\(\text { If } y=\left(\log \left(x+\sqrt{x^2+a^2}\right)\right)^2 \text { and } x \neq \frac{1-a^2}{2}\)then \(\left(x^2+a^2\right) \frac{d^2 y}{d x^2}+x \frac{d y}{d x}\) is equal to :

The value of \(k\) for which the function \(f(x)=\left\{\begin{array}{ll}\frac{1-\cos 8 x}{16 x^2} & , \text { if } x \neq 0 \\ k & , \text { if } x=0\end{array}\right.\) is continuous at \(x=0\) is :

If \(A = \mathbb{R} - \left\{\frac{3}{2}\right\}\) and function \(f: A \rightarrow A\) is defined by \(f(x) = \frac{3x-2}{2x-3}\), then

If X is a normal variate with mean 16 and standard deviation 4, then the value of the standard normal variate Z corresponding to X = 17 is :

If \(a, b\) and \(c\) are all different from zero and \(\left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|=0\), then the value of \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\) is :

If \(\cos y=x \cos (a+y)\), then \(\frac{d y}{d x}=\)

The vector in the direction of the vector \(2 \hat{i}-\hat{j}-2 \hat{k}\) that has magnitude 9 units is :

If \(y=\frac{1}{\sqrt[3]{1-x^3}}\), then \(\frac{d y}{d x}\) is equal to :

Match the complex given in List - I with the number of unpaired electrons given in List - II

List-I (Complex)	List-II (Number of unpaired electrons (n))
(A) \(\left[ NiCl _4\right]^{2-}\)	(I) 5
(B) \(\left[ Co \left( NH _3\right)_6\right]^{3 +}\)	(II) 1
(C) \(\left[ FeF _6\right]^{3-}\)	(III) 2
(D) \(\left[ Fe ( CN )_6\right]^{3-}\)	(IV) \(0\)

Choose the correct answer from the options given below:

The reaction of phenol with chloroform in the presence of sodium hydroxide gives

Read the passage carefully and answer the questions based on the passage:
Pollen pistil interaction involves all events from the landing of pollen grains on the stigma until the pollen tube enters the embryo sac (when the pollen is compatible). When a pollen tube grows through the style and enters into the ovules, it finally discharges two male gametes in one of the synergids. Syngamy and triple fusion are two fusion events occur in angiosperms. Thus, angiosperms exhibit double fertilization. The products of these fusions are the diploid zygote and triploid primary endosperm nucleus. Zygote develops into embryo and primary endosperm cell forms the endosperm tissue. The developing embryo passes through different stages before maturation.
The coconut water from tender coconut, a good source of nutrition is nothing but:

Match List - I with List - II.

List I (Name)	List - II (Functions)
(A) mRNA	(I) amino acid carrier
(B) rRNA	(II) structural and catalytic role during translation
(C) tRNA	(IV) template for protein synthesis
(D) cistron	(III) gene

Choose the correct answer from the options given below:

The \(\Lambda_m^{\circ}\) for \(CaSO _4\) at 298 K , if \(\lambda_{ Ca ^{+2}}^{\circ}=119.0 Scm ^2 mol^{-1}\) and \(\lambda_{ SO _4^{2-}}^{\circ}=160.0 Scm ^2 mol^{-1}\) will be: