XAT 2017 Question Paper

Instructions

For the following questions answer them individually

Question 51

If f(x) = ax + b, a and b are positive real numbers and if f(f(x)) = 9x + 8, then the value of a + b is:

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Question 52

Arup and Swarup leave point A at 8 AM to point B. To reach B, they have to walk the first 2 km, then travel 4 km by boat and complete the final 20 km by car. Arup and Swarup walk at a constant speed of 4 km/hr and 5 km/hr respectively. Each rows his boat for 30 minutes. Arup drives his car at a constant speed of 50 km/hr while Swarup drives at 40 km/hr. If no time is wasted in transit, when will they meet again?

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Question 53

Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.

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Question 54

In a True/False quiz, 4 marks are awarded for each correct answer and 1 mark is deducted for each wrong answer. Amit, Benn and Chitra answered the same 10 questions, and their answers are given below in the same sequential order.
AMIT     T T F F T T F T T F
BENN    T T T F F T F T T F
CHITRA T T T T F F T F T T
If Amit and Benn both score 35 marks each then Chitra’s score will be:

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Question 55

In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?

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Question 56

If 5° $$\leq$$ x° $$\leq$$ 15°, then the value of sin 30° + cos x° - sin x° will be :

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Question 57

The Volume of a pyramid with a square base is 200 cubic cm. The height of the pyramid is 13cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?

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Question 58

A dice is rolled twice. What is the probability that the number in the second roll will be higher than that in the first?

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Question 59

An institute has 5 departments and each department has 50 students. If students are picked up randomly from all 5 departments to form a committee, what should be the minimum number of students in the committee so that at least one department should have representation of minimum 5 students?

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Question 60

If $$N = (11^{p + 7})(7^{q - 2})(5^{r + 1})(3^{s})$$ is a perfect cube, where $$p, q, r$$ and $$s$$ are positive integers, then the smallest value of $$p + q + r + s$$ is :

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