Match List-I with List-II

List I (Function)	List II (Derivative with respect to ' x ')
(A) \(f(x)=x^x\)	(I) \(a x^{a-1}\)
(B) \(f(x)=a^x\)	(II) 0
(C) \(f(x)=a^a\)	(III) \(a^x \log _e a\)
(D) \(f(x)=x^a\)	(IV) \(x^x\left(1+\log _e x\right)\)

Choose the correct answer from the options given below:

For the following probability distribution:

X	-4	-3	-2	-1	0
p(x)	0.1	0.2	0.3	0.2	0.2

The order and degree of the differential equation \(\frac{d^2 y}{d x^2}+2 e^{-x}=0\), respectively are :

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0},|\vec{a}|=7,|\vec{b}|=3\) and \(|\vec{c}|=5\), then angle between \(\vec{b}\) and \(\vec{c}\) is

The solution of the differential equation \(\left(x^2+x y\right) d y=\left(x^2+y^2\right) d x\) is

For the LPP :
Maximise \(z=4 x+y\)
subject to constraints
\(x+y \leq 50, \quad 3 x+y \leq 90, \quad x \geq 0, y \geq 0\) the maximum value of \(z\) is :

A unit vector perpendicular to the vectors \(\hat{i}-\hat{j}\) and \(\hat{i}+\hat{j}\) is

The standard reduction potentials of \(Mg^{2+}/Mg, Pb^{2+}/Pb\) and \(Sn^{2+}/Sn\)
are \(-2.36, -0.13\) and \(-0.14\) V respectively.
The reaction \(X + Y^{2+} \rightarrow X^{2+} + Y\) will be spontaneous when :

Read the passage carefully and answer the questions
Replacement of a hydrogen atom in a hydrocarbon by an alkoxy or carboxyl group yields a class of compounds known as ethers. Ethers are classified as symmetrical or unsymmetrical on the basis of groups attached to the oxygen atoms. Diethyl ether, a symmetrical ether, has been widely used as an inhalation anesthetic. Ethers can be prepared by acid catalyzed intermolecular dehydration of alcohols and Williamson's synthesis. Acid catalyzed dehydration of alcohols is not generally preferred as it gives a mixture of elimination and substitution products. In Williamson's synthesis, an alkyl halide is allowed to react with sodium alkoxide. Ethers containing substituted Alkyl groups may also be prepared by this method. The C-O bond in ether is weakly polar and is cleaved under drastic conditions with excess of hydrogen halides. In electrophilic substitution, the alkoxy group deactivates the aromatic ring and directs the incoming group to ortho and para positions.
Which is most reactive hydrogen halide for cleavage of ethers?

Which of the following is NOT correct in the case of the output obtained from a full wave rectifier?

Match List I with List II

List-l (Name of compound)	List-II (Structure)
(A). Resorcinol	(I).
(B). Catechol	(II).
(C). Hydroquinone	(III).
(D). p-Cresol	(IV).

Choose the correct answer from the options given below :

Sex determination in grasshopper is of -

Identify the correct statements among the following.
(A) The number of electrons (\( n_e \)) is more than the number of holes (\( n_h \)) in intrinsic conductors.
(B) Semiconductors are elements (Si, Ge) type as well as compounds (GaAs, CdS).
(C) The number of charge carriers can be changed by 'doping' of a suitable impurity in pure semiconductors.
(D) Holes are essentially electron vacancies in a valence band.
Choose the correct answer from the options given below: