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- Question
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
Options- A.
1 2 - B.
3 4 - C.
3 8 - D.
5 16 - Correct Answer
-
3 4
ExplanationIn a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),
(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),
(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}∴ n(E) = 27.
∴ P(E) = n(E) = 27 = 3 . n(S) 36 4
More questions
- 1. The banker's gain of a certain sum of money is Rs. 36 and the true discount on the same sum for the same time and at the same rate is Rs. 30. The sum is?
Options- A. Rs. 1080
- B. Rs. 180
- C. Rs. 500
- D. Rs. 300 Discuss
Correct Answer: Rs. 180
Explanation:
Sum = (B.D. x T.D.) / (B.D. - T.D.) = Rs. (36 x 30) / 6
= Rs. 180- 2. The H.C.F. of 9⁄10, 12⁄25, 18⁄35 and 21⁄40 is:
Options- A. 3⁄5
- B. 252⁄5
- C. 3⁄1400
- D. 63⁄700 Discuss
Correct Answer: 3⁄1400
Explanation:
Required H.C.F. = H.C.F. of 9, 12, 18, 21 = 3 L.C.M. of 10, 25, 35, 40 1400 - 3. If 7 spiders make 7 webs in 7 days, then how many days are needed for 1 spider to make 1 web?
Options- A. 10
- B. 7
- C. 3
- D. 4 Discuss
Correct Answer: 7
Explanation:
7 spiders make 7 webs in 7 days.
? 1 spiders make 7 webs in 7 x 7 days.
? 1 spiders make 1 webs in 7 x 7 / 7 days.
? 1 spiders make 1 webs in 7 days.- 4. 134% of 3894 + 38.94 % of 134 =?
Options- A. 5000
- B. 5300
- C. 5500
- D. 5270 Discuss
Correct Answer: 5270
Explanation:
134% of 3894 + 38.94% of 134 = ?
? ? = (3894 x 134)/100 + (38.94 x 134)/100
= 5217.96 + 52.1796
= 5270.1396 ? 5270- 5. Find the value of 2 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
Options- A. 800
- B. 500
- C. 900
- D. 1600 Discuss
Correct Answer: 1600
Explanation:
2 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
= 2 x [(36 x 48 x 250) / (12 x 9 x 5)]
= 2 x 4 x 4 x 50 = 1600- 6. Ram and Mohan are friends. Each has some money. If Ram gives ? 30 to Mohan, Then Mohan will have twice the money left with Ram. But if Mohan gives ? 10 to Ram, Then Ram will have thrice as much as is left with Mohan. How much money does each have?
Options- A. ?62,?34
- B. ?6,?2
- C. ?170,?124
- D. ?43,?26 Discuss
Correct Answer: ?62,?34
Explanation:
Let us assume Ram has R rupees and Mohan has M rupees.
According to question,
If Ram gives 30 rupees to Mohan, then
Ram has left money = R - 30 and Mohan has money = M + 30
Then Mohan will have twice the money left with Ram,
M + 30 = 2(R - 30)
M + 30 = 2R - 60
2R - M = 90................................(1)
Again According to question,
if Mohan gives 10 rupees to Ram, then
Mohan has left the money = M - 10 and Ram has the money = R + 10
Then According to question,
Ram will have thrice as much as is left with Mohan,
R + 10 = 3 (M - 10 )
? R + 10 = 3M - 30
? 3M - R = 10 + 30
? 3M - R = 40..................................(2)
After Multiplying 2 with Equation (2) , add with the equation (1),
6M - 2R + 2R - M = 80 + 90
? 6M - M = 170
? 5M = 170
? M = 170/5
? M = 34
Put the value of M in equation (1), we will get
? 2R - 34 = 90
? 2R = 90 + 34
? 2R = 124
? R = 124/2
? R = 62- 7. Two men start together to walk a certain distance, one at 4 km/h and another at 3 km/h. The former arrives half an hour before the latter. Find the distance.
Options- A. 6 km
- B. 9 km
- C. 8 km
- D. 7 km Discuss
Correct Answer: 6 km
Explanation:
Let total distance = x km
According to the question,
x/3 - x/4 = 1/2;
? x/12 = 1/2
? x = 6 km- 8. A positive number, when increased by 10 equal 200 times its reciprocal . What is the number?
Options- A. 100
- B. 10
- C. 20
- D. 200 Discuss
Correct Answer: 10
Explanation:
Let the positive number be N.
According to the question,
N + 10 = 200/N
? N2 + 10N = 200
? N2 + 10N - 200 = 0
? ( N - 10) ( N + 20) = 0
&ythere4; N = 10 and N = -20
But N ? -20, since N is a positive number.
So, the required number is 10.- 9. From a 15 m high bridge on the river, the angle of depression of a boat is 30°. If the speed of the boat be 6 Km/h, then the time taken by the boat to reach exactly below the bridge will be :
Options- A. 9 ?3 second
- B. 19 / ?3 second
- C. 3 ?3 second
- D. None of these Discuss
Correct Answer: 9 ?3 second
Explanation:
- 10. Which of the following statements is not correct?
Options- A. log10 10 = 1
- B. log (2 + 3) = log (2 x 3)
- C. log10 1 = 0
- D. log (1 + 2 + 3) = log 1 + log 2 + log 3 Discuss
Correct Answer: log (2 + 3) = log (2 x 3)
Explanation:
(a) Since loga a = 1, so log10 10 = 1.(b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3
∴ log (2 + 3) ≠ log (2 x 3)
(c) Since loga 1 = 0, so log10 1 = 0.
(d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.
So, (b) is incorrect.
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