GATE Practice Question and Answer
8Q: How many four digit even numbers can be formed using the digits {2, 7, 5, 3, 9, 1} ? 2407 05b5cc6d7e4d2b4197774e705
5b5cc6d7e4d2b4197774e705- 159false
- 260true
- 361false
- 464false
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Answer : 2. "60"
Explanation :
Answer: B) 60 Explanation: The given digits are 1, 2, 3, 5, 7, 9 A number is even when its units digit is even. Of the given digits, two is the only even digit.Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways. Number of even numbers = ⁵P₃ = 60.
Q: 12 men complete a work in 9 days. After they have worked for 6 days, 4 more men join them. How many days will they take to complete the remaining work ? 1398 05b5cc6d7e4d2b4197774e700
5b5cc6d7e4d2b4197774e700- 12 daysfalse
- 22.5 daysfalse
- 32.25 daystrue
- 43 daysfalse
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Answer : 3. "2.25 days"
Explanation :
Answer: C) 2.25 days Explanation: 1 man's 1 day work = 1/108 12 men's 6 day's work = 1/9 x 6 = 2/3 Remaining work = 1 - 2/3 = 1/3 16 men's 1 day work = 1/108 x 16 = 4/274/27 work is done by them in 1 day. 1/3 work is done by them in 27/4 x 1/3 = 9/4 days.
Q: In an election between two candidates K and L, the number of valid votes received by K exceeds those received by L by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did L get ? 3323 05b5cc6d7e4d2b4197774e6fb
5b5cc6d7e4d2b4197774e6fb- 13241false
- 22457false
- 32642false
- 42834true
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Answer : 4. "2834"
Explanation :
Answer: D) 2834 Explanation: Let the total number of votes polled in the election be 100k.Number of valid votes = 100k - 20% (100k) = 80kLet the number of votes polled in favour of K and L be a and b respectively.a - b = 15% (100k) => a = b + 15k=> a + b = b + 15k + bNow, 2b + 15k = 80k and hence b = 32.5kIt is given that 100k = 872032.5k = 32.5k/100k x 8720 = 2834 The number of valid votes polled in favour of L is 2834.
Q: A sum of money at simple interest amounts to Rs. 415 in 2 years and to Rs. 514 in 4 years. The sum is ? 2483 05b5cc6d7e4d2b4197774e6f6
5b5cc6d7e4d2b4197774e6f6- 1Rs. 316true
- 2Rs. 251false
- 3Rs. 154false
- 4Rs. 294false
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Answer : 1. "Rs. 316"
Explanation :
Answer: A) Rs. 316 Explanation: S.I. for 2 years = (514 - 415) = Rs. 99S.I. for 1 year = 99/2 Principal = (415 - 99) = Rs. 316.
Q: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is ? 1681 05b5cc6d7e4d2b4197774e6e2
5b5cc6d7e4d2b4197774e6e2- 142 secfalse
- 244 secfalse
- 346 secfalse
- 448 sectrue
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Answer : 4. "48 sec"
Explanation :
Answer: D) 48 sec Explanation: Relative speed = 60 + 90 = 150 km/hr. = 150 x 5/18 = 125/3 m/sec. Distance covered = 1.10 + 0.9 = 2 km = 2000 m. Required time = 2000 x 3/125 = 48 sec.
Q: Let K and L be events on the same sample space, with P (K) = 0.8 and P (B) = 0.6. Are these two events are disjoint ? 1668 05b5cc6d7e4d2b4197774e6c6
5b5cc6d7e4d2b4197774e6c6- 1B) = 0.6. Are these two events are disjoint ? A)false
- 2= 0.6. Are these two events are disjoint ? A) TRUE B) FALSE Answer & Explanation Answer: B) FALSE Explanation: These two events cannot be disjoint because P(K) + P(L) > 1. P(AꓴB) = P(true
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Answer : 2. "= 0.6. Are these two events are disjoint ?
A) TRUE
B) FALSE
Answer & Explanation
Answer: B) FALSE
Explanation: These two events cannot be disjoint because P(K) + P(L) > 1.
P(AꓴB) = P("
Explanation :
Answer: B) FALSE Explanation: These two events cannot be disjoint because P(K) + P(L) > 1. P(AꓴB) = P(A) + P(B) - P(AꓵB). An event is disjoint if P(A ꓵ B) = 0. If K and L are disjoint P(K ꓴ L) = 0.8 + 0.6 = 1.4 And Since probability cannot be greater than 1, these two mentioned events cannot be disjoint.
Q: A fair six-sided die is rolled twice. What is the probability of getting 4 on the first roll and not getting 6 on the second roll ? 1935 05b5cc6d7e4d2b4197774e6c1
5b5cc6d7e4d2b4197774e6c1- 11/36false
- 25/36true
- 31/12false
- 41/9false
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Answer : 2. "5/36"
Explanation :
Answer: B) 5/36 Explanation: The two events mentioned are independent. The first roll of the die is independent of the second roll. Therefore the probabilities can be directly multiplied. P(getting first 4) = 1/6 P(no second 6) = 5/6 Therefore P(getting first 4 and no second 6) = 1/6 x 5/6 = 5/36
Q: Statement : The byproducts obtained from animals such as hairs, skins, horns, etc. contain at least 45 per cent food protein. Indian scientists have developed methods to segregate 50 per cent of this protein. They have used an enzyme developed in Russia for destruction of soya-proteins. Conclusions: A. Indian scientists cannot develop enzymes. B. If a suitable method involving less cost is developed then many more food protein would be obtained. 1152 05b5cc6d6e4d2b4197774e6a7
5b5cc6d6e4d2b4197774e6a7- 1Only A followsfalse
- 2Only B followsfalse
- 3Neither A nor B followstrue
- 4Both A & B followsfalse
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Answer : 3. "Neither A nor B follows"
Explanation :
Answer: C) Neither A nor B follows Explanation: There is no indication that Indian scientists are incapable of developing enzymes. There could be any number of reasons why Indian scientists used Russian enzymes. So conclusion A does not follow. In addition, cost is not discussed in the passage at all. There is no mention of a correlation between cost and extraction of proteins. Thus, conclusion B does not follow either.