### CTS PAPER - 2003

**CTS 2003 - nit jsr**

**Aptitude test**: 60Qs Time 1 hr

Booklet color : Blue

1)

Diameter of circle is d, Find length of string.(outer string that covers the circle)

Ans: d (pi + 3)

2) Diamond's value is proportional to its weight2 .When the diamond broke wts of pieces in ratio 1:2:3;4:5.

Total loss in value is 85,000.What is the value of the diamond twice the wt of the original diamond.

Ans : 45,000

3)Person X join a job at 20 yrs.First 3 years sal =10,000 p.a. Afterwards every year inc of 2,000 per year for 10 year. Then sal become const till retirement. at retirement avg sal is 25,000. ( thro'out career) what age he retires.?

4)In an island there r tribals who speak lang of atmost 4 words.Lang consists of 4 alphabets.How many words can be formed in that language? Ans 340

5) It was found that the cause for the malaria was the swamp marsh and so r swamps were drained .Mosquito the real cause for malaria due to lack of breeding grounds (Swamps) also was wiped out. What does this illustrate?

(Ans : (Possible) when many conditions form a result eradication of one cause also eradicates the result)

6)An officer kept files on his table at various times in the order 1,2,3,4,5,6 .Typist can take file from top whenever she has time and type it.What order she cann't type.?

(Ans : 4,5,6,2,3,1)

7)A and B r fighting .B fires 3 times as many missiles as A. Total hits: total misses = 1/7 .B's misses 357.B's hits - A's hits = 66.A's hits?

8)40 shots taken.50p for a hit.10p for a miss.(he have to give).Finally he has Rs.5.How many hits.? Ans 15

9)Find avg of a,b,c,d,e .Given data : avg of any 4 num =avg of any 3 num 2)(a+b)(a+b) = 36

Which of the abv are sufficient?

10)What is the difference in times btwn clk 1 & clk2.

1) both show same time 6 hrs back 2 ) 1 clk gains 1 min an hr,clk2 gains 2 min an hour.

Like abv

11)A takes 9 strides to B's 7 strides. A stride = 1meter.B stride =1.2m B gets the start of 24m.What dist should A travel to overtake B?

12) Tortoise gets 100 m head start. Hare is 10 times faster as tort. What is the dist traveled by hare to catch up tort.?

13)4 weights r weighed in pairs. Weights of pairs are determined as 103,105,106,106,107,109 What is the min wt?

Ans 51

14) Constant cost = 300 and 1.75 / copy. How many copies should he sell at 7.75 /copy to make a profit.

15)

Find the perimeter ? ANs 28

16) 20 members avg =10.5. 3 memb of 11.5,12.5,13.5 left and 3 memb of 10.5,12.5,14.5 joined along with a teacher of 21 yr.Now avg = ..Ans 11.

17)

Find the area of shaded. Radius of circle = 1cm..Arcs r drawn with center at circumference.

18)

Find the area of the shaded portion?

19) Solid cube of 6 * 6 * 6. This cube is cut into to 216 small cubes.(1 * 1 * 1).the big cube is painted in all its faces. Then how many of cubes are painted at least 2 sides. (Ans 56)

20) A Bacteria is doubling at every 4 min. After 40 min 1024 bact. Then 256 when>.? Ans : 32 min

21) A bag contains 3 balls of 11 different colors each. Find the min no of chances to find at least 3 balls of same color?

Ans : 23

22) If square of x< 4 then 100/x is..? Ans : 100/x > 50 & 100/x < -50.

23) If [x] is the int less than x and |x| is the abs val of x.Then max of [x]/|x| is Ans d)none

24) A work in 12 days b in 15 days. Find the no of days if they work on alternate days. Ans 13 1/4

25) A,B,C r positive int.Out of them 2 r odd. Then 5a5a + ( b-5)3 (c-3)(c-3) = ? Ans : always odd.

26) A squarer side is 5cm.If a square of side 10cm is hinged @ the center of the prev square. when they r rotated common area to both squares (Ans : Does not change)

27) 3p.p + pq + 5q.q is even. If

a) If p is odd, q is odd

b) If p is even, q is odd

c) If p is odd ,p is even

d) Atleast one of p and q is odd.

Choices are given. Ans : 4) None of these

28) A lady has to feed a dog for the one week from Monday to Sunday. She has food types M,N,O,P,Q,R,S .

MNOP - protein enriched RS - vitamin enriched. Vitamin enriched cannot be fed on consecutive days.

Conditions given : M should be fed before S.

M should be fed before Q.

R Should be fed before S.

Before N and Q there should be four types.

**Ba**sed on this 3 ?s are asked.All r easy to answer..

29) A man bought at the cost of 5 plums a rupee and 2 oranges a rupee.He sells 10 plums and 6 oranges at the selling price of 4 plums a rupee and 3 oranges a rupee.What is his gain or loss? Ans loss of 50p.

30) Out of 32 books the cost of 10 books is Rs. 50 each and he got a profit of 4%. He sells 15 books at a profit of 3.8461% on the selling price of Rs 70. The remaining cost is 576. The remaining books are sold at Rs 74. What is his total profit.

31) Two solutions have milk & water in the ratio 7:5 and 6:11.Find the proportion in which these two solutions should Be mixed so that the resulting solution has 1 part milk and 2 parts water?

a)35:3 b)21:36 c)not possible Ans :c

Further qs are from reading comprehension.(verbal reasoning) All are easy to answer if u read carefully.

We are not able to get the remaining questions.

**CTS Apti Question paper (Colour: Yellow)**

**There are other three colours also. We received only yellow Question papers.**

**1. If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by Ans: 330**

2. The total no. of numbers that are divisible by 2 or 3 between 100 and 200(both inclusive) are Ans:67

3. From a pack of cards Jack, Queen, King & ace are removed. Then the algebraic sum of rest of the cards is Ans:216

4. The average temperature of days from Monday to Wednesday is 37 degree Celsius and that of from Tuesday to Thursday is 34 degrees. The temperature of Thursday is 4/5th of Monday. Then the temperature of Thursday is Ans: 36 degrees

5. Swetha, Tina, Uma and Vidya are playing a gambling. In this different people lose in different games-in the reverse alphabetical order. The rule is that if one loses she should double the amount of others. At the end of 4th Which one of them started with the least amount? (6) Which one of them started with the largest amount of money? (7.) At the end of the 2nd game what is the amount of money with uma? game each of them have same amount of money (Rs.32).

Ans: Vidya, Swetha, Rs.8

8. A cube of 12 mm is painted on all its side. If it is made up of small cubes of size 3mm. If the big cube is splitted into those small cubes, the number of cubes that remain unpainted is Ans: 8

9. B is 50% faster than A. If A starts at 9 A.M. and B starts at 10 A.M. A travels at a speed of 50 km/hr. If A and B are 300 kms apart, The time when they meet when they travel in opposite direction is Ans:12 noon

10. A graph will be there. Inside the graph sheet there will be a Quadrilateral. We have to count the number of squares in the Quadrilateral.

11. You are having 31kg of rice. You are provided with a 1kg stone for weighing. In how many weights the 31kg of rice can be weighed. Ans: 5

12. A starts at 11:00AM and travels at a speed of 4km/hr. B starts at 1:00PM and travels at 1km/hr for the first 1hr and 2km/hr for the next hr and so on. At what time they will meet each other. Ans:

13. There are 80 coins, among them one coin weighs less compared to other. You are given a physical balance to weigh. In how many wieghings the odd coin can be found. Ans:

14. Dia of the circle 4cm. The shaded part is 1/3 of the square area. What is the side of the square. Ans: root of 3pi

15. A,B,C, can do a work in 8,14,16 days respectively. A does the work for 2 days. B continues from it and finishes till 25% of the remaining work. C finishes the remaining work. How many days would have taken to complete the work Ans:

16. Raja went to a beauty contest .his wife was eager to know the result he told that the lady wear a yellow sari was winner. Miss. Andhra Pradesh Miss. Utter Pradesh, Miss. Maharashtra, Miss. West Bengal were the participants all the participants sat in a row. The conditions are (A) The woman wore yellow sari won the competition. (B) Miss. West Bengal was neither the runner-up or winner.(C) Miss. West Bengal was not at either ends.(D) Miss. Maharastra wore the white sari.(E) The women wore white sari and yellow sari sat at extreme ends.(F) The runner-up and winner did not sit together. [This was the passage given and the questions were easy]

17. The ratio of white balls and black balls is 1:2. If 9 gray balls is added it becomes 2:4:3. Then what is number of black balls. Ans:12

18. There are 10 coins. 6 coins showing head. And 4 showing tail. Each coin was randomly flipped (not tossed) seven times successively.after flipping the coins are 5 heads 4 tails one is hided the hided coin will have what.

19. Two cars are 500 cm apart. each is moving forward for 100 cm at a velocity of 50 cm/s and receding back for 50 cm at 25 cm/s at what time they will collide with each other.

20. People near the sea shore are leading a healthy life as they eat fish.but people at other part of the city are also healthy. Inference.

21. It is found from research that if u r a drunken then u have a less chance for chronic heart diseases. Inference.

22. A-B+c>A+B-C i) B is +ve, ii) B is -ve when it will hold true.

23. i) C.P is Rs 120 and profit is 30%

ii) C.P is Rs 210 and profit is 20%

we can find the S.P by using

i)only ii)only both i &ii neither i&ii

24. How will u find distance between Nagpur and Mumbai?

I took one hour more when I travel at 80 km/hr than at 90 km/hr.

25. 100 coins were collected by four persons each collected more than 10 each collected a different number each was an even number find what is the max possible no of coins, two more questions based on the same passage.

26. A car travels from B at a speed of 20 km/hr. The bus travel starts from A at a time of 6 A.M. There is a bus for every half an hour interval. The car starts at 12 noon. Each bus travels at a speed of 25 km/hr. Distance between A and B is 100 km. During its journey , The number of buses that the car encounter is

27. The ratio of the ages of the father and the son is 5:3, After 10 years it will be in the ratio 3:2. What will be their ages.

28. There was a Island. In that Island there was Rubys and Emeralds. Those were available in plenty. 0.3 kg of ruby is 4 lakhs and 0.4 kg of emeralds is 5 lakhs. Jayanth is buying 12 kg of Ruby and emerald. Choices will be given . Jayanth has to carry both ruby and emerald to the maximum profit.

29. Varun buys 8 books,10 pens and 2 pencils and Babu buys 6 books, 5pens and 5 pencils. Babu pays 50% more than Varun. What is the amount Varun spends in buying pencils.

30. Prakash and Revathi rent a fancy shop. Prakash imposes the following restrictions on Revathi for buying clips,stickers and lip sticks. The number of clips is twice the no. of stickers. The no. of lipsticks should be more than the sum of clips and stickers. Cost of clip is 1 rupee. Cost of lipstick is twice the clips. Cost of 1 lipstick is the cost of four stickers. Then What is the amount that Prakash spents for Revathi. Answer choices will be given.

1.Train A starts from station A at 11.am.Train B starts from station B at 12 noon.the speed of train A is 4 kmph,train B is 1 kmph for the first hour,2 kmph for the 2nd hour,3 kmph for the 3rd hour etc.At what time do the two trains meet? ans:2 PM

2.There is a coin collection.100 coins in all.4 peopke collect coins.Each collects a minimum of 10 coins.and each has different number of coins.the numbers are even. (4 questions based on this)

3.Moped problem based on time and distance

4.Find the number of integers divisible by either 3 and 12 from 1 to 999.

5.Find the number of integers divisible by either 3 or 2 from 100 to 200 including both,

6.There is a cube of side 4 cm.The faces are coloured in red.the cube is cut into pieces of size 1 cm.How many cubes have no colour Ans:8

7.There are 80 coins.One coin is counterfeit in weight.How many minimum weighings are required to find out the counterfeit coin? Ans 4

8.There are 31 kgs of rice .With a 1 kg weight,Find out the minimum number of weighings required to weigh 31 kgs.

9.there are four contestants in a beauty contest.they aer Ms.UP,Ms. MP,

Ms.AP and Ms.WB.each is wearing a different colour saree(red,blue,green and white).They are seated in a row.The winner and runner are not sitting near each other.Ms.WB is noehter the winner nor the runner.the green and white saree contestans are sitting in either end and the green color saree contestant is the runner up.

4 questions based on this

10.there is a pack of cards.Find the sum of integers excluding all the picture cards. Ans.216

11.Two questions based on figure. Given at the end.

12.There are 2 cars moving in opposite directions.the distance between them is 300cm.They move forward for 100cm with a speed of 50 cm/s,and omes back 50 cms at 25cm/s.after how many seconds will the cars collide?

13) There is a room with 12 slots for painting. The details about the paintings are as follows:

18th century paintings - 3

19th century paintings - 2

20th century paintings - 4

Make up a sequence so that the paintings may be arranged with the following rules.

1) The 5th slot is always empty.

2) There must be an empty slot between paintings of different groups (century).

3) The paintings of the same group can be placed together.

A set of questions were asked with the pattern that was framed.

14)

Find the area of the square which is covered by the circle.

The area is 1/3 area of the square. Find the side of the square.

15)

Find the number of squares.

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