The particular solution of the differential equation \(\cos \left(\frac{d y}{d x}\right)=a,(a \in R ) ; y=2\) at \(x=0\) is given by

If \(\left[\begin{array}{ccc}a-b & 0 & 0 \\ 0 & b-c & 0 \\ 0 & 0 & c-2\end{array}\right]\) is a scalar matrix such that a + b + c = 0, then, which of the following are TRUE?
(A) a = 0
(B) b = 0
(C) a = 1
(D) c = 1
Choose the correct answer from the options given below:

The probability distribution of a random variable \(X\) is given below :

x	0	1	2	3
\(P ( x )\)	\(\frac{k}{3}\)	\(\frac{k}{2}\)	\(\frac{k}{4}\)	\(\frac{k}{7}\)

Then the value of \(k\) is

Increase in the number of patients in the hospitals due to heat stroke is:

If the points \(( a , b ),( c , d )\) and \(( a + c , b + d )\) are collinear, then

The values of ' \(a\) ' and ' \(b\) ' such that the function defined by is a continuous function :
\(f(x)=\left\{\begin{array}{ll}3 & x \leq 5 \\ a x+b & 5 < x \leq 15 \\ 18 & x > 15\end{array}\right.\)

The value of \(\int_0^{\pi / 2} \log _e\left(\frac{5+2 \sin x}{5+2 \cos x}\right) d x\) is

A p-type semiconductor can be obtained by doping of:

Why do the actinoids exhibit a higher number of oxidation states than lanthanoids?

Answer the question on basis of passage given below :
Molecular nitrogen is very little reactive chemically. During lightning discharge, atmospheric nitrogen and oxygen combines to form nitric oxide which also combines with oxygen to form nitrogen dioxide. Both NO and \(NO _2\) constitute smog which is very poisonous. It can cause burning sensation in the eyes and adversely affect respiratory system.
Oxidation state of nitrogen in nitric oxide and nitrogen dioxide respectively is :

Read the passage carefully and answer the Questions
The term vitamin was coined from the word vital +amine since the earlier identified compounds had amino groups. Later work showed that most of them didn't contain amino groups, so the letter "e" was dropped and ther term vitamin is used these days.
Vitamins are classified into two groups depending upon their solubility in water or fat. Fat soluble vitamins are soluble in fat and oils but insoluble in water. They are stored in liver and adipose (fat storing) tissues. Water-soluble vitamins are soluble in water. They must be supplied regularly in the diet as they are readily excreated in urine.
What are the sources of Vitamin B12?

A radioactive sample has \(4.0 \times 10^{18}\) active nuclei at a certain instant. How many of these nuclei will still be in the same active state after three half lives ?

Match List - I with List - II.

List - I	List - II
(A) Oxalic acid	(I) Hexane-1,6-dioic acid
(B) Acetophenone	(II)Ethane-1,2-dioic acid
(C) Phthalic acid	(III) Benzene-1,2-dicarboxylic acid
(D) Adipic acid	(IV) \(\Delta T_b=k_b m\)

Choose the correct answer from the options given below :