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CLASS – XII, SUB – MATH, , REVISION SET- 02, 𝑖, , TIME – 2 Hrs., F.M. – 100, , 1) Construct a 3 X 4 matrix A =[aij] whose elements are., i) aij = 𝑗, 𝑥+𝑦, 2, 3 2, 2) If, =, , then x = …… y = ………, 1, 𝑥−𝑦, 1 7, 2a + b a − 2b, 4 −3, 3) Find a,b,c,d if., =, 5c − d 4c + 3d, 11 24, 2, 2, 2, 2, 4) Compute the following :- cos2 𝑥 sin 2𝑥 + sin 2𝑥 cos2 𝑥, sin 𝑥 cos 𝑥, cos 𝑥 sin 𝑥, 𝑦 0, 1 3, 5 6, 5) Find the values of x and y satisfying the equation., 2, +, =, 0 𝑥, 1 2, 1 8, 2 3, −2 2, 6) If 2x + 3y =, and 3x + 2y =, , find X and Y., 4 0, 1 −5, a − b 2a + c, −1 5, 7) Find the value of a, if, =, 2a + b 3c + d, 0 13, 1 −1, 2 1 3, 8) If A =, and B = 0 2 , find AB and BA, 4 1 0, 5 0, cos 𝜃 sin 𝜃, cos 𝜃 sin 𝜃, 9) If A =, , B =, , show that AB = BA., sin 𝜃 cos 𝜃, sin 𝜃 cos 𝜃, 1, 3, 3 −2, 1 3 5, 10) Evaluate the following :+, −1 −4, −1 1, 2 4 6, 𝑐𝑜𝑠𝑥 −𝑠𝑖𝑛𝑥 0, 11) If f(x) = 𝑠𝑖𝑛𝑥 𝑐𝑜𝑠𝑥 0 , show that f(x).f(y) = f(x + y), 0, 0, 1, cos2 𝜃 sin2 𝜃, 12) If A =, , Find A2 ., −sin2 𝜃 cos2 𝜃, 1, 0, 1, 𝜔 𝜔2, 𝜔 𝜔2 1, 2, 2, 13) Show that, +, =, 𝜔, 0 ., 𝜔 𝜔, 1, 𝜔, 1 𝜔, 2, 2, 2, 𝜔, 0, 𝜔, 1, 𝜔, 𝜔 𝜔, 1, 1 2 3, −7 −8 −9, 14) Find the matrix X so that, X, =, ., 4 5 6, 2, 4, 6, 3 −5, 15) If A =, , Find A2-5A-14 I, where I is a unit matrix., −4 2, cos 𝛼 sin 𝛼, 16) If A =, , prove by mathematical induction that,, −sin 𝛼 cos 𝛼, 17) A trust fund has Rs. 30,000 that must be invested in two different type of bonds. The first bond pays, 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication,, determine how to divide Rs. 30,000 among the two types of bonds. If the trust fund must obtain an, annual total interest of. (a) Rs. 1800, (b) Rs. 2000, 1 −1, 2 1 3, 18) If A =, and B = 0 2 , verify that (AB), = B, A,, 4 1 0, 5 0, 3 −4, 19) If A =, , show that ( A - AT) is a skew – symmetric matrix, where AT is the transpose of matrix A., 1 −1, 20) Using elementary transformations (operations), Find the inverse of the following matrices, if it exists., 2, 1 3, 4 −1 0, −7 2 1