If A and B are two matrices such that A + B and AB are both defin

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

21.

Let Q = cosπ4- sinπ4sinπ4cosπ4 and x = 1212, then Q3x is equal to

  • 01

  • - 1212

  • - 10

  • - 12- 12


22.

If the matricx A = 200020202, then Ana000a0b0a, n N where

  • a = 2n, b = 2n

  • a = 2n, b = 2n

  • a = 2n, b = n2n - 1

  • a = 2n, b = n2n


23.

If f(x) = 1xx + 12xx(x - 1)x + 1x3xx - 1x(x - 1)x - 2x + 1xx - 1

Then, f(100) is equal to

  • 0

  • 1

  • 100

  • 10


24.

For a matrix A = 100210321, if U1, U2, and U3. are 3 × 1 column matrices satisfying AU1 = 100, AU2 = 230, AU3 = 231 and U is 3 × 3  matrix whose columns are U1, U2, and U3.  Then, sum of the elements of U- 1

  • 6

  • 0

  • 1

  • 2/3


Advertisement
25.

Let I denote the 3 x 3 identity matrix and P be a matrix obtained by rearranging the columns of I. Then,

  • there are six distinct choices for P and det (P) = 1

  • there are six distinct choices for P and det (P) =  ± 1

  • there are more than one choices for P and some of them are not invertible

  • there are more than one choices for P and P- 1 = I in each choice


26.

If I = 100010001 and P = 1000- 1000- 2. Then, the matrix P3 + 2P2 is equal to

  • P

  • I - P

  • 2I + P

  • 2I - P


27.

If P = 2- 2- 4- 1341- 2- 3, then P5 is equal to

  • P

  • 2P

  • - P

  • - 2P


28.

The system of linear equations λx + y + z = 3,  x - y - 2z = 6, - x + y + z = µ has

  • infinite number of solutions for λ -1 and all µ

  • infinite number of solutions for λ = - 1 and μ = 3

  • no solution for λ  - 1

  • unique solution for λ = - 1 and μ = 3


Advertisement
Advertisement

29.

If A and B are two matrices such that A + B and AB are both defined, then

  • A and B can be any matrices

  • A, B are square matrices not necessarily of the same order

  • A, B are square matrices of the same order

  • number of columns of A = number of rows of B


C.

A, B are square matrices of the same order

Let A and B both have a matrices of order m x n.

Also, AB is defined, it means m = n.

Hence, A and B are square matrices of same order.


Advertisement
30.

If A = 3x - 12x +3x + 2 is a symmetric matrix, then the value of x is

  • 4

  • 3

  • - 4

  • - 3


Advertisement