Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
The feasible region determined by the constraints, x + y ≤ 4, x ≥ 0, y ≥ 0, is as follows.
The corner points of the feasible region are O (0, 0), A (4, 0), and B (0, 4). The values of Z at these points are as follows.
Corner point |
Z = 3x + 4y |
|
O(0, 0) |
0 |
|
A(4, 0) |
12 |
|
B(0, 4) |
16 |
→ Maximum |
Therefore, the maximum value of Z is 16 at the point B (0, 4).
Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
Represent graphically a displacement of 40 km, 30° east of north.
If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
Show that the Signum Function f : R → R, given by
is neither one-one nor onto.
Consider f : R+ → [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with the inverse f–1 of f given by , where R+ is the set of all non-negative real numbers.
Determine order and degree(if defined) of differential y' + y =ex
Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.
The order of the differential equation
\begin{align}2x^2\frac{d^2y}{dx^2}\;- \;3\frac{dy}{dx}\;+ y=\;0\end{align}
is (A) 2 (B) 1 (C) 0 (D) not defined
Letbe a function defined as
. The inverse of f is map g: Range
(A)
(B)
(C)
(D)
If f: R → R be given by f(x) = , then fof(x) is
(A)
(B) x3
(C) x
(D) (3 – x3).
Let f: X → Y be an invertible function. Show that the inverse of f –1 is f, i.e., (f–1)–1 = f.
Thanku sir