Two point charges placed a distance d apart in vacuum exert a force of magnitude F on each other. One of the two charges is doubled. To keep the magnitude of force same the separation between the charges should be changed to

An oil drop of mass m carrying a charge +q is held stationary in air by an electric field E. The electric field is correctly given by

A straight wire of mass 200 g and length 1.5 m carrying a current of 2 A is placed in a uniform magnetic field at right angles to its direction, is suspended in mid air. The magnitude of magnetic field is : \(\left(g=9.8 m / s ^2\right)\)

What is the particle X in the fusion reaction shown below ?
\({ }_1^2 H +{ }_1^2 H \rightarrow{ }_2^3 He + X +3.27 MeV\)

An angular magnification of 30 X is desired using an objective lens of focal length 1.25 cm and an eyepiece of focal length 5 cm. What should be the separation between objective and eyepiece when the final image is formed at the near point ?

When a convex lens of glass is immersed in water, its power will

A surface of area \( \vec{A} = 2\hat{i} - 3\hat{k} \) exists in a region of electric field \( \vec{E} = a\hat{i} + b\hat{j} \). The net flux passing through the surface is

Which of the following could not be a rate determining step?

Read the passage carefully and answer the questions
The carbonyl group of aldehydes and ketones is highly polar. The positively charged carbon is readily attacked by electron-rich nucleophile and the negatively charged oxygen atom is attacked by an electro-deficient electrophile. Aldehydes and ketones undergo nucleophilic addition reactions in the presence of acid or a base. The mechanism involves attack of a nucleophile on the electron deficient carbonyl carbon to form a tetrahedral intermediate. A new bond is formed between the carbon and oxygen. Protonation of the anion furnished by the reaction medium yields a neutral addition product. The addition product is same whether the reaction is catalyzed by acid or a base. For example in the presence of base aldehydes and ketones react with hydrogen cyanide to form cyanohydrin.
The source of nucleophile in the base catalyzed cyanohydrin formation is:

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The term vitamin was coined from the word vital +amine since the earlier identified compounds had amino groups. Later work showed that most of them didn't contain amino groups, so the letter "e" was dropped and ther term vitamin is used these days.
Vitamins are classified into two groups depending upon their solubility in water or fat. Fat soluble vitamins are soluble in fat and oils but insoluble in water. They are stored in liver and adipose (fat storing) tissues. Water-soluble vitamins are soluble in water. They must be supplied regularly in the diet as they are readily excreated in urine.
Among the following, water-soluble vitamin is

If \(\int \frac{2 x}{x^2+3 x+2} d x=m \log |x+2|+n \log |x+1|+C\), then the values of m and n are:

Consider a line \(\vec{r}=(\hat{i}+4 \hat{j})+\lambda(2 \hat{i}-2 \hat{j}+3 \hat{k})\), then which of the following statements are correct?
(A) It passes through point \((9,-4,12)\)
(B) It passes through point \((1,4,-1)\)
(C) Its direction cosine's are \(\frac{2}{\sqrt{17}}, \frac{-2}{\sqrt{17}}, \frac{3}{\sqrt{17}}\)
(D) Its Cartesian equation is \(\frac{x-1}{2}=\frac{y-4}{-2}=\frac{z}{3}\)
Choose the correct answer from the options given below:

Which of the following has the highest molar conductivity?