SAMPLE QUESTION PAPER
CLASS – X
Time : 3 hrs. M.M. 80

SECTION A

1. Solve for x and y :
311 x +125 y = 747 ; 125 x + 311 y = 561

2. If ( x – 5 ) is a factor of , find the values of c and d.

3. In fig, L and M are the midpoints of equal chords AB and CD of a circle, with centre O. prove that
(i) ÐOLM = ÐOML
(ii) ÐALM = ÐCML

4. A walkman is available for Rs 500 cash or Rs 150 cash down payment followed by 4 monthly instalments of Rs 90 each. Find the rate interest charged under the instalment plan.

5. A loan has to be returned in three equal annual instalments. If the rate of interest is 10 % p.a compounded annually and each instalment is Rs 1331, Find the sum borrowed and the total interest paid.

6. D is appoint on the side BC of ?ABC such that ?ADC = ?BAC, prove that

7. Which term of the A.P 3 ,6 ,9 , …. is 36 more than its 24th term?
OR
For what value of n , the nth terms of the two A.P ‘s given below are same:
(i) 2 , -3 , -8 , ………. (ii) -26 , -27 , -28 ,,…..

Reduce the following rational expression into its lowest terms :
6. Using sridharacharyas’s formula, solve for x:
OR
The sum of the squares of two consecutive odd natural numbers is 34. find the numbers

SECTION B

8. Solve the following system of linear equations graphically: Also shade the region between the lines and X – axis.

9. Solve for x :
10. Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 9

11. Construct a ? ABC in which AB = 4 cm , BC = 6 cm and AC = 4 cm. Draw its incircle and measure its radius.

12. A right triangle with sides 3 cm and 4 cm is revolved around its hypotenuse. Find the volume of the double cone thus generated.
13. Prove that:
OR
Evaluate:

14. A conical tent is to accommodate 11 persons. Each person must have 4 sq. metres of the space on the ground and 20 cubic metres of air to breath. Find the height of the cone.

15. Show that the points ( 4 , 4 ) , ( -4 , -4 ) and ( -4v3, 4v3) form the vertices of an equilateral triangle.
OR
Show that the point ( 1 , 4 ) , ( 4 , 4 ) , ( 4 , 8 ) , ( 1 , 8 ) are the vertices of a parallelogram

16. In what ratio does the point ( 3, 12 ) divide the line segment joining the points ( 1 , 4 ) and ( 4 , 16 ).

17. Using step deviation method, find the mean of the following data.

Class
350-450
450-550
550-650
650-750
750-850
850-950
Total

Frequency 14 46 58 70 48 14 250

18. A bag contains 100 identical tokens on which numbers 1 to 100 are marked. A token is drawn. What is the probability that the number, which leaves the remainder 3 when divided by 5
19. The pie chart given shows the enrolment
of students in different classes of a school.
If the total enrolment of all classes is 2400,
Answer the following:
(i) Which class has more enrolment than class IX and by how much?
(ii) Which pair of classes have equal enrolment? Write their enrolments also.
(iii) The class X has how many students less than class VI?

SECTION C

20. Prove that angles in the same segment of a circle are equal .Using the above, find the following:
In fig, ÐBAC = 60o , ÐCDE = 30o and ÐDBC = 40o . Find ÐDCE

21. In a right triangle, Prove that the square on the hypotenuse is equal to the sum of the squares on the other two sides. Using the above, do the following:
ABC is a right triangle , right angled at CD ^ AB . If CD = p , AC = b , BC = a and AB = c ,
Show that pc = ab
OR

Prove that the ratio of the areas of similar triangles is equal to the ratio of the squares on their corresponding sides. Using the above, do the following:
The perimeters of two similar triangles ABC and A’B’C’ are 60 cm and 36 cm respectively. If A’B’ = 9 cm, find AB and the ratio of the areas of two triangles
22. An aeroplane flying horizontally 1 km above the ground, is observed at an angle of 60o from a point on the
ground. After 10 seconds of flight, the angle of elevation is observed to be 30o. Find the speed of the
aeroplane ( in m/second).

23. The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city.

Expenditure
(in Rs.)
100-150
150-200
200-250
250-300
300-350
350-400
400-450
450-500

Frequency 24 40 33 28 30 22 16 7

Find the average expenditure (in Rs.) per household.
24. A cone is divided into two parts by drawing a plane through the mid point of its axis, parallel to the base.
Find the ratio of the volumes of two parts into which the plane divides the cone.
OR
A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. Find the total surface area and volume of the toy.
25. Lakshmi’s annual income is Rs 3,96,000. She contributes Rs 6,500 per month in her PF and pays quarterly premium of Rs 2,500 for her LIC policy.She contributes RS 10,000 towards Prime minister’ relief fund( 100 % exemption) and Rs 10,000 to a charitable trust ( 50% exemption ) . If Rs 2,000 is deducted per month from her salary towards income tax, find the income tax to be paid by her in the last month