Ganit Pradnya(VII VIII)

JMO / HPR LEV / 06022011 / VII / VIII 7 8 Marks 100

(Time) : 2 (Hours)

Name of the Student

School :

(Place) (District) :

Seat No (If Given) :

Invigilator’s Signature

Instructions :

Attempt all questions.

Write explanation in the space provided for all the questions.

Separate answerbook or sheet is not allowed.

Use provided space for rough work.

Q. 1 to 4 carries 4 marks each,

Q. 5 to 7 carries 5 marks each,

Q. 8 to 11 carries 6 marks each,

Q. 12 to 14 carries 7 marks each,

Q. 15 to 17 carries 8 marks each.

There are 17 questions in this question paper. Ensure it.

Examiner’s Signature :

Q. No. Marks

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

Total Marks

In Words :

Junior Maths Olympiad

Specimen Paper

- 2 -

JMO – 2011 (VII / VIII)

Q. 1 Find the next two terms of the following series of numbers. (4 Marks)

(a) 6, 15, 35, 77, 143, ……….., ………

(b) 3137, 4143, 4753, 5961, …….., ……….

Solution :

Rough Work /

Ans.

a

b

- 3 -

JMO – 2011 (VII / VIII)

Q. 2 Divide 237 into three parts in such a manner that 3 times the first shall be equal

to 5 times the second and 8 times the third.

Solution :

(4 Marks)

Rough Work /

Ans.

Part 1

Part 2

Part 3

- 4 -

JMO – 2011 (VII / VIII)

Q. 3 Find the last digit of the number 12 + 2

2 + …….. + 99

2 (4 marks)

12 + 2

2 + …….. + 99

2

Solution :

Rough Work /

Ans.

- 5 -

JMO – 2011 (VII / VIII)

Q. 4 Which are the two numbers less than 260 that divide 232

– 1 exactly ? (4 marks)

232

– 1

Solution :

Rough Work /

Ans.

- 6 -

JMO – 2011 (VII / VIII)

Q. 5 If 3! = 3 2 1 4! = 4 3 2 1 5! = 5 4 3 2 1 (5 marks)

then find the value of 1.1 ! + 2.2! + 3.3! + 4.4! + …… + 99.99!

3! = 3 2 1 4! = 4 3 2 1 5! = 5 4 3 2 1

1.1 ! + 2.2! + 3.3! + 4.4! + …… + 99.99!

Solution :

Rough Work /

Ans.

- 7 -

JMO – 2011 (VII / VIII)

Q. 6 (AUM)2 = UMOUM, then AUM + MOU = ? (5 marks)

(AUM)2 = UMOUM, AUM + MOU = ?

Solution :

Rough Work /

Ans.

- 8 -

JMO – 2011 (VII / VIII)

Q. 7 Five friends A, B, C, D, E studying in std. VIII appeared for GAT examination

held recently. When their class teacher asked their marks, everyone told the

average marks of remaining four classmates instead of telling individual own

score. Their answers were as follows.

A B C D E

Answers 90.25 88 89 90.5 89.25

Find the marks obtained by each of them and find the average marks of all five

friends.

A, B, C, D, E GAT

A B C D E

90.25 88 89 90.5 89.25

Solution :

Rough Work /

Ans.

(5 Marks)

A B C D E

- 9 -

JMO – 2011 (VII / VIII)

Q. 8 A teacher said that there were 100 students in his class. 24 of whom were boys

and 32 of whom were girls. Which number system did the teacher use in this

statement ?

Solution :

(6 Marks)

Rough Work /

Ans.

- 10 -

JMO – 2011 (VII / VIII)

Q. 9 In the adjoining figure 40 match sticks are arranged in a square pattern, such

that there are 30 squares in all. Now remove 9 match sticks such that there

won’t be any square and draw such figure in place of answer.

Solution :

Rough Work /

Ans.

(6 Marks)

- 11 -

JMO – 2011 (VII / VIII)

Q.10 Study the following arrangement of numbers and answer the following

questions.

a) Find the sum of numbers in 50th

row at first and then find the sum of

numbers in nth

row.

b) Find the first and last number in 50th

row.

a) ‘n’

b)

Solution :

Rough Work /

Ans.

A

B

(6 Marks)

- 12 -

JMO – 2011 (VII / VIII)

Rough Work For Q. 11

- 13 -

JMO – 2011 (VII / VIII)

Q.11 Simplify :

5

15

11

5

15

11

5

15

11

5

15

11

5

15

11

5

15

11

Solution :

(6 Marks)

Ans.

- 14 -

JMO – 2011 (VII / VIII)

Rough Work For Q. 12

- 15 -

JMO – 2011 (VII / VIII)

Q.12 Find the sum of all four digit numbers using the digits 0, 1, 2 only, using each

digit atleast once.

Solution :

(7 Marks)

Ans.

- 16 -

JMO – 2011 (VII / VIII)

Rough Work For Q. 13

- 17 -

JMO – 2011 (VII / VIII)

Q.13 How many pairs of rabits can be produced from a single pair in a year; if each

pair begets a new pair every month onwards and no rabit dies ?

For example - On 1st Jan. 1 pair of rabbits.

then on 1st Fab. 1 + 1 = 2 pairs of rabbits.

Solution :

(7 Marks)

Ans.

- 18 -

JMO – 2011 (VII / VIII)

Rough Work For Q. 14

- 19 -

JMO – 2011 (VII / VIII)

Q.14 If x = 111 ………. 11 (20 digit number), y = 333 ….. 3 (10 digit number)

z = 444 ………. 4 (10 digit number) find the value of z

yx 2.

x = 111 ………. 11 (20 ), y = 333 ….. 3 (10 )

z = 444 ………. 4 (10 ) z

yx 2

Solution :

(7 Marks)

Ans.

- 20 -

JMO – 2011 (VII / VIII)

Rough Work For Q. 15

- 21 -

JMO – 2011 (VII / VIII)

Q.15 In the adjoining fig. ABCD is a square, E is a midpoint of AD.

EB = EF, AFGH is also a square. Find the ratio AB : AH.

ABCD E AD

EB = EF. ABCD AB : AH

Solution :

A B

C D

E

F G

H

Ans.

(8 Marks)

- 22 -

JMO – 2011 (VII / VIII)

Rough Work For Q. 16

- 23 -

JMO – 2011 (VII / VIII)

Q.16 For a natural number n, let an denotes the sum of the squares of the digits of n.

For example a249 = 22 + 4

2 + 9

2 = 101. Find the sum of a1 + a2 + a3 + …… + a1000.

‘n’ an ‘n’

a249 = 22 + 4

2 + 9

2 = 101 a1 + a2 + a3 + …… + a1000

Solution :

(8 Marks)

Ans.

- 24 -

JMO – 2011 (VII / VIII)

Rough Work For Q. 17

- 25 -

JMO – 2011 (VII / VIII)

Q.17 A closed vessel in the form of a right circular cone of height ‘h’ contains some

water. When the vertex of the conical vessel is downward, water in it stands at

1/3rd

of the height. It is now inverted so that the vertex is upward. At what

height the water now stands ?

h

Solution :

(8 Marks)

Ans.