TCS 2015 off campus all india exam held on 20th February questions-3

8.The diagonal of a square is twice the side of an equatorial triangle.The ratio of the area of the triangle to the area of square is

1.A passenger train takes 5hrs less for a journey of
396 kmif its speed is increased by 55kmph from its normal speed.The normal
speed (to the nearest kmph) is

a)None b)44 c)55 d)66

2.The value of the expression

1%2%3%5%7%11%13

Can be altered by including parenthesis.If we are
allowed to place as many parenthesis as we want,how many distinct values can be
obtained from this expression?

Clue:which of the numbers can appear in the
numerator and which are in the denominator of the fraction obtained after
inserting parenthesis?

a)32
b)64 c)16 d)128

3.A pair of 8 slided dice has sides numbered 1 to
8.Each side has same probability or chance of landing face up.The probability
that the product of 2 numbers on the sides that land face up exceeds 36 is

a)11/64
b)5/32 c)3/16 d)1/4

4.A series of books was published at 10years
intervals when the 10

^{th}book was issued the sum of publication years was 19,560when was the 1^{st}book published
a)1910 b)1914
c)1911 d)1909

5.given the digits 1,3,6,9 find the probability that
a 3 digit number formed by using them with no digit repeated is divisible by 4

a)None b)1/4
c)1/6 d)1/12

6. An entry in an unshaded square
is obtained by adding the entries connected to it from the row above (11 is one
such number). Write the value of n.

a)10 b)11
c)9 d)none

7.While planning their outing,abhishek understood that
their boat could travel with a speed of 12kmph in still water.The group decided
to travel 24 minutes downstream.Aarti had prior experience in that route and
mentioned that the speed of stream was 4kmph.How many kms will the group travel
downstream?

a)6.4
b)3.2 c)4 d)4.8

8.The diagonal of a square is twice the side of an equatorial triangle.The ratio of the area of the triangle to the area of square is

a)sqrt(3):8
b)sqrt(2):4 c)sqrt(2):5 d)sqrt(3):6

9.On a
26-question test, five points were deducted for each wrong answer and eight
points were added for each correct answer. If all the questions were answered,
how many were correct if the score was zero?

A. 10

B. 11

C. 12

D. 13

A. 10

B. 11

C. 12

D. 13

10.Adarsh went
to a casino with Rs.6400 and played a certain game 6 times.Each time he bet
half the money he had the time the chance of winning this game was ½ and
adharsh won three of the 6 games even though he did not remember which 3 games
he won.In each of these games he won the amount equal to his bet.After the 6
games the money was

a)3200 b)2700
c)1280 d)cannot be

11.Jake runs
faster than paul.Jake and paul each walk 24kms.the sum of the speeds is 7km/hr
and the sum of the time taken by them is 14 hrs then jake's speed is?

a)6kmph b)2kmph
c)4kmph d)8 kmph

12.If
(3a+6b)/(5a+12b)=12/23 determine the
value of 3a

^{2}+5b^{2}/ab
a)19/2 b)32/3
c)9 d)31/3

13.Y can do a
work in 2/3 the time it takes X.Z can do the same work in ¾ the time it takes
Y.When all three are typing at the same time what fraction of their total work
does Y do

a)1/3 b)4/13
c)9/23 d)8/29

14.The number
of different non congruent triangles with integer side and perimeter 15 is

a)9 b)7
c)10 d)6

15.The number
of committes of size 10 that could be formed from 10 men & 10 women such
that committee has atleast 6 women is

a)60626 b)210
c)10210 d)none

16.How many
positive multiples of 10 that are less than 1000 are the sum of 4 consecutive
integers

a)51 b)50
c)49 d)none

17.I just
finished 3 marble games & have 21 marbles.In the 1

^{st}game I lost half of my marbles.Inthe 2^{nd}game I won 11 times what I had at the end of the 1^{st}game.In the 3^{rd}game I won 9 marbles.How many marbles Did I have when I started playing?
a)6 b)4
c)8 d)2

18.A shop
sells chocolates,it used to sell chocolates for Rs4.50 each but there were no
sales at that price.When it reduced the price all chocolates sold but enabling
to realize at 342.86 from chocolates alone.If the new price was not less than
half of the original price.How many chocolates are sold

a)62 b)79
c)65 d)81

19. Four
of the six numbers is 1867456,1993764,2019657,2025189,2109472,2121346
have a mean of 2068916.What is the mean of other two numbers

a)2006710.5 b)2067330.5 c)1930610 d)2022423

20.Let f be a
function such that f(f(x))=f(x+2)-3 for
all intergersx,if f(1)=4 and f(4)=3,then f(5) is

a)12 b)15
c)6 d)9

21. George,
Paul and Hari start a business by contributing Rs. 30000/-, Rs. 40000/- and Rs.
50000/- respectively. After ½ a year George withdraws half his contribution. At
the end of the year the business showed a profit of Rs 90000 which was divided
amongst the 3 men proportionate the to amount and duration of their investment
in the enterprise. Paul got,

Options

a) Rs 25000 b)Rs 18000 c) Rs 32000 d)Rs 24000

Options

a) Rs 25000 b)Rs 18000 c) Rs 32000 d)Rs 24000

22.The sum of
first n terms in a sequence is always 1/n.Find the product of the first 2014
terms (n! denotes the factorial of n,that is the product of the
numbers(1,2……n))

a)-1/(2013!2013!)

b)
1/(2013!2013!)

c)
1/(2013!2014!)

d)-
1/(2013!2014!)

23.Inabhi’s
class of 44 students,28 students speak malayalam,26 students speak tamil,9
students speak none of the two languages.How many students speak both
tamil& Malayalam

a)54 b)38
c)19 d)10

24.If [x]
denotes greatest integer less than equal to x,the value of ∑[log

_{2}n] ,n ranging from 1 to 1024 is
a)2048 b)8204
c)1024 d)10120

25.A sequence
u

_{1},u_{2}……….is defined by u_{1}=√2,u_{2}=π,u_{n}=u_{n-1}-u_{n-2 }for n>=3.What is u_{1000}?
a)1000(√2-1000π) b)-√2
c)π d)1000√2 –π

26.A swimming
pool whos surface forms a rectangle measures 25 m long by 15 m wide The pool is
2 m deep at the shallow end and the depth increases at a constant rate to 4 m
deep at the other end How many cubic meters of water will pool hold

a)1250 b)975
c)1000 d)1125

27.The sum of
two numbers is 2016 and their product is 32.The sum of their reciprocals is

a)63 b)9 c)32+√2014 d)32-√2014

28.100
students appeared for two different examinations 60 passed the first,50 the
second and 30 both the examinations.Find the probability that a student
selected at random failed in both the examination

a)5/6 b)1/5 c)1/7 d)5/7