If \(f(x)=2 x^3-15 x^2+36 x+1, x \in[1,5]\), then the absolute minimum value of \(f(x)\) is:

The value of \(\tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]\) is :

If a random variable \(x\) follows Polseon's distribution such that \(P(x=2)=9 P(x=4)+90 P(x=6)\), them sum of the mean and variance of \(x\) is

The value of \(\left|\begin{array}{ccc}7! & 8! & 9! \\ 8! & 9! & 10! \\ 9! & 10! & 11!\end{array}\right|\) is :

If \(0<2 x<1\), which of the following is smallest?

The effective rate, which is equivalent to a nominal rate of \(12 \%\) compounded semi-annually, is

If \(A=\left[\begin{array}{ll}3 & -5 \\ 4 & -7\end{array}\right]\), then \(A^{-1}\) is:

Which one of the following is not practiced in the organic farming?

Identify the correct statement(s) among the following:
(A) If three electrical cells each of emf, E and internal resistance r are connected in series to a resistance R, the current drawn from them is 3E/(R+3r).
(B) If these three cells are connected in parallel combination, across resistance R then the current drawn will be E/(3R+r).
(C) If the two cells are connected in series and then one in parallel which are then connected across resistance R, then the current drawn will be 2E/(2R+2r).
(D) In a mixed grouping of cells, current will be maximum when total external resistance is equal to total equivalent internal resistance.
Choose the correct answer from the options given below :

Which one of the following takes place in all eukaryotic organisms as a method of cellular defense?

The integral value of \(k\) for which the system of linear equations
\(\begin{array}{l}k x+y+2 z=0 \\k y=x-3 z \\2 x+y+k z=0\end{array}\)
has a non-zero solution is :

Two lenses of power 3D and -1D are kept in contact. The focal length of the combined lens would be :

Identify the correct order of organic compounds in the following chemical reaction: ? + Mg → ? → ? → ?
(A) CH 3 MgBr
(B) CH 3 B
(B) CH 3 B
(D) CH 4
Choose the correct answer from the options given below :