# 10 Class Maths Paper

SAMPLE PAPER - 2008

Class - X

SUBJECT – MATHEMATICS

Time: 3 hrs Marks: 80

General Instructions:

( I ) All questions are compulsory.

( ii ) The question paper consists of 30 questions divided into four sections –A, B, C and D. Section A contains 10 questions of 1 mark each, Section B is of 5 questions of 2 marks each, Section C is of 10 questions of 3 marks each and section D is of 5 questions of 6 marks each. . ( iii ) There is no overall choice. However, an internal choice has been provided in one question of two marks each, three questions of three marks each and two questions of six marks each.

( iv ) In question on construction, the drawing should be neat and exactly as per the given measurements.

( v ) Use of calculator is not permitted.

SECTION A

( Qns 1 – 10 carry 1 mark each )

1. If HCF ( a, b ) = 12 and a x b = 1800. Find LCM ( a, b ).

2. Find the zeros of the quadratic polynomial from the graph.

Y

4

3

2

1

X X’ -4 -3 -2 -1 0 1 2 3 4

-1

-2

-3

Y’

3. If the pair of linear equations x – y = 1 and x + ky = 5 has a unique solution x = 2, y = 1, find the value of k.

4. If x = 4sin2θ and y = 4 cos2θ + 1. Find the value of x + y.

5. Find the value of P, if cos( 810 + θ ) = sin( P/3 - θ ).

6. A horse is tied to a peg at one corner of an equilateral triangle shaped grass field of side 15m by means of a 7m rope. Find the area of that part of the field in which the horse can graze.

7. Two tangents PQ and PR are drawn from an external point P to a circle with centre O. If LQOR = 1200, then what is the value of LOPQ? Q

O P

R

8. An observer 1.5m tall is 28.5m away from a tower. The angle of elevation of the top of the tower from her eye is 450. What is the height of the tower?

A

B 450 C

1.5m

D 28.5m E

9. The graph of the less than ogive and more than ogive intersect at the point ( 4, 15). What is the value of the median?

10. Suppose you drop a die on the rectangular region shown in fig. What is the probability that it will land inside the circle with diameter 1m ?

2m

3m

SECTION B

( Qns 11 – 15 carry 2 marks each )

11. If 9th term of an A.P is 99 and 99th term is 9, find its 108th term.

12. A letter of English alphabet is chosen at random. What is the probability that the chosen letter is ( i ) a vowel ( ii ) a consonant.

13. If 2x + y = 35 and 3x + 4y = 65, find the value of x/y.

14. Show that the three points ( 3, 3 ), ( h, 0 ) and ( 0, k ) are collinear if 1/h + 1/k = 1/3

15. Find the zeros of the quadratic polynomial x2 + 11x + 30, and verify the relationship between the zeros and coefficients. OR

Divide the polynomial p ( x ) by g ( x ) and find the quotient and remainder. p( x ) = x4 – 3x2 + 4x + 5

g ( x ) = x2 + 1 - x

SECTION C

( Qns 16 – 25 carry 3 marks each )

16. A shopkeeper buys a number of books for Rs80. If he had bought 4 more books for the same amount, each book would cost him Re 1 less. How many books did he buy? 17. Prove that √3 is irrational.

18. Find...

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