Match the complex species given in List-l with the possible isomerism given in List-ll:

List-l Complex species	List-ll Isomerism
(A) \(\left[ Co \left( NH _3\right)_4 Cl _2\right]^{+}\)	(I) optical
(B) cis- \(\left[ Co ( en )_2 Cl _2\right]^{+}\)	(II) ionization
(C) \(\left[ Co \left( NH _3\right)_5\left( NO _2\right)\right] Cl _2\)	(III) coordination
(D) \(\left[ Co \left( NH _3\right)_6\right]\left[ Cr ( CN )_6\right]\)	(IV) geometrical

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n-Hexane is obtained when glucose is

What is the product of the following reaction?
\[R-CN \frac{H_2 / Ni}{Na(Hg) / C_2 H_5 OH}\]
The options are:

Which structure of proteins gives rise to fibrous and globular proteins?

Answer the question on the basis of passage given below :
Nitrogen differs from rest of the members of group 15 due to its small size, high electronegativity, high ionization enthalpy and non-availability of d orbitals. Nitrogen has unique ability to form pa - pa multiple bonds with itself and with other elements having small size and high electronegativity. Heavier elements of this group do not form pa - pr bonds as their atomic orbitals are so large and diffuse that they cannot have effective overlapping.
Linear structure is exhibited by:

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Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms.
They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O_H bond along with the reactions involving the complete -COOH group.
The products formed when 2,2-Dimethylpropan-1-al is heated with concentrated KOH are :

Converting \(\text{[A]}\) into \(\text{[C]}\) is called :

Match List I with List II

List - I (Organism)	List - II (Product)
(A) Streptococcus	(I) Citric acid
(B) Aspergillus niger	(II) Streptokinase
(C) Monascus purpureus	(III) Ethanol
(D) Saccharomyces cerevisiae	(IV) Statin

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The sum of the order and degree of the differential equation \(\frac{d^2 y}{d x^2}+\sqrt[3]{\frac{d y}{d x}}+(1+x)=0\) is :

Choose the incorrect statements from the options given below:
(A) In making a full wave rectifier, the two diodes are connected, with one in forward bias and the second in reverse bias.
(B) In a full wave rectifier, the output frequency is twice the input frequency.
(C) In a full wave rectifier, the current through the load resistance flows in one direction for half cycle and in the reverse direction for the other half cycle.
(D) In a full wave rectifier having two diodes and a resistance, the output voltage is uniform
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The materials and devices do not obey Ohm's law when
(A) The relation between V and I is not unique, i.e., there is more than one value of V for the same current I
(B) The relation between V and I depends on the sign of V
(C) V ceases to be proportional to I
(D) The relation between V and I is linear
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The corner points of the feasible region determined by the system of Linear Constraints are \((0,3),(1,2)\) and \((3,0)\). Let \(z=p x+q y\), where \(p, q>0\), be the objective function. Find the condition on \(p\) and \(q\) so that the minimum of \(z\) occurs at \((3,0)\) and \((1,2)\) :

Match List-I with List-II

List-I (Definite integral)	List-II (Value)
(A) \(\int_0^1 \frac{2 x}{1+x^2} d x\)	(I) 2
(B) \(\int_{-1}^1 \sin ^3 x \cos ^4 x d x\)	(II) \(\log _e\left(\frac{3}{2}\right)\)
(C) \(\int_0^\pi \sin x d x\)	(III) \(\log _e 2\)
(D) \(\int_2^3 \frac{2}{x^2-1} d x\)	(IV) 0

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