Match List-I with List-II

Llst-I	Llst-(II)
(A) \(f(x)=[x]\)	(I) Continuous everywhere but not differentiable at \(x=-1\)
(B) \(f(x)=|x-1|\)	(II) Continuous everywhere except at all integral values
(C) \(f(x)=e^{|x|}\)	(III) Continuous everywhere but not differentiable at \(x=1\)
(D) \(f(x)=|x+1|\)	(IV) Continuous everywhere but not differentiable at \(x=0\)

Choose the correct answer from the options given below:

The principal value of \(\cot ^{-1}\left(-\frac{1}{\sqrt{3}}\right)\) is

\(\int \frac{d x}{\sqrt{5-x}}=\) (where \(C\) is arbitrary constant.)

A specific characteristic of a sample is known as a:

The radius of spherical balloon is decreasing at the rate of \(0.1 cm / sec\), the rate at which its volume is decreasing, when its radius is 0.5 cm is:

If the function \(f(x)=x^2\) is one-to-one and onto, then the domain D and range R of \(f(x)\) are respectively :

The distance of a point \((1, -1, 0)\) from the plane \(\vec{r} \cdot (3\hat{i} - 2\hat{j} - 6\hat{k}) = 4\) is:

Match List-I with List-II

List-I	List-II
A. Impedance of a series LCR circuit at resonance	(I) Voltage across L and C are 180 degree out of phase
B. For a series LC Circuit	(II) Current in L and C are 180 degree out of phase
C. For a parallel LC circuit	(III) Minimum
D. Reactance of a capacitor in a DC circuit	(IV) Infinite

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Match List I with List II

List I	List ll
(A) hPL	(I) Maternal pituitary
(B) Relaxin	(II) Placenta
(C) Oxytocin	(III) Thyroid
(D) Thyroxine	(IV) Ovary

Choose the correct answer from the options given below:

A dentist has a small mirror of focal length \(1 . 6 ~ c m\). He observes the cavity in the tooth of a patient by holding the mirror at a distance of 8 mm . from the cavity. The magnification is:

Identify the correct statement about the electric charges \( q_1 \) and \( q_2 \) from the figure given below.

Read the passage carefully and answer the questions
Alcohols and phenols are formed when a hydrogen atom in a hydrocarbon, aliphatic and aromatic respectively is replaced by -OH group. These are further classified on the basis of number of hydroxy groups and according to the hybridization of the carbon atom \(sp ^2\) or \(sp ^3\) to which the -OH group is attached. They find applications in industry as well as in day-to-day life. One of the most commercially obtained alcohol also known as wood spirit is obtained by destructive distillation of wood. Both alcohols and phenols are acidic in nature. The acidity of alcohols and phenols vary according to the nature of substituent(s) attached to them. Alcohols and phenols react with carboxylic acids, acid chlorides and acid anhydrides to form esters. Introduction of acetyl group in alcohols and phenols is called acetylation. Phenol undergo electrophilic aromatic substitution reaction because the -OH activates the benzene ring. It undergoes nitration, halogenation and sulphonation reactions.
Which of the following compound lacks a phenolic group?

A parallel beam of monochromatic light of wavelength \( 460 \text{ nm} \) passes through a long slit of width \( 0.1 \text{ mm} \). What is the angular divergence in which most of the light is diffracted ?