question_answer3) Two identical p-n junctions are connected in series in three different ways as shown below to a battery. The potential drop across the p-n junctions are equal in:
question_answer7) Radar waves are sent towards a moving aeroplane and the reflected waves are received. When the aeroplane is moving towards the radar, the wavelength of the wave:
question_answer10) The antenna current of an AM transmitter is 8 A when only the carrier is sent, but it increases to 8.93 A when the carrier is modulated by a single sine wave. Find the percentage modulation.
question_answer11) Two point like charges Q1 and Q2 of whose strengths are equal in absolute value are placed at a certain distance from each other. Assuming the field strength to be positive in the positive direction of x-axis, the signs of the charges \[{{Q}_{1}}\] and \[{{Q}_{2}}\] for the graphs (field strength versus distance) shown in Fig. 1, 2, 3 and 4 are :
A)
\[{{Q}_{1}}\] positive, \[{{Q}_{2}}\] negative; both positive; \[{{Q}_{1}}\] negative, \[{{Q}_{2}}\] positive; both negative
doneclear
B)
\[{{Q}_{1}}\] negative \[{{Q}_{2}}\] positive; \[{{Q}_{1}}\] positive, \[{{Q}_{2}}\] negative; both positive; both negative
doneclear
C)
\[{{Q}_{1}}\] positive, \[{{Q}_{2}}\] negative; both negative; \[{{Q}_{1}}\] negative, \[{{Q}_{2}}\] positive; both positive
doneclear
D)
both positive; \[{{Q}_{1}}\] positive, \[{{Q}_{2}}\] negative; \[{{Q}_{1}}\] negative, \[{{Q}_{2}}\] positive; both negative
question_answer12) ABCD is a rectangle. At comers B, C and D of the rectangle are placed charges \[+10\,\times \,{{10}^{-10}}\,C,-20\,\times \,{{10}^{-12}}\,and\,10\,\times \,{{10}^{-12}}C,\]respectively. Calculate the potential at the fourth comer. (The side \[AB=4\text{ }cm\] and \[BC=3\text{ }cm\])
question_answer13) A parallel plate capacitor of capacitance 100 pF is to be constructed by using paper sheets of 1 mm thickness as dielectric. If the dielectric constant of paper is 4, the number of circular metal foils of diameter 2 cm each required for the purpose is:
question_answer14) The electric field intensity \[\overrightarrow{E}\], due to an electric dipole of moment \[\overrightarrow{P}\], at a point on the equatorial line is:
A)
parallel to the axis of the dipole and opposite to the direction of the dipole moment \[\overrightarrow{P}\]
doneclear
B)
perpendicular to the axis of the dipole and is directed away from it
doneclear
C)
parallel to the dipole moment
doneclear
D)
perpendicular to the axis of the dipole and is directed towards it
question_answer15) Twelve wires of each of resistance 60 are connected to form a cube as shown in the figure. The current enters at a comer A and leaves at the diagonally opposite corner G. The joint resistance across the comers A and G are:
question_answer16) A conductor and a semiconductor are connected in parallel as shown in the figure. At a certain voltage both ammeters register the same current. If the voltage of the DC source is increased then the:
A)
ammeter connected to the semiconductor will register higher current than the ammeter connected to the conductor
doneclear
B)
ammeter connected to the conductor will register higher current than the ammeter connected to the semiconductor
doneclear
C)
ammeters connected to both semiconductor and conductor will register the same current
doneclear
D)
ammeters connected to both semiconductor and conductor will register no change in the current
question_answer17) A uniform copper wire of length 1 m and cross-sectional area 8 x 10-7m2 carries a current of 1 A. Assuming that there are \[8\times {{10}^{28}}\]free electron/ m3 in copper, how long will an electron take to drift from one end of the wire to the other?
question_answer18) The temperature coefficient of resistance of a wire is 0.00125 / K. At 300 K, its resistance is 1\[\Omega \]. The resistance of the wire will be 2 0 at:
question_answer19) A rectangular coil ASCD which is rotated at a constant angular velocity about an horizontal as shown in the figure. The axis of rotation of the coil as well as the magnetic field B are horizontal. Maximum current will flow in the circuit when the plane of the coil is:
question_answer20) If the total emf in a thermocouple is a parabolic function expressed as \[E=at+\frac{1}{2}b{{t}^{2}},\]which of the following relation does not hold good?
A)
neutral temperature \[{{t}_{n}}=-\frac{a}{b}\]
doneclear
B)
temperature of inversion, \[{{t}_{i}}=\frac{-2a}{b}\]
question_answer21) The proton of energy \[1MeV\] describes a circular path in plane at right angles to a uniform magnetic field of \[6.28\times {{10}^{-4}}T\]. The mass of the proton is \[1.7\times {{10}^{-27}}kg\]. The cyclotron frequency of the proton is very nearly equal to:
question_answer22) The magnetic field at the centre of a loop of a circular wire of radius r carrying current I may be taken as B0. If a panicle of charge q moving with speed v passes the centre of a semicircular wire, as shown in figure, along the axis of the wire, the force on it due to the current is:
question_answer23) There are two solenoids of same length and inductance L but their diameters differ to the extent that one can just fit into the other. They are connected in three different ways in series. (1) They are connected in series but separated by large distance, (2) they are connected in series with one inside the other and senses of the turns coinciding, (3) both are connected in series with one inside the other with senses of the turns opposite as depicted in figures 1, 2 and 3, respectively. The total inductance of the solenoids in each of the case 1, 2 and 3 are respectively:
question_answer24) From figure shown below a series L-C-R circuit connected to a variable frequency\[200\text{ }V\]source. \[L=5H,\]\[\text{C=80 }\!\!\mu\!\!\text{ F}\]and \[\text{R = 40 }\Omega \]. Then the source frequency which drive the circuit at resonance is:
question_answer25) If the coefficient of mutual induction of the primary and secondary coils of an induction coil is\[\text{5 H}\]and a current of \[10\text{ A}\] is cut-off in \[5\times {{10}^{-4}}s\], the emf inducted (in volt) in the secondary coil is:
question_answer26) A voltage of peak value 283 V and varying frequency is applied to a series L-C-R combination in which \[R=3\,\Omega \], \[\text{L = 25 mH}\]and \[\text{C = 400 }\!\!\mu\!\!\text{ F}\]. The frequency (in Hz) of the source at which maximum power is dissipated in the above, is:
question_answer27) Pour independent waves are represented by equations: (1) \[{{X}_{1}}={{a}_{1}}\,\sin \,\omega t\] (2) \[{{X}_{2}}={{a}_{1}}\,\sin \,2\omega t\] (3) \[{{X}_{3}}={{a}_{1}}\,\sin \,{{\omega }_{1}}t\] (4) \[{{X}_{4}}={{a}_{1}}\,\sin \,\left( \omega t+\delta \right)\] Interference is possible between waves represented by equations:
question_answer28) Following diffraction pattern was obtained using a diffraction grating using two different wavelengths \[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\]. With the help of the figure identify which is the longer wavelength and their ratios.
A)
\[{{\lambda }_{2}}\]is longer than \[{{\lambda }_{1}}\]and the ratio of the longer to the shorter wavelength is 1.5
doneclear
B)
\[{{\lambda }_{1}}\] is longer than \[{{\lambda }_{2}}\] and the ratio of the longer to the shorter wavelength is 1.5
doneclear
C)
\[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\] are equal and their ratio is 1.0
doneclear
D)
\[{{\lambda }_{2}}\] is longer than \[{{\lambda }_{1}}\] and the ratio of the longer to the shorter wavelength is 2.5
question_answer29) In Youngs double slit experiment, the interference pattern is found to have an intensity ratio between bright and dark fringes is 9. This implies that:
A)
the intensities at the screen due to two slits are 5 units and 4 units respectively
doneclear
B)
the intensities at the screen due to the two slits are 4 units and 1 units, respectively
question_answer37) Two electrons are moving in opposite direction with speeds 0.8 c and 0.4 c, where c is the speed of light in vacuum. Then the relative speed is about:
question_answer38) A photo-sensitive material would emit electrons, if excited by photons beyond a threshold. To overcome the threshold, one would increase the:
question_answer46) Given: \[2C+2{{O}_{2}}(g)\xrightarrow{{}}2C{{O}_{2}}(g);\] \[\Delta H=-787kJ\] \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l);\] \[\Delta H=-286kJ\] \[{{C}_{2}}{{H}_{2}}(g)+2\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}2C{{O}_{2}}(g)+{{H}_{2}}O(l);\] \[\Delta H=-1310kJ\] The heat of formation of acetylene is :
question_answer47) Given the equilibrium system : \[N{{H}_{4}}Cl(s)\xrightarrow{{}}NH_{4}^{+}(aq)+C{{l}^{-}}(aq)\] \[(\Delta H=+3.5kcal/mol.)\] What change will shift the equilibrium to the right?
A)
Decreasing the temperature
doneclear
B)
Increasing the temperature
doneclear
C)
Dissolving \[NaCl\] crystals in the equilibrium mixture
doneclear
D)
Dissolving \[N{{H}_{4}}N{{O}_{3}}\] crystals in the equilibrium mixture
question_answer49) Equivalent amounts of \[{{H}_{2}}\] and \[{{I}_{2}}\] are heated in a closed vessel till equilibrium is obtained. If 80% of the hydrogen can be converted to \[HI\], the \[{{k}_{c}}\] at this temperature is:
question_answer53) If the molar conductance values of \[C{{a}^{2+}}\] and \[C{{l}^{-}}\] at infinite dilution are respectively \[118.88\times {{10}^{-4}}{{m}^{2}}mho\,mo{{l}^{-1}}\] and \[77.33\times {{10}^{-4}}{{m}^{2}}m\hom o{{l}^{-1}}\] then that of \[CaC{{l}_{2}}\] is (in \[{{m}^{2}}\,mho\,mo{{l}^{-1}}\]):
question_answer54) The standard reduction potentials at 298 K for the following half reactions are given against each: \[Z{{n}^{2+}}(aq)+2{{e}^{-}}\to Zn(s)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{E}^{o}}=-0.762V\] \[C{{r}^{3+}}(aq)+3{{e}^{-}}\to Cr(s)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{E}^{o}}=-0.740V\] \[2{{H}^{+}}(aq)+2{{e}^{-}}\to {{H}_{2}}(s)\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{E}^{o}}=-0.00V\] \[F{{e}^{3+}}(aq)+3{{e}^{-}}\to F{{e}^{2+}}(aq)\,\,\,\,\,\,\,\,\,\,{{E}^{o}}=-0.762V\] The strongest reducing agent is:
question_answer59) Give the IUPAC name for \[{{H}_{3}}C-C{{H}_{2}}-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-{{H}_{2}}C-C{{H}_{2}}-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-OC{{H}_{3}}\]
question_answer60) In which of the below reaction do we find \[\alpha \], \[\beta \]-unsaturated carbonyl compounds undergoing a ring closure reaction with conjugated dienes?
question_answer73) A nuclear reaction of \[_{92}^{235}U\] with a neutron produces \[_{36}^{90}Kr\] and two neutrons. Other element produced in this reaction is:
question_answer81) If the normal to the curve \[y=f(x)\] at (3, 4) makes an angle \[\frac{3\pi }{4}\] with the positive x-axis, then \[f(3)\] is equal to :
question_answer86) The area of the region bounded by the straight lines \[x=0\]and \[x=2,\] and the curves \[y={{2}^{x}}\] and \[y=2x-{{x}^{2}}\] is equal to :
question_answer89) If \[x\sin \left( \frac{y}{x} \right)dy=\left[ y\,\sin \left( \frac{y}{x} \right)-x \right]dx\] and \[y(1)=\frac{\pi }{2},\]then the value of \[\cos \left( \frac{y}{x} \right)\] is equal to:
question_answer95) Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is :
question_answer97) A box contains 9 tickets numbered 1 to 9 inclusive. If 3 tickets are drawn from the box one at a time, the probability that they are alternatively either {odd, even, odd} or {even, odd, even}is:
question_answer99) If the probability density function of a random variable X is \[f(x)=\frac{x}{2}\] in \[0\le x\le 2,\]then \[P(X>1.5\left| X>1 \right.)\] is equal to :
question_answer100) If X follows a binomial distribution with parameters n = 100 and \[p=\frac{1}{3},\] then \[P(X=r)\] is maximum when r is equal to :
question_answer102) If \[x=-\,5\] is a root of \[\left| \begin{matrix} 2x+1 & 4 & 8 \\ 2 & 2x & 2 \\ 7 & 6 & 2x \\ \end{matrix} \right|=0,\] then the other roots are :
question_answer104) If the rank of the matrix \[\left| \begin{matrix} -1 & 2 & 5 \\ 2 & -4 & a-4 \\ 1 & -2 & a+1 \\ \end{matrix} \right|\] is 1 then the value of a is :
question_answer109) If \[\overrightarrow{b}\] is a unit vector, then\[(\overrightarrow{a}\cdot \overrightarrow{b})\overrightarrow{b}+\overrightarrow{b}\times (\overrightarrow{a}\times \overrightarrow{b})\]is:
question_answer110) It \[\theta \] is the between the lines AB and AC where A, B and C are the three points with coordinates (1, 2, -1), (2, 0, 3), (3, -1, 2) respectively, then\[\sqrt{462}\]is equal to :
question_answer111) Let the pairs \[\overrightarrow{a},\,\overrightarrow{b}\] and \[\overrightarrow{c},\,\overrightarrow{d}\] each determine a plane. Then the planes are parallel, if:
question_answer113) If \[\cos x+{{\cos }^{2}}x=1,\]then the value of \[{{\sin }^{12}}x+3{{\sin }^{10}}x+3{{\sin }^{8}}x+{{\sin }^{6}}x-1,\] is equal to :
question_answer118) If the normal at \[(a{{p}^{2}},\,\,2ap)\]on the parabola\[{{y}^{2}}=4ax,\]meets the parabola again at\[(a{{q}^{2}},\,\,2aq),\] then :