A transformer with turns ratio \( \frac{N_1}{N_2} = \frac{100}{1} \) is connected to a 240 V ac supply. If the primary and secondary resistance are \( 1.0 \text{ k}\Omega \) and \( 1 \ \Omega \) respectively, then find the output power ?

In series LCR circuit, the rms potential drop across R, L and C are V, 2 V and 2 V volts respectively. The source voltage is:

Two identical capacitors are connected in parallel combination. Their equivalent capacitance is \( C_1 \). If the plate area is halved and separation between plates is doubled for both the capacitors, their equivalent capacitance now is \( C_2 \). Find the ratio \( C_1/C_2 \).

In Rutherford's scattering experiment, if impact parameter \( b = 0 \), then the value of the scattering angle will be :

Which of the following statements are correct?
(A) Permeability of soft iron < permeability of steel
(B) Susceptibility of soft iron > susceptibility of steel
(C) Retentivity of soft iron > Retentivity of steel
(D) Coercivity of soft iron > coercivity of steel
Choose the correct answer from the options given below :

A charge of \( Q = 8.0 \times 10^{-9} \text{ C} \) is uniformly distributed on the surface of a spherical shell of radius \( R = 10 \text{ cm} \). The electric field at a distance of 10 cm from the outer surface of the shell is

The electric field amplitude of an electromagnetic wave is \(100 N C ^{-1}\) and its frequency is 50 MHz . What is the magnitude of wave vector \(k\), (given speed of electromagnetic wave is \(3 \times 10^8 m s ^{-1}\) )

Select the correct statements for Hoffmann bromamide degradation reaction:
(A) Used to prepare primary amines
(B) Amides are treated with bromine in aqueous solution.
(C) NaOH is used in this reaction.
(D) HCI is used in this reaction
Choose the correct answer from the options given below:

Total internal reflection of a ray of light is possible when the ray goes from

Read the passage carefully and answer the questions
Ethers with the general formula \(C _n H _{2 n+2} O\) and functional group C-O-C may be divided as symmetrical and unsymmetrical.
Lower symmetrical ether may be obtained by the dehydration of alcohols at low temperatures in the presence of protic acids,
such as \(H _2 SO _4\) and \(H _3 PO _4\) whereas at high temperature intramolecular dehydration takes place.
Formation of ether from primary alcohols is also accompanied by the formation of small amount of alkenes.
Due to the steric hinderance, secondary and tertiary alcohols undergo elimination reaction rather than substitution reaction yielding alkene as major product. Ethers can also be obtained by heating alkyl halides with sodium or potassium alkoxides.
Substituted Ethers (secondary & tertiary) can also be prepared using this method.
If primary halides are replaced with secondary and tertiary halides, alkenes are the major products.
The major product in the following reaction is \(ROH + HOR \xrightarrow{ H _2 SO _4, 140^{\circ} C }\)

Identify the correct statement about decomposition
(A) The rate of decomposition is quicker, if detritus is rich in nitrogen and sugar.
(B) Decomposition is largely an oxygen requiring process.
(C) The rate of decomposition is slow, if detritus is rich in chitin and lignin.
(D) The rate of decomposition is slow, if detritus is rich in nitrogen and sugar.
Choose the correct answer from the options given below:

The magnetic flux (Φ) through the area of cross-section of a current-carrying coil is proportional to the current (i) i.e., Φ = Li.
(A) L is self-inductance of the coil
(B) The self-inductance of the coil does not depend on its geometry
(C) self-inductance is the electromagnetic analogue of mass in mechanics
(D) The self-inductance of the coil depends on the permeability of the medium inside coil
Choose the correct answer from the options given below:

If \(x=\frac{1-t}{1+t}\) and \(y=\frac{2 t}{1+t}\), then \(\frac{d^2 y}{d x^2}\) is equal to :