1.For real number x, int(x) denotes integer part of x.int(x) is the largest integer less than or equal to x.int(1,2)=1,int(-2,4)=-3. Find the value of int(1/2)+int(1/2+ 100)+int(1/2+2/100)+….+int(1/2+99/100)

a.100

b.120

c.130

d.150

Answer:d

Explaination:

int (1/2) = 0

int (1/2 + 100 ) = 100

into (1/2 + 2/100) = 0

……

int ( 1/2 + 50/100 ) = 1

int (1/2 + 51 /100) = 1

…….

int (1/2 + 99/100) = 1

So 100 + 1 + 1 + …..50 times = 150

2.There are 100 wine glasses. I offered my servant to 3 paise for every broken glass to be delivered safely and forfeit 9 paisa for every glass broken at the end of day. He recieved Rs.2.40 .how many glass did he break.

a.20

b.73

c.5

d.8

Answer:c

Explaination:If a glass has been broken, he has to loose 3 paisa + 9 paise = 12 paise

Assume K glasses got broken

100 x 3 – 12 x K = 240 ⇒K=5

3.If f(f(n))+f(n)=2n+3 and f(0)=1, what is the value of f(2012)?

a) 2011

b) 2012

c) 2013

d) 4095

Answer: C

Explaination: Put n = 0

Then f(f(0))+f(0) = 2(0) + 3 f(1) + 1 = 3 f(1) = 2

Put n = 1

f(f(1)) + f(1) = 2(1) + 3 f(2) + 2 = 5 ⇒f(2) = 3

Put n = 2

f(f(2)) + f(2) = 2(2) + 3 ⇒ f(3) + 3 = 7 ⇒ f(3) = 4

……

f(2012) = 2013

4.The average mark obtained by 22 candidates in an examination is 45. The average of the first ten is 55 while the last eleven is 40 .The marks obtained by the 11th candidate is ?

a.1

b.2

c.3

d.0

Answer : d

Explaination:It is clear that 22 x 45 = 10 x 55 + K + 11 x 40 ⇒ K = 0

5:If f(1)=4 and f(x+y)=f(x)+f(y)+7xy+4,then f(2)+f(5)=?

a.150

b.135

c.115

d.125

Answer : d

Explaination: Let x =1 and y = 1

f(1 + 1) = f(1) + f(1) + 7 x 1 x 1 + 4 ⇒ f(2) = 19

Let x =2 and y = 2

f(2 + 2) = 19 + 19 + 7 x 2 x 2 + 4 ⇒ f(4) = 70

Let x = 1 and y = 4

f( 1 + 4) = 4 + 70 + 28 + 4 = 106

f(2) + f(5) = 125

7.How many two digit numbers are there which when subtracted from the number formed by reversing it’s digits as well as when added to the number formed by reversing its digits, result in a perfect square.

a.1

Given that, 10x+y – (10y – x) = 9(x-y) is a perfect square

So x-y can be 1, 4, 9. ——– (1)

So given that 10x+y +(10y +x) = 11(x+y) is a perfect square.

So x+y be 11. Possible options are (9,2), (8,3),(7,4),(6,5) ———(2)

From the above two conditions only (6,5) satisfies the condition

Only 1 number 56 satisfies.

8.Four times the first of three consecutive odd integers is 6 more than twice the third. The third integer is?

9.If 43 times of two digit numbers is 34 times of two digit no .and sum of ( number and reverse of the number) is 14 then what is the number?

a.68

b.66

c.67

d.69

Answer:a