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

Solve the following LPP graphically:
Maximise Z = 2x + 3y, subject to x + y ≤ 4, x ≥ 0, y ≥ 0

A manufacturing company makes two types of television sets; one is black and white and the other is colour. The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a coloured set. The company can spend not more than Rs 648000 a week to make television sets. If it makes a profit of Rs 510 per black and white set and Rs 675 per coloured set, how many sets of each type should be produced so that the company has maximum profit? Formulate this problem as a LPP given that the objective is to maximise the profit.

Minimise Z = 3x + 5y subject to the constraints:
x + 2y ≥ 10
x + y ≥ 6
3x + y ≥ 8
x, y ≥ 0

The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is ______.

Feasible region (shaded) for a LPP is shown in the Figure Minimum of Z = 4x + 3y occurs at the point ______.

The common region determined by all the linear constraints of a LPP is called the ______ region.

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

The area of a trapezium is defined by function f and given by f(x) = `(10 + "x") sqrt(100 - "x"^2)`, then the area when it is maximised is:

The point(s) on the curve y = x³ – 11x + 5 at which the tangent is y = x – 11 is/are:

In maximization problem, optimal solution occurring at corner point yields the ____________.

If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA  "n" in "I"`, then x = ____________.

`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.

`2"tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`

If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt "cos" alpha) = "x",` then sinx is equal to ____________.

`"cos"^-1 ("cos" ((7pi)/6))` is equal to ____________.

`"tan"^-1 sqrt3 - "sec"^-1 (-2)` is equal to ____________.

`lim_("x"-> 0) sqrt(1/2 (1 - "cos"  2"x"))/"x"` is equal to

The number of roots of x³- 3x + 1 = 0 in [1, 2] is ____________.

Using integration, find the area of the region in the first quadrant enclosed by the line x + y = 2, the parabola y² = x and the x-axis.

Using integration, find the area of the region `{(x, y): 0 ≤ y ≤ sqrt(3)x, x^2 + y^2 ≤ 4}`