tn 12std maths chapter1 free

www.CellExam.com TN 12thStd (+2 ) Maths Chapter 1 Questions

1 Cell Exam – 142 Venkateswara Layout, Phase -2, Hosur 635109. [email protected] Cell Exam : +91 94421 100 10

I. Choose the most suitable answer. [ 20 x 1 = 20]

1.The rank of the matrix A = ……..

(a) 2 (b) 3 (c) 1 (d) 4

2. The rank of a matrix of order n is ……..

(a) 1 (b) n (c) (n-1) (d) 2n

3. ˉ¹ is equal to …..

( a) A ¹̄ (b) (c) A (d)

4. Every homogeneous system ………..

(a) is always consistent (b) has only trivial solution

(c) has infinitely many solutions (d) need not be consistent

5. Cramer`s rule is applicable only ( with three unknowns ) when ……

(a) ≠ 0 (b) ∆ = 0 (c) ∆ = 0, ≠ 0 (d) , = = = 0

6. The values of λ and μ in which λx +2y = μ, 3x + 2y = 4 have many solution are given by …….

(a) λ = 0, μ = 1 (b) λ = 3, μ = any value (c) λ ≠ 3, μ = 4 (d) λ = 3, μ = 4

7. The equation 2x + 3y = 7 and ax + 6y = b have no solution if …….

(a) a = 4, b = 14 (b) a = 4, b = 9 (c) a = 2, b = 7 (d) a = 2, b = 14

8. If A = and B = ( 4 5 6 ) the rank of AB is ………

(a) 0 (b) 3 (c) 1 (d) 2

9. The equations x + y - z = 1, 2x + y + z = 1, x – y + 2z = 2 have ……..

(a) Unique solutions (b) no solutions (c) infinitely many solutions

(d) more than one solution

10. The inverse of A = is ……..

(a) A (b) –A (c) (d) -



11. If A and B are matrices such that ≠ 0 and ≠ 0 than is …….

(a) A ¹̄Bˉ¹ (b) (AB) ¹̄ (c) Bˉ¹A ¹̄ (d) BA

12. For what values a, so that the system of equations 2x - 3y + 4z = a, x – y + 5z = 1 and x – 2y – z = 2

are consistent.

(a) a = 2 (b) a = -2 (c) a = 3 (d) a = -3

13. If p (A) ≠ p (A,B), then the system is …..

(a) consistent and has infinitely many solutions (b) consistent and has a unique solution

(c) consistent (d) inconsistent

14. Given ∆ = 3, 3 , =6 and = 3 are the value of the simultaneous equation the solution is …….

(a) ( 1,1,2) (b) ( 2,1,1) (c) (1,2,1) (d) ( 2,1,2)

15. If the rank of the matrix is 2, then λ is …..

(a) 1 (b) 2 (c) 3 (d) any real number

16. If A is a square matrix of order n then * adj.A+ is ……..

(a) ² (b) (c) (d)

17. If A is a matrix of order 3, then det ( KA) …..

(a) k³ det (A) (b) k² det (A) (c) k det (A) (d) det (A)

18. If A and B are any two matrices such that AB = 0 and A is non- singular, then ……

(a) B = 0 (b) B is singular (c) B is non- singular (d) B = A

19. If A = [2 0 1], than rank of is ……..

(a) 1 (b) 2 (c) 3 (d) 0

20. If 1 is the unit matrix of order n, where k ≠ 0 is a constant, then adj (K I ) is ………

(a) (adj I ) (b) k ( adj I) (c) k² [ adj (I) ] (d) (adj I )

II. Answer any five question [ 5 x 6 = 30]



21. If A = and B = verify that (AB)ˉ¹ = Bˉ¹ A ¹̄

22. Solve by matrix inversion method . x +y + z = 9, 2x + 5y + 7z = 52, 2x + y –z = 0

23. Find the rank of the following matrices. .

24. Solve the following non-homogeneous system of linear equations by determinant method.

x + y + z = 4, x – y + z = 2, 2x + y –z = 1

25. Show that the equation x + y +z = 6, x +2y + 3z = 14, x + 4y + 7z = 30 are consistent and solve them.

26. Examine the consistency of the equations.

2x – 3y + 7z = 5, 3x + y -3z =13, 2x + 19y – 47z = 32

27. Solve the following system of linear equations by determinant method:

x + y = 3, 2x + 3y = 7

III. Answer any five questions: [ 5 x 10 = 50]

28. If A = , verify A ( adj . A ) = (adj. A ) A = I₃.

29. Find the inverse of the matrix A = and verify that A³ = Aˉ¹.

30. Solve by matrix inversion method each of the following system of linear equations;

x – 3y – 8z + 10 = 0, 3x + y = 4, 2x + 5y + 6z = 13

31. Solve the following non- homogeneous system of linear equations by determinant method.

+ - = 1; + + = 5; - - = 0

32. Investigate for what values of λ, μ the simultaneous equations

x + y + z = 6, x + 2y + 3z = 10, x + 2y + λz = μ have (i) no solutions (ii) a unique solution and (iii) an infinite

number solutions.

33. Discuss the solutions of the system of equations for all values of λ.



x+ y +z = 2; 2x + y -2z = 2; λx + y + 4z = 2

34. For what values of k, the system of equations. Kx + y + z = 1; x + ky + z = 1; x + y + kz = 1 have (i)

unique solutions, (ii) more than one solutions and ( iii) no solution.

35. Solve by matrix inversion method each of the following system of linear equations

x – 3y - 8z +10=0, 3x +y = 4, 2x + 5y + 6z = 13.

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tn 12std maths chapter1 free

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