Discussion
Home ‣ Aptitude ‣ Surds and Indices Comments
- Question
- If ?2n = 64 , what will be the value of n?
Options- A. 8
- B. 4
- C. 12
- D. 16
- 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. - 1. If m = 7 - 4?3, then (?m + 1/?m) =?
Options- A. 8
- B. 3
- C. 4
- D. 9 Discuss
- 2. 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
- 3. if a = 2 + ?3, then what is the value of (a2 + a -2)?
Options- A. 12
- B. 14
- C. 16
- D. 18 Discuss
- 4. 1/1 + xb - a + xc - a + 1/1 + xa-b + xc - b + 1/1 + xb - c+ xa - c =?
Options- A. xa - b - c
- B. 1
- C. 0
- D. 3 Discuss
- 5. If a = ?3/2, then ?1 + a + ?1 - a =?
Options- A. (2- ?3)
- B. (2 + ?3)
- C. ?3/2
- D. ?3 Discuss
- 6. (100)0 is equivalent to :
Options- A. 0
- B. 10
- C. 1
- D. 100 Discuss
- 7. 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 Discuss
- 8. (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
- 9. [(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
- 10.
[(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
Surds and Indices problems
Search Results
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
Explanation:
? = 1/ ( 1 + xb - a + xc - a ) + 1/ ( 1 + xa - b + xc - b ) + 1 / ( 1 + xb - c + xa - c )
Apply the law of algebra and solve the given equation.
? ? =1/ ( 1 + xb/xa + xc/xa ) + 1/ ( 1+ xa/xb + xc/xb ) + 1/ ( 1 + xb/xc + xa/xc )
? ? = xa/ ( xa+xb+xc ) + xb/ ( xb + xa+ xc ) + xc/ ( xc+xb+xa )
? ? = ( xa + xb + xc ) / ( xa + xb + xc ) = 1
Correct Answer: ?3
Explanation:
Let us assume
P = ?1 + a + ?1 - a
Square on both side,
P 2 = ( ?1 + a + ?1 - a ) 2
Use the formula ( a + b ) 2 = a 2 + b 2 + 2ab
we will get
? P 2 = (1 + a) + (1- a) + 2 ?1 + a x ?1 - a
? P 2 = (1 + a) + (1- a) + 2 ?(1 + a ) x ( 1 - a )
? P 2 = 2 + 2 ?1 - a2
? P 2 = 2 (1 + ?1 - a2)
Now put the value of a which is given in question;
? P 2 = 2 (1 + ?1 - ( ?3/2 )2)
? P 2 = 2(1 + ?1 - 3/4 )
? P 2 = 2(1 + ?1/4 )
? P 2 = 2(1 + 1/2) = 2 x 3/2 = 3
? P= ?3
? (?1 + a + ?1 - a) = ?3
Correct Answer: 1
Explanation:
If any given number (suppose x) is a rational number other than zero, then x0 = 1.
Correct Answer: 3a b 2 c
Explanation:
Correct Answer: 1 2
Explanation:
Correct Answer: 32 a6
Explanation:
Correct Answer: 9
Explanation:
Comments
There are no comments.More in Aptitude:
Programming
Copyright ©CuriousTab. All rights reserved.