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- Question
- Form a quadratic equation whose one root is 3 - ?5 and the sum of roots is 6
Options- A. x2 ? 6x + 4 = 0
- B. x2 + 6x + 4 = 0
- C. x2 ? 6x ? 4 = 0
- D. None of these
- Correct Answer
- x2 ? 6x + 4 = 0
ExplanationGiven : - Sum of the roots ( k1 + k2 ) = 6
One root k1 = 3 - ?5
? the other root k2 = 6 - ( 3 - ?5) = 3 + ?5
? Product of roots k1k2 = ( 3 - ?5 ) ( 3 + ?5 )
product of roots = 9 - 5 = 4
Hence , the required equation is x2 - (sum of the roots)x + (product of roots) = 0
? x2 - 6x + 4 = 0. - 1. A tank be filled by one tap in 20 min. and by another in 25 min. Both the taps are kept open for 5 min. and then the second is turned off. In how many minutes more is the tank completely filled?
Options- A. 171/2 min.
- B. 12 min.
- C. 11 min.
- D. 6 min. Discuss
- 2. The simple interest on a sum of money will be ? 600 after 10 yr. It the principle is trebled after 5 yr, what will be the total interest at the end of tenth year?
Options- A. ? 600
- B. ? 900
- C. ? 1200
- D. ? 1500 Discuss
- 3. In a class of 50 students, 35 opted for mathematics and 37 opted for Biology. How many have opted for both Mathematics and Biology? How many have opted for only Mathematics? (Assume that each student has to opt for at least one of the subjects).
Options- A. 15
- B. 17
- C. 13
- D. 19 Discuss
- 4. The probability that a man will be alive for 10 more years is 1/4 and the probability that his wife will alive for 10 more years is 1/3 .The probability that none of them will be alive for 10 more years, is
Options- A. 5/12
- B. 1/2
- C. 7/12
- D. 11/12 Discuss
- 5. Two trains running at 36 km/hr and 54 km/hr are running parallel in the opposite direction. If their lengths are 200m and 300m respectively. Then how much time will they take to cross each other?
Options- A. 20 sec
- B. 25 sec
- C. 30 sec
- D. 35 sec Discuss
- 6. In the given figure, DE || BC and DE : BC = 3 : 5 the ratio of the areas of ? ADE and the trapezium BCED.
Options- A. 9 25
- B. 12 25
- C. 3 4
- D. 9 16 Discuss
- 7. A certain sum becomes 8 fold in 15 yr at simple interest. What will be the rate interest?
Options- A. 465/3%
- B. 462/3%
- C. 465/8%
- D. 4612/11% Discuss
- 8. Four boys and three girl stand in queue for an interview. The probability that they stand in alternate position is
Options- A. 1/34
- B. 1/35
- C. 1/17
- D. 1/68 Discuss
- 9. A and B together can do a work in 24 days. B alone does its 1/3 part in 12 days. How long will A alone take to do the remaining work?
Options- A. 48 days
- B. 36 days
- C. 24 days
- D. 72 days Discuss
- 10. The sides AB and AC of ?ABC have been produced to D and E respectively. The bisectors of ?CBD and ?BCE meet at O. If ?A = 40°, then ?BOC is equal to:
Options- A. 60°
- B. 65°
- C. 75°
- D. 70° Discuss
More questions
Correct Answer: 11 min.
Explanation:
Work done by both the taps in 5 min
= 5 (1/20 +1/25) = (5 x 9)/100 = 9/20
Remaining part = (1 - 9/20) = 11/20
Now, 1/20 part is filled in 1 min.
So, 11/20 part will be filled in 11 min.
Hence, the tank will be full in 11 more min.
Correct Answer: ? 1200
Explanation:
Let the principle and rate of interest be P and R%
Then, (P x R x 10)/100 = 600
? PR = 6000
Total interest at the end of year = 300 + (3P x R x 5)/100 = 300 + (15 x 6000)/100 = ? 1200
Correct Answer: 13
Explanation:
Given in the question,
n(M ? B) = 50, n(M) = 35, n(B) = 37, n(M ? B) =?
use the below formula
n(M ? B) = n(M) + n(B) ? n(M ? B)
We get 50 = 35 + 37 ? n(M ? B)
? n(M ? B) = 35 + 37 ? 50 = 72 ? 50 = 22
? 22 students have opted for both Mathematics and Biology.
Again number of students who have opted for only Mathematics = n(M) ? n(M ? B) = 35 ? 22 = 13.
Correct Answer: 1/2
Explanation:
Required probability = P(A) x P(B)
= (1 - 1/4) x (1 - 1/3) = 3/4 x 2/3 = 1/2
Correct Answer: 20 sec
Explanation:
Relative speed, when the trains are running in the opposite direction = Sum of the speed
Therefore, Relative speed = 36 km/hr +72 km/hr = 90 km/hr
Relative speed in m/sec = 90 km/hr x 5/18= 25 m/sec
Distance covered = sum of the lengths of the train = 200 m+ 300 m = 500m
Therefore, time taken = 500m / 25 m/sec = 20 sec
Correct Answer: 9 16
Explanation:
Correct Answer: 462/3%
Explanation:
Let sum = p
Then, after 15 yr
Sum = 8p
? SI = 8p - P = 7P
Now, 7P = (P x R x 15)/100
? 7 = 15R/100 = 3R/20
? R = (20 x 7)/3 = 140/3
= 462/3%
Correct Answer: 1/35
Explanation:
Total number of possible arrangement for 4 boy and 3 girls in a queue = 7!
when they occupy alternate position then the arrangement would be like
BGBGBGB. Thus the total number of possible arrangement = 4! x 3!
? Required probability = 4! x 3! / 7!
= (4 x 3 x 2 x 3 x 2) / (7 x 6 x 5 x 4 x 3 x 2) = 1/35
Correct Answer: 48 days
Explanation:
Work done by (A + B) in 1 day = 1/24
Work done by B alone in 1 day = 1/(3 x 12) = 1/36
? Work of A for 1 day = 1/24 - 1/36 = 1/72
After 12 days the remaining work = 1 - 1/3 = 2/3
? 1/72 work is done by A in 1 day
? 2/3 work is done by A in (1 x 72)/(1 x 2/3) = 48 days
Correct Answer: 70°
Explanation:
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