SAMPLE PAPER

Class-VII

Foundation

For IIT-JEE

& Medical

MATHEMATICS

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Sample Paper Foundation for IIT / NTSE / Olympiad

1

Time: 3 hours MM: 90

Instructions: 1. All questions are compulsory.

2. Section A carries 6 parts, one mark for each part.

3. Section B carries 10 blanks, one mark for each blank.

4. Section C carries 6 questions, two marks for each question.

5. Section D carries 8 questions, four marks for each question.

6. Section E carries 6 questions, five marks for each question.

SECTION A 1. Choose the correct option out of the following

i) The number of vertices in a cuboid

(a) 8 (b) 10 (c) 4 (d) 12

ii) (ab)4

is equal to

(a) ab4

(b) ba4

(c) 4ab (d) a4

b4

iii) In ΔPQR, the angle opposite to side PQ is

(a) ∠P (b) ∠L (c) ∠Q (d) ∠R

iv) The supplementary angle of 44° is

(a) 36° (b) 136° (c) 44° (d) 144°

v) The product of and is 75 57

(a) 25/49 (b) 1 (c) 49/25 (d) 12 /7

vi) If the integers 11, –6, –10, 7, 8, –4 and –3 are marked on the number line, the integer on the extreme right is

(a) –10 (b) –8 (c) 11 (d) –3

SECTION B

2. Fill in the blanks:

a) 27.3 ÷ 100 = ___________.

b) The mode of 1,2,3,5,5,3,5,7,3,2,2,5 is ___.

c) A sphere has ____ edges.

d) Fractions representing the same value are called ____ fractions.

e) If a ray stands on a line, then the sum of adjacent angles so formed is ____.

f) ____ is a solid which has two edges and no vertex.

g) The reciprocal of 2 3

5 8

is ____.

h) The value of the expression (5)0

+ (50)0

+ (500)0

is __________

i) Seven times a number equals 56 : The equation for this is _____.

j) Multiplicative inverse of an integer ‘b’ is ___ .

SECTION C

3. Draw a triangular prism and write its number of vertices.

4. Solve for ‘x’ for 7x + 13 – 4x = 4x + 43 – 4x

5. Find the sum of 4 1

&7 1 4

6. Write down a pair of a negative and a positive integer whose sum is 4.

7. Is it possible to have a triangle with sides 6 cm, 3 cm and 7 cm? Give reason(s).

8. Find the median of the given data: 22, 34, 21, 44, 21, 22, 45, 44, 22

SECTION D

9. (a) Find the probability of choosing E from the word TEMPERATURE.

(b) Find the mean of 2, 4, 8, 6, 5.

Head Office: 62, Nitikhand-III, Indirapuram GZB | Cont. +91-9990495952,+91-9990495952 .| www.apexiit.co.in

Sample Paper Foundation for IIT / NTSE / Olympiad

2

10. Solve for ‘p’ : 2 ( 1) 5 1

25 3

p p

11. In a class test of 20 questions, 4 marks are awarded for every correct answer, 1 mark is deducted for every incorrect

answer and 0 is awarded for a question not attempted. What will be Nitish's score, if he gets 4 correct and 6 incorrect

answers?

12. Simplify

3

3 2 3

9 7 1 0

3 7 1 0

13. Evaluate3 6 2 5 5 1 0

2 1 5 3 6 7 1 4

.

14. Find ‘x’ and 'y', if AB is a straight line.

15. In the given figure, find x, y, z.

16. Simplify: 11.001 – 2.36 + 4.965 – 5.7

SECTION E

17. a) In the given figure, l || m. Find ∠1, ∠2, ∠3 and ∠4.

b) Find the measure of an angle which is three times its supplement.

18. a) A piece of wire is 19.63 m long. If it is cut into 13 equal parts, find the length of each piece.

b) By what fraction should be multiplied to1 1

6 get

5 5

6?

19. Find two numbers whose sum is 16 and the first number is 6 more than the second number.

20. a) Simplify: (26

x 215

) ÷ 221

b) Express 231200000000 in the standard form.

21. A tree broke at a point in a storm but did not separate. The top touched the ground at a distance of 12 metre from its

base. Find the height of the tree if the length from the base to the broken point is 5 m.

22. The performance of a student in 1st term and 2nd term is given.

Construct a double bar graph and answer the following questions

i) In which subject the child has shown the maximum improvement?

ii) In which subject the performance has gone down.

60%

Dhwani Jain is pursuing Chemical Engineering from N.U.S. (National university of Singapore) Ranked 2nd University in Asia. she was our two years classroom program Student.

Prakhar Goel is studying in Maulana Azad Medical College Delhi. He was our One year Dropper Batch Student

Prerna Kashyap is pursuing B.Tech (EC) fromNIT Kurukshetra. She was our Two years classroom program Student

Shubham Mukherjee is studying in IIT-Guwahati. He was our One year Dropper Batch Student

Shiddhant Rathore is pursuing B.Tech (Mechanical) from BITS Goa.He was our Three years Classroom Program Student.

AIR 427(GE)

Arindham Roy is pursuing B.Tech from NIT Patna. He was our Two years classroom program Student

AIR 1823(GE)

AIR 5982 (IITAdvanced)

Arindham Roy

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