Tata Consultancy Services
Placement Paper
1. 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.
2. One card is drawn from a well shuffled deck of 52 cards.
Find the probability of getting -
a. a king of red color
b. a black card
3. 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
4. If cosec 18º = sec A, then the measure of A is ___________
5. 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?
6. 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
7. 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
8. 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
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
10. A long thin strip of width 7 cm is kept on a flat surface. Another identical strip is kept on it in an overlapping manner such that the combined width of the two is 11 cm. What is the width of 55 such strips kept like this?
11. A telephone company charges 80 paisa /min for first 80 min of talk, 70 paisa/ min subsequently up to 130 min and 55 paisa/min beyond 130 min. What would be the amount paid by a subscriber who has used a total of 110 min of talk time?
12. Alan, Steven and Marwick dug up 9 nuggets. Their weights were 154,16,19,101,10,17,13,46 and 22 kgs. They took 3 each. Alan’s weighed twice as much as Steven’s. How heavy were Marwick’s nuggets?
13. If mt=1 & m is greater than 0, which of the following is True?
• When m is greater than 1, t is greater than 1.
• When m is less than 1, t is less than 1
• As m increases t increases
• As m decreases t decreases
14. If the radii of umbra and penumbra cast by an object on a wall are of the ratio 2:6, what is the area of the penumbra ring around the umbra of the latter’s radius is 40 cms?
15. Fred is a researcher at the Sun Computer Centre. He is also a jazz musician. He wrote a program that recognized his pattern of musical play and predicted his notes. Notes were first converted to numbers through complex statistical techniques. The first few numbers are 26, 25, 23, 20, and 16. What should come next?
16. Using only the digit from 0 to 5. How many 5 digit codes can be constructed? If the first digit cannot be 3 and number of digits cannot be used more than once.
17. In a box there are X green balls, 3X+6 red balls and 2 yellow ones. If there are no other colors what is the probability?
18. Find the number of trailing Zeroes in 52!
19. The Vertices of ABC are point A(1,2), B(4,6), C(-4,12). Which of the following is true?
a) ABC is not a Right ∆
b) It is a right ∆ with right angle at C
c) It is a right ∆ with right angle at B
d) It is a right ∆ with right angle at A
20. 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
21. The fundamental theorem of arithmetic states that every natural number greater than 1 can be written as a unique product of prime numbers. What is the smallest number by which 4732 must be divided in order to make it into a perfect square?
22. From the top of a 9m 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
23. 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.
24. If x+y = 4 and x–y = 8, then x = ___ and y = ___
25. Two dice are thrown simultaneously. Find the probability of :
a) The sum of the numbers appearing on the top of the two dice being 6.
b) The numbers appearing on the top of both dice being same.
Placement Paper
1. 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.
2. One card is drawn from a well shuffled deck of 52 cards.
Find the probability of getting -
a. a king of red color
b. a black card
3. 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
4. If cosec 18º = sec A, then the measure of A is ___________
5. 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?
6. 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
7. 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
8. 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
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
10. A long thin strip of width 7 cm is kept on a flat surface. Another identical strip is kept on it in an overlapping manner such that the combined width of the two is 11 cm. What is the width of 55 such strips kept like this?
11. A telephone company charges 80 paisa /min for first 80 min of talk, 70 paisa/ min subsequently up to 130 min and 55 paisa/min beyond 130 min. What would be the amount paid by a subscriber who has used a total of 110 min of talk time?
12. Alan, Steven and Marwick dug up 9 nuggets. Their weights were 154,16,19,101,10,17,13,46 and 22 kgs. They took 3 each. Alan’s weighed twice as much as Steven’s. How heavy were Marwick’s nuggets?
13. If mt=1 & m is greater than 0, which of the following is True?
• When m is greater than 1, t is greater than 1.
• When m is less than 1, t is less than 1
• As m increases t increases
• As m decreases t decreases
14. If the radii of umbra and penumbra cast by an object on a wall are of the ratio 2:6, what is the area of the penumbra ring around the umbra of the latter’s radius is 40 cms?
15. Fred is a researcher at the Sun Computer Centre. He is also a jazz musician. He wrote a program that recognized his pattern of musical play and predicted his notes. Notes were first converted to numbers through complex statistical techniques. The first few numbers are 26, 25, 23, 20, and 16. What should come next?
16. Using only the digit from 0 to 5. How many 5 digit codes can be constructed? If the first digit cannot be 3 and number of digits cannot be used more than once.
17. In a box there are X green balls, 3X+6 red balls and 2 yellow ones. If there are no other colors what is the probability?
18. Find the number of trailing Zeroes in 52!
19. The Vertices of ABC are point A(1,2), B(4,6), C(-4,12). Which of the following is true?
a) ABC is not a Right ∆
b) It is a right ∆ with right angle at C
c) It is a right ∆ with right angle at B
d) It is a right ∆ with right angle at A
20. 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
21. The fundamental theorem of arithmetic states that every natural number greater than 1 can be written as a unique product of prime numbers. What is the smallest number by which 4732 must be divided in order to make it into a perfect square?
22. From the top of a 9m 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
23. 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.
24. If x+y = 4 and x–y = 8, then x = ___ and y = ___
25. Two dice are thrown simultaneously. Find the probability of :
a) The sum of the numbers appearing on the top of the two dice being 6.
b) The numbers appearing on the top of both dice being same.