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- Question
- If (a2 + 1/a2) = 17/4, then what is (a3 - 1/a3) equal to?
Options- A. 75/16
- B. 63/8
- C. 95/8
- D. None of these
- Correct Answer
- 63/8
Explanation(a2 + 1/a2) = 17/4
subtracts 2 and Add 2 from above equation, we will get
? a2 + 1/a2 - 2 + 2 = 17/4
? a2 + 1/a2 - 2a x 1/a + 2 = 17/4
Now apply the formula, x2 + x2 - 2xy
? (a - 1/a)2 + 2 = 17/4
? (a - 1/a)2 = 17/4 - 2
? (a - 1/a)2 = (17 - 8)/4
? (a - 1/a)2 = 9/4
? (a - 1/a) = ?9/4
(a -1/a) = 3/2
After that, cubing On both sides, we get
(a -1/a)3 = (3/2)3
Apply the formula (x ? y)3 = x3 ? 3x2y + 3xy2 ? c3
? (x ? y)3 = x3 ? 3xy(x - y) ? y3
? a3 - 1/a3 - 3 x a x 1/a (a - 1/a) = 27/8
? a3 - 1/a3 = 27/8 + 3 x (3/2)
? a3 - 1/a3 = 27/8 + 9/2
? (a3 - 1/a3) = 63/8 - 1. What is the probability that a non-leap year contains 52 Tuesday only?
Options- A. 1/7
- B. 2/7
- C. 3/7
- D. 6/7 Discuss
- 2. 7 1/ 2 - [ 2 1/ 4 ÷ { 1 1/ 4 - 1/2(1 1/ 2 - 1/3 - 1/6)}] is equal to?
Options- A. 2/9
- B. 1
- C. 41/2
- D. 177/288 Discuss
- 3. The radius of a circle is increased so that its circumference increase by 5%. The area of the circle will increase by?
Options- A. 10 %
- B. 10.25 %
- C. 8.75 %
- D. 10.5 % Discuss
- 4. Yogesh can run 1km in 6 min 20 s and Vijay can cover the same distance in 6 min 40 s . By what distance can Yogesh beat Vijay?
Options- A. 50 m
- B. 90 m
- C. 45 m
- D. 30 m Discuss
- 5. There are three pipes connected with a tank. The first pipe can fill 1/2 part of the tank in 1 h, second pipe can fill 1/3 part of the tank in 1 h. Third pipe is connected to empty the tank. After opening all the three pipes, 7/12 part of the tank can be filled in 1 h, then how long will third pipe take to empty the full tank.
Options- A. 3 h
- B. 4 h
- C. 5 h
- D. 6 h Discuss
- 6. The value of (0.96) 3 - (0.1) 3/ [(0.96) 2 + (0.096) + 0.01] is?
Options- A. 0.86
- B. 1.06
- C. 0.95
- D. 0.97 Discuss
- 7. A boy goes to school with a speed of 3 km/hr. and return to the village with a speed of 2 km/hr. If he takes 5 hours in all, then distance between the village and the school is?
Options- A. 6 km.
- B. 7 km.
- C. 8 km.
- D. 9 km. Discuss
- 8. Solve [(238 + 131) 2 + (238 - 131) 2] / (238 x 238 + 131 x 131)
Options- A. 4
- B. 2
- C. 8
- D. 9 Discuss
- 9. A train 200 m long is running at a speed of 36 km/hr. It crosses a bridge in 30 sec. What is the length of the bridge?
Options- A. 150m
- B. 200m
- C. 125m
- D. 100m Discuss
- 10. A cistern can be filled by two pipes. A and B in 12 minutes and 14 minutes respectively and can be emptied by a third pipe C in 8 minutes. If all the taps be turned on at the same moment, what part of cistern will remain unfilled at the end of 7 minutes?
Options- A. 5/24
- B. 19/24
- C. 7/24
- D. 17/24 Discuss
More questions
Correct Answer: 6/7
Explanation:
A non-leap year has 365 days, each day repeats for 52 times with 1 day left
This one can be {Sun, Mon, Wed, Thu, Fri, and Sat}.
? p = 6/7
Correct Answer: 41/2
Explanation:
Given expression = 15/2 -[9/4 ÷ {5/4 - 1/2(3/2 - 1/3 - 1/6)}]
= 15/2 -[9/4 ÷ {5/4 - 1/2 x 1}]
= 15/2 -[9/4 ÷ {5/4 - 1/2}]
= 15/2 -[9/4 ÷ 3/4] = 15/2 - [9/4 x 4/3]
= (15/2 - 3)
= 9 / 2 = 41/2
Correct Answer: 10.25 %
Explanation:
Let circumference = 100 cm .
Then, ? 2?r = 100
? r = 100/2?
=50/?
? New circumference
= 105 cm
Then, 2?R = 105
? R = 105 / (2?)
&rArr Original area = [ ? x (50/?) x (50/?) ]
= 2500/? cm2
? New Area = [? x (105/2?) x (105/2?)]
= 11025 / (4?) cm2
? Increase in area = [11025/(4?)] - 2500/? cm2
= 1025 / 4? cm2
Required increase percent [1025/(4?)] x 2500/? x 100 = 41/4%
= 10.25%
Correct Answer: 50 m
Explanation:
Clearly, Yogesh beats vijay by 20 s.
Distance covered by vijay in 400 s = 1000 m
[? 6 min 40 s = 400 s]
Distance covered by Vijay in 20 s = (1000/400) x 20 m = 50 m
? Yogesh beats Vijay by 50 m.
Correct Answer: 4 h
Explanation:
1st pipe takes 1 h to fill 1/2 part of the tank.
So, time taken to fill the whole tank (m) = 2 h
2nd pipe takes 1 h to 1/3 part of the tank
So, time taken to fill the whole tank (n) = 3 h
Let 3rd pipe takes P h to empty the tank = x
? 1/m + 1/n - 1/x = 7/12 ? 1/2 + 1/3 - 1/x = 7/12
? 1/x = (6 + 4 - 7)/12 = 3/12 = 1/4
? x = 4 h
Correct Answer: 0.86
Explanation:
(0.96)3 - (0.1)3/ [(0.96)3 + 0.096 + 0.01]
= (0.96)3 - (0.1)3 = (0.96 - 0.1) [(0.96)2 + 0.96 x 0.1 + (0.1)2]
[? a3 - b3 = (a - b) (a2 + ab + b2)]
= (0.96 - 0.1) [(0.96)2 + 0.096 + 0.01]/(0.96)2 + 0.096 + 0.01
= 0.96 - 0.1 = 0.86
Correct Answer: 6 km.
Explanation:
Let The required distance be y km.
Then, y/3 + y/2 = 5
? 2y + 3y = 30
? y = 6 km
Correct Answer: 2
Explanation:
Given expression
= [(a + b)2 + (a - b)2] / [a2 + b2]
= 2(a2 + b2) / (a2 + b2)
= 2
where, a = 238, b = 131
Correct Answer: 100m
Explanation:
Speed in m/sec = 36 km/hr x 5/18 = 10m/sec
Distance covered by train in crossing the bridge = Speed of train in m/sec x time in sec = 10 m/sec x 30 sec = 300 m
Now, we know that
Distance covered by train in crossing the bridge= Length of train + Length of bridge
Therefore, Length of bridge = 300m - 200m = 100m
Correct Answer: 19/24
Explanation:
Time taken to fill the whole tank = (12 x 14 x 8) / (14 x 8 + 12 x 8 - 12 x 14) = 168/5 minutes
? In 7 minutes 5/168 x 7 = 5/24 part of the tank will be filled
? Requied answer = 1 - 5/24 = 19/24 part
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