If \(A=\left[\begin{array}{ccc}2 & -2 & 1 \\ 0 & 4 & 2\end{array}\right]\) and \(B=\left[\begin{array}{ccc}1 & -2 & 7 \\ 2 & 0 & 6\end{array}\right]\) are two matrices such that 3A - 2B + 4C = O, then matrix C is equal to:

In which of the following interval the function \(f(x)=x^x, x>0\) is strictly increasing?

The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^3+x \cos x+\tan ^5 x+1\right) d x\) is:

Let X be a random variable. Let E(X) and Var(X) denote the mean and the variance of X respectively.
Match List - I with List - II

List - I	List - II
(A) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(2 X +3)\) is	(I) \(11 \alpha\)
(B) If \(E ( X )=\alpha\), then \(E (2 X )\) is	(II) \(6 \alpha\)
(C) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(3 X -\alpha)+\operatorname{Var}(\sqrt{2} X +\beta)\) is	(III) \(4 \alpha\)
(D) If \(E(X) = 3\) \(\frac{5\alpha}{12}, \text{ then E(12X + } \alpha)\) is	(IV) \(2 \alpha\)

Choose the correct answer from the options given below:

The set of points where the function given by \(f(x) = |x - 2|\) is differentiable is:

The function \(f(x)=-\frac{3}{4} x^4-8 x^3-\frac{45}{2} x^2+163\) has a local maxima at

For which of the following functions, the second order derivative is \(2 e^2\)?

There are four particles A, B, C and D with the same mass and equal kinetic energy K. If the kinetic energy of particle A becomes 4 K, B becomes 9 K, C becomes 64 K and D becomes 16 K times, respectively, the fractional change in the de Broglie wavelength of the particles arranged in increasing order is

India has more than 1000 varieties of mango. This is an example of:

Two similar magnetic poles having pole strengths in the ratio 1 : 4 are placed 6 cm apart. The distance from a smaller pole in strength where net magnetic field is zero will be :

The value(s) of K, for which the system of linear equations 2x + y + x = 1, x + Ky - x = \(\frac{3}{2}\) and 3y - 5x = 9 does not possess a unique solution is

Arrange the following in increasing order of their \(pK _a\) values.
(A) o-nitrophenol
(B) m-nitrophenol
(C) Phenol
(D) Ethanol
Choose the correct answer from the options given below:

Benzene ring in phenol is expected to give the characteristic substitution or replacement reactions i.e. halogenation, nitration, sulphonation, alkylation etc. In these reactions, the attacking reagent is electrophile. The phenolic group activates the ortho and para positions in the ring due to conjugation. Disubstitution reactions are quite fast as the electron density in the ring has increased considerably. Phenols do not respond to nucleophilic substitution reactions as it is influenced by phenolic group.
Victor Meyer test gives following observations. Match List I with List II:

List-I	List-II
A. Blood red colouration	I. Tertiary alcohol
B. Blue colouration	II. Phenols
C. Colourless solution	III. Primary alcohol
D. Violet colouration with \(\text{FeCl}_3\)	IV. Secondary alcohol

Choose the correct answer from the options given below: