CMAT 2021 Slot-1

Instructions

For the following questions answer them individually

Question 1

Two pipes A and B can fill a tank in 5 hours and 20 hours respectively. Both pipes together can fill the same tank in:

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Question 2

In June-2020, the ratio of boys to girls in a college was 3 : 2. In September-2020, there were 80 fewer boys and 20 fewer girls in the college and the ratio of boys to girls was 7 : 5. What was the total number of students in the college in June-2020?

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Question 3

M is a 4-digit number. If the left most digit is removed, then the resulting three digit number is $$\frac{1}{9}^{th}$$ of M. How many such M's are possible?

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Question 4

L and M together can complete a piece of work in 72 days, M and N together can complete it in 120 days, and L and N together in 90 days. In what time can L alone complete the work?

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Question 5

Given below are two statements
Statement I : The set of numbers(5,6, 7, p, 6, 7, 8, q) has an arithmetic mean of 6 and mode (most frequently occurring number) of 7. Then $$p\times q=16$$.
Statement II: Let p and q be two positive integers such that $$p+q+p\times q=94$$. Then $$p+q=20$$.
In light of the above statements, choose the correct answer from the options given below

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Question 6

A milkman adds 10 litres of water to 90 litres of milk. After selling $$\frac{1}{5}^{th}$$ of the total quantity, he adds water equal to the quantity he sold. The proportion of water to milk he sells now would be:

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Question 7

In a $$\triangle ABC,D,E$$ and $$F$$ are the mid-points of the sides AB, BC and CA respectively. Then the ratio of the area of a $$\triangle DEF$$ and the area of a $$\triangle ABC$$ is:

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Question 8

A 100-meter long train crosses a 200-meter long and 20-meter wide bridge in 20 seconds. What is the speed of the train in Km/hour?

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Question 9

Given below are two statements:
Statement I: $$\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}=2$$
Statement II: If $$a+b+c=0$$, then $$(a^{3}+b^{3}+c^{3})\div abc=3$$
In light of the above statements, choose the correct answer from the options given below

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Question 10

Given below are two statements:
Statement I : Acoin is tossed three times. The probability of getting exactly two heads is 3/8
Statement II: In tossing of 10 coins, the probability of getting exactly 5 heads is 63/256

In the light of the above statements, choose the correct answer from the options given below.

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