| 1 | Relation R on Real Numbers is defined as R = {(a, b): a ≤ b}. The relation is : |
| 2 | Let f: [-2,2] → [-2,2] be a function defined by f(x) = x/xl, then f is : |
| 3 | For real numbers x and y, we write xRY → x - y + V2 is an irrational number. Then, check the relation R is reflexive, symmetric or |
| 4 | Let N denote the set of all natural numbers and R be the relation on N x N defined by (a, b)R(c, d) if ad (b + c) = bc(a + d). Show that R is an equivalence relation. |
| 5 | Consider f: R+ → [-5, ∞) given by f(x) = 9x2 + 6x - 5 where R, is the set of all nonnegative real numbers. Prove that f is one- one and onto function. |
| 6 | Let N be the set of natural numbers and R be the relation on N x N defined by (a, b)R (c, d) iff ad = bc for all a, b, c, d € N. Show that R is an equivalence relation. |
| 7 | If A and B are matrices of order 3 X n and m x 5 respectively, then find the order of matrix 5A - 3B, given that it is defined. |
| 8 | Given that matrices A and B are of order 3 x n and m x 5 respectively, then the order of matrix C = 5A +3B is: |
| 9 | A is a skew-symmetric matrix of order 3, then prove that det A = 0. |
| 10 | The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is |
| 11 | If A is a 3 × 2 matrix, B is a 3 x 3 matrix and C is a 2 x 3 matrix, then the elements in A, B and C are respectively |
| 12 | If A a non-singular square matrix of order 3 and A2 = 2A, then find the value of | A|. |
| 13 | Given that A is a square matrix of order 3 X 3 and |A| = -4. Find | adj A | |
| 14 | Let A = [a] be a square matrix of order 3 X 3 and |A| = -7. Find the value of a11 A21 + a12 A22 + a13 A23 where Aij is the cofactor of element aj |
| 15 | If A and B are square matrices of the same order 3, such that |A| = 2 and AB = 2l, write the value of | B. |
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