Page 1 :
REVISION SET- 03, , CLASS – XII, SUB – MATH, 2, , * Evalute the following :- 1) 𝑥 – 𝑥 + 1 𝑥 − 1, 𝑥+1 𝑥+1, , 2), , TIME – 2 Hrs., F.M. – 100, , a−b b−c c−a, b−c c−a a−b, c−a a−b b−c, , 3) Write the minor, and cofactor of each element of the following determinants and also evaluate the, 1 0 4, the determinant in each case. 3 5 − 1, 0 1 2, 1 0 1, 4) If A = 0 1 2 , show that 3A = 27 A ., 0 0 4, x y z, 5) Prove that 𝑥 2 𝑦 2 𝑧 2 = (y-z) (z-x) (x-y) (yz+zx+xy)., yz zx xy, a, b−c c+b, a+c, b c−a, 6) Prove that, = (a+b+c) (a2+b2+c2)., a−b a+b, c, 7) Show without expanding at any stage that :-, , x a x+a, y b y+b =0, z c z+c, , 3x − 8, 3, 3, 3, 3x − 8 3 = 0, 3, 3, 3x − 8, 10) Find the area of triangle whose vertices are :- (-2,4), (2,-6), (5,4)., 11) Find the value of K if area of triangle is 4 sq. units and vertices are (-2,0), (0,4), (0,k)., 𝑥 𝑦, 12) Show that the points (a,0), (0,b) and (x,y) are collinear if 𝑎 + 𝑏 = 1., 2 −1 2, 13) Find the adjoint of the matrices :2, 3 5 ., −2, 0 1, 1 −1, 2, 14) Find inverse of the matrices :0, 2 −3 ., 3 −2 4, −1 − 1, 2, 15) If A =, , show that A +3A+4I2 = O and hence find A-1 ., 2 −2, 2 −3, 16) If A =, , verify that {a} adj A’ = (adj A)’, {b} (adj A)-1 = adj(A-1), 4, 6, * Solve the following system of equations by matrix method :17) 2x – y = -2, 18) 2x - 3y + 5z = 11, (19) x + y – z = 1, (20) 3x + y + z = 3, 3x + 4y = 3, 3x + 2y + -4z = -5, x – y –z = -1, 2x – y – z = 2, x + y – 2z = -3, 3x + y - 2z = 3, -x -y+z=1, * Solve the equations :-, , (8), , 2 3, x 3, =, ., 4 5, 2x 5, , (9)