111)Evaluate:log(a

^{2}bc^{3})^{5}^{}
a. 32log a + 5log b + 243log c b. (10log a + 5log b + 15log c) c. 15(log a + log b + log c) d. 5log (a

^{2}bc^{3})
Ans: (B)

112) if p varies directly as the square of q and inversely as the square root of r,which of the following would be true if k represents constant of variation?

a.p(q)

^{2}= √k b.k= r^{2}* p *q^{-2 }c.p/k(q)^{2}=√r d. √p =1/k(q)^{2}
113) what is the loss percentage incurred by a company when it buys an asset for Rs 1,50,000 and sells it for Rs 75,500?

a.49.67% b.49.34% c.98.68% d.98.34%

A) c.p = 1,50,000rs

s.p= 75,500

loss = c.p – s.p

= 1,50,000 – 75,500

= 74,500

Loss% = (loss/c.p)*100

= (74,500/1,50,000)*100

= 49.67%

114)If a positive integer n is divided by 5 then the remainder is 3. Which of the following numbers gives remainder 0,when it is divided by 5? a. n + 3 b. n – 2 c. n + 2 d. n + 1

Ans: n+2;

115) Find the greatest 5 digit number that is exactly divisible by 3, 4, 5 and 7?

a.99940 b.99960 c.99970 d.99990

Ans: 99999 / LCM(3,4,5,7) = 99999 / 420 = 238 ( quotient)

238 * 420 = 99960

116)Probability of one of the power plants over heating is 0.15 per day and the probability of failure of the backup cooling system is 0.11 .If these events are independent.What is the probability of ‘big trouble’(i.e . both events taking place)? a.0.35 b.0.0185 c. 0.0165 d.0.26

Ans: big trouble occur when overheating and failure of cooling system happens at the same time.

0.15 * 0.11 = 0.0165

117)If the selling price of a watch is halved,the profit becomes quartered.Find the profit percentage of the watch?

a.50% b.66.67% c.100% d.200%

let c.p=x

s.p=y

((y/2)-x)/x=((y-x)/x)*(1/4)

y=3x

profit%=((3x-x)/x)*100

=200%

118)Simplify the expression 7log

_{5}p + √3 /2 log_{5}q – ½ log_{5}2r
a.log

_{5}p^{7}+ q^{(}√3^{)/2}– (√2)( √r) b.log_{5}(p^{7}+ q^{(}√3^{)/2})/r c.log p^{7}.q^{(}√3/2^{)}/(( √2)( √r)) d. log5 p^{7}. q^{(√3/2}^{)}– ((√2)( √r))
7logp+((3)^(1/2))/2logq-(1/2)log2r

=logp^(7)+logq^((3^(1/2))/2)-log2r^(1/2)

=log((p^(7)*q^((3^(1/2))/2))/(2r^(1/2))

119)There are 5 clients and 5 consultants in a round table meeting.In how many ways can the clients be seated such that no consultant is next to the other consultant?

a. 5! 6! b.4! 4! c.4! 5! d.9! e.c5 5! 4!

Ans: 5 clients can be arranged in 4! Ways as it is a circular arrangement.

Now 5 places left in between 5 clients. So 5 consultants can be arranged in 5! Ways.

Total: 4! * 5!

120)A company decides to reorganise its financial transaction files and put all such files into various drawers. In how many ways can 7 files be put into 3 drawers ,if any number of files can be put in each drawer?

a.7

^{3 }b.^{7}p3 c.7!/4! d.3^{7 }e.^{7}c3