Radiation of frequency \(2 v _0\) incident on a metal with threshold frequency \(v _0\) results in maximum kinetic energy of photoelectrons as :

If \(A\) and \(B\) are symmetric matrices of order \(3 \times 3\) then the matrix \(2 A B-B A\) is :

Which of the following statements is NOT CORRECT.

Which one of the following inequalities is redundant for the shaded feasible region (ABCDA) shown below?

The area bounded by the curve \(|x|+y=1\) and the axis of \(x\) is :

The function \(f(x)=\left|\begin{array}{cc}x^2 & x \\ 3 & 1\end{array}\right|, x \in R\) has a:

Match List - I with List - II.

LIST-I	LIST-I
(A) \(\csc ^{-1} x\)	(I) \((0, \pi)\)
(B) \(\sec ^{-1} x\)	(II) \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}\)
(C) \(\tan ^{-1} x\)	(III) \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
(D) \(\cot ^{-1} x\)	(IV) \([0, \pi]-\left\{\frac{\pi}{2}\right\}\)

Choose the correct answer from the options given below:

Match List - I with List - II

List - I (Complex)	List - II (Hybridisation)
(A) \([CoF_6]^{3-}\)	(I) \(sp^3\)
(B) \([Co(NH_3)_6]^{3+}\)	(II) \(dsp^2\)
(C) \([NiCl_4]^{2-}\)	(III) \(d^2sp^3\)
(D) \([Ni(CN)_4]^{2-}\)	(IV) \(sp^3d^2\)

Choose the correct answer from the options given below :

The integrating factor of the differential equation \(\frac{d y}{d x}=x+x y\) is:

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 oxidixing 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 starting compound (Y) in the following reaction is
\(Y \xrightarrow{\text { axidation }} \text { aldehyde } \xrightarrow{\text { oxidation }} \text { carboxylic acids }\)

Read the following passage carefully and answer the given questions.
Plasmodium, a tiny protozoan is responsible for the disease malaria. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. Innate immunity consist of four types of barriers. These are – (i) Physical barriers- skin on our body is the main barrier which prevents entry of the micro-organisms. (ii) Physiological barriers- Acid in the stomach, saliva in the mouth, tears from eyes-all prevent microbial growth. (iii) Cellular barriers- Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. (iv) Cytokine barriers- virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Allergy is due to the release of chemicals like histamine and serotonin from the mast cells. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused.
Which one of the following drugs or chemicals can not quickly reduce the symptoms of allergy?

Let \(A=\{1,2,3\}\), then the possible equivalence relations on \(A\) are :
(A) \(\{(1,1),(2,2),(3,3)\}\)
(B) \(\{(1,1),(2,2),(3,3),(1,2),(2,1)\}\)
(C) \(\{(1,1),(2,2),(3,3),(1,2),(2,1),(1,3)\}\)
(D) \(\{(1,1),(2,2),(3,3),(1,3),(3,1)\}\)
Choose the correct answer from the options given below :

If charge is moving perpendicular to uniform magnetic field then its time period of revolution is: