In the following reaction, identify Product 'A' :
\(Phenol\ \xrightarrow[(3)\ HCl]{(1)\ NaOH, (2)\ CO_2}\ A\)

The amines which are soluble in water
(A) Methanamine
(B) Ethanamine
(C) Propanamine
(D) Benzylamine
Choose the correct answer from the options given below:

Which type of isomerism is shown by the complex compounds?
\(\left[ Co \left( NH _3\right)_5 Br \right] SO _4\) and \(\left[ Co \left( NH _3\right)_3 SO _4\right]\)Br

Acylation of aniline with acetic anhydride gives :

Read the passage carefully and answer the Questions:
According to Valence Bond theory, the metal atom or ion under the influence of ligands can use its \((n-1) d, n s, n p\) or \(n s, n p, n d\) orbitals for hybridisation to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on. These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding.
While the VB theory, to a larger extent, explains the formation, structures and magnetic behaviour of coordination compounds, it suffers from the many shortcomings. The Crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. The five \(d\) orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion. However, when this negative field is due to ligands in a complex, it becomes asymmetrical and the degeneracy of the \(d\) orbitals is lifted. It results in splitting of the \(d\) orbitals. The pattern of splitting depends upon the nature of the crystal field.
The spin only magnetic moment of \(\left[ MnBr _4\right]^{2-}\) is 5.9 BM. Predict the geometry of the complex ion?

Isotonic solutions must have the same
(A) Solute
(B) Density
(C) Elevation in boiling point
(D) Depression in freezing point
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Which of the following reactions are given by Phenols?
(A) Nitration
(B) Halogenation
(C) Oxidation
(D) Acetylation
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The particular solution of the differential equation \(\frac{d y}{d x}=8 y x\) when \(y=1\) at \(x=0\) is:

A random variable y has the following probability distribution

y	1	2	3	4	5
P(y)	2k	3k	k	4k	5k

Match List-l with List-ll

List - I	List - II
(A) P(y > 2)	(I) \(\frac{2}{5}\)
(B) k	(II) \(\frac{2}{3}\)
(C) \(P(y \leq 3)\)	(II) \(\frac{8}{15}\)
(D) \(P(2 \leq y \leq 4)\)	(II) \(\frac{1}{15}\)

Choose the correct answer from the options given below

Aspartame is most successful artificial sweetener but is only limited to cold food and cold drinks because:

The probability distribution of a random discrete variable is given

X	-1	0	1	2	3
P(X)	0.1	p	0.3	q	r

If it is known that \(P(X=1)\) is the mean of \(P(X=0)\) and \(P(X=2)\).Then the value of \(r\) is :

If A is an invertible matrix of order 3, then

List-I	List-II
(A) \(|\operatorname{adj} A|\)	(I) \(8|A|\)
(B) \(|A(\operatorname{adj} A)|\)	(II) \(|A|^2\)
(C) \(|2 A|\)	(III) \(\frac{1}{|A|}\)
(D) \(\left|A^{-1}\right|\)	(IV) \(|A|^3\)

Choose the Correct answer from the options given below :

A solenoid with \(2 \times 10^4\) turns per meter, diameter 0.1 m , has a coil of 100 turns and 0.01 m radius placed inside. If solenoid current decreases from 4 A to 0 in 0.05 s , total charge through coil is :