Question 1:
The sum of three consecutive terms in a geometric progression is 14. If 1 is added to the first and the second terms and 1 is subtracted from the third, the resulting new terms are in arithmetic progression. Then the lowest of the original term is
(A) 1
(B) 2
(C) 4
(D) 8
Question 2:
In the polynomial ( x – 1)( x – 2)( x – 3)...........( x – 100) the coefficient of x99 is
(A) 5050
(B) – 5050
(C) 100
(D) 99
Question 3:
India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points, is:
(A) 0.8750
(B) 0.0875
(C) 0.0625
(D) 0.0250
Question 4:
An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4,.......,12 is picked and the number on the card is noted. The probability that the noted number is either 7 or 8, is
(A) 0.24
(B) 0.244
(C) 0.024
(D) None of these
Question 5:
There exists a function f(x) satisfying f(0) = f(1), f’(0)= - 1 , f(x)>0 for all x ,and
(A) f’’(x)>0 for all x
(B) - 1 < f’’(x)<0 for all x
(C) - 2 < f’’(x)≤-1 for all x
(D) f’’(x) <-2 for all x
