CBSE Question Paper 2016 class 10 Mathematics

Section-A

Question number 1 to 4 carry one mark each

1. In ,S and T are points in the sides PQ and PR respectively such that. If PS = 4 cm, PQ = 9 cm and PR = 4.5 cm, then find PT.

2. Find the value of , when it is given that

3. If, find the value of.

4. Find the sum of upper limit and lower limit of the class interval in which the 20^th observation of the following data lies:

SECTION-B

Question number 5 to 10 carry two marks each.

5. Find the prime factorization of the denominator of the rational number equivalent to 8.39.

6. Show that is an irrational number

7. Find the quadratic polynomial whose zeroes are and.

8. State which of the two triangles given in the figure are similar. Also, state the similarity criterion used.

9. Prove that:

10. Determine missing frequency x, from the following data, when Mode is 67.

SECTION C

Questions number 11 to 20 carry three marks each.

11. Use Euclid division lemma to show that square of any positive integer cannot be of the from 5m+2 or 5m +3 for some integer m.

12. A man has certain note of denomination 20 and 5 which amount to 380. If the number of notes of each kind are interchanged, they amount to 60 less than before. Find the number of notes of each denomination.

13. Divide the polynomial by the polynomial and verify the division algorithm.

14. Show graphically the following pair of linear equations if inconsistent:
2x – 2y – 2 = 0
3x – 3y + 5 = 0

15. are in the same base BC. If AE produced intersects BC at D then, prove that

16. In a , AD is perpendicular to BC and AD² =BD x CD, Prove that ABC is a right-angled Triangle.

17.

18. Prove that:
(sin A + cosec A )² + (cos A + sec A)² = 7 + tan² A + cot² A

19. The following data gives the information on the observed lifetimes (in hours) of 150 electrical components:

Find the mode of the distribution.
20. The weekly pocket money of the students of class ix of a school are given in the following table:

Find the median for the above data.

Section D

Question numbers 21 to 31 carry four marks each.

21. Can the number 6ⁿ,n being a natural number, end with the digit 5? Give reasons.

22. Draw the graph of the following pair of linear equations:
X + 3y = 6 and 2x – 3y = 12
Find the ratio of the areas of the two triangles formed by first line, x = 0, y = 0 and second line x = 0, y = 0

23. Obtain all other zeroes of the polynomial if two of its zeroes are and .

24. Mr. Sharma and Mr. Arora are family friends and they decided to go for a trip with family. For the trio they reserved their rail tickets. Mr. Arora has not taken a half ticket for his child who is 6 years old where as Mr. Sharma has taken half tickets for his two children who are 65 years and 8 years old. A railway half ticket costs half of the full fare but the reservation charges are the same as in a full ticket. Mr. and Mrs. Arora paid 1700, while Mr. and Mrs. Sharma paid 2700. Find the full fare of one ticket and the reservation charges per ticket what difference you find in their behavior and which one you will choose for you self?

25. In the given figure, ABC is a triangle and GHED is a rectangle. BC = 12 cm, HE = 6cm, FC = BF and altitude AF = 24 cm. Find the area of the rectangle.

26. “In a triangle if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle’. Prove it.

27. If, verify the following:
i) ,
ii)

28. Prove that:

29.

30. The daily income of 150 families if given below. Calculate the arithmetic mean.

31. The following table gives the daily income of 50 workers of a factory. draw both types (“less than type’ and ‘greater than type’) gives