Match \(List - I\) with \(List - II\)

\(List - I\)	\(List - II\)
(A) \(\frac{d}{d x}\left(\sin x^2\right)\)	(I) \(\frac{1}{5}\)
(B) \(\frac{d}{d x}\left(e^{\sin x}\right)\)	(II) 0
(C) \(f(x)=\tan ^{-1} x\) then \(f^{\prime}(2)\)	(III) \(2 x \cos x^2\)
(D) If \(y=3 \cos x-2 \sin x\), then \(\frac{d^2 y}{d x^2}+y\)	(IV) \(e^{\sin x} \cos x\)

Let \(\vec{a}=\hat{i}+4 \hat{j}, \vec{b}=4 \hat{j}+\hat{k}\) and \(\vec{c}=\hat{i}-2 \hat{k}\). If \(\vec{d}\) is a vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) such that \(\vec{c} \cdot \vec{d}=16\), then \(|\vec{d}|\) is equal to:

The maximum value of the objective function \(Z=10 x+15 y\) of an L.P.P, whjected to the constraints
\(2 x+4 y \leq 8,\)
\(3 x+y \leq 6\)
\(-x-y \geq-4\)
\(x \geq 0, y \geq 0\) is :

If \(a_{i j}\) represents the element of \(i^{\text {th }}\) row and \(j^{\text {th }}\) column and \(A_{i j}\) is the corresponding cofactor, then for the matrix \(A=\left[\begin{array}{ccc}1 & -1 & 0 \\ 2 & 0 & 1 \\ 3 & 4 & 2\end{array}\right]\) the value of \(a_{11} A_{21}+a_{12} A_{22}+a_{13} A_{23}\) is:

The maximum value of a LPP \(z=3 x+4 y\) subject to the constraints: \(x+y \leq 6, x \geq 0, y \geq 0\) is:

If \(\left|\begin{array}{ccc}p-a & 0 & c-r \\ 0 & q-b & c-r \\ a & b & r\end{array}\right|\) =0 then the value of \(\frac{p}{p-a}+\frac{q}{q-b}+\frac{r}{r-c}\) is

Match List-l with List-ll

List-l	List-ll
(A) \(f(x)=x \cdot \sin x\)	(I) is not continuous at \(x=-3\)
(B) \(f(x)=\frac{|x|}{x}, x \neq 0\) and \(f(x)=1\) at \(x=0\)	(II) is continuous everywhere
(C) \(f(x)=x-[x],[x]\) denotes greatest integer function	(III) is not differentiable at \(x=1\)
(D) \(f(x)=e^{|x-1|}\)	(IV) is not continuous at \(x=0\)

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If the corner points of the bounded feasible region of an LPP with objective function maximize \(Z=2 x+3 y\) are \((0,0),(1,2)\) and \((1,1)\), then its optimal value is

Reaction of \(C _6 H _5 CH _2 Br\) with aqueous sodium hydroxide follows preferably:

Match List I with List II

List I – Name of the part	List II – Characteristics
A. Non-albuminous seed	III. Residual endosperm absent
B. Albuminous seed	I. Residual endosperm present
C. Perisperm	IV. Residual nucellus
D. Pericarp	II. Fruit wall

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\(\left[ Ag \left( NH _3\right)_2\right] OH\) forms silver when it reacts with:

Match the property given in List-l with the element given in List-Il

List-I (Property)	List-ll (Element)
(A) Lanthanoid, which can show +2 oxidation state	(I) Pm
(B) Radioactive lanthanoid	(II) Lu
(C) Lanthanoid which has \(4 f^{\wedge} 7\) electronic configuration in +3 oxidation state	(III) Eu
(D) Lanthanoid which has \(4 f^{\wedge}\{14\}\) electronic configuration in +3 oxidation state	(IV) Gd

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Answer the question on basis of passage given below :
Transition metals form a large number of complexes or coordination compounds in which the metal atoms are bound to a number of anions or neutral molecules. The valence bond theory explain the formation, magnetic behaviour and geometrical shapes while the crystal field theory explains the effect of different crystal fields on the degeneracy of d-orbitals energies of the central metal atom/ion. This provides for the quantitative estimation of orbital separation energies, magnetic moments and spectral and stability parameters.

List - I	List - II
A. Mn2+	I. Yellow
B. \(F e 3+\)	II. Green
C. \(N i 2+\)	III. Blue
D. \(Cu 2+\)	IV. Pink

Choose the correctanswer from the options given below: