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- Question
- If a = ( ?2 -1)1/3, then the value of (a - a-1)3 + 3 ( a - a -1 ) is?
Options- A. -2
- B. 2
- C. 2?2
- D. ?2
- Correct Answer
- -2
ExplanationGiven that,
a = (?2 - 1)1/3
By cubing the both side of the given equation.
a3 = ?2 - 1
Then 1/a3 = 1/?2 - 1
Now multiply and divide the above equation by ?2 + 1
? 1/a3 = ( ?2 + 1 ) / ( ?2 + 1 ) x 1/(?2 - 1 )
? 1/a3 = ( ?2 + 1 ) x 1 / ( ?2 + 1 ) x (?2 - 1 ) [ Use the formula (A + B)(A - B) = A2 - B2 ]
? 1/a3 = ( ?2 + 1 ) / ( 2 - 1 )
? 1/a3 = ?2 + 1
According to the question
( a - a-1 )3 + 3 ( a - a-1 )
= (a - 1/a)3 + 3(a - 1/a) Use the formula [ ( A - B)3 = A3 - B3 + 3AB(A - B) ]
= a3 - 1/a3 - 3 a x 1/a (a -1/a) + 3(a - 1/a)
= a3 - 1/a3 - 3 (a -1/a) + 3(a - 1/a)
= a3 - 1/a3
Pu the value of a3 and 1/a3
= ?2 -1 - ( ?2 + 1 )
= ?2 -1 - ?2 - 1
= -2 - 1. Two train start at the same time Aligarh and Delhi and processed toward each other at 16 km/hr and 21 km/hr respectively when they meet, it is found that one train has travelled 60 km more than the other. The distance between two station is?
Options- A. 445 km.
- B. 444 km.
- C. 440 km.
- D. 450 km. Discuss
- 2. If Reena?s age was twice of her present age, when subtracted from four times three years from hence, with three times the three years before her present age. What will be her age after one year ?
Options- A. 22 yrs
- B. 21 yrs
- C. 20 yrs
- D. 24 yrs Discuss
- 3. A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B ?
Options- A. 10 yrs
- B. 11 yrs
- C. 12 yrs
- D. 13 yrs Discuss
- 4. The sum of the ages of father and a son presently is 70 years. After 10 years, the son's age is exactly half that of the father. What are their ages now?
Options- A. 45 years, 25 years
- B. 50 years, 20 years
- C. 47 years, 23 years
- D. 50 years, 25 years Discuss
- 5. The ages of Sunil and Anil are in the ratio 8:7, after 6 years, the ratio of their ages will be 19 : 17. What is the difference in their present ages?
Options- A. 10 years
- B. 6 years
- C. 8 years
- D. 4 years Discuss
- 6. The average age of a class of 6 girls is x years. Four new girls having ages x ? 2, x + 2, x + 4 and x + 6 joins the class. What is the new average age (in years) of the class?
Options- A. x + 1
- B. x + 2
- C. 2.5x
- D. x + 2.5 Discuss
- 7. The ratio of the present ages of Aman and Ankit is 2 : 1 and the sum of their present ages is 72 years. What will be the Aman's age (in years) after 6 years?
Options- A. 30
- B. 48
- C. 52
- D. 54 Discuss
- 8. Ratio of A's age to B's age is 4:3. 'A' will be 26 years old after 6 years. The age of B now is
Options- A. 12 years
- B. 21 years
- C. 13 years
- D. 15 years Discuss
- 9. K is 5 years older to H. H is 3 years younger to R. R is 6 years older to C. C is 7 years younger to L. Who is the eldest?
Options- A. H
- B. K
- C. R
- D. L Discuss
- 10. The ratio of ages of the father and mother was 11:10 when their son was born. The ratio of ages of the father and mother will be 19:18 when the son will be twice his present age. What is the ratio of present ages of father and mother?
Options- A. 15 : 14
- B. 14 : 13
- C. 16 : 15
- D. 17 : 16 Discuss
More questions
Correct Answer: 444 km.
Explanation:
Suppose they meet after y hours .
Then, 21y - 16y = 60
? y = 12
?required distance = (16 x 12 + 21 x 12) km.
= 444 km.
Correct Answer: 22 yrs
Explanation:
Let Reena?s present age be 'K' yrs.
Given:{(K+3) x 4} - {(K-3) x 3)}
=> K = 21 yrs
So her present age is 21 yrs.
Then, her age after 1 year is 22 yrs.
Correct Answer: 10 yrs
Explanation:
Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25 => x = 5
Hence, B's age = 2x = 10 years.
Correct Answer: 50 years, 20 years
Correct Answer: 4 years
Explanation:
suppose the ages of Sunil and Anil are 8x yr and 7x yr, respectively.
After 6 yr, = 136x + 102 = 133x + 114
136x ? 133x = 114 ? 102
3x = 12 X = 12/3 = 4
Age of Sunil = 8x = 8 × 4 = 32 yr
Present age Anil = 7x = 7 × 4 = 28 yr
Required difference = (32 ? 28) = 4 yr
Correct Answer: x + 1
Correct Answer: 54
Correct Answer: 15 years
Correct Answer: K
Correct Answer: 15 : 14
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