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GRADE 12 NEB MATHS, TIME 3HRS, , FULL MARK 75, , GROUP A( 1X 11 = 11), Write the correct option in your answer sheet., 1. Which of the following is correct ?, (a), 0! = 1, 𝑛!, , (b), , C (n, r ) = (𝑛−𝑟)!𝑟!, , (c), , P ( n , r ) = (𝑛−𝑟)!, , 𝑛!, , (d), All, 2. Sum of cube roots of unity is …., (a) 1, (b) -1, (c) 0, (d) 𝜔, 3. If sin x = 0 then x = …, (a) n𝜋, 𝑛𝜋, (b) 2, (c), (d), , 𝑛(𝜋+1), 2, 𝑛𝜋, 3, , 4. sin−1 𝑥 + cos −1 𝑥 =…..

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(a), (b), (c), (d), , 1, √1−𝑥 2, 1, √1+𝑥 2, 1, √𝑥 2 −1, 1, 𝑥 2 +1, , 9. Solution of xdx – ydy = 0 is.…, (a) 𝑥 2 − 𝑦 2 = 𝑐, (b) 𝑥 2 + 𝑦 2 = 𝑐, (c) 𝑥 2 𝑦 2 = 𝑐, (d) Not defined, 10. In Gauss Elimination method , coefficient of the, first variable in the first equation must be, (a) -ve, (b) +ve, (c) 0, (d) Non zero, 11. If line of action of two forces never meet then, they are called…., (a) Like, (b) Unlike, (c) Perpendicular, (d) Parallel, , GROUP B(5 X 8 = 40 )

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12. Derive the condition when one root of given two, quadratic equations is common., 13. Use De-Moivre’s theorem to find fourth root of, 8+8√3 i., 14. (a) Use vector method to prove cosine law., (b) solve : √3sin x +cos x = 1, 15. find regression equation of X on Y, X : 10 , 20 , 30 , 40 , 50, Y : 11 , 22 , 33 , 44 , 55, 16 . Find equation of tangent and normal to y = x ^3, at x = 2., 1, , 17 . integrate : ∫ (𝑥−1)2 (𝑥−2)3 𝑑𝑥, 18 . maximize by simplex method, Objective function : Z = 9x+y, 2x+y ≤ 8 , 4x + 3y ≤ 18 , x≥ 0 and y ≥0, 19.find magnitude of resultant of two like and also find, the point of application of resultant force., GROUP ‘C’ ( 8 X 3 =24 )

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20. (a) prove, , 𝑛2, ∞, :∑1 (𝑛+1)!, , = e-1, , (b) In how many ways can you invite your 6 friends out of, 10 friends in a party where one particular is always, included ?, 21. (a) find equation of ellipse in standard form., 𝑎+𝑏, , (b)prove : tan−1 𝑎 + tan−1 𝑏 = tan−1 1−𝑎𝑏, 22.(a) find derivative by first principle : f(x) = 𝑒 √𝑠𝑖𝑛𝑥, 𝑑𝑦, , 𝑦, , ( b) solve : 𝑑𝑥 − 𝑥 = 2𝑥 2