(i) \(\begin{vmatrix}2 & 4\\2 & 1\end{vmatrix}\) = \(\begin{vmatrix}2x & 4\\6 & x\end{vmatrix}\)
⇒2 x 1 – 5 x 4 = 2x x x – 6 x 4)
⇒ 2- 20 = 2x2 – 24
⇒2x2 = 6
⇒ x2 = 3
⇒ x = ±√3
(ii) \(\begin{vmatrix}2 & 3\\4 & 5\end{vmatrix}\) = \(\begin{vmatrix}x & 3\\2x & 5\end{vmatrix}\)
⇒ 2 x 5 – 3 x 4 = x x 5 – 3 x 2x
⇒10 – 12 = 5x – 6x
⇒ -2 = -x
⇒ x = 2
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.
Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
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).
Determine order and degree(if defined) of differential equation yn + 2y' + siny = 0
The rate of change of the area of a circle with respect to its radius r at r = 6 cm is
(A) 10π (B) 12π (C) 8π (D) 11π
If a line has the direction ratios −18, 12, −4, then what are its direction cosines?
Let f : N → N be defined by
State whether the function f is bijective. Justify your answer.