Instructions

For the following questions answer them individually

Question 91

There are 6 boxes numbered 1,2,… 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is

Question 92

Consider the following two curves in the x-y plane:

$$y = x^3 + x^2 + 5$$

$$y = x^2 + x + 5$$

Which of following statements is true for $$-2 \leq x \leq 2$$ ?

Question 93

In a certain examination paper, there are n questions. For j = 1,2 …n, there are $$2^{n-j}$$ students who answered j or more questions wrongly. If the total number of wrong answers is 4095, then the value of n is

Question 94

If x, y, z are distinct positive real numbers the $$(x^2(y+z) + y^2(x+z) + z^2(x+y))/xyz$$ would always be

Question 95

A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph with 3 edges and 3 points. The degree of a point is the number of edges connected to it. For example, a triangle is a graph with three points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any point through a sequence of edges. The number of edges, e, in the graph must satisfy the condition

Question 96

The number of positive integers n in the range $$12 \leq n \leq 40$$ such that the product (n -1)*(n - 2)*…*3*2*1 is not divisible by n is

Question 97

Let T be the set of integers {3,11,19,27,…451,459,467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S is

Instructions

DIRECTIONS for the following two questions: Answer the questions on the basis of the information given below.

Some children were taking free throws at the basketball court in school during lunch break. Below are some facts about how many baskets these children shot.

i. Ganesh shot 8 baskets less than Ashish.

ii. Dhanraj and Ramesh together shot 37 baskets.

iii. Jugraj shot 8 baskets more than Dhanraj.

iv. Ashish shot 5 baskets more than Dhanraj.

v. Ashish and Ganesh together shot 40 baskets.

Instructions

DIRECTIONS for the following three questions: Answer the questions on the basis of the information given below.

A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1 the south end point of OR to E2, the east end point of IR. Traffic moves at a constant speed of $$30\pi$$ km/hr on the OR road, 20$$\pi$$ km/hr on the IR road, and 15$$\sqrt5$$ km/hr on all the chord roads.

Question 99

Amit wants to reach N2 from S1. It would take him 90 minutes if he goes on minor arc S1 - E1 on OR, and then on the chord road E1 - N2. What is the radius of the outer ring road in kms?

Question 100

Amit wants to reach E2 from N1 using first the chord N1 - W2 and then the inner ring road. What will be his travel time in minutes on the basis of information given in the above question?

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