Jharkhand Board Sample Paper
Subject – Mathematics
Class 10th
Total No. of Questions : 25 Time : 3 Hours Full Marks : 80
GENERAL INSTRUCTIONS :
1. All questions are compulsory.
2. This question paper consists of 25 questions divided into three Sections A, B and C. Section A contains 10 questions of 2 marks each, Section B contains
10 questions of 3 marks each and Section C contains 5 questions of 6 marks each.
3. Only sketches are to be given in the answers of construction.
4. Answers of the questions must be in the context of the instructions given there in.
5. Do all rough work only on the last pages of the Question-Cum-Answer Booklet and nowhere else.
SECTION – A
( Question Nos. 1 to 10 carry 2 marks each )
1. A fraction becomes 4/5 if 1 is added to each of the numerator and the denominator. However, if we subtract 5 from each, the fraction becomes 1/2 . Find the fraction.
2. Find the value of k for which the HCF of x^{2} + 2kx + 3k + 3 and x^{2} + x – 5k is x + 5.
3. Solve : ( x + 5 )^{2} – 36 = 0
4. Find the common difference of the A.P. of 119, 136, 153, 170, ........ and write the next two terms.
5. A briefcase is available for Rs. 800 cash or for Rs. 500 cash down payment and Rs. 320 to be paid after six months. Find the rate of interest charged under the installment plan.
6. A loan has to be returned in two equal annual installments. If the rate of interest is 16% per annum compounded annually and each instalment is Rs.1,682, find the sum ( loan ) borrowed and the total interest charged.
7. Show that: tan^{4} A + tan^{2} A = sec^{4} A – sec^{2} A.
8. Evaluate: sin^{2} 20° + sin^{2} 70°.
9. The radius of the base and the height of a right circular cone are 7 cm and 24 cm respectively. Find the volume of the cone.
Represent the following data in the form of a pie-chart :
Items | Clothing | Food | House rent | Education | Miscellaneous |
Amount Spent (Rs) | 600 | 4,000 | 1,200 | 400 | 1,000 |
10. A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at random, find the probability that it is black.
SECTION – B
( Question Nos. 11 to 20 carry 3 marks each )
11. Solve graphically ( Use the graph paper given on Page No. 00 ) :
x – y = 0; x + y = 2.
12. Solve the system of equations :
11/v – 7/u = 1; 9/v – 4/u = 6.
13. Simplify : 1/(x-1) – 1/(x+1) – 2/(x^{2}+1) – 4/(x^{4}+1).
14. Find the roots of the equation : 6x^{2} + x – 2 = 0
15. Prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.
16. Construct an incircle of a triangle whose sides are 5 cm, 12 cm and 13 cm and measure its radius.
17. A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.
18. If the radii of the ends of a bucket 45 cm high are 28 cm and 7 cm, determine its capacity.
19. Find a point on the X-axis which is equidistant from the points ( 5, 4 ) and ( – 2, 3 ).
20. Find the coordinates of the point which divides the line-segment joining the points ( – 7, 4 ) and ( – 6, – 5 ) internally in the ratio 7 : 2.
SECTION – C
( Question Nos. 21 to 25 carry 6 marks each )
21. The angles of elevation of the top of rock from the top and bottom of a 100 m high tower are 30° and 45° respectively. Find the height of the rock.
22. Prove that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
23. The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. Prove it.
4. Calculate the mean of the following frequency distribution :
Class-interval | 0-80 | 80-160 | 160-240 | 240-320 | 320-400 |
Frequency | 22 | 35 | 44 | 25 | 24 |
5. Rajinder Kaur’s monthly salary is Rs. 15,400. She contributes Rs. 1,000 per month towards PF and pays Rs. 1,000 quarterly on LIC premium during the year. She donates Rs. 3,100 to Medical Research Centre and earns a relief of 100% on the donation. Find the amount of income tax paid by her.
Use the following for calculating income tax :
(a) Standard deduction : If the salary exceeds Rs. 1,50,000 but does not exceed Rs. 3,00,000, then Rs. 25,000.
(b) Rates of income tax :
Slab | Income Tax |
(i) Upto Rs. 50,000 | NIL |
(ii) Rs. 50,001 to Rs. 60,000 | 10% of the amount exceeding Rs. 50,000 |
(iii) Rs. 60,001 to R s . 1,50,000 | Rs. 1,000 + 20% of amount exceeding Rs. 60,000 |
(iv) Above Rs. 1,50,000 | Rs. 19,000 + 30% of the amount exceeding Rs. 1,50,000 |
(c) Rebate in income tax : 15% of the total savings and Rs. 5,000 extra for female.
(d) Surcharge : 5% of the income tax payable.