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- Question
- If a + b + 1 = 0, then the value of (a 3 + b 3 + 1 ? 3ab) is
Options- A. 3
- B. 0
- C. ?1
- D. 1
- Correct Answer
- 0
ExplanationAs we know from the formula,
A3 + B3 + C3 = ( A + B + C) (A2 + B2 + C2 ? AB ? BC ? CA) + 3ABC
If A + B + C = 0 then,
A3 + B3 + C3 = 0 x (A2 + B2 + B2 ? AB ? BC ? CA) + 3ABC
A3 + B3 + C3 = 0 + 3ABC
A3 + B3 + C3 - 3ABC= 0
As we know that from given question,
A = a, B = b and C = 1, Put these value in above equation, we will get
a3 + b3 + 13 - 3 x a x b x 1 = 0
a3 + b3 + 1 - 3ab = 0 - 1. 2508 ÷ 15.02 +? x 11 = 200
Options- A. 13
- B. 8
- C. 3
- D. 4 Discuss
- 2. When the speed of a boat in still water is 4 km/h and the rate of stream is 2 km/h, find upstream speed of the boat.?
Options- A. 6 km/h
- B. 5 km/h
- C. 2 km/h
- D. 7 km/h Discuss
- 3. The sum of three consecutive odd number is 57. The middle one is?
Options- A. 19
- B. 21
- C. 23
- D. 17 Discuss
- 4. Without stoppages, the speed of a train is 150 km/h and with stoppages, it is 100 km/h. How many minutes does the train stop?
Options- A. 20
- B. 15
- C. 25
- D. 45 Discuss
- 5. Raman's present age is three times his daughter's and nine-thirteenth of his mother's present age. The sum of the present ages of all three of them is 125 yr. What is the difference between the present ages of Raman's daughter and Raman's mother?
Options- A. 45 yr
- B. 40 yr
- C. 50 yr
- D. Connot be determined Discuss
- 6. A boat running upstream takes 528 min to cover a certain distance, while it takes 240 min to cover the same distance running downstream. What is the ratio between the speed of the water current, respectively?
Options- A. 2 : 1
- B. 3 : 2
- C. 8 : 3
- D. Couldn't be determined Discuss
- 7. Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4. What will be the total of their present ages?
Options- A. 8 years
- B. 20 years
- C. 35 years
- D. 45 years Discuss
- 8. In ten years, A will be twice as old as B was 10 years ago. If A is now 9 years older then B. Find the present age of B?
Options- A. 39 year
- B. 40 year
- C. 36 year
- D. 49 year Discuss
- 9. Mahatma Gandhi was born on October 2, 1869. The day of the week was:
Options- A. Sunday
- B. Monday
- C. Saturday
- D. Friday Discuss
- 10. Change 75/100 into decimal number.
Options- A. 0.075
- B. 0.75
- C. 0.0075
- D. 7.5 Discuss
More questions
Correct Answer: 3
Explanation:
2508 ÷ 15.02 ÷ ? x 11 = 200
? 2508/15 + ? x 11 = 200
? ? = (200 - 167.2) x 1/11 = 2.98 ? 3
Correct Answer: 2 km/h
Explanation:
Upstream speed of boat = Boat's speed in still water - Rate of stream = 4 - 2 = 2 km/h
Correct Answer: 19
Explanation:
Let the requirement odd integers be N, N +2 and N + 4
Then, N + (N + 2) + (N + 4) = 57
? 3N = 51
? N = 17
? The integers are 17, 19, 21.
Correct Answer: 20
Explanation:
Because of stoppages, train covers 50 km less per hour.
? Time taken taken to cover 50 km = 50/150 h = (50/150) x 60 = 20 min
Correct Answer: 50 yr
Explanation:
Let age of Raman's daughter = N yr
Then, age of Raman's = 3N yr
and age of Raman's mother = (13/9) x 3N = 13N/3 yr
According to the question, N + 3N + 13N/3 = 125
? 3N + 9N + 13N = 125 x 3
? N = (125 x 3)/25 = 15
Hence, required difference = 13N/3 - N = 10N/3
= (10 x 15)/3 = 50 yr
Correct Answer: 8 : 3
Explanation:
Let boat's rate upstream be U and boat's rate downstream = V
According to the question.
Distance covered in 528 min = Distance covered in 240 min
? Distance covered in 8 h 48 min = Distance covered in 4 h
? U x 84/5 = V x 4
? (44 x U)/5 = 4V
? V = (11 x U)/5
? Required ratio = (V + U)/2 : (V - U)/2
? = (11U/5 + U)/2 : (11U/5 - U)/ 2
? = 16U/5 : 6U/5 = 8 : 3
Correct Answer: 35 years
Explanation:
Let A's age 10 years ago = x years
Then, B's age 10 years ago = 2x years
? (x + 10) / (2x + 10) = 3 / 4
? 4(x + 10) = 3(2x + 10)
? x(6 - 4) = 40 - 30
? x = 5
&ther4; Total of their present ages = (x + 10) + (2x + 10)
= (3x + 20)
= 35 years
Correct Answer: 39 year
Explanation:
Let B's present age be x years then A's present age be (x + 9) years
As per the given condition
(x + 9 + 10) = 2(x - 10)
? x = 39
? The present age of B = 39 years
Correct Answer: Saturday
Explanation:
Correct Answer: 0.75
Explanation:
75/100 = 0.75
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