 ## Friday, 26 May 2017

1 . There are 12 people to be seated around a round table. In how many ways we can arrange them such that 3 particular person A, B and C are all ways together ?

 A.   10 ! B.   9 ! C.   10 ! × 3 ! D.   9 ! × 3 !
2 . Of the different words that can be formed from letters of word MIRROR, how many begins with M and Ends with O ?

 A.   $6!\over3!$ B.   6 ! C.   $4!\over3!$ D.   $6!\over4!$
3 . A box contains 10 balls out of which 3 are green and rest are yellow. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 green balls are included in the sample and no sample has all the 6 balls of the same colour ?

 A.   110 B.   179 C.   189 D.   168
4 . Which of the following values of X satisfy the inequality .
x (x – 4) < 3 x – 10 ?

 A.   2 < x < 5 B.   x = 5, x = 2 C.   8 < x < 11 D.   None of these
5 . What would be the maximum value of R in the given equation ?
3 P 8 + 2 R 6 + 4 Q 5 = 989

 A.   5 B.   6 C.   8 D.   7
6 . Three pens and 5 books cost Rs 250. Six pens and 2 books cost Rs 130. What is the difference between the cost of a pen and that of a book ?

 A.   35 B.   45 C.   40 D.   20
7 . Direction (Q. 7-8 ) : For the given equations A and B, give answer, from following options :

I)${x^2}$ + 6x + 9 = 0 II)${y^2}$+ 9y + 20 = 0

 A.   If x is smaller than y. B.   If x is greater than y. C.   If x is equal to y. D.   If x is either equal to or greater than y
8 . . I)${4x^2}$– 9x – 9 = 0 II)${2y^2}$ – 13y + 21 = 0

 A.   If x is smaller than y B.   If x is greater than y. C.   If x is equal to y. D.   If x is either equal to or smaller than y.
9 . If a card is picked up at random from a pack of 52 cards. Find the probability that it is a king or queen ?

 A.   $7\over52$ B.   $1\over13$ C.   $2\over13$ D.   none of these
10 . Three coins are tossed. Find the probability of no heads ?

 A.   $3\over8$ B.   $1\over2$ C.   $2\over3$ D.   $1\over8$

1 .
 Answer : Option D Explanation : Let those three peoples as single group now 10 objects (9 people and a group) which can be arrange in (10 – 1)! ways = 9 ! ways But 3 person of group can be arranged in 3 ! ways Hence total possible no. of arrangements = 9 ! × 3 !
2 .
 Answer : Option C Explanation : M and O are fixed at the start and end positions, Hence, we have to arrange 1, R, R, R among themselves ( i.e. in 4 places), and since R is 3 times. This can be done in $4!\over3!$ ways
3 .
 Answer : Option D Explanation : 4 .
 Answer : Option A Explanation : x ( x – 4) < 3x – 10=${x^2}$– 7x + 10 < 0 = (x – 2) ( x – 5) < 0∴this possible when :Case I ; (x – 2 ) > 0 then (x – 5 ) < 0 –––∴x > 2 and x < 5Case II ; (x – 2) < 0 then (x – 5) > 0∴ x < 2 and x > 5
5 .
 Answer : Option D Explanation : 3 P 8 + 2 R 6 + 4 Q 5 = 989For maximum value of R, the value of P and Q should be minimum (i.e. zero)∴308 + 2 R 6 + 405 = 989= 2 R 6 = 989 – 713 →2 R 6 = 276 ∴ R = 7
6 .
 Answer : Option C Explanation : 7 .
 Answer : Option B Explanation : 8 .
 Answer : Option D Explanation : 9 .
 Answer : Option C Explanation : 4 king or 4 queen = 8∴ Req. probability = $8\over52$=$2\over13$
10 .
 Answer : Option D Explanation : Sample space, S = ( HHH, HHT, HTH, HTT, THT, THH, TTH, TTT)Number of exhaustive cases = 8Favourable cases is TTT ( no head probability to be found),BR. ∴ P(E)=$1\over8$ ∴ Probability of no heads =$Number of favourable cases\over Number of favourable cases$=$1\over8$