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Mathematics
Submitted by: Suresh Gyanchandani (jaipur)
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Pre-Board (Sample Paper)
Class: X M.M. 80
Subject: Mathematics Time: 3 hrs
GENERAL INSTRUCTIONS
1. The question paper consists of three sections: A, B and C.
2. Internal choices have been provided in some questions. Attempt any one of them.
3. Q. No. 1-7 in section A are of 2 marks each.
4. Q. No. 8-19 in section B are of 3 marks each.
5. Q. No. 20-25 in section C are of 5 marks each.
6. Use of calculators is not permitted.
SECTION – A
1. Solve for x and y: 31/x + 43/y = 105/xy; 43/x + 31/y = 117/xy
2. If the 12th term of an A.P. is –13 and the sum of first four terms is 24, find the A.P.
3. Simplify as one rational expression: x6 – 64
x4 + 4x2 + 16
4. A T.V. is available for Rs.18000 cash or for Rs.6000 cash down payment along with 4 equal monthly instalments of Rs.3100 each. Find the rate of interest charged.
5. In an equilateral triangle ABC, D is a point on the side BC, such that BD = 1/3 BC. Prove that 9AD2 = 7 AB2.
6. If (x2 – x + 6) is H.C.F. of polynomials p(x) = (x2 – 4x + 3)(x2 – 5x + a) and q(x) = (x2 + 5x + 6)(2x2 – 3x + b), find the values of a and b.
7. A card is drawn from a pack of 52 cards. Find the probability that the drawn card is neither spade nor ace.
8. Two circles intersect each other at A and B. Their common tangents meet the two circles in C and D.Prove that ÐCAD + ÐCBD = 1800.
9. Find the nth term of an AP, the sum of whose n terms is given by an2+bn.
10. Solve the quadratic equation for x: 10ax2 – 6x +15ax – 9 = 0.
11. A loan of Rs.12,750 is to be paid back in two equal half yearly instalments. If the interest is compounded half yearly at 8% p.a., how much is each instalment. Also calculate the total interest charged.
12. Solve graphically the following system of linear equations: 2x + 3y = 12; 2y – 1 = x. Shade the area enclosed between these lines and y-axis and calculate the area also.
13. If the points (6, 6), (10, 5) and (8, 4) are mid points of the sides of a triangle, find the three vertices of a triangle.
14. 300 apples are distributed equally among a certain number of children. Had there been 10 more students, each would have received one apple less. Find the number of students.
15. A conical vessel whose internal radius is 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the water rises.
17. Find the ratios in which the co-ordinate axes divide the line joining the points (–2 ,5) and (1, – 9).
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