Identify " \(Y\) " in the following reaction:

Match List I with List II

LIST - I	LIST - II
A. Cubic cell	I. \(\alpha=\beta=\gamma=90^{\circ}\)
B. Monoclinic cell	II. \(\alpha=\beta=90^{\circ}, \gamma=120^{\circ}\)
C. Triclinic cell	III. \(\alpha=\gamma=90^{\circ}, \beta \neq 90^{\circ}\)
D. Hexagonal cell	IV. \(\alpha \neq \beta \neq \gamma \neq 90^{\circ}\)

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Which of the following is an example of a minimum boiling azeotrope?

Match List-I with List-II

List-I (Reagent)	List-II (Characteristic of Compound)
(A) Tollen's Reagent	(I) Aliphatic aldehyde
(B) Iodoform test	(II) Tertiary alcohol
(C) Lucas Reagent	(III) Methyl ketone
(D) Fehling's Reagent	(IV) Aliphatic and aromatic aldehydes

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Arrange the following compounds in the decreasing order of reactivity towards Sn1 reaction
(A) (Ph)3C-1
(B) (Ph)3C-Br
(C) (Ph)3C-Cl
(D) (Ph)3C-F
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Answer the question on the basis of passage given below :
Adsorption is a surface phenomenon which can be expressed by means of an empirical relationship know as Freundlich Adsorption isotherm. The relationship given by \(\frac{x}{m} = Kp^{\frac{1}{n}}\ (n > 1)\)
x = Mass of the gas adsorbed
m = Mass of adsorbent
p = Pressure at which adsorption takes place
K and n are constant
The curve of above relationship indicate that at a fixed pressure there is a decrease in physical adsorption with increase in temperature. At high pressure, curves become parallel to pressure axis, indicating saturation of the surface of adsorbent.
Adsorption of a gas follow Freundlich isotherm shown below. \(\frac{x}{m}\) is proportional to

Read the Passage carefully and answer the Questions:
Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered. The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction.
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(=k[A]^{ a }[B]^{ y }\)
Here \(k\) is the rate constant
\(x+y\) gives the overall order of a reaction, whereas \(x\) and \(y\) represent the order with respect to the reactants \(A\) and \(B\), respectively.
The unit of rate constant for first order reaction is:

Which of the following statements are true?
(A) Degree of the differential equation \(\frac{d^2 y}{d x^2}+y=1\) is 2.
(B) Number of arbitrary constants in the particular solution the differential equation of order 4 are 4.
(C) \(y^2=a\left(b^2-x^2\right)\) will be the general solution of a differential equation of order 2; where a and b are two arbitrary constants.
(D) \(f(x, y)=\frac{2 x-y}{x+3 y}\) is a homogeneous function of degree 1.
(E) Integrating factor of \(x \frac{d y}{d x}-y=2 x^2\) is \(\frac{1}{x}\).
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The area of the region bounded by the circle \(x^2+y^2=1\) is ___________ sq. units.

Match List - I with List - II.

List - I	List - II
(A) If A and B are mutually exclusive events, then \(P ( A \cup B )=\)	(I) \(\frac{ P ( A \cap B )}{ P ( B )}, P ( B ) \neq 0\)
(B) If A and B are independent events, then \(P ( A \cap B )=\)	(II) \(\frac{ P ( A \cap B )}{ P ( A )}, P ( A ) \neq 0\)
(C) If A and B are two events of a sample space of an experiment, then \(P ( A / B )=\)	(III) \(P ( A ) \cdot P ( B )\)
(D) If A and B are two events of a sample space of an experiment, then \(P ( B / A )=\)	(IV) \(P ( A )+ P ( B )\)

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The angle between the vectors \(\hat{i}-2 \hat{j}+\hat{k}\) and \(3 \hat{i}+2 \hat{j}+\hat{k}\) is:

If the lines \(\frac{1-x}{3}=\frac{y-2}{2 \lambda}=\frac{z-3}{2}\) and \(\frac{x-1}{3 \lambda}=\frac{y-1}{1}=\frac{6-z}{5}\) are perpendicular, then \(\lambda\) is equal to

Using monochromatic light for diffraction in a single slit of width 0.1 mm , with a central maximum of 5 mm width on a screen 50 cm away, the wavelength of light used is :