Gujarat Board Maths Sample Paper Gujarat Board Maths Sample Paper 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 Know More About :- Botany Andhra Pradesh Board Sample Paper
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08. ABC is a triangle in which AB = AC and D is a point on AC such that, BC2 = AC × CD. Prove that BD = BC. 09. 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. 10. 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. 11. Divide 3x2 – x3 – 3x + 5 by x – 1 – x2, and verify the division algorithm. 12. In an equilateral triangle ABC, D is a point on side BC such that BD = 1 / 3 BC. Prove that 9 AD2 = 7 AB2. 13. Show that one and only one out of n , n+2 or n+4 is divisible by 3. Where ‘n’ is any positive integers. 14. On a multiple choice examination with three possible answers (out of which only one is correct) for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing? 15. Using properties of determinants, prove that following:
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