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Find $\lim_{x\rightarrow1}\frac{x^{3}-3x+2}{x^{2}-5x+4}.$

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Evaluate $\int_{0}^{\pi}\frac{x\,sin\,x}{1+cos^{2}\,x}dx.$

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Question:

Find $\frac{\mathrm{d} y}{\mathrm{d} x},$ if $y=xsin^{-1}\,x+\sqrt{1-x^{2}}.$

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Question:

With suitable example and figure explain the integrated rate law for first order reaction.

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Question:

What is meant by rate of a reaction? List and explain different types of rates used in chemical kinetics.

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Question:

Explain the pressure and volume correction terms to the ideal gas equation, and deduce van der Waals equation.

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Question:

State the Dalton’s law of partial pressure and give its significance.

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Question:

Calculate the i) average speed ii) root mean square speed and iii) most probable speed of

oxygen molecules at 515 K. (Given $M_{m(O_{2})}=0.0016$ kg mo $1^-10)$

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Question:

$y=-x^{2}$ is increasing in [− 5, − 3] .

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Question:

$y=x^{2}-3x^{3}$ has no points of inflection.

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Question:

Which are the cases when tetrahedral geometry is favoured over octahedral geometry for metal complexes? Why are they so?

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Question:

Give the possible electronic configurations for $d^{3}$ and $d^{6}$ systems in a tetrahedral crystal field.

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Question:

The function f, defined by $f(x)=\left | x-2 \right |,$ is differentiable in [0,1].

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Question:

Give the CFSE of an octahedral complex with seven electrons in the d orbitals.

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Question:

Explain the directional properties of the five d orbitals in a free transition metal ion with the help of suitable diagrams.

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Question:

$\frac{\mathrm{d} }{\mathrm{d} x}\left [ \int_{2}^{e^{x}}ln\, t\,dt \right ]=x-ln\,2.$

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Question:

Give the hybridized orbitals and the corresponding geometries of $[Ti(H_{2}O)_{6}]^{3+}$ and $[CoC1_{4}]^{2-}.$

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Question:

The function f, defined by )x(f = cos x + sin ,x is an odd function.

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Question:

What type of isomerism is exhibited in the complexes $[Co(NH_{3})_{5}(SO_{4})]$ Br and $[Co(NH_{3})C1_{2}]^{+}?$

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Question:

The measurements of the bulk modulus of a material at different temperatures is as follows:

$T(\degree C)$	20	500	100	1200	1400	1500
K (G Pa)	203	197	191	188	186	184

Determine the regression equation for this data.

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