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- Question
A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
Options- A. 45 m
- B. 50 m
- C. 54 m
- D. 72 m
- Correct Answer
- 50 m
Explanation2 kmph = ❨ 2 x 5 ❩ m/sec = 5 m/sec. 18 9 4 kmph = ❨ 4 x 5 ❩ m/sec = 10 m/sec. 18 9 Let the length of the train be x metres and its speed by y m/sec.
Then, ❨ x ❩ = 9 and ❨ x ❩ = 10. y - 5 9 y - 10 9 ∴ 9y - 5 = x and 10(9y - 10) = 9x
⟹ 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
∴ Length of the train is 50 m.
- 1. If U = {a, b, c, d, e, f}, A = {a, b, c}, B = {c, d, e, f}, C = {c, d, e}, find (A ? B) ? (A ? C).
Options- A. {c}
- B. {a}
- C. {b}
- D. {d} Discuss
- 2. If a and b are the roots of the equation x 2 - 6x + 6 = 0, find the value of 2(a 2 + b 2).
Options- A. 40
- B. 42
- C. 48
- D. 46 Discuss
- 3. The simple interest on a certain sum of money for 3 yr at 8 % pa is half the compound interest on ? 8000 for 2 yr at 10 % pa. Find the sum on which simple interest is calculated
Options- A. ? 3500
- B. ? 3800
- C. ? 4000
- D. ? 3600 Discuss
- 4. The value of k for which the roots ?, ? of the equation : x2 ? 6x + k = 0 satisfy the relation 3? + 2? = 20, is
Options- A. 8
- B. - 8
- C. 16
- D. - 16 Discuss
- 5. What amount will be received on a sum of ? 1750 in 2 1/ 2 yr, if the interest is compounded at the rate of 8% pa?
Options- A. ? 2125
- B. ? 2122.85
- C. ? 2100
- D. ? 2200 Discuss
- 6. Find what is that first years in which a sum of money will become more than double in amount if put out at compound interest at the rate of 10% per annum?
Options- A. 6th years
- B. 7th years
- C. 8th years
- D. Data inadequate Discuss
- 7. A sum of ? 8448 is to be divided between A and B who are respectively 18 and 19 yr old, in such a way that if their shares be invested at 6.25 % per annum at compound interest, they will receive equal amounts on attaining the age of 21 yr. The present share of A is
Options- A. ? 4225
- B. ? 4352
- C. ? 4096
- D. ? 4000 Discuss
- 8. What is the difference between the compound interest and simple interest calculated on an amount of ? 16200 at the end of 3 yr at 25% pa? (Rounded off to two digits after decimal)
Options- A. ? 3213.44
- B. ? 3302.42
- C. ? 3495.28
- D. ? 3290.63 Discuss
- 9. How many times do the hands of a clock coincide in a day?
Options- A. 20
- B. 21
- C. 22
- D. 24 Discuss
- 10. x = 3a solution of the equation 3x2 + (k ? 1)x + 9 = 0 if k has value
Options- A. 13
- B. ?13
- C. 11
- D. ?11 Discuss
More questions
Correct Answer: {c}
Explanation:
A ? B = {a, b, c} ? {c, d, e, f}
A ? B = { c }
A ? C = { a, b, c } ? { c, d, e }
A ? C = { c }
? (A ? B) ? (A ? C) = { c }.
Correct Answer: 48
Explanation:
a and b are the roots of the equation
x2 - 6x + 6 = 0
? a + b = -B/A = 6 and ab = C/A = 6
We know that,
a2 + b2 = (a + b)2 - 2ab
= (6)2 - 2 x 6 = 36 - 12 = 24
? 2(a2 + b2) = 2 x 24 = 48
Correct Answer: ? 3500
Explanation:
CI = 8000 x (1 + 10/100)2 - 8000
= 8000 x (11/10) x (11/10) - 8000
= ? 9680 - 8000
= ? 1680
? Sum = (840 x 100)/(3 x 8) = ? 3500
[ ? SI is half of CI ]
? SI = 1680/2 = ? 840
Correct Answer: 8
Explanation:
According to question , we have
The roots ?, ? of the equation : x2 ? 6x + k = 0
On comparing with ax2 + bx + c = 0 , we get a = 1 , b = - 6 , c = k
Now , ? + ? = ( - b/a ) = 6
? + ? = 6 and 3? + 2? = 20
On solving ,
? ? = 4, ? = 2
Product of the roots = k
So, k = ?? = 4 × 2 = 8.
Hence , required answer will be option A .
Correct Answer: ? 2122.85
Explanation:
Given, P = ? 1750, R = 8%,
n = 2 and a/b = 1/2
According to the formula,
Amount = P(1 + R/100)n x [1 + {(a/b) x R}/100]
=1750 (1 + 8/100 )2 [1 + {(1/2) x 8} /100]
=1750 (27/25)2 x 26/25
= 1750 x (27/25) x (27/25) x (26/25)
=? 2122.848
= ? 2122.85
Correct Answer: 8th years
Explanation:
Here, P(1 + 10/100)t > 2P
? (11/10)t > 2
When t = 8 ? (11/10)8 = 2.14358
t =7 ? (11/10)7 = 1.9487
By trial, [11 x 11 x 11 x 11 x 11 x 11 x 11 x 11] / [10 x 10 x 10 x 10 x 10 x 10 x 10 x 10] >2
Hence, the first years in which sum of money will become more than double in amount is 8th year
Correct Answer: ? 4096
Explanation:
Let shares of A and B be ? N and ? (8448 - N), respectively,
Amount got by A after 3 yr = Amount got by B after 2 yr
N(1 + 6.25/100)3 = (8448 - N) x (1 + 6.25/100)2
? 1 + 6.25/100 = (8448 - N)/N
? 1 + 1/16 = (8448 - N)/N
? 17/16 = (8448 - N)/N
? 17N = 135168 - 16N
? N = 4096
Correct Answer: ? 3290.63
Explanation:
Let required difference be ? D.
By formula,
D = P x (R/100)2 x [(3 + R)/100]
= 16200 x (25/100)2 x [(3 + 25)/100]
= 16200 x 625/10000 x 13/4
= 162 x 625 x 13/4 x 100 = ? 3290.63
Correct Answer: 22
Explanation:
AM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
PM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
The hands overlap about every 65 minutes, not every 60 minutes.
∴ The hands coincide 22 times in a day.
Correct Answer: ?11
Explanation:
The given quadratic equation 3x2 + (k ? 1)x + 9 = 0
Putting x = 3 in above given eq. , we get
27 + 3(k ? 1) + 9 = 0
? 27 + 3k - 3 + 9 = 0
? 3k = ?33 ? k = ?11.
Hence , the value of k is ?11.
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