CAT Practice Question and Answer
8Q: For x∈N, x>1, and p=logxx+1, q=logx+1x+2 then which one of the following is correct? 6993 25b5cc7d0e4d2b419777511ff
5b5cc7d0e4d2b419777511ff- 1p < qfalse
- 2p = qfalse
- 3p > qtrue
- 4can't be determinedfalse
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- SingleChoice
Answer : 3. "p > q"
Explanation :
Answer: C) p > q Explanation: kl>k+1l+1 for (k,l) > 0 and k > l Let k = x+1 and l = x Therefore, x+1x>(x+1)+1(x)+1 (x + 1) > x Therefore, log(x+1)log(x)>log(x+2)log(x+1) ⇒logxx+1 >logx+1x+2
Q: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold ? 6944 05b5cc6ebe4d2b4197774eeb4
5b5cc6ebe4d2b4197774eeb4- 1360 litfalse
- 2480 littrue
- 3320 litfalse
- 4420 litfalse
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Answer : 2. "480 lit"
Explanation :
Answer: B) 480 lit Explanation: 1/k - 1/20 = -1/24 k = 120 120 x 4 = 480 Therefore, the capacity of the cistern is 480 liters.
Q: 45% of 750 - 25% of 480 = ? 6902 05b5cc6dde4d2b4197774e9d8
5b5cc6dde4d2b4197774e9d8- 1337.50false
- 2217.50true
- 3376.21false
- 4120false
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Answer : 2. "217.50"
Explanation :
Answer: B) 217.50 Explanation: Given expression = (45 x 750/100) - (25 x 480/100) = (337.50 - 120) = 217.50
Q: A cube is painted blue on two adjacent surfaces and black on the surfaces opposite to blue surfaces and green on the remaining faces .Now the cube is cut into 216 smaller cubes of equal size. 6851 05b5cc76fe4d2b4197774ff12
5b5cc76fe4d2b4197774ff12- 156false
- 248false
- 332false
- 464true
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Answer : 4. "64"
Explanation :
Answer: D) 64 Explanation: We know that Cubes with no surface painted can be find using x-23, where x is number of cuttings. Here x=6. ∴ 6-23=64
Q: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples ? 6796 05b5cc6e3e4d2b4197774ec98
5b5cc6e3e4d2b4197774ec98- 16/7false
- 219/21false
- 37/31false
- 45/21true
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Answer : 4. "5/21"
Explanation :
Answer: D) 5/21 Explanation: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ x ⁶C₁) As remaining person can be any one among three couples left. Required probability = (⁵C₂ x ⁶C₁)/¹⁰C₅= (10 x 6)/252 = 5/21
Q: In a purse there are 30 coins, twenty one-rupee and remaining 50-paise coins. Eleven coins are picked simultaneously at random and are placed in a box. If a coin is now picked from the box, find the probability of it being a rupee coin? 6784 05b5cc60de4d2b4197774b618
5b5cc60de4d2b4197774b618- 14/7false
- 22/3true
- 31/2false
- 45/6false
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Answer : 2. "2/3"
Explanation :
Answer: B) 2/3 Explanation: Total coins 30 In that, 1 rupee coins 20 50 paise coins 10Probability of total 1 rupee coins = 20C11 Probability that 11 coins are picked = 30C11 Required probability of a coin now picked from the box is 1 rupee = 20C11/30C11 = 2/3.
Q: In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group, none can speak any other language. If 2 persons in the group can speak two languages and one person can speak all the three languages, then how many persons are there in the group ? 6759 05b5cc718e4d2b4197774f4d6
5b5cc718e4d2b4197774f4d6- 121false
- 222false
- 323true
- 424false
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Answer : 3. "23"
Explanation :
Answer: C) 23 Explanation: Let us assume the two persons who can speak two languages speak Hindi and Tamil. The third person then speaks all the three languages. Tamil – Number of persons who can speak is 6. Only Tamil 6 – 2 – 1 = 3 Hindi - Number of persons who can speak is 15. Only Hindi 15 – 2 – 1 12 Gujarati – Number of persons who can speak is 6. Only Gujarati 6 – 1 = 5 Thus the number of persons who can speak only one language is 3 + 12 + 5 = 20 Number of persons who can speak two languages = 2 Number of person who an speak all the languages = 1 Total number of persons = 23.
Q: Find the missing number? 15, 30, ? , 40, 8, 48 6747 05b5cc6afe4d2b4197774d264
5b5cc6afe4d2b4197774d264- 121false
- 28false
- 319false
- 410true
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Answer : 4. "10"
Explanation :
Answer: D) 10 Explanation: Given nuber series is 15, 30, ? , 40, 8, 48 Here the number series follows a pattern that 15 15 x 2 = 30 30 ÷ 3 = 10 10 x 4 = 40 40 ÷ 5 = 8 8 x 6 = 48 Hence, the missing number in the series is 10.