Six charges each +3q are placed at the corners of a regular hexagon of each side 'a'. The electric field at the center of the hexagon is:

A closely wound solenoid of 1000 turns and area of cross section \( 1.2 \text{ cm}^2 \) carries a current of 5 A. It is suspended horizontally in uniform magnetic field of \( 5 \times 10^{-2} \text{ T} \) making an angle of \( 30^\circ \) with the axis of solenoid. The torque acting on the solenoid is:

The radius of curvature of the path of a charged particle in a uniform magnetic field is directly proportional to the

What is the unit of electric flux in terms of the base units of SI?

A deutron and an \(\alpha\)-particle moving with the same velocity enter into a uniform magnetic field acting normal to the plane of their motion. The ratio of the circular paths described by the deutron and \(\alpha\)-particle is

In forward bias and in reverse bias, respectively, the width of the depletion layer of a p-n junction

Which of the following are true for optical instruments?
(A) A simple microscope is a converging lens of large focal length.
(B) A telescope is used to provide angular magnification of distant objects.
(C) The objective lens of a telescope has a smaller focal length than the eyepiece.
(D) The magnifying power of a telescope is the ratio of the focal length of the objective lens
to the focal length of the
eyepiece.
(E) A simple microscope is a converging lens of small focal length
Choose the correct answer from the options given below :

Haloalkanes can be represented by the formula

A wire of resistance \( 18 \, \Omega \) is bent in the form of an equilateral triangle. The effective resistance between any two corners of the triangle is :

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 followings is not an example of physiological barriers?

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
\(Y \xrightarrow{\text { axidation }} \text { aldehyde } \xrightarrow{\text { oxidation }} \text { carboxylic acids }\)

Match List - I with List - II.

LIST - I	LIST - II
(A) \(x^x\) has a stationary point at \(x\) equal to	(I) \(e\)
(B) For \(x>0\), minimum value of \(x^x\)	(II) \(1 / e\)
(C) The greatest value of \(\left(\frac{1}{x}\right)^x\)	(III) \(e^{1 / e}\)
(D) The stationary point of \(\frac{\log x}{x}\) for \(x\), where \(x>0\), is	(IV) \(e^{-1 / e}\)

Choose the correct answer from the otions given below:

The slope of the normal to the curve \(y=2 x^2\) at \(x=1\) is: