If \(f(x)\) and \(g(x)\) are continuous functions and \(f \circ g\) is an identity function such that \(g^{\prime}(b)=5\) and \(g(b)=a\), then \(f(a)\) is :

The values of \(\lambda\) for which the following system of equations has unique solution:
\(\begin{array}{l}\lambda x+3 y-z=1 \\x+2 y+z=2 \\-\lambda x+y+2 z=-1\end{array}\)

The maximum value of \(y=x^3-3 x\) is :

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards.
The probability distribution of number of aces is given by :

The point which lies in the half plane \(2 x-y \geq 6\) is:

The function \(y=f(x)\) has extreme values at the points where ___________ .

If A is a square matrix of order 3, B = kA and |B| = x|A| then,

The area enclosed between \(y^2=4 x\) and \(x^2=4 y\) is:

In agarose gel electrophoresis, the separated DNA fragments can be visualised by staining the DNA with a compound, known as

Identify the gene which is not effective against cotton boll worms?

Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor is

"Choose the reactions given by \(\text{Cr}_2\text{O}_7^{2-}\)
(A)\(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{Fe}^{2+} \rightarrow 2\text{Cr}^{3+} + 6\text{Fe}^{3+} + 7\text{H}_2\text{O}\)
(B) \(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 3\text{H}_2\text{S} \rightarrow 2\text{Cr}^{3+} + 3\text{SO}_4^{2-} + 7\text{H}_2\text{O}\)
(C) \(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 3\text{Sn}^{2+} \rightarrow 2\text{Cr}^{3+} + 3\text{Sn}^{4+} + 7\text{H}_2\text{O}\)
(D) \(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ \rightarrow 3\text{Cr}^{3+} + 2\text{H}_2\text{O}\)
(E) \(\text{Cr}_2\text{O}_7^{2-} + 2\text{OH}^- \rightarrow 2\text{CrO}_4^{2-} + \text{H}_2\text{O}\)
Choose the correct answer from the options given below:"

If the speed of rotation of the armature of a generator is increased, how would it effect (i) The maximum emf produced (ii) The frequency of the emf?