Arts (English Medium) Class 12 - CBSE Important Questions for Mathematics

A dealer in rural area wishes to purchase a number of sewing machines. He has only Rs 5,760 to invest and has space for at most 20 items for storage. An electronic sewing machine cost him Rs 360 and a manually operated sewing machine Rs 240. He can sell an electronic sewing machine at a profit of Rs 22 and a manually operated sewing machine at a profit of Rs 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit? Make it as a LPP and solve it graphically.

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

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?

A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs 100 and that on a bracelet is Rs 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit?

It is being given that at least one of each must be produced.

The objective function Z = ax + by of an LPP has maximum vaiue 42 at (4, 6) and minimum value 19 at (3, 2). Which of the following is true?

Solve the following Linear Programming Problem graphically:

Maximize: P = 70x + 40y

Subject to: 3x + 2y ≤ 9,

3x + y ≤ 9,

x ≥ 0,y ≥ 0.

Consider `f:R - {-4/3} -> R - {4/3}` given by f(x) = `(4x + 3)/(3x + 4)`. Show that f is bijective. Find the inverse of f and hence find `f^(-1) (0)` and X such that `f^(-1) (x) = 2`

Show that the relation R on R defined as R = {(a, b): a ≤ b}, is reflexive, and transitive but not symmetric.

A function f : [– 4, 4] `rightarrow` [0, 4] is given by f(x) = `sqrt(16 - x^2)`. Show that f is an onto function but not a one-one function. Further, find all possible values of 'a' for which f(a) = `sqrt(7)`.

Let A = {3, 5}. Then number of reflexive relations on A is ______.

If `sin (sin^(−1)(1/5)+cos^(−1) x)=1`, then find the value of x.

Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`

Prove that `tan {pi/4 + 1/2 cos^(-1)  a/b} + tan {pi/4 - 1/2 cos^(-1)  a/b} = (2b)/a`

Solve: tan^-1 4 x + tan^-1 6x `= π/(4)`.

Evaluate `sin^-1 (sin  (3π)/4) + cos^-1 (cos π) + tan^-1 (1)`.

Draw the graph of cos^–1 x, where x ∈ [–1, 0]. Also, write its range.

`sin[π/3 + sin^-1 (1/2)]` is equal to ______.

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

If A is a skew symmetric matric of order 3, then prove that det A  = 0