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www.kalvikadal.in, , https://material.kalvikadal.in, , https://t.me/Join_kalvikadal, , NITHISH PUBLISHERS, Chennai - 62, Cell: 98435 25224, 90032 12319, , REVISION EXAM - I (2022), (Chapter 1, 2, 3, 4), MODEL PAPER - I, Std: XII, Subject: MATHS, , Time : 3 hrs, Marks : 90, 20  1  20, , PART - I, (i), , All Questions are Compulsory, , l.i, n, , Note:, , (ii) Choose the most appropriate answer from the given four alternatives and write the, option code and the corresponding answer., , 2. 4, , 2., , A 1, 2, , al, , 1. A 1, , 4. 5, , 5, 3, 3. , , 1, 2, , , , , 5, 2, 4. , , 1, 3, , , , , vi, , 3 1, 2. The inverse of ,  is, 5 2,  3 1,  2 1, 1. , 2. , , 5, 3, 3 , , , , , 5, 7 3, 3. If A  , , then 9I  A , 4 2, , 3. 2, , ka, , 1. 3, , da, , 1. If |adj adj A  |A|9, then the order of the square matrix A is, , 3. 3A 1, , w, , .k, , 2, 1 3, 4. If the matrix  1 k  3  has an inverse then the values of k,  1 4, 5, , , 1. k is any real number 2. k   4, 3. k  4, , 4. 2A 1, , 4. k  4, , 5. If A  [2 0 1], then rank of AAT is, 2. 2, , w, , 1. 1, , 3. 3, , 4. 0, , 6. If A, B and C are invertible matrices of same order, these which one of the following is not true?, , w, , 1. adj A  |A| A 1, 1, , 3. det A, , 2. adj AB  adj A adj B, 1, , 4. ABC 1  C 1  B 1  A 1, ,  det A, , 2, 3, 4,  1, , 7. The rank of the matrix  2, 4, 6, 8  is, 1 2 3 4, , , 1. 1, 2. 2, 3. 4, , 4. 3, ,  12  17 ,  1 1, 1, 8. If AB 1  , and A 1  , ,  then B , 19, 27, 2, 3, , , , , , ,  2 5, 3 1, 8 5, 3. , 2. , 1. , , , , 2, 3, 3, 8, , 2 1, , , , , ,  8 5, 4. , 2 , 3, , 1, , Please send your Materials & Question Papers to [email protected] (OR) Whatsapp - 9385336929

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www.kalvikadal.in, , https://material.kalvikadal.in, , https://t.me/Join_kalvikadal, ,  cos  sin  , k 0, and A adj A  , 9. If A  , ,  then k , 0 k,   sin  cos  , 1. 0, 2. sin , 3. cos , , 4. 1, , 10. in  in  1  in  2  in  3 is _____, 1. 0, , 2. 1, , 3. – 1, , 4. i, , 3.  1, , 4. 1, , 1. 1, , 2. i, , 3, 12. If  z    2 then the least value of |z| is, z, , 1. 1, 2. 2, , 3. 3, , 4. 4, , 13. The solution of the equation |z|  z  1  2i is, 3,  2i, 2, , 2., , 3,  2i, 2, , 3. 2 , , 14. The modulus of a complex number 2  i , 3 is, 2. , 13, , , 4. 2 , , 3, i, 2, , 3. , 7, , 4. 7, , 3. x2  8x  25  0, , 4. x2  8x  25  0, , ka, , 1. , 3, , 3, i, 2, , da, , 1., , l.i, n, , 11. The value of the complex number i253 is, , 15. The equation having 4  3i and 4  3i as roots is, 2. x2  8x  25  0, , vi, , 1. x2  8x  25  0, , 1. 0, , 2. 4, , al, , 16. A zero of x3  64 is, , 3. 4i, , 4.  4, , 17. A polynomial equation in x of degree n always has, 2. n real roots, , .k, , 1. n distinct roots, , 3. n imaginary roots, , 4. atmost one root, , w, , x 1 is, 18. The domain of the function defined by f x  sin 1 , , 1. [1, 2], , 2. [ 1, 1], , 3. [0, 1], , 4. [ 1, 0], , 3. 0, , 4. does not exist, , w, , 19. The value of tan [tan 1 2019] is, 1.  2019, , 2. 2019, , w, , 20. The principal value of sec 1  2 is, , , 1., 2., 3, 3, , 3., , 2, 3, , PART - II, Note:, , (i), , 4., ,  2, 3, 7  2  14, , Answer any seven Questions, , (ii) Question number 30 is Compulsory., 4, 2, 21. Find the inverse (if it exists) , ,  1 3, 3  4i, 22. Write, in the x  iy form, hence find its real and imaginary parts., 5  12i, 2, , Please send your Materials & Question Papers to [email protected] (OR) Whatsapp - 9385336929

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www.kalvikadal.in, , https://material.kalvikadal.in, , https://t.me/Join_kalvikadal, , z1, 23. If z1  3  2i and z2  6  4i find,  z2, 24. Show that the equation z3  2 z  0 has five solution., 25. Construct a cubic equation with roots 1, 2 and 3., 26. Find a polynomial equation of minimum degree with rational co-efficients having 2i  3 as a root., 27. Show that the equation x9  5x5  4x4  2x2  1  0 has atleast 6 imaginary solutions., 28. If cos 1  x    cos 1 x true. Justify your answer., 29. Find all values of x such that  5  x  5 and cos x  1., , l.i, n, , 30. Find the principal value of tan 1 , 3 ., 7  3  21, , PART - III, (i), , Answer any seven Questions, , (ii) Question number 40 is Compulsory., , da, , Note:, , ka, , 2,  3 8 5, , 31. Find the rank of  2  5 1, 4, 1, 2 3 2, , , 32. Solve by using matrix inversion method 2x  y  8; 3x  2y   2., , vi, , 33. Find the value of the real numbers x and y if the complex numbers 2  i x  1  i y  2i  3, and x   1  2i y  1  i are equal., , al, , 34. If |z|  3, show that 7  |z  6  8i|  13., , .k, , 35. If p and q are the roots of the equation lx2  nx  n  0 show that, 36. Form a polynomial equation with integer co-efficients with, , q  , , p  , l, p, , q, , n, ,  0., , , , , 2, , as a root, 3, , , w, , w, , 5, 5, , , , cos  cos, sin , 37. Find the value of sin 1  sin, 9, 9, 9, 9, ,  2  sin x , 38. Find the domain of cos 1 , , 3, , , , w, , 1, 39. Find the value of sin 1  1  cos 1    cot 1 2, 2, 40. Find the square root of 6  8i, PART - IV, 7  5  35, , Note: Answer all Questions,  cos  0 sin  , , , 41. (a) If F    0, 1, 0  show that [F ] 1  F  ,   sin  0 cos  , , , (Or), 3, , Please send your Materials & Question Papers to [email protected] (OR) Whatsapp - 9385336929

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www.kalvikadal.in, , https://material.kalvikadal.in, , https://t.me/Join_kalvikadal, , (b) 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), 42. (a) Solve by using Cramer’s method, , 1 2 1, 2 5 4, 3 4 2,   10;   20;   10, x y z, x y z, x y z, (Or), , l.i, n, , (b) Let z1, z2 be complex numbers such that |z1|  |z2|  |z3|  r  0 and z1  z2  z3  0 prove that,  z1 z2  z2 z3  z3 z1 , ,   r., z1  z2  z3, , , , (Or), 12, ,  20  5i , , ,  7  6i , , is real., , ka, , 12, ,  19  7i , (b) Show that , ,  9i , , da, ,  2z  1 , 43. (a) If z  x  iy is a complex number such that Im ,   0. Show that the locus of z is,  iz  1 , 2x2  2y2  x  2y  0, , 44. (a) Solve the equation 6x4  35x3  62x2  35x  6  0, , vi, , (Or), , al, , (b) Find all zeros of the polynomial x6  3x5  5x4  22x3  39x2  39x  135, if it is known that, 1  2i and , 3 are two of its zeros., , w, , .k, ,  x2  1 , 45. (a) Find the domain of f x  sin 1 , ,  2x , (Or), , w, ,  , 3 , 1, (b) Find the value of cot 1 1  sin 1  , 2 .,   sec  , 2, , , , w, , , 1, 1, 46. (a) Show that the value of tan 1  1  cos 1    sin 1 ,  is 12, 2, 2, , ,  , (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., 47. (a) Solve the following system of equations using matrix inversion method:, 2x1  3x2  3x3  5 ; x1  2x2  x3   4 ; 3x1  x2  2x3  3., (Or), (b) Show that the point 1,, , 3, 3, 1 i, 1 i, and  , are the vertices of an equilateral triangle., , 2, 2, 2, 2, , 4, , Please send your Materials & Question Papers to [email protected] (OR) Whatsapp - 9385336929

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n, , www.kalvikadal.in, , da, l.i, , • 1st – 9th Reduced Syllabus Portions Released by TN Educational Dept. (2021-2022), • 10th Reduced Syllabus Portions Released by TN Educational Dept. (2021-2022), • 11th Reduced Syllabus Portions Released by TN Educational Dept. (2021-2022), , ka, , • 12th Reduced Syllabus Portions Released by TN Educational Dept. (2021-2022), , vi, , 9th – 12th Refresher Course Module and Answer Key 2021 - 2022, , al, , • 9th Reduced Syllabus Study Materials , Guides and Question Papers 2021 – 2022, • 10th Reduced Syllabus Study Materials , Guides and Question Papers 2021 – 2022, , .k, , • 11th Reduced Syllabus Study Materials , Guides and Question Papers 2021 – 2022, , Book back, Questions, , Penguin Full, Guide, , Dolphin, Guide, , Sura, Guide, , EC Loyola, Guide, , Question, Papers, , 9th, , Click Here, , Click Here, , Click Here, , Click Here, , Click Here, , Click Here, , 10th, , w, , w, , STD, , w, , • 12th Reduced Syllabus Study Materials , Guides and Question Papers 2021 – 2022, , Click Here, , Click Here, , Click Here, , Click Here, , Click Here, , Click Here, , 11th, , Click Here, , Click Here, , Click Here, , Click Here, , Click Here, , Click Here, , 12th, , Click Here, , Click Here, , Click Here, , Click Here, , Click Here, , Click Here