List of practice Questions

The amplitude of upper and lower side bands of A.M. wave where a carrier signal with frequency 11.21 MHz, peak voltage 15 V is amplitude modulated by a 7.7 kHz sine wave of 5 V amplitude are $\frac{a}{10}$V and $\frac{b}{10}$V respectively. Then the value of $\frac{a}{b}$ is _________.
The parameters of the unit cell of a substance are a = 2.5, b = 3.0, c = 4.0, $\alpha=90^\circ, \beta=120^\circ, \gamma=90^\circ$. The crystal system of the substance is :
Given below are two statements:
Statement I : Rutherford's gold foil experiment cannot explain the line spectrum of hydrogen atom.
Statement II : Bohr's model of hydrogen atom contradicts Heisenberg's uncertainty principle.
In the light of the above statements, choose the most appropriate answer from the options given below:
The statement that is INCORRECT about Ellingham diagram is :
In a uniform magnetic field, the magnetic needle has a magnetic moment $9.85 \times 10^{-2}$ A/m$^2$ and moment of inertia $5 \times 10^{-6}$ kg m$^2$. If it performs 10 complete oscillations in 5 seconds then the magnitude of the magnetic field is _________ mT. [Take $\pi^2$ as 9.85]
A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section $10^{-6}$ m$^2$ stretched by an amount 0.04 m. The velocity of the projected stone is _________ m/s. (Young's modulus of rubber = $0.5 \times 10^9$ N/m$^2$)
A particle of mass $9.1 \times 10^{-31}$ kg travels in a medium with a speed of $10^6$ m/s and a photon of a radiation of linear momentum $10^{-27}$ kg m/s travels in vacuum. The wavelength of photon is _________ times the wavelength of the particle.
A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance 200 $\mu$F is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of 'R' should be _________ $\Omega$.
In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 Å. If the speed of the electron is $2.2 \times 10^6$ m/s, then the current associated with the electron will be _________ $\times 10^{-2}$ mA. [Take $\pi$ as 22/7]
A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching $\frac{h}{3}$ in both the directions.
A body takes 4 min. to cool from 61$^\circ$C to 59$^\circ$C. If the temperature of the surroundings is 30$^\circ$C, the time taken by the body to cool from 51$^\circ$C to 49$^\circ$C is :
The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy $2 \times 10^{-9}$ J per molecule is :
If 'f' denotes the ratio of the number of nuclei decayed Nd to the number of nuclei at t=0 N0 then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as: [$\lambda$ is the radioactive decay constant]

The truss shown is subjected to a force \( P \). All members of the truss have the same length \( L \). The reaction at A and force in member AB are 

For a state of plane strain, the normal strains are given by \(\epsilon_{xx} = 1000 \times 10^{-6}, \epsilon_{yy} = 200 \times 10^{-6}, \) and the maximum shear strain is \( \gamma_{\text{max}} = 1000 \times 10^{-6}. \)The value of shear strain\( \, \gamma_{xy} \, \)for this strain state is

A force \( F = 40 \, \text{kN} \) is applied on the hook as shown. The equivalent force-couple system at B is

The figure shows a structure with supports. The correct free body diagram when the supports are removed is 
 

Match the different transformations/reactions in Column I with the most suitable information in Column II. 

A magnet of mass 50 g has a magnetic moment of \( 4.2 \times 10^{-7} \, \text{A m}^2 \). The density of the magnet is 7.2 g/cm3. The intensity of magnetization in A/m is \(\underline{\hspace{2cm}}\) (round off to 3 decimal places).

In the context of scanning electron microscopy, match the information in Column I with the most appropriate information in Column II.

Match the heat treatment processes given in Column I with the most suitable outcomes in Column II. 

A co-joined cross-ply laminate composite, as shown in the figure, is distorted upon heating. What are the resultant shapes of edges XY and YZ? 

Fe - 10 atom % C austenite (fcc), having no Fe vacancies, has a lattice parameter of 4 Å. The density of austenite in g/cm3 is \(\underline{\hspace{2cm}}\) (round off to 2 decimal places).

An element transforms from \( \alpha \) to \( \beta \) at 773 K and 1 atm pressure with 912 J mol\(^{-1}\) as enthalpy of transformation. The molar volumes of \( \alpha \) and \( \beta \) phases are 7.377 cm3 and 7.317 cm3, respectively. Assume that the difference in molar volumes of \( \alpha \) and \( \beta \) is independent of pressure. The pressure (in atm) required for \( \alpha \) to \( \beta \) transformation to occur at 723 K is \(\underline{\hspace{2cm}}\) (round off to nearest integer).

The two-dimensional velocity field \( \mathbf{V} \) of a flow in a Cartesian coordinate system is given in dimensionless form by \( \mathbf{V} = (x^2 - axy) \hat{i} + \left( bxy - \frac{y^2}{2} \right) \hat{j} \). Here, \( \hat{i} \) and \( \hat{j} \) are the unit vectors along the \( x \) and \( y \) directions respectively, \( a \) and \( b \) are independent of \( x \), \( y \) and time. If the flow is incompressible, then the value of \( (a - b) \), up to one decimal place, is \(\underline{\hspace{1cm}}\).