Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions

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

If the Cartesian equations of a line are ` (3-x)/5=(y+4)/7=(2z-6)/4` , write the vector equation for the line.

Evaluate :

`∫(x+2)/sqrt(x^2+5x+6)dx`

A line passes through (2, −1, 3) and is perpendicular to the lines `vecr=(hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr=(2hati-hatj-3hatk)+mu(hati+2hatj+2hatk)` . Obtain its equation in vector and Cartesian from. 

Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. School A wants to award Rs x each, Rs y each and Rs z each for the three respective values to 3, 2 and 1 students, respectively with a total award money of Rs 1,600. School B wants to spend Rs 2,300 to award 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is Rs 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for an award.

Evaluate :   `∫1/(cos^4x+sin^4x)dx`

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)]`