Instructions

For the following questions answer them individually

Question 81

Two students X and Y are best friends. They sit randomly in a row of 9 seats with 7 other friends to watch a movie. What is the probability that the friends sit together?

Question 82

Suppose the equations $$3x^{2} — 7x + k = 0$$ and $$—7x^{2} + kx + 3 = 0$$ have a common root, then the value of $$k$$ is:

Question 84

Let the quotient be f(x) when $$5x^{4} —3x^{3} + 2x^{2} — 1$$ is divided by $$x^{2} + 4$$, the remainder be g(x) when $$2x^{3} — x + 1$$ with $$x^{2} + x + 1$$. The remainder when f(x) is divisible by g(x)

Question 85

Read the given statements and select the most appropriate option

Statement-I: If the sum of remainders obtained when 3864335 divisible by 382 and 300 is twice the remainder when a least four-digit number is divisible by 32, then that number is 1021

Statement-II: 45!-1 is a prime number.

Question 86

SUPPOSE $$M_{(base-n)}$$ Means m is a number in base-n system. It for $$a > b, a_{(base-10)} + b_{(base-10)} = 20_{(base-3)}$$ and $$a^{2}_{(base-10)} + b^{2}_{(base-10)} = 202_{(base-3)}$$, then what are $$a_{(base-3)}$$ and $$b_{(base-3)}$$?

Question 87

From his house, David walks 70 steps forward to the East then without reversing his back, he walks 30 steps backward. Then he reverses his back and walks 20 steps forward. What is the distance (in feet) between his final position and his house if one step measures 2 feet?

Question 88

A cubic room, with lateral surface area 2304 $$m^{2}$$ is to be divided into 4 m wide small rooms, by inserting plywood sheets in the room. To minimise the expenditure on purchase of these sheets, how many such sheets will be required to construct maximum number of such small rooms, if the length and the height of the small rooms remains same as that of the cubic room?

Question 89

If $$x^{2} — 4y^{2} — x + \lambda y — 2 = 0$$ is to represent a pair of straight lines, then the product of the possible values of $$\lambda$$ is

Question 90

Suppose xy are positive integers such that xy = 2835. If the HCF of x and y is 9, then what are the possible values of 2x +y ?