Guess Paper – 2011
Class – X
Subject – Mathematics

1. Solve the following pair of linear equation graphically: 3x-2y-1 =0, 2x-3y+6=0.

2. Find the H.C.F. of 65 and 117 and express it in the form of 65m+117n.

3. Using Euclid’s division algorithm, find the HCF of 144, 180 and 192.

4. In a two digit number, unit’s digit is twice the ten’s digit. If the digits are reversed, new number is 27 more that the original number. Find the number.

5. If 7sin²θ + 3 sin²θ = 4, then show that tanθ = 1/√3.

6. Prove that area of equilateral triangle described on the side of a square is half the area of equilateral triangle described on its diagonal.

7. Prove that:

            [{(cos³θ + sin³θ)/ (cosθ + sinθ)} + {(cos³θ - sin³θ)/ (cosθ - sinθ)}] = 0

8. Find the median of following distribution:

Class	5-10	10-15	15-20	20-25	25-30	30-35	35-40	40-45
Frequency	5	6	15	10	5	4	2	2

9. Solve the following system of equations by the method of elimination (substitution).

                (a + b) x + (a – b) y = a² + b²

                (a – b) x + (a + b) y = a² + b²

10. ABC is a triangle in which AB = AC and D is a point on AC such that, BC² = AC × CD. Prove that BD = BC.

11. Solve the following system of linear equations graphically: 4x – 5y – 20 = 0; 3x +5y – 15 = 0. Determine the area of triangle formed by these lines, and the line x=0.

12. 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 to the first side is a right angle. Using the above do the following: In quadrilateral ABCD, ÐB = 90⁰. If AD² = AB² + BC² + CD², then prove that ÐACD = 90⁰.

13. Divide 3x² – x³ – 3x + 5 by x – 1 – x², and verify the division algorithm.

14. In an equilateral triangle ABC, D is a point on side BC such that BD = 1 / 3 BC. Prove that 9 AD² = 7 AB².

15. Show that one and only one out of n , n+2 or n+4 is divisible by 3. Where ‘n’ is any positive integers.