Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

If for any 2 x 2 square matrix A, `A("adj"  "A") = [(8,0), (0,8)]`, then write the value of |A|

A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event "number obtained is even" and B be the event "number obtained is red". Find if A and B are independent events.

Find `int dx/(5 - 8x - x^2)`

Find the value of x, y and z from the following equation:

`[(4, 3),(x, 5)] = [(y, z),(1, 5)]`

Find the value of x, y and z from the following equation:

`[(x + y, 2),(5 + z, xy)] = [(6, 2), (5, 8)]`

Find the value of x, y, and z from the following equation:

`[(x + y + z), (x + z), (y + z)] = [(9), (5), (7)]`

Find the value of a, b, c and d from the equation:

`[(a - b, 2a + c),(2a - b, 3c + d)] = [(-1, 5),(0, 13)]`

`A = [a_(ij)]_(m xx n)` is a square matrix, if ______.

If A = `[(0, -tan  α/2), (tan  α/2, 0)]` and I is the identity matrix of order 2, show that I + A = `(I - A)[(cos α, -sin α),(sin α, cos α)]`

Let A = `[(0,1),(0,0)]`show that (aI+bA)ⁿ  = aⁿI + na^n-1 bA , where I is the identity matrix of order 2 and n ∈ N

if A = [(1,1,1),(1,1,1),(1,1,1)], Prove that A" = `[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))]` `n in N`

if `A = [(3,-4),(1,-1)]` then prove A"=` [(1+2n, -4n),(n, 1-2n)]` where n is any positive integer

Find the matrix X so that X`[(1, 2, 3),(4, 5, 6)]= [(-7, -8, -9),(2, 4, 6)]`

If A and B are square matrices of the same order such that AB = BA, then prove by induction that AB" = B"A. Further, prove that (AB)" = A"B" for all n ∈ N

If A = `[(α, β),(γ, -α)]` is such that A² = I, then ______.

If A is a square matrix such that A² = A, then (I + A)³ – 7A is equal to ______.

If `P(A)  = 3/5 and P(B) = 1/5` , find P (A ∩ B) if A and B are independent events.

A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.

Let E and F be events with `P(E) = 3/5, P(F) = 3/10 and P(E ∩ F) = 1/5`.  Are E and F independent?

Given that the events A and B are such that `P(A) = 1/2, PA∪B=3/5 and P (B) = p`. Find p if they are

1. mutually exclusive
2. independent.