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- Question
- If a + 1/a = ? 3, then the value of a6 - 1/a6 + 2 will be
Options- A. 3?3
- B. 5
- C. 1
- D. 2
- Correct Answer
- 2
ExplanationGiven equation is,
a + 1/a = ?3 .............................(i)
On squaring both sides
? a2 + 1/a2 + 2 = 3
? a2 + 1/a2 = 1 ..............................(ii)
Now, multiplying Equation (i) and (ii), we get
(a + 1/a) (a2 + 1/a2) = ?3
? a3 + a/a2 + a2/a + 1/a3 = ?3
? a3 + 1/a3 + ( a + 1/a ) = ?3
now put the value of a + 1/a in above equation,
? a3 + 1/a3 + ?3 = ?3 [from Eq. (i)]
? a3 + 1/a3 = 0
? ( a6 + 1 ) /a3 = 0
? a6 + 1 = 0 x a3
? a6 + 1 = 0
? a6 = -1
? a6 - 1/a6 + 2
put the value of a6
= (-1)6 - 1/(-1)6 + 2
= 1 - 1 + 2 = 2 - 1. If the price of 357 apples is Rs. 1517.25, what will be the approximate price of 49 dozens of such apples?
Options- A. Rs. 2500
- B. Rs. 2800
- C. Rs. 2900
- D. Rs. 2400 Discuss
- 2. 15 years later, A will be twice as old as B but five years ago A was 4 times as old as B. Find the difference of their present ages?
Options- A. 15 years
- B. 45 years
- C. 30 years
- D. 25 years Discuss
- 3. The ratio of the present ages of a son and his father is 1 : 5 and that of his mother and father is 4 : 5. After 2 years the ratio of the age of the son to that of his mother becomes 3 : 10. What is the present age of the father?
Options- A. 30 years
- B. 28 years
- C. 27 years
- D. None of these Discuss
- 4. Two trains of length 512 m and 528 m are running towards each others on parallel lines at 84 km/h and 60 km/h, respectively. In what time, will they be clear of each other from the moments they meet?
Options- A. 26 s
- B. 25 s
- C. 15 s
- D. 27 s Discuss
- 5. Shantanu completes 5/8 of a job in 20 days. At this rate, how many more days will he take to finish the job?
Options- A. 6 days
- B. 18 days
- C. 5 days
- D. 12 days Discuss
- 6. Two unbiased dice are thrown simultaneously. the probability of getting the sum divisible by 3, is?
Options- A. 11/36
- B. 12/36
- C. 13/36
- D. 17/36 Discuss
- 7. 1 + 1 ÷ {1 + 1 ÷ (1 + 1/3)} =?
Options- A. 11/3
- B. 14/7
- C. 11/8
- D. 12/3 Discuss
- 8. The present worth of a sum due sometimes hence is Rs. 576 and the banker's gain is Re. 1. The true discount is?
Options- A. Rs. 16
- B. Rs. 18
- C. Rs. 24
- D. Rs. 32 Discuss
- 9. A businessman purchased 30 TV sets in ? 300000, If the average cost of 15 TV sets is ? 9000 then find out the average cost of remaining TV sets.
Options- A. ?20000
- B. ? 12000
- C. ? 11000
- D. ?10000 Discuss
- 10. Ten years ago the average age of a family of 4 members was 24 years. Two children having been born average age of the family is same today. What is the present age of the youngest child if they differ in age by 2 years?
Options- A. 1 year
- B. 2 years
- C. 3years
- D. 5 years Discuss
More questions
Correct Answer: Rs. 2500
Explanation:
As we know that,
1 Dozen = 12 piece
49 Dozen = 49 x 12 piece
Price of 357 apples is Rs. 1517.25.
Price of 1 apples is Rs. 1517.25 / 357.
Price of 49 x 12 apples is Rs. 1517.25 x 49 x 12 / 357.
Price of 49 x 12 apples is Rs. 1517.25 x 7 x 12 / 51.
Price of 49 x 12 apples is Rs. 1517.25 x 7 x 4 / 17.
Price of 49 x 12 apples is Rs. 2499.
So Price will be around 2500 and answer will be 2500.
Correct Answer: 30 years
Explanation:
Let A's age = x years and B's age = y years
As per the first condition,
? (x + 15) = 2(y + 15)
? x - 2 y = 15 ....(i)
As the per second condition,
? (x - 5) = 4(y - 5)
? x - 4 y = -15 ....(ii)
Solving (i) and (ii) one get's, x = 45, y = 15
? A's age = 45 years
B's age = 15 years
? Difference of their ages = 45 - 15 = 30 years
Correct Answer: None of these
Explanation:
? S / F = 1 / 5
? F = 5 S, .....(i)
? M / F = 4 / 5
? M = 4 / 5 F ....(ii)
? (S + 2) / (M + 2) = 3 / 10
? 10S + 20 = 3M + 6 ....(iii)
From (i), (ii) and (iii)
? (12 - 10)S = 20 - 6
? 2S = 14
? S = 7 years
? F = 5S = 5 x 7 = 35 years.
Correct Answer: 26 s
Explanation:
Relative speed = (84 + 60) km/h = 144 km/h = 144 x (5/18) = 8 m/s
Distance covered in passing each other = 512 + 528 = 1040 m
? Required time = 1040/40 = 26 s
Correct Answer: 12 days
Explanation:
Let the required number of days be N.
Remaining work = 1 - 5/8 = 3/8
Less work, Less days (Direct proportion)
5/8 : 3/8 : : 20 : N
? N = (3/8) x 20 x 8/5
? N = 12 days
Correct Answer: 12/36
Explanation:
n(S) = 6 x 6 = 36
n(E) = (1, 2) (2, 1), (1, 5) (2, 4) (3, 3) (4, 2) (5, 1) (3, 6) (4, 5) (5, 4) (6, 3) (6, 6) = 12
? P(E) = 12/36
Correct Answer: 14/7
Explanation:
Given expression = 1 + 1 ÷ {1 + 1 ÷ (1 + 1/3)}
= 1 + 1 ÷ { 1 + 1 ÷ 4/3}
= 1 + 1 ÷ { 1 + 3/4}
= 1 + 1 ÷ 7/4
= 1 + 1 x 4/7
= 1 + 4/7
= 14/7
Correct Answer: Rs. 24
Explanation:
T.D. = ?(P.W.) X {(B.G.)
= ?(576 x 1) = Rs. 24
Correct Answer: ? 11000
Explanation:
Total cost of 30 TV sets = ? 300000
Total cost of 15 TV sets = 9000 x 15 = 135000
Total cost of remaining 15 TV sets = 300000 - 135000 = 165000
? Average cost of remaining TV sets = 165000/15 = ? 11000
Correct Answer: 3years
Explanation:
Let the age of youngest child be y.
Then y + ( y + 2 ) = ( 24 x 6 ) - ( 24 x 4 + 4 x 10)
= 144 - 136
? 2y + 2 = 8
? y =3 years
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