Arts (English Medium) Class 12 - CBSE Question Bank Solutions

If A, B be two square matrices such that |AB| = O, then ____________.

A square matrix A is invertible if det A is equal to ____________.

If A `= [(0,-1,2),(1,0,3),(-2,-3,0)],` then A + 2A^T equals

Find the adjoint of the matrix A `= [(1,2),(3,4)].`

Find the adjoint of the matrix A, where A `= [(1,2,3),(0,5,0),(2,4,3)]`

Find x, if `[(1,2,"x"),(1,1,1),(2,1,-1)]` is singular

Find the value of x for which the matrix A `= [(3 - "x", 2, 2),(2,4 - "x", 1),(-2,- 4,-1 - "x")]` is singular.

For what value of x, matrix `[(6-"x", 4),(3-"x", 1)]` is a singular matrix?

If the equation a(y + z) = x, b(z + x) = y, c(x + y) = z have non-trivial solutions then the value of `1/(1+"a") + 1/(1+"b") + 1/(1+"c")` is ____________.

The value of `abs (("cos" (alpha + beta),-"sin" (alpha + beta),"cos"  2 beta),("sin" alpha, "cos" alpha, "sin" beta),(-"cos" alpha, "sin" alpha, "cos" beta))` is independent of ____________.

Find the position vector of a point A in space such that `vec"OA"` is inclined at 60º to OX and at 45° to OY and `|vec"OA"|` = 10 units.

Maximise and Minimise Z = 3x – 4y subject to x – 2y ≤ 0, – 3x + y ≤ 4, x – y ≤ 6, x, y ≥ 0

Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy, where p, q > 0. Condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1) is ______.

If A = [a_ij] is a square matrix of order 2 such that a_ij = `{(1","  "when i" ≠ "j"),(0","  "when"  "i" = "j"):},` then A² is ______.

For matrix A = `[(2,5),(-11,7)]` (adj A)' is equal to:

For A = `[(3,1),(-1,2)]`, then 14A⁻¹ is given by:

The maximum value of `["x"("x" − 1) + 1]^(1/3)`, 0 ≤ x ≤ 1 is:

A feasible region in the set of points which satisfy ____________.

Of all the points of the feasible region for maximum or minimum of objective function the points.

A set of values of decision variables which satisfies the linear constraints and nn-negativity conditions of an L.P.P. is called its ____________.