Assume the earth to be a spherical conductor of radius 6400 km. Calculate the capacitance of earth.

The ratio of equivalent capacitance in series and parallel combinations of two capacitors of capacity 5 F and 20 F will be

If \(E _{ p }\) and \(E _{ k }\) represents the potential and kinetic energy respectively of an orbital electron, then according to Bohr's theory.

An electric dipole is kept in an electric field which is increasing in the +x direction.
The dipole moment of the dipole is also along the +x direction.
Which of the following options is correct for the electric dipole?

A current of 10 A is flowing in a wire of length 1.5 m. When placed in a uniform magnetic field of 2 T, it experiences a force 15 N. The angle between the magnetic field and the direction of flow of current is

A p-n junction diode can be used :

A 400 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 400 pF capacitor. The electrostatic energy lost in the process is

The interval on which the function \(f(x)=x^4-\frac{x^3}{3}\) is strictly decreasing, is :

Which of the following enzymes join the sticky ends in recombinant DNA technology?

The point on the curve \(\frac{x^2}{4}+\frac{y^2}{9}=1\) at which the tangent to the curve is parallel to the \(x\)-aris is

Read the passage carefully and answer the questions based on the passage:
Alcohols are versatile compounds as they can act as both nucleophile and electrophile. They undergo reactions based on cleavage of O-H and C-O bonds. The cleavage of O-H bond reflects the acidic character of alcohols. However they are weaker acids than water, phenol and carboxylic acids. Alkoxide ion formed by loss of proton from the OH group of alcohols reacts with water to form the corresponding conjugate acid - base pair. They act as Bronsted base due to presence of unshared electron pairs on oxygen.Both alcohols and phenol react with carboxylic acids, acid chlorides and anhydrides to form esters. The introduction of acetyl group in alcohols or phenol is known as acetylation. Alcohols react with hydrogen halides to form alkyl halides which form the basis of Lucas test. They also undergo acid catalyzed dehydration to form alkenes. Alcohols can be easily oxidized with variety of oxidizing agents. The nature of the product depends on the type of oxidizing agent and the nature of alcohol.
Which of the following gives the correct sequential steps for dehydration of alcohol?

If \(A=\left[\begin{array}{cc}\sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha\end{array}\right]\), and \(A+A^{\prime}=I\), then the value of \({ }^{\prime} \alpha^{\prime}\) is :

Which techniques are commonly used for early diagnosis of a disease.
(A) Serum analysis
(B) ELISA
(C) PCR
(D) Recombinant DNA technology
Choose the correct answer from the options given below: