Rajasthan Board Secondary Examination 2013 – Maths Paper
PART – A
1. Find the H.C.F. of numbers 44 and 99.
2. Total price of 7 pencils and 5 pens is Rs. 29. Write it down in the algebraic form.
3. Find the eleventh term of the A.P. 2, 7, 12, …… .
4. Find the coordinates of the point which divides the join of points ( – 1, 7 ) and ( 4, – 3 ) in the ratio 2 : 3.
5. Write down the distance of the point ( 7, – 3 ) from y-axis.
6. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°, then find ∠ POA.
7. If the radius of a circle is 14 cm, then find the area of the circle.
8. Divide the line segment of 7·5 cm in the ratio of 2 : 3. Draw figure only.
9. Radius of the circle is r and θ is the angle of the sector in degree. Write down the formula of length of corresponding arc.
10. Write down the sum of the probabilities of all the elementary events of an experiment.
PART – B
11. If DE | | BC in ∆ ABC, AD = 1·5 cm, BD = 3 cm and AE = 1 cm, then find EC.
12. If sin A = 3/5 , then find cos A and cosec A.
13. Find the value of tan 65°/cot 25° .
14. Find the value of sin 35° cos 55° + cos 35° sin 55°.
15. A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.
PART – C
16. Find the highest positive integer by which dividing the numbers 396, 436 and 542 remainders are 5, 11 and 15 respectively.
17. Divide x³ – 3x² + 3x – 5 by x – 1 – x² , and verify the division algorithm.
18. Suresh started work in 1985 at an annual salary of Rs. 5,000 and received an increment of Rs. 200 each year. In which year did his income reach Rs. 7,000 ?
19. If tan 2A = cot ( A – 18° ), where 2A is an acute angle, then find the value of A.
20. The shadow of a tower standing on a plane ground is found to be 40 m longer when the sun’s altitude reduces to 30° from 60°. Find the height of the tower.
21. Prove that the lengths of tangents drawn from an external point to the circle are equal.
22. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 times of the corresponding sides of the first triangle. Write down steps of construction.
23. Find the area of the sector of a circle with radius 4 cm and of angle 60°. Also find the area of the corresponding major sector. ( Use π = 3·14 ).
24. A metallic sphere of radius 4·2 cm is melted and recast into the shape of a cylinder of radius 7 cm. Find the height of the cylinder.
25. 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether it is defective or not. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.
PART – D
26. Coach of a cricket team buys one bat and 2 balls for Rs. 300. Later he buys another 2 bats and 3 balls of the same kind for Rs. 525. Represent this situation algebraically and solve it by graphical method. Also find out that how much money coach will pay for the purchase of one bat and one ball.
27. A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so ? If yes, at what distances from the two gates should the pole be erected ?
28.If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then prove that the two sides are divided in the same ratio.
Prove that 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.
29.Find the area of the triangle formed by joining the mid-points of the sides of the triangle ABC whose vertices are A ( 0, – 1 ), B ( 2, 1 ) and C ( 0, 3 ). Find the ratio of this area to the area of the triangle ABC.
30. A Life Insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years.
Age ( in years ) Number of policy holders
Below 20 2
Below 25 6
Below 30 24
Below 35 45
Below 40 78
Below 45 89
Below 50 92
Below 55 98
Below 60 100
The marks distribution of 30 students in a mathematics examination are as follows :
Class-interval of marks 10-25 25-40 40-55 55-70 70-85 85-100
Number of students 2 3 7 6 6 6
Find the mean by assume mean method and find also the mode of given data.