A galvanometer of resistance G is converted into a voltmeter to measure upto V volts by connecting a resistance \( R_1 \) in series with the coil. If a resistance \( R_2 \) is connected in series with it, then it can measure the \( \frac{V}{3} \) volts. Find the resistance \( R_3 \) in terms of \( R_1 \) and \( R_2 \) required to be connected to convert it into a voltmeter that can read upto 3V volts :

Two sources of equal emf are connected in series. This combination is connected to an external resistance R.
The internal resistance of two sources are \( r_1 \) and \( r_2 \) (\( r_2 > r_1 \)).
If the potential difference across the source of internal resistance \( r_2 \) is zero, then R equals to:

The condition for observing diffraction from a single slit is that the light wavefront incident on the slit should be

Read the following statements regarding energy levels, and identify the correct statements.
(A) The energy of an atom is least when its electron is revolving in an orbit closest to the nucleus
(B) the energy levels of the excited states come closer and closer together as principal quantum number increases
(C) ionisation energy of the hydrogen atom is the minimum energy required to free the electron from the ground state of the hydrogen atom
(D) as the excitation of hydrogen atom increases, the value of minimum energy required to free the electron from the excited atom decreases.
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A double slits is illuminated by light of wavelength 600 nm. The slits are 0.1 cm apart and the screen is placed 1 m away. The width of maxima is:

Choose the correct statements :
(A) A nuclide is represented as \( ^A_Z X \)
(B) Nuclids with same number of protons are called isotopes
(C) \( \alpha \)-ray scattering experiments allow determination of the nuclear radius
(D) Nuclids with same number of neutrons are called isotones
(E) The nuclear force distinguishes between neutron and proton
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In an AC generator, a 100 turns coil of area \( 0.10 \text{ m}^2 \) rotates at 50 Hz in a uniform magnetic field of 0.01 T. The maximum voltage generated in the coil is:

The rate constant for a first order reaction becomes 2 times when the temperature is raised from 330 K to 380 K . Then the energy of activation for the reaction will be:\[[\log 2=0.3010]\]

Let \(A=\left[a_{i j}\right]_{3 \times 2}\) and \(B=\left[b_{i j}\right]_{3 \times 4}\) be two matrices.
Then the order of the matrix \(\left(A^T \cdot B\right)^T\) is :

A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, the probability of exactly 6 successe, is:

The mass of urea (\(NH_2CONH_2\)) required to make 2.5 kg of 0.25 molal aqueous solution will be :

The demand function for a certain product is represented by the equation: p = 20 + 5x - \(3 x^2\), where \(x\) is the number of units demanded and p is the price per unit (in Rs.), then the marginal revenue when 2 units are sold, is:

Answer the question on the basis of passage given below:
Aldehydes are generally more reactive than ketones in nucleophilic addition reactions due to steric and electronic reasons. Sterically, the presence of two relatively large substituents in ketones hinders the approach of nucleophile to carbonyl carbon more than aldehydes having only one such substituent Electronically aldehydes are more reactive than ketones because two alkyl groups reduce the elctrophilicity of the carbonyl more effectively than in former.
For preparation of phenylethanoic acid from benzyl alcohol, reagents required are
A. HBr
B. \(CO _2\)
C. \(K C N\)
D. \(\Delta / H_3 O^{+}\)
E. \(AgNO _3\)
Choose the correct answer from the options given below: