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**71. Find the remainder when 2**

^{21 }is divided by 6.

A. 0 B. 1 c. 2 D. 3

72. Which of the following numbers is the smallest number?

A. 1/12 B. 1/6 C. ¼ D. 1/3

Ans: (A)

A. 1/12 B. 1/6 C. ¼ D. 1/3

Ans: (A)

73. A phone company offers 5 phone plan options: call waiting, call forwarding, voice mail, conferencing, and caller ID. A customer can choose 3 options. The number of ways one can avail the plan options is:

A. 5 B. 10 C. 3 D. 20

Solution:

5c3 =10 is correct answer

A. 5 B. 10 C. 3 D. 20

Solution:

5c3 =10 is correct answer

74. If log

A. 8 B. 5 C. 16 D. 32

Solution:

log

so log

log

x/8 = 32

x/8 = 2

x= 16

_{32}x + log_{32 }(1/8) = 1/5, then the value of x is equal to:A. 8 B. 5 C. 16 D. 32

Solution:

log

_{b}x+ log_{b}y = log_{b}xyso log

_{32}x + log_{32 }(1/8) = 1/5log

_{32}x(1/8) = 1/5x/8 = 32

^{1/5}x/8 = 2

x= 16

75. Length and breadth of a rectangle are directly proportional. If length increases from 6 cm to 21 cm and if breadth now is 14 cm, then what was the breadth before any change in length occurred?

A. 4 cm B. 1.5 cm C. 2 cm D. 3 cm

A. 4 cm B. 1.5 cm C. 2 cm D. 3 cm

Solution:

since they are directly proportional

6/21=x/14

x=(14*6)/21=4

breadth=4cm..

76. At an election there are 5 candidates among which 3 members are to be elected and a voter may vote for any number of candidates not greater than the number to be elected. Then the number of ways in which a voter may vote are ?

A. 25 B. 30 C. 32 D. None of the above

A. 25 B. 30 C. 32 D. None of the above

Solution:

77. One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is '9' of hearts.

A. 1/13 B. 1/26 C. 1/52 D. 3/52

A. 1/13 B. 1/26 C. 1/52 D. 3/52

Solution:

78. If 2

A. 0 B. 1 C. 2 D. 3 E. None of the above

Solution:

second equation can be written as,

2^x*2^x*3^y=36. substituting the first equation value,

2^x*18=36.

2^x=2^1;

a^m=a^n, then m=n, so we get x=1

^{x}* 3^{y}= 18 and 2^{2x}* 3^{y}=36, the value of x isA. 0 B. 1 C. 2 D. 3 E. None of the above

Solution:

second equation can be written as,

2^x*2^x*3^y=36. substituting the first equation value,

2^x*18=36.

2^x=2^1;

a^m=a^n, then m=n, so we get x=1

79. An unbiased coin is tossed 5 times. If tail appears on first 4 tosses, then probability of tail appearing on the fifth toss is: A. ½ B. 1 C. 0 D. 4/5

Solution: (A) Appearing tail on fifth toss is independent of first 4 tosses.

80. In a single throw of dice, what is the probability to get a number greater than or equal to 4

A. 1/3 B. 2/3 C. ½ D. None of the above

Solution: Getting number greater than or equal to 4 means 4,5 and 6 are possibilities.

Total case for a dice is 6.

ans: 3/6 = 1/2

A. 1/3 B. 2/3 C. ½ D. None of the above

Solution: Getting number greater than or equal to 4 means 4,5 and 6 are possibilities.

Total case for a dice is 6.

ans: 3/6 = 1/2