If \(f(x)=x+\frac{1}{x}\). Which of the following is not a correct option?

If \(\left[\begin{array}{ll}1 & 3 \\ 2 & 4\end{array}\right]\left[\begin{array}{cc}3 & 5 \\ -1 & 3\end{array}\right]=\left[\begin{array}{cc}m & 14 \\ 2 & n\end{array}\right]\), then m + n is equal to:

The function \(f(x)=x^3-3 x\) is :

If \(|\vec{a}|=a\), then the value of \(|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2\) is :

Consider two lines \(l_1\) and \(l_2\) with cartesian equations \(\frac{x}{2}=\frac{1-y}{-2}=\frac{z}{1}\) and \(\frac{2 x-5}{16}=\frac{y-2}{-1}=\frac{z-5}{4}\) respectively. Which of the following is/are true?
(A) Direction ratio of \(l_1\) are \(2,2,1\)
(B) Direction cosines of \(l_1\) are \(\frac{2}{3}, \frac{-2}{3}, \frac{1}{3}\)
(C) Direction ratio of \(l_2\) are \(16,-1,4\)
(D) Angle between \(l_1\) and \(l_2\) is \(\cos ^{-1}\left(\frac{38}{3 \sqrt{273}}\right)\)
Choose the correct answer from the options given below:

The linear inequalities satisfying the shaded feasible region given in the figure are

(A) \(x \geq 0, \quad y \geq 0, \quad 2 x+y \geq 2\)
(B) \(x \geq 0, \quad y \geq 0, \quad 2 x+y \leq 2\)
(C) \(x \geq 0, \quad y \geq 0, \quad 2 x+y \geq 2, \quad x+2 y \leq 8, \quad x-y \leq 1\)
(D) \(x+2 y \geq 8, \quad x-y \geq 1\)
Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{ll}1 & 2 \\ 4 & 5\end{array}\right]\) then
Match List-I with List-II

List-I	List-II
(A) \(\operatorname{det}(A)\)	(I) \(-\frac{1}{3}\)
(B) \(\operatorname{det}\left(A^{-1}\right)\)	(II) \(- 12\)
(C) \(\operatorname{det}(2 A)\)	(III) \(- 3\)
(D) \(\operatorname{det}\left( 3 A ^T\right)\)	(IV) \(- 27\)

Choose the Correct answer from the options given below :

Choose the correct statement(s) from the following:
(A) With increasing reverse bias voltage, the barrier potential across the junction of p-n diode decreases.
(B) A p-type semiconductor can be obtained by doping Si or Ge with trivalent atoms.
(C) A rectifier rectifies dc voltages.
(D) Pure semiconductors are called extrinsic semiconductors.
Choose the correct answer from the options given below:

Match List-l with List-ll
Let \(A\) be any invertible square matrix. Then

List-l	List-ll
(A) \(A-A^T\)	(I) \(|A| A^{-1}\)
(B) \(A A^T\)	(II) Skew-symmetric
(C) \(\operatorname{det}\left(A^{-1}\right)\)	(III) Symmetric
(D) \(\operatorname{adj} A\)	(IV) \([\operatorname{det}(A)]^{-1}\)

Choose the correct answer from the options given below :

The electric field intensity produced by the radiations coming from a 200 W bulb at 6 m distance is E . What is the electric field intensity produced by the radiations coming from 100 W bulb at the same distance?

Read the passage carefully and answer the Questions
Aldehydes and ketones are important organic compounds prepared mainly by oxidation of alcohols. Primary alcohols give aldehyde and secondary alcohols yield ketones. Aldehydes can also be formed by partial reduction of acid chlorides, reduction of esters or by Gattermann-Koch reaction. Ketones are prepared by Friedel-Craft's acylation, hydration of alkyne and reaction of Grignard's reagent with nitriles. Chemically, aldehydes and ketones are reactive in nature due to the carbonyl group and undergo nucleophilic addition reactions. Aldehydes are more reactive than ketones and can be oxidized to carboxylic acids, while both can be reduced to alcohols or hydrocarbons and exhibit condensation reaction.
When two moles of benzaldehyde are heated with concentrated NaOH solution, the product/s obtained is/are:

The value of \(\int_0^1[\log x-\log (1-x)] d x\) is

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability \( \frac{4}{3} \) for this wavelength, will be :