question_answer2) A slit of width a is illuminated with a monochromatic light of wavelength \[\lambda \] from a distant source and the diffraction pattern is observed on a screen placed at a distance D from the slit. To increase the width of the central maximum one should
question_answer3) A thin film of soap solution (n = 1.4) lies on the top of a glass plate (n = 1.5). When visible light is incident almost normal to the plate, two adjacent reflection maxima are observed at two wavelengths 400 and 630 nm. The minimum thickness of the soap solution is
question_answer5) A light whose frequency is equal to 6 x 1014 Hz is incident on a metal whose work function is \[2eV\left[ h=6.63\,\times \,{{10}^{-34}}\,Js,1eV=1.6\,\times \,{{10}^{-19}}J \right]\] The maximum energy of the electrons emitted will be
question_answer6) An electron microscope is used to probe the atomic arrangements to a resolution of 5 A. What should be the electric potential to which the electrons need to be accelerated?
question_answer9) An observer A sees an asteroid with a radioactive element moving by at a speed \[=0.3c\] and measures the radioactivity decay time to be\[{{T}_{A}}\]. Another observer B is moving with the asteroid and measures its decay time as\[{{T}_{B}}\]. Then \[{{T}_{A}}\] and \[{{T}_{B}}\] are related as
A)
\[{{T}_{B}}<\text{ }{{T}_{A}}\]
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B)
\[{{T}_{A}}={{T}_{B}}\]
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C)
\[{{T}_{B~}}>{{T}_{A}}\]
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D)
Either [A] or [C] depending on whether the asteroid is approaching or moving away from A
question_answer10) \[^{234}U\]has 92 protons and 234 nucleons total in its nucleus. It decays by emitting an alpha particle. After the decay it becomes
question_answer12) A certain radioactive material \[_{Z}{{X}^{A}}\]starts emitting \[\alpha \] and \[\beta \] panicles successively such that the end product is \[_{Z-3}{{Y}^{A-8}}.\]. The number of \[\alpha \]and \[\beta \] particles emitted are
question_answer13) In the circuit shown above, an input of 1 V is fed into the inverting input of an ideal Op-amp A. The output signal \[{{\text{V}}_{\text{out}}}\] will be
question_answer15) A \[p-n\] junction has acceptor impurity concentration of \[{{10}^{17}}\]\[c{{m}^{-3}}\]in the \[P\] side and donor impurity concentration of \[{{10}^{16}}c{{m}^{-3}}\]in the \[N\] side. What is the contact potential at the junction? (\[kT=\]thermal energy, intrinsic carrier concentration \[{{n}_{i}}1.4\times {{10}^{10}}c{{m}^{-3}}\])
question_answer16) A Zener diode has a contact potential of 1 V in the absence of biasing. It undergoes Zener breakdown for an electric field of \[{{10}^{6}}\,\,V/m\] at the depletion region of \[p-n\] junction. If the width of the depletion region is 2.5 \[\mu \]m, what should be the reverse biased potential for the Zener breakdown to occur?
question_answer22) The energy stored in the capacitor as shown in Fig. [a] is \[\text{4}\text{.5}\times \text{1}{{\text{0}}^{\text{-6}}}\text{J}\]. If the battery is replaced by another capacitor of 900 pF as shown in Fig. [b], then the total energy of system is
question_answer23) Equal amounts of a metal are converted into cylindrical wires of different lengths L and cross-sectional area A. The wire with the maximum resistance is the one, which has
A)
length \[=\text{ }L\] and area \[=\text{ }A\]
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B)
length = \[\frac{L}{2}\] and area \[=\text{ }2A\]
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C)
length \[=\text{ }2L\] and area = \[\frac{A}{2}\]
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D)
All have the same resistance, as the amount of the metal is the same
question_answer24) If the force exerted by an electric dipole on a charge \[q\] at a distance of 1 m is \[F\], the force at a point 2 m away in the same direction will be
question_answer25) A solid sphere of radius\[{{R}_{1}}\] and volume charge density \[\rho =\frac{{{\rho }_{0}}}{r}\]is enclosed by a hollow sphere of radius \[{{R}_{2}}\]with negative surface charge density \[\alpha \], such that the total charge in the system is zero, \[{{\rho }_{0}}\]is a positive constant and \[r\] is the distance from the centre of the sphere. The ratio \[\frac{{{R}_{2}}}{{{R}_{1}}}\]is
question_answer26) A solid spherical conductor of radius R has a spherical cavity of radius \[a\left( a<R \right)\] at its centre. A charge \[+Q\] is kept at the centre. The charge at the inner surface, outer surface and at a position \[r\left( a<r<R \right)\] are respectively
question_answer27) A cylindrical capacitor has charge Q and length L. If both the charge and length of the capacitors are doubled, by keeping other parameters fixed, the energy stored in the capacitor
question_answer28) Three resistances of 4\[\Omega \] each are connected as shown in figure. If the point D divides the resistance into two equal halves, the resistance between point A and D will be
question_answer31) A meter bridge is used to determine the resistance of an unknown wire by measuring the balance point length l. If the wire is replaced by another wire of same material but with double the length and half the thickness, the balancing point is expected to be
question_answer33) A sample of \[\text{HCl}\] gas is placed in an electric field of \[3\times {{10}^{4}}\text{N}{{\text{C}}^{\text{-1}}}\]. The dipole moment of each\[\text{HCl}\]molecule is \[6\times {{10}^{-30}}\text{Cm}\]. The maximum torque that can act on a molecule is
question_answer36) Two identical incandescent light bulbs are connected as shown in the figure. When the circuit is an AC voltage source of frequency \[f\], which of the following observations will be correct?
A)
Both bulbs will glow alternatively
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B)
Both bulbs will glow with same brightness provided frequency \[f=\frac{1}{2\pi }\sqrt{1/LC}\]
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C)
Bulb \[{{b}_{1}}\]will light up initially and goes off, bulbs \[{{b}_{2}}\]will be constantly
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D)
Bulb \[{{b}_{1}}\] will blink and bulb \[{{b}_{2}}\] will be ON constantly
question_answer37) A transformer rated at 10 kW is used to connect a 5 kV transmission line to a 240 V circuit. The ratio of turns in the windings of the transformer is
question_answer38) Three solenoid coils of same dimension, same number of turns and same number of layers of winding are taken. Coil 1 with inductance \[{{L}_{1}}\] was wound using a Mn wire of resistance 11\[\Omega /m;\]Coil 3 with inductance \[{{L}_{3}}\] was wound using the similar wire but the direction of winding was reversed in each layer; Coil 3 with inductance \[{{L}_{3}}\] was wound using a superconducting wire. The self-inductance of the coils \[{{L}_{1}}\], \[{{L}_{2}}\], \[{{L}_{3}}\] are
question_answer39) Light travels with a speed of \[2\times {{10}^{8}}\,m/s\] in crown glass of refractive index 1.5. What is the speed of light in dense flint glass of refractive index 1.8?
question_answer40) A parallel beam of fast moving electrons is incident normally on a narrow slit. A screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statement is correct?
A)
Diffraction pattern is not observed on the screen in the case of electrons
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B)
The angular width of the central maximum of the diffraction pattern will increase
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C)
The angular width of the central maximum will decrease
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D)
The angular width of the central maximum will remains the same
question_answer56) The number of formula, units of calcium fluoride, \[Ca{{F}_{2}}\] present in 146.4 g of \[Ca{{F}_{2}}\] (the molar mass of \[Ca{{F}_{2}}\] is 78.08 g/mol) is
question_answer62) The standard free energy change of a reaction is \[\Delta {{G}^{o}}=-115kJ\] at 298 K. Calculate the equilibrium constant \[{{K}_{P}}\] in \[\log {{K}_{P}}\] \[(R=8.314\,\,J{{K}^{-1}}mo{{l}^{-1}}).\]
question_answer67) The molar conductivities of \[KCl,Nacl\] and \[KN{{O}_{3}}\] are 152, 128 and \[111\,\,S\,\,\,c{{m}^{2}}\,\,mo{{l}^{-1}}\] respectively. What is the molar conductivity of \[NaN{{O}_{3}}\]?
question_answer81) If \[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\] be three unit vectors such that \[\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})=\frac{1}{2}\overrightarrow{b},\]\[\overrightarrow{b}\] and \[\overrightarrow{c}\] being non-parallel. If \[{{\theta }_{1}}\] is the angle between \[\overrightarrow{a}\] and \[\overrightarrow{b}\] and \[{{\theta }_{2}}\] is the angle between \[\overrightarrow{a}\] and \[\overrightarrow{c}\], then
question_answer86) In a triangle ABC, the sides b and c are the roots of the equation \[{{x}^{2}}-61x+820=0\] and\[A={{\tan }^{-1}}\left( \frac{4}{3} \right)\] then \[{{a}^{2}}\] is equal to
question_answer87) The shortest distance between the straight lines through the points \[{{A}_{1}}=(6,\,2,\,2)\] and \[{{A}_{2}}=(-4,\,0,\,-1),\]in the directions of \[(1,\,-2,\,\,2)\] and\[(3,\,-2,-\,2)\]is
question_answer89) Let A and B are two fixed points in a plane, then locus of another point C on the same plane such that CA + CB = constant, (> AB) is
question_answer91) If \[g(x)\] is a polynomial satisfying \[g(x)g(y)=g(x)+g(y)+g(xy)-2\] for all real \[x\] and \[y\] and \[g(2)=5,\] then \[\underset{x\to 3}{\mathop{\lim }}\,g(x)\] is
question_answer94) A spherical balloon is expanding. If the radius is increasing at the rate of 2 cm/min, the rate at which the volume increases (in cubic centimetres per minute) when the radius is 5 cm, is
question_answer99) Let y be the number of people in a village at rime\[t\]. Assume that the rate of change of the population is proportional to the number of people in the village at any time and further assume that the population never increases in time. Then, the population of the village at any fixed time\[t\]is given by
A)
\[y={{e}^{kt}}+c,\] for some constant \[c\le 0\] and \[k\ge 0\]
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B)
\[y=c{{e}^{kt}},\] for some constants \[c\ge 0\] and \[k\le 0\]
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C)
\[y={{e}^{ct}}+k,\] for some constants \[c\le 0\] and \[k\ge 0\]
doneclear
D)
\[y=k{{e}^{ct}},\] for some constants \[c\ge 0\] and \[k\le 0\]
question_answer107) A manufacturer of cotter pins knows that 5% of his product is defective. He sells pins in boxes of 100 and guarantees that not more than one pin will be defective in a box. In order to find the probability that a box will fail to meet the guaranteed quality, the probability distribution one has to employ is
question_answer108) The probability that a certain kind of component will survive a given shock test is\[\frac{3}{4}.\]The probability that exactly 2 of the next 4 components tested survive is
question_answer109) Mean and standard deviation from the following observations of marks of 5 students of a tutorial group (marks out of 25) 8 12 13 15 22 are
question_answer113) If \[D=\] diag \[({{d}_{1}},{{d}_{2}},\,......\,{{d}_{n}}),\]where \[{{d}_{i}}\ne 0,\]for\[i=1,\,2,\,.....\,n,\]then \[{{D}^{-1}}\]is equal to
question_answer114) If x, y, z are different from zero and\[\Delta =\left| \begin{matrix} a & b-y & c-z \\ a-x & b & c-z \\ a-x & b-y & c \\ \end{matrix} \right|=0,\] then the value of the expression \[\frac{a}{x}+\frac{b}{y}+\frac{c}{z}\] is
question_answer117) Let \[\alpha ,\beta \] be the roots of the equation \[{{x}^{2}}-ax+b=0\] and \[{{A}_{n}}={{\alpha }^{n}}+{{\beta }^{n}}.\] Then, \[{{A}_{n+1}}-a{{A}_{n}}+b{{A}_{n-1}}\] is equal to
question_answer119) The plane through the point \[\left( -1,\,\,-1,\,\,-1 \right)\] and containing the line of intersection of the planes\[\vec{r}\cdot (\hat{i}+3\hat{j}-\hat{k})=0\]and \[\vec{r}\cdot (\hat{j}+2\hat{k})=0\] is
question_answer120) \[\vec{a}=\hat{i}-\hat{j}+\hat{k}\] and \[\vec{b}=2\hat{i}+4\hat{j}+3\hat{k}\] are one of the sides and medians respectively, of a triangle through the same vertex, then area of the triangle is