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

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 ____________.

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

Assertion (A): The domain of the function sec^–12x is `(-∞, - 1/2] ∪ pi/2, ∞)`

Reason (R): sec^–1(–2) = `- pi/4`

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

Write the antiderivative of `(3sqrtx+1/sqrtx).`

Let A = {1, 2, 3,......, 9} and R be the relation in A × A defined by (a, b) R (c, d) if a + d = b + c for (a, b), (c, d) in A × A. Prove that R is an equivalence relation. Also, obtain the equivalence class [(2, 5)].

Evaluate : `∫(sin^6x+cos^6x)/(sin^2x.cos^2x)dx`