 27
- D. 1 3 Discuss
- 9. ? x6 ÷ ? x12 × x - 3 × ? x9 is equivalent to :
Options- A. 2x
- B. 1
- C. 1 3x2
- D. 1 x Discuss
- 10. If 3x - 3x-1 = 18, then xx is equal to
Options- A. 3
- B. 8
- C. 27
- D. 216 Discuss
Surds and Indices problems
Search Results
Correct Answer: 1
Explanation:
If any given number (suppose x) is a rational number other than zero, then x0 = 1.
Correct Answer: 12
Explanation:
?2n = 64 ? 2n = (64)2
? 2n = (2 × 2 × 2 × 2 × 2 × 2)2
? 2n = (26)2 ? 2n = 26 × 2 = 212
? n = 12.
Correct Answer: 4
Explanation:
Given that ,
m = 7 - 4?3
Then I/m = 1/7 - 4?3......................(1)
Now multiply and divide with 7 + 4?3 in Eq. (1)
We will get,
1/m = ( 1/7 - 4?3 ) x ( 7 + 4?3 / 7 + 4?3)
?1/m = ( 7 + 4?3 )/ ( 7 - 4?3 ) x ( 7 + 4?3
?1/m = ( 7 + 4?3 ) / ( 72 - ( 4?3)2 )
?1/m = ( 7 + 4?3 ) / ( 49 - 4 x 4 x 3 )
?1/m = ( 7 + 4?3 ) /49 - 48
?1/m = ( 7 + 4?3 ) / 1
?1/m = 7 + 4?3
? m + 1/m = 14
? ( m + 1/m ) + 2 = 14 + 2 = 16
? (?m + 1/?m)2 = ( m + 1/m )+ 2
? (?m + 1/?m)2 = 16
? (?m + 1/?m)2 = 42
? (?m + 1/?m) = 4
Correct Answer: irrational unless n is the mth power of an integer
Explanation:
If m and n are natural numbers, then m?n is irrational unless n is mth power of an integer.
Correct Answer: 14
Explanation:
Given that, a = 2 + ?
Then, 1/a = 2 - ?3 [ by conjugate property ]
Conjugate law is below,
if x = p + ?
then 1/x = p - ?
Apply the law of algebra in above equation.
Now, we have, a
2 + a
-2
= ( a + 1/a )
2 - 2
= ( 2 + ?
3 + 2 - ?
3)
2 - 2
= (4)
2 - 2 = 16 - 2 = 14
Correct Answer: 1 2
Explanation:
Correct Answer: 32 a6
Explanation:
Correct Answer: 9
Explanation:
Correct Answer: 1
Explanation:
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
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