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### TCS touch stone Sample questions

Q. 1 If x + y = 4 and x – y = 8, then x =      and y =

Q. 2 A sum of Rs. 400 is to be used to give four cash prizes to students of a school for their overall performance. If each prize is Rs. 20 less than its preceding prize, find the value of each prize.

Q. 3 After 2 years of time, Paul will be 2 times as old as Alice. Presently he is 4 times as old. How old is Paul now

Q. 4 One card is drawn from a well shuffled deck of 52 cards.
Find the probability of getting
i) a king of red colour
ii) a black card

Q. 5 Two dice are thrown simultaneously. Find the probability of
i) the sum of the numbers appearing on the top of the two dice being 6.
ii) the numbers appearing on the top of both dice being same.

Q. 6 Two vertical poles of heights 6m and 11m stand on a plane ground. The distance between their feet is 12m. A rope is tied tightly from the top of one pole to the top of the other. Find the length of the rope.

Q. 7 From the top of a 9 metres high building AB, the angle of elevation of the top of a tower CD is 30º C and the angle of depression of the foot of the tower is 60º. Find the height of the tower

Q. 8 The radius of a circle is 21 cms . Therefore its circumference is _________cms.

Q. 9 A vessel is in the form of a hollow cylinder mounted on a hollow hemisphere. The diameter of the hemisphere is 14 cms, and the total height vessel is 3 cms. Find the outer surface area of the vessel

Q. 10 If cosec 18º = sec A, then the measure of A is ___________

Q. 11 A point A(x,y) divides the segment joining point B(5,-1) and
C(-10,4) in the ratio 3:2. Find the value of x and y

Q. 12 A man is standing in front of a painting of a man, and he tells us the following: "Brothers and sisters have I none, but this man's father is my father's son". Who is on the painting?

Q. 13.The fundamental theorem of arithmetic states that every natural number greater than 1 can be written as a unique product of prime numbers. Now what is the smallest number by which 4732 must be divided in order to make it into a perfect square

Q. 14. In the reading room of a library, there are 10 reading spots. Each reading spot consists of a round table with 4 chairs placed around it. There are some readers such that in each occupied reading spot there is different number of readers. If in all there are 10 readers, how many reading spots do not have even a single reader