Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

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?

Evaluate :

`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`

Find the value of p, so that the lines `l_1:(1-x)/3=(7y-14)/p=(z-3)/2 and l_2=(7-7x)/3p=(y-5)/1=(6-z)/5 ` are perpendicular to each other. Also find the equations of a line passing through a point (3, 2, – 4) and parallel to line l₁.

Find the vector and cartesian equations of the line passing through the point (2, 1, 3) and perpendicular to the lines

`(x-1)/1=(y-2)/2=(z-3)/3 and x/(-3)=y/2=z/5`

If A= `[(cos alpha, -sin alpha), (sin alpha, cos alpha)]` then A + A' = I then the value of α is  ______.

Find the adjoint of the matrices.

`[(1,2),(3,4)]`

Find the adjoint of the matrices.

`[(1,-1,2),(2,3,5),(-2,0,1)]`

Verify A(adj A) = (adj A)A = |A|I.

`[(2,3),(-4,-6)]`

Verify A(adj A) = (adj A)A = |A|I.

`[(1,-1,2),(3,0,-2),(1,0,3)]`

Find the inverse of the matrices (if it exists).

`[(2,-2),(4,3)]`

Find the inverse of the matrices (if it exists).

`[(-1,5),(-3,2)]`

Find the inverse of the matrices (if it exists).

`[(1,2,3),(0,2,4),(0,0,5)]`

Find the inverse of the matrices (if it exists).

`[(1,0,0),(3,3,0),(5,2,-1)]`

Find the inverse of the matrices (if it exists).

`[(2,1,3),(4,-1,0),(-7,2,1)]`

Find the inverse of the matrices (if it exists).

`[(1,-1,2),(0,2,-3),(3,-2,4)]`

Find the inverse of the matrices (if it exists).

`[(1,0,0),(0, cos alpha, sin alpha),(0, sin alpha, -cos alpha)]`

Let A = `[(3,7),(2,5)]` and B = `[(6,8),(7,9)]`. Verify that (AB)⁻¹ = B⁻¹A⁻¹.

If A = `[(3,1),(-1,2)]` show that A² – 5A + 7I = 0. Hence, find A^–1.

For the matrix A = `[(3,2),(1,1)]` find the numbers a and b such that A² + aA + bI = 0.

For the matrix A = `[(1,1,1),(1,2,-3),(2,-1,3)]` show that A³ − 6A² + 5A + 11 I = 0. Hence, find A⁻¹.