If \(\mathrm{x}=\mathrm{t}^{2}+2\) and \(\mathrm{y}=2 \mathrm{t}\) represent the parametric equation of the parabola

If \(\sin 3 \theta=\sin \theta\), how many solutions exist such that \(-2 \pi < \theta < 2 \pi\) ?

Recent studies suggest that \(12\%\) of the world population is left handed. Depending on parents' hand usage, the chances of having left handed children are as follows:
A: Both parents are left handed, chances of having left handed children \(= 24\%\)
B: Both parents are right handed, chances of having left handed children \(= 9\%\)
C: Father left handed and mother right handed, chances of having left handed children \(= 17\%\)
D: Father right handed and mother left handed, chances of having left handed children \(= 22\%\)
Given \(P(A) = P(B) = P(C) = P(D) = 1/4\) and L denotes child is left handed. What is the probability that \(P(A \mid L)\)?

\(\frac{d}{d x}\left[\cos ^2\left(\cot ^{-1} \sqrt{\frac{2+x}{2-x}}\right)\right]\) is

The maximum value of \( \left(\frac{1}{x}\right)^{x} \) is

The foot of the perpendicular from the point \((2,4)\) upon \(x+y=4\) is

If linear function \( f(x) \) and \( g(x) \) satisfy
\( \int[(3 x-1) \cos x+(1-2 x) \sin x] d x=f(x) \cos x+g(x) \sin x+C \), then

For a given half cell, \(\mathrm{Al}^{3+}+3 \mathrm{e}^{-} \rightarrow \mathrm{Al}\) on increasing of aluminium ion, the electrode potential will

The IUPAC name for

Catalysts are used to increase the rate of a chemical reaction. Because it

Silencing of specific mRNA in RNAi is by

The human protein \(\alpha-1\) antitrypsin is obtained from

A nucleus of mass \( 20 \mathrm{u} \) emits a \( \mathrm{y} \) photon of energy \( 6 \mathrm{MeV} \). If the emission assume to occur
when nucleus is free and rest, then the nucleus will have kinetic energy nearest to
(take \( 1 \mathrm{u}=1.6 \times 10^{-27} \mathrm{~kg} \) )