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

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is `(4r)/3`. Also find maximum volume in terms of volume of the sphere

A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at Rs 7 profit and  B at a profit of Rs 4. Find the production level per day for maximum profit graphically.

Find graphically, the maximum value of z = 2x + 5y, subject to constraints given below :

2x + 4y ≤ 83

x + y ≤ 6

x + y ≤ 4

x ≥ 0, y≥ 0

If A and B are two independent events such that `P(barA∩ B) =2/15 and P(A ∩ barB) = 1/6`, then find P(A) and P(B).

If A is a square matrix, such that A²=A, then write the value of 7A−(I+A)³, where I is an identity matrix.

If `[[x-y,z],[2x-y,w]]=[[-1,4],[0,5]]` find the value of x+y.

A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30, respectively. The company makes a profit of Rs 80 on each piece of type A and Rs 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?

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)]`