TCS exam conducted on 2^{nd} December 2015
1. What are the last two digits of the given number having
200 digits?
123412344123444123444412.....
a)12 b)23 c)34 d)41 e)44
123412344123444123444412.....
a)12 b)23 c)34 d)41 e)44
Answer: 44
2. How many
squares are there between 2013,2020,2027,...................... and 2300.
Clue: 44^2=1936
A) 1 B) 4 C)
2 D) 3
Ans: 1 ( 47^{2})
3. If a pipe
can fill the tank within 6hrs.But due to leak it takes 30 min more. Now the
tank is full then how much time will it take to empty the tank through the leak?
Ans: 78 hours
4. Two
trains running in opposite directions cross a man standing on the platform in
27 seconds and 17 seconds respectively and they cross each other in 23 seconds.
The ratio of their speeds is:
Ans: 3:2
Ans: 3:2
5. If f(x) = x^{4}
+ax^{3} + bx^{2} + cx +d. If f(1)=f(2)=f(3)=f(4). find b
a. 30 b. 35 c. can't be determined d.
10
ans: 35
Solution: ans b=35
f(1)=1+a+b+c+d
f(2)=16+8a+4b+2c+d
f(3)=81+27a+9b+3c+d
f(4)=256+64a+16b+4c+d
given
f(1)=f(2)=f(3)=f(4)
firstly
f(1)=f(2)
1+a+b+c+d=16+8a+4b+2c+d
7a+3b+c=15...........................................................equ(1)
then
f(1)=f(3)
we get
13a+4b+c=40...........................................................equ(2)
then
f(1)=f(4)
we get
21a+5b+c=85..........................................................equ(3)
solve equ(2)equ(1)
we get
6a+b=25......................................equ(4)
solve equ(3)equ(2)
we get
8a+b=45......................................equ(5)
solve equ(4) and equ(5) and put the value in other equactions for all the values
we get
a=10 ,b=35,c=50
proof
put the value of a ,b,c
we get
f(1)=f(2)=f(3)=f(4)
f(1)=1+a+b+c+d
f(2)=16+8a+4b+2c+d
f(3)=81+27a+9b+3c+d
f(4)=256+64a+16b+4c+d
given
f(1)=f(2)=f(3)=f(4)
firstly
f(1)=f(2)
1+a+b+c+d=16+8a+4b+2c+d
7a+3b+c=15...........................................................equ(1)
then
f(1)=f(3)
we get
13a+4b+c=40...........................................................equ(2)
then
f(1)=f(4)
we get
21a+5b+c=85..........................................................equ(3)
solve equ(2)equ(1)
we get
6a+b=25......................................equ(4)
solve equ(3)equ(2)
we get
8a+b=45......................................equ(5)
solve equ(4) and equ(5) and put the value in other equactions for all the values
we get
a=10 ,b=35,c=50
proof
put the value of a ,b,c
we get
f(1)=f(2)=f(3)=f(4)
6. if f(x+y)= f(x)+f(y)+xy and f(1)=5 then f(5)+f(7)=
Ans: 56
7. The diagonal of a square field is 200, and then find the area of a square.
Ans: 2*10^4
8. Eesha can run 224m in 28 seconds. Usha can run same
distance in 32 seconds. By how distance (in metres) would Eesha beat Usha?
A.28m B.32m
A.28m B.32m
Ans: 28m
9. Filling in a square grid.. Sudoku type …Each block can be
filled by only one of digits from 1,2,3,4,5. The digits can’t repeat either
vertically or horizontally or diagonally. Find the value of x
Ans: 2
1

2

3

4

5

4

5

1

2

3

2

3

4

5

1

5

1

2

3

4

3

4

5

1

2
