Match List - I with List - II.

List - I	List - II
(A) The common region determined by all the constraints of LPP is called	(I) objective function
(B) Minimize \(z=c_1 x_1+c_2 x_2+\cdots+c_n x_n\) is	(II) convex set
(C) A solution that also satisfies the non-negative restrictions of a LPP is called	(III) feasible region
(D) The set of all feasible solutions of a LPP is a	(IV) feasible solution

Choose the correct answer from the options given below :

During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has \(45\%\) chance of having heart attack, but yoga and meditation assumed to reduce the chance of heart attack by \(25\%\) and \(20\%\) respectively. He has option to choose any of the two options with equal probabilities.
If Amit goes through one of the two options selected at random and suffers a heart attack, then the probability that he had selected yoga is:

If \(\frac{3 x-5}{6}+8 \geq 4+\frac{2 x}{3}\), then

If \(\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi\) then the value of \(\alpha^2 \beta^2 \gamma^2+3(\alpha+\beta+\gamma)\) 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 \(x=0\)

Choose the correct answer from the options given below :

\(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{d x}{1+\sqrt{\tan x}}\) is equal to:

The direction cosines of the line
\(x-y+z-5=0\) and \(x-3 y-6=0\) are:

Chlorine is extracted from brine by:

Read the passage carefully and answer the Questions
Carbonyl compounds such as aldehydes, ketones, and carboxylic acids play an important role in the biochemical process of plants and animal kingdom.
Many aldehydes and ketones find applications in dye, perfumery and other industries.
The carbonyl carbon atom is \(s p^2\)-hybridized forming three sigma and one pi-bond with oxygen.
C-O bonds are polar bond due to high electronegativity of oxygen than carbon.
Hence the carbonyl carbon behaves as an electrophilic center and oxygen as a nucleophilic centre.
Primary and secondary alcohols yield aldehydes and ketones respectively upon oxidation with variety of oxidizing agents.
The boiling points of aldehydes and ketones differ from hydrocarbons and ethers.
Aldehydes and ketones undergo nucleophilic addition reaction due to presence of electrophilic carbonyl carbon.
Nucleophile and a proton add across the carbon oxygen double bond.
The alcohol which cannot be used to prepare carbonyl compound through oxidation is

Primary productivity does not depends upon which one of the following factors?

The wavelength of light from the spectral emission line of sodium is 662 nm.
The kinetic energy at which an electron would have the same de-Broglie wavelength would be:
(Given: \( h = 6.62 \times 10^{-34} \text{ J s}, m_e = 9 \times 10^{-31} \text{ kg} \))

Match List-l with List-ll

List-l (Microbes)	List-II (Products or uses)
(A). Trichoderma polysporum	(I). Blood cholesterol lowering agent
(B). Streptococcus	(II). Citric acid
(C). Aspergillus niger	(III). Clot buster to remove blood clots
(D). Monascus purpureus	(IV). Cyclosporin A

Choose the correct answer from the options given below:

Match List-I with List-II

List-I (Quantity)	List-II (Formula)
(A) Einstein's Photoelectric Equation	(I) \( K_{max} / e \)
(B) De-Broglie Wavelength	(II) \( K_{max} = hc/\lambda - \phi \)
(C) Stopping potential	(III) \( hc/\phi \)
(D) Threshold wavelength	(IV) \( h/p \)

Choose the correct answer from the options given below: