APTITUDE : TCS MODEL PAPER

[TCS COMPLETELY SOLVED MODEL PAPER]

1.) There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is

a)1/2 b)14/19 c)37/38 d)3/4
Ans: 14/19

sol:- the probability for selecting red box is 1/2 but randomly if we select green box, the probability will be 0.
So, total probability for this case is 0.5.

Now consider the other case, 9 red balls are transferred to green ball box. now total balls in that box will be 19.

Total probability = probability to select 1st box + probability to select 2nd box

= (1/2)*(1C1/1C1)+(1/2)*(9C1/19C1)

= (1/2)*(1+9/19)

= (1/2)*(28/19)

= 14/19

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APTITUDE :

APTITUDE :

1. How many times in a day, are the hands of a clock in straight line but opposite in direction? A. 20 B. 22 C. 24 D. 48 Answer: Option B Explanation: The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only). So, in a day, the hands point in the opposite directions 22 times. Learn more problems on : Clock Discuss about this problem : Discuss in Forum Rough 2.  252 can be expressed as a product of primes as: A. 2 x 2 x 3 x 3 x 7 B. 2 x 2 x 2 x 3 x 7 C. 3 x 3 x 3 x 3 x 7 D. 2 x 3 x 3 x 3 x 7 Answer: Option A Explanation: Clearly, 252 = 2 x 2 x 3 x 3 x 7. Learn more problems on : Problems on H.C.F and L.C.M Discuss about this problem : Discuss in Forum Rough Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. 3. What is the speed of the train? I.  The train crosses a tree in 13 seconds. II.  The train crosses a platform of length 250 metres in 27 seconds.  III.  The train crosses another train running in the same direction in 32 seconds. A. I and II only II and III only C. I and III only D. Any two of the three E. None of these Answer: Option A Explanation: Let the speed of the train be x metres/sec. Time taken to cross a tree = Length of the train Speed of the train Time taken to cross a platform = (Length of the train + Length of the Platform) Speed of the train I gives, 13 = l     13x. x II gives 27 = l + 250 x 13x + 250 = 27 x x = 125 m/sec. 7 Thus I and II give the speed of the train. The correct answer is (A.) Learn more problems on : Problems on Trains Discuss about this problem : Discuss in Forum Rough

4.	Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
	A. 1.45 B. 1.88 C. 2.9 D. 3.7

	5. If 5 = 2.236, then the value of 5 - 10 + 125 is equal to: 2 5
	A. 5.59 B. 7.826 C. 8.944 D. 10.062 Answer: Option B Explanation: 5 - 10 + 125 = (5)2 - 20 + 25 x 55 2 5 25 = 5 - 20 + 50 25 = 35 x 5 25 5 = 355 10 = 7 x 2.236 2 = 7 x 1.118 = 7.826 Learn more problems on : Square Root and Cube Root Discuss about this problem : Discuss in Forum Rough

6.

Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

A. 7 hours 30 minutes B. 8 hours C. 8 hours 15 minutes D. 8 hours 25 minutes Answer: Option C Explanation: Number of pages typed by Ravi in 1 hour = 32 = 16 . 6 3 Number of pages typed by Kumar in 1 hour = 40 = 8. 5 Number of pages typed by both in 1 hour = 16 + 8 = 40 . 3 3 Time taken by both to type 110 pages = 110 x 3 hours 40 = 8 1 hours (or) 8 hours 15 minutes. 4 Learn more problems on : Time and Work Discuss about this problem : Discuss in Forum Rough

7.	The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
	A. 20 B. 23 C. 169 D. None of these Answer: Option B Explanation: Let the numbers be x and y. Then, xy = 120 and x2 + y2 = 289. (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529 x + y = 529 = 23. Learn more problems on : Problems on Numbers Discuss about this problem : Discuss in Forum Rough

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
8.	What is the area of a right-angled triangle? I.  The perimeter of the triangle is 30 cm. II.  The ratio between the base and the height of the triangle is 5 : 12.  III.  The area of the triangle is equal to the area of a rectangle of length 10 cm.
	A. I and II only B. II and III only C. I and III only D. III, and either I or II only E. None of these Answer: Option A Explanation: From II, base : height = 5 : 12. Let base = 5x and height = 12x. Then, hypotenuse = (5x)2 + (12x)2 = 13x. From I, perimeter of the triangle = 30 cm. 5x + 12x + 13x = 30         x = 1. So, base = 5x = 5 cm, height = 12x = 12 cm. Area = 1 x 5 x 12 cm2 = 30 cm2. 2 Thus, I and II together give the answer. Clearly III is redundant, since the breadth of the rectangle is not given. Correct answer is (A). Learn more problems on : Area Discuss about this problem : Discuss in Forum Rough

9.	Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
	A. Rs. 9,423 B. Rs. 10,250 C. Rs. 12,500 D. Rs. 10,500 Answer: Option D Explanation: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4. Simran's share = Rs. 24500 x 3 = Rs. 10,500. 7 Learn more problems on : Partnership Discuss about this problem : Discuss in Forum Rough

10.	A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
	A. 28  4 years 7 B. 31  5 years 7 C. 32  1 years 7 D. None of these Answer: Option B Explanation: Required average = 67 x 2 + 35 x 2 + 6 x 3 2 + 2 + 3 = 134 + 70 + 18 7 = 222 7 = 31  5 years. 7 Learn more problems on : Average Discuss about this problem : Discuss in Forum Rough

11.

Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

A. 8 kmph B. 11 kmph C. 12 kmph D. 14 kmph Answer: Option C Explanation: Let the distance travelled by x km. Then, x - x = 2 10 15 3x - 2x = 60 x = 60 km. Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs. 10 So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M. Required speed = 60 kmph. = 12 kmph. 5 Learn more problems on : Time and Distance Discuss about this problem : Discuss in Forum Rough

12.	A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
	A. 3.6 sec B. 18 sec C. 36 sec D. 72 sec Answer: Option C Explanation: Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.    = 36 x 5 m/sec 18    = 10 m/sec. Distance to be covered = (240 + 120) m = 360 m. Time taken = 360 sec = 36 sec. 10 Learn more problems on : Problems on Trains Discuss about this problem : Discuss in Forum Rough

13.	How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
	A. 25 B. 30 C. 40 D. 45 Answer: Option B Explanation: Speed of the train relative to man = (63 - 3) km/hr = 60 km/hr = 60 x 5 m/sec 18 = 50 m/sec. 3 Time taken to pass the man = 500 x 3 sec 50 = 30 sec. Learn more problems on : Problems on Trains Discuss about this problem : Discuss in Forum

Direction (for Q.Nos. 14 - 16): Insert the missing number.
14.	1, 4, 9, 16, 25, 36, 49, (....)
	A. 54 B. 56 C. 64 D. 81 Answer: Option C Explanation: Numbers are 12, 22, 32, 42, 52, 62, 72. So, the next number is 82 = 64. Learn more problems on : Odd Man Out and Series Discuss about this problem : Discuss in Forum

15.	16, 33, 65, 131, 261, (....)
	A. 523 B. 521 C. 613 D. 721 Answer: Option A Explanation: Each number is twice the preceding one with 1 added or subtracted alternatively. So, the next number is (2 x 261 + 1) = 523. Learn more problems on : Odd Man Out and Series Discuss about this problem : Discuss in Forum Rough

16.	7, 26, 63, 124, 215, 342, (....)
	A. 481 B. 511 C. 391 D. 421 Answer: Option B Explanation: Numbers are (23 - 1), (33 - 1), (43 - 1), (53 - 1), (63 - 1), (73 - 1) etc. So, the next number is (83 - 1) = (512 - 1) = 511. Learn more problems on : Odd Man Out and Series Discuss about this problem : Discuss in Forum Rough

Direction (for Q.Nos. 17 - 18): Find the odd man out.
17.	10, 14, 16, 18, 21, 24, 26
	A. 26 B. 24 C. 21 D. 18 Answer: Option C Explanation: Each of the numbers except 21 is an even number. Learn more problems on : Odd Man Out and Series Discuss about this problem : Discuss in Forum

18.	331, 482, 551, 263, 383, 362, 284
	A. 263 B. 383 C. 331 D. 551 Answer: Option B Explanation: In each number except 383, the product of first and third digits is the middle one. Learn more problems on : Odd Man Out and Series Discuss about this problem : Discuss in Forum   Rough

19.	What is the probability of getting a sum 9 from two throws of a dice?
	A. 1 6 B. 1 8 C. 1 9 D. 1 12 Answer: Option C Explanation: In two throws of a die, n(S) = (6 x 6) = 36. Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}. P(E) = n(E) = 4 = 1 . n(S) 36 9 Learn more problems on : Probability Discuss about this problem : Discuss in Forum Rough

20.	The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
	A. 2.3 m B. 4.6 m C. 7.8 m D. 9.2 m Answer: Option D Explanation: Let AB be the wall and BC be the ladder. Then, ACB = 60º and AC = 4.6 m. AC = cos 60º = 1 BC 2 BC = 2 x AC = (2 x 4.6) m = 9.2 m. Learn more problems on : Height and Distance Discuss about this problem : Discuss in Forum Rough

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