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ISHA VIDHYA MATRICULATION HIGHER SECONDARY SCHOOLS, REVISION EXAM- MATHEMATICS, TIME: 3 hours, CLASS-12, MARKS: 90, PART–I, , 20 x1= 20, , Note : i) Answers all the questions, ii) Choose the most appropriate answer from the given four, alternatives and write the option code with the corresponding answer., 3, 1. The inverse of[, 5, 3 −1, a) [, ], −5 −3, , 1, ] is, 2, 2 −1, b)[, ], −5 3, , −3 5, c)[, ], 1 −2, , d) [, , −2 5, ], 1 −3, , 2 3 , -1,  be such that λA = A is, 5, −, 2, , , , 2. If A= , , a) 17, , b) 14, , c) 19, , d) 21, , 1 x 0 , 3. If p = 1 3 0  is the adjoint of 3x3 matrix A and A = 4 then x is, , , 2 4 − 2, a) 15, , b) 12, , c) 14, , d) 11, , 4. If A, B and C are invertible matrices of same order, thesewhich of the following is not, true?, a) adj A = A A-1, , b) adj(AB) = (adj A) (adj B), , c) det A-1 = (det A)-1, , d) (ABC)-1 = C-1 . B-1 . A-1, ,  12 − 17,  1 − 1, and A-1 = , then B-1 =, , , − 19 27 , − 2 3 , , 5. If (AB)-1= , ,  2 − 5, − 3 8 , , , , a), , 8 5, , 3 2, , 3 1, , 2 1, , b) , , c) , , 7 3 ,  , then 9I2 - A =,  4 2, , 6. If A = , a) A-1, , b) A-1/2, , c) 3A-1, , d) 2A-1, , c) AT, , d) (A-1)2, , c) -1, , d) i, , 7. If ATA-1 is symmetric, then A2 =, a) A-1, , b) (AT)2, , 8. in+ in+1 + in+2 +in+3 is _____., a) 0, , b) 1, ,  8 − 5, , − 3 2 , , d) 

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9. The solution of the equation z - z = 1 + 2i is, a), , 3, -2i, 2, , b), , −3, +2i, 2, , c) 2 -, , 3, I, 2, , d) 2 +, , 3, i, 2, , 1+𝑧, , 10. If |𝑧| = 1, then the value of 1+𝑧̅, a) z b) 𝑧̅, , 1, , c) 𝑧, , d) 1, , 11. The principle argument of (sin 40° + icos 40°)5 is, a) -110°, , b) -70°, , c) 70°, , d) 110°, , 12. If z = x + iy is a complex number such that z + 2 = z − 2 then the locus of z is, a) Real axis b) imaginary axis, , c) ellipse, , d) circle, , 13. A zero of x3 + 64 is, a) 0, , b) 4, , c) 4i, , d) -4, , 14. The value of the complex number (i25)3 is, a) 1, , b) i, , c) -1, , d) 1, , 15. The number of real number in [ 0 , 2π] satisfying sin4x – 2sin2x +1 is, a) 2 b) 4, , d) ∞, , c) 1, , 16. A polynomial equation in x of degree n always has, a) n distinct roots, , b) n real roots, , b) c) n imaginary roots, , d) atmost one root, , 17. If cot-12 and cot-13 are two angles of a triangle then the third angle is, a), , 𝜋, 4, , b), , 3𝜋, , 𝜋, , 𝜋, , c) 6, , 4, , d) 3, , 18. The number of positive roots of the polynomial ∑𝑛𝑗=0 𝑛𝐶𝑟 (−1)𝑟 𝑥 𝑟 is, a) 0, , b) n, , c) <n, , d) r, , 19. If the functions f(x) = sin-1(x2 – 3 ) then x belongs to, a) [-1 , 1], , c) [-2 , √2] ∪ [√2 , 2] d) [2,√2] ∪ [-1,1], , b) [√2 , 2], , 20. The value of sin-1 (cos x), 0 ≤ 𝑥 ≤ 𝜋 is, a) π-x, , b )𝑥, , −𝜋, 2, , 𝜋, , c) 2 -x, , d) x-π

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PART–II, , 7X2=14, , Note: i) Answer any 7 questions., ii) Question no. 30 is compulsory, ,  8 − 4,  , find A (adj A)., − 5 3 , , 21. If A= , , − 2 4 , ,  1 − 3, , 22. Find the inverse ( if it exists) , , 23. Construct a cubic equation with roots 1,2 and 3., 24. Find the polynomial equation of minimum degree with rational co-efficient having 2i, + 3 as a root., 25. Show that the equation x9 – 5x5 +4x4 +2x2 + 1 =0 has at least 6 imaginary solutions., 26. If cos-1 (-x) = 𝜋 – cos-1 (x) true. Justify your answer., 𝑛, 27. Simplify ∑102, 𝑛=1 𝑖, , 28. Find z-1 if z = (2 + 3i) (1- i), −𝜋, , 29. State the reason for cos-1[𝑐𝑜𝑠 ( 6 )] ≠, , −𝜋, 6, , 30. Find the principal value of tan-1(√3)., , PART–III, Note: i ) Answer any 7 questions., , 7X3=21, , ii) Question no.40 is compulsory., , 2 9, , 1 7 , , 31. Verify the property (AT)-1 = (A-1)T with A= , , 4,  1 −2 3, , 32. Find the rank of − 2 4 − 1 − 3, , ,  − 1 2, 7, 6 , 1, , 33. In a competitive examination , one mark is awarded for every correct answer while 4, mark is deducted for every wrong answer . A student answerd 100 questions and got, 80 marks. How many questions did he answer correctly?(use Cramer’srule to solve the, problem), , 1+ i  1− i , 34. Simplify ,  −, , 1− i  1+ i , 3, , 3, , into rectangular form., , 35. State and prove triangle inequality.

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36. Solve the cubic equation 2x3 – x2 – 18x + 9 =0 if sum of its roots vanishes., 37. Find the value of sin-1(𝑠𝑖𝑛, , 5𝜋, 9, , 2+ 𝑠𝑖𝑛 𝑥, , 38. Find the domain of cos-1(, , 𝜋, , 𝑐𝑜𝑠 9 + 𝑐𝑜𝑠, , 3, , 5𝜋, 9, , 𝜋, , 𝑠𝑖𝑛 9 ), , ), 1, , 39. Find the value of sin-1 (-1) + cos-1 (2) + cot −1 (2), 40. Find the square root of 6 – 8i., PART–IV, , 7x5 =35, , Note: Answer all the questions., 41. a) A boy is walking along the path y= ax2 + bx +c through the points (-6,8), , (-2,-12), , and (3,8). He want to meet his friend at p(7,60) will be meet his friend? ( use, Gaussian elimination method), , (OR), , −8 1 4, 1, b) If A = 9 [ 4, 4 7] prove that A-1 = AT, 1 −8 4, 42. a) Solve by using Cramer’s method, 4, 𝑧, , 3, 𝑥, , 4, , −, , 𝑦, , 2, , 1, , − 𝑧 − 1 = 0; 𝑥 +, , + 1 = 0;, , 2, 𝑦, , +, , 1, 𝑧, , – 2 = 0;, , 2, 𝑥, , −, , 5, 𝑦, , −, , (OR), 𝑧−4𝑖, , b) If z = x + iy is a complex number such that |𝑧+4𝑖| = 1, show that the locus of z is, real axis., ,  19 − 7i ,  20 − 5i , 43. a) Show that ,  +,  is real.,  9+i ,  7 − 6i , 12, , 12, , (OR), , b) Solve the equation 6x4 – 35x3 + 62x2-35x + 6 =0, 𝑥 2 +1, , 44. a) Find the domain of f(x) = sin-1 (, , 2𝑥, , ), , (OR), , b) Determine k and solve the equation 2x3 – 6x2 + 3x + k = 0. If one of its roots it twice, the sum of the other two roots., 45. a) Find the value of i) cot-1(1) + sin-1(, , −√3, 2, , ) - sec-1(−√2)., , ii) tan-1(√3) – sec-1 (-2)., , (OR), , b) Solve the following system of equations using matrix inversion method, 2x1 + 3x2 + 3x3 = 5; x1 -2x2 + x3 = -4; 3x1 – x2 -2x3 =3.