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Class: X Time: 2 hours Maximum Marks: 100

Name of the Candidate: _________________________________________________

Roll Number: __________________________________________________________

Candidate’s Signature: ________________ Invigilator’s Signature: _______________

Instructions

A. General:

1. This booklet is your Question Paper containing

9Printed Pages. Do not open this booklet before

being instructed to do so by the invigilators.

2. Blank papers, clipboards, log tables, slide rules,

calculators, cameras, cellular phones, pagers and

electronic gadgets are NOT allowed inside the

examination hall.

3. Write your name and roll number in the space

provided below.

4. Use a black ball point pen/HB pencil to darken the

bubbles on the OMR sheet.

B. Question Paper Format:

The question paper consists of two sections.

1. Section 1 contains 20 multiple choice questions of

MATHEMATICS. Each question has four choices (A),

(B), (C) and (D) out of which ONLY ONE is correct.

2. Section 2 contains 20 multiple choice questions of

APTITUDE. Each question has four choices (A), (B), (C)

and (D) out of which ONLY ONE is correct.

C. Marking Scheme:

1. For each question in Section 1, you will be awarded

3 marks if you darken the bubble corresponding to

the correct answer and zero mark if no bubbles are

darkened. In all other cases, minus ONE(–1) mark will

be awarded.

2. For each question in Section 2, you will be awarded

2 marks if you darken all the bubble(s) corresponding

to only the correct answer and zero mark if no

bubbles are darkened. In all other cases, minus

HALF(–1/2) mark will be awarded.

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Space for Rough Work

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Section-I 1. If a three digit number ‘abc’ has three factors,how many factors does the 6-

digit number ‘abcabc’ have?

A) 13 or 29 factors B) 15 or 27 factors

C) 16 or 24 factors D) 15 or 20 factors

2. The sum of the factors of a number is 124.What is the number?

A) Number lies between 40 and 50 B) Number lies between 50 and 60

C) Number lies between 60 and 70 D) More than one such number exists

3. In a quadrilateral ABCD, AB=3, BC=4, CD=5, ∠ABC = ∠BCD=120 degrees.

Find the area of the quadrilateral

A) 41.625 B) 43.759 C) 45.941 D) 49.147

4. Determine the number of three digit numbers in base 10 having at least one 5

and at most one 3?

A) 221 B) 236 C) 249 D) 254

5. Let P(x)=x2+ax+b be a quadratic polynomial where a is real and b is not equal

to 2 and is rational. Suppose P(0)2 ,P(1)2,P(2)2 are integers. Then a and b are:

A) a is irrational but b is rational B) both a and b are integers

C) a is integer but b is not integer D) no such a and b exist

6. Find the number of integer solutions of (a,b,c) satisfying the given below

condition a2=bc+4 , b2=ac+4

A) 11 B) 12 C) 13 D) 14

7. There are four basket-ball players A,B,C,D. Initially the ball is with A. The ball

is always passed from one person to a different person. In how many ways can

the ball come back to A after seven passes?

A) 183 B) 546 C) 693 D) 721

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8.let I1,I2 be any two parallel lines and B,C be any two points on I1 and A1 , A2 , ……. ,A2016 be points on I2 .If Di denotes the area of triangle Ai BC and if (sigma runs from 1 to 2016 ) Di =2016. Then area of triangle A2016 BC is?

A)1 B)1/2 C)2 D)2016

9. Let { an } be a sequence of integers such that a1 =1 ; am+n=am+an+mn for all positive integers m, n. Then a12 is?

A) 71 B) 70 C) 78 D) 76

10. The number of solutions of the equation (xy)(x+y)=2010 , where x and y denotes positive prime numbers , is ?

A) 10 B) 11 C) 12 D) 13

11. Let ABC be a triangle in which AB=AC . Suppose the orthocenter of the triangle lies on the incircle. Find the ratio of AB/AC?

A) 1 B)1 2 C)1 4 D) 3 4

12.For any natural number n , let S(n) denotes the sum of digits of n . Find the number of all the three digits of n such that S(S(n))= 2

A) 84 B) 88 C) 97 D) 100

13. Three positive real numbers a, b, c are such that a2 + 5b2 +4c2 -4ab-4bc=0. Let a, b, c be the lengths of the sides of the triangle

A) Triangle is possible for all values of a, b, c.

B) No such triangle exists

C) Triangle exists only under some conditions

D) None

14. The sum of two positive integers is 52 and their L.C.M is 168, Find the units digit in the product of those numbers?

A) 2 B) 4 C) 0 D) 8

15. Points E, F on the sides of CA, AB of triangle ABC are such that FE is parallel BC ; BE and CF intersect at X then AX is ?

A) Median B) angular bisector C) altitude D) none of the above

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16. The number of even factors of the number 25200 is ?

A) 90 B) 80 C) 72 D) 45

17.If a,b,c are real numbers with a<b<c and a+b+c=6,ab+bc+ca=9 . Then range

of c is ?

A)0<c<1 B)1<c<2 C)2<c<3 D)3<c<4

18. If transversal cut the side AB,BC,CD,DA of a quadrilateral ABCD at P,Q,R,S.

Find the value of 8(AP/RD)(BQ/PB)(DS/QC)(CR/SA) ?

A)4 B)8 C)6 D)1

19.Two circles of radii a,b touch each other externally and they touch a line . A

circle is inscribed in the region between the circles and the line so that it touches

two circles and the line. If a=4,b=9 then the radius of inscribed circle is ?

A)81/16 B)25/16 C)36/16 D)81/16

20.111111111111 is perfectly divisible by ?

A)101 B)307 C)407 D)207.

Section-II

1. What day of the week does 28 May, 2006 fall on?

A) Saturday B) Monday C) Sunday D) Thursday

2. Find the odd one?

396 ; 462 ; 572 ; 427 ; 671 ; 264

A) 396 B) 427 C) 671 D) 264

3.Which is the number that comes next in the sequence : 0,6,24,60,120,210?

A) 240 B) 290 C)336 D) 504

4. Fill up the blank by following the given sequence :

1,2,3,6,4,5,6,60,5,6,7,………..

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A) 120 B) 210 C)150 D) 125

5. Folowing the given sequence find the blank space left:

8,4,4,7,8,1,3,9,3,2,1,……..

A) 1 B) 2 C)3 D) No logic

6. Observing the first series apply the same logic to the second sequence and

find the value of e?

5 6 11 28 71 160 ?

2 3 a b c d e

A) 25 B) 68 C)157 D) 318

7. Pointing to a man in the photograph, a woman said, “His brother’s father is the

only son of my grandfather.” How is the woman related to the man in

photograph?

A) Sister B) Aunt C) Grandmother D) Daughter

8. A man to photograph says “ The lady in the photograph is my nephew’s

maternal grandmother ” How is lady in the photograph related to the man’s sister

who no other sister ?

A) Mother-in-law B) Cousin C) Sister-in-law D) Mother

9. Find out the wrong term in the series 2,5,10,50,500,5000

A) 5000 B) 500 C) 50 D) 10

10. 4, 18, ?, 100, 180, 294, 44

A) 48 B) 50 C) 58 D) 60

11. What is the next number in the given sequence?

1, 11, 21, 1211, 111221, ……………..

A) 13112221 B) 12112211 C) 11221212 D) 13122121

12. Which number replaces the question mark?

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A) 8 B) 2 C) 6 D) 4

13. Which number replaces the question mark?

A) 10 B) 11 C) 12 D) 13

14. Which number replaces the question mark?

A) 4 B) 8 C) 10 D) 13

15. Which number replaces the question mark?

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A) 0 B) 4 C) 10 D) 8

16. F21, S23, T25, T27, S29, M31, __? Find out the next term in the series A) P33 B) B31 C) W02 D) K33

17. There are 35 steps in a temple. By the time Chithra comes down two steps, Madhu goes up one step. If they start simultaneously and keep their speed uniform, then at which step from the bottom will they meet? A) 11th step B) 12th step C) 13th step D) None of the above 18. Find the odd one among the following 396, 462, 572, 427, 671, 264

A) 396 B) 427

C) 671 D) 264

19 .Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:

A. 5 min. B. 9 min.

C. 10 min. D. 15 min

20. In a certain code, BREAKTHROUGH is written as EAOUHRBRGHKT. How is DISTRIBUTION written in that code?

A) TISTBUONDIRI B) STTIBUONRIDI

C) RISTTIBUDION D) STTIBUDIONRI

SPACE FOR ROUGH WORK

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Wissenaire

Wissenaire is the annual techno-management festival of Indian Institute of Technology

Bhubaneswar held in the Arugul campus of the prestigious IIT Bhubaneswar. It is one

of the most awaited technical festival of East India. It is a three day long event usually

held during first week of January. The word Wissenaire is derived from the German

word ‘Wissen’ meaning knowledge and ‘air’ meaning free. Thus it is justified by its

tagline Knowledge Runs Free. Wissenaire encompasses various sectors of technology,

science and management. These including quizzing, coding, designing, robotics, planning

and testing the creativity and innovative spirit of young technical minds. With this

motive Wissenaire’17 is conducting Qwissenaire’17, the Talent Test to ignite minds of

8th, 9th and 10th class students.