question_answer2) In a vernier calipers, one main scale division is x cm and n divisions of the vernier scale coincide with \[(n-1)\] divisions of the main scale. The least count (in cm) of the calipers is
question_answer3) If \[\overset{\hat{\ }}{\mathop{\text{i}}}\,,\]\[\overset{\hat{\ }}{\mathop{\text{j}}}\,\] and \[\overset{\hat{\ }}{\mathop{k}}\,\]represent unit vectors along the x, y and z-axes respectively, then the angle 9 between the vectors i + j + k and i + j is equal to
question_answer4) A particle goes from point A to point B, if moving in a semicircle of radius 1.0 m, in 1.0 s, as shown in the figure. The magnitude of the average velocity of the particle is
question_answer5) A body starting from rest, accelerates at a constant rate a\[\text{m}{{\text{s}}^{-2}}\]for some time after which it decelerates at a constant rate b \[\text{m}{{\text{s}}^{\text{-2}}}\]to come to rest finally. If the total time elapsed is t sec, the maximum velocity attained by the body is given by
question_answer6) A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected at an angle of \[0{}^\circ \] with the vertical with the same initial speed. At highest points of their journey, the ratio of their potential energies will be
question_answer7) A 10 kg stone is suspended with a rope of breaking strength 30 kg-wt. The minimum time in which the stone can be raised through a height 10 m starting from rest is \[\left( \text{Taking g}=\text{ 1}0\text{ Nk}{{\text{g}}^{-1}} \right)\]
question_answer8) Two bodies A and B of masses 10 kg and 15 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. If T represents the tension in the string when a horizontal force F = 500 N is applied to A (as shown in figure 1) and T be the tension when it is applied to B (figure 2), then which of the following is true?
question_answer10) Two springs A and B are identical but A is harder than B \[B({{k}_{A}}>{{k}_{g}}).\] Let \[{{W}_{A}}\]and \[{{W}_{B}}\] represent the work done when the springs are stretched through the same distance and \[W{{}_{A}}\] and \[W{{}_{B}}\]are the work done when these are stretched by equal forces, then which of the following is true?
A)
\[{{\text{w}}_{\text{A}}}>{{\text{W}}_{\text{B}}}\text{ and W}{{\text{ }\!\!\!\!\text{ }}_{A}}=\text{W}{{\text{ }\!\!\!\!\text{ }}_{B}}\]
doneclear
B)
\[{{\text{w}}_{\text{A}}}>{{\text{W}}_{\text{B}}}\text{ and W}{{\text{ }\!\!\!\!\text{ }}_{A}}\text{W}{{\text{ }\!\!\!\!\text{ }}_{B}}\]
doneclear
C)
\[{{\text{w}}_{\text{A}}}>{{\text{W}}_{\text{B}}}\text{ and W}{{\text{ }\!\!\!\!\text{ }}_{A}}\text{W}{{\text{ }\!\!\!\!\text{ }}_{B}}\]
doneclear
D)
\[{{\text{w}}_{\text{A}}}\text{}{{\text{W}}_{\text{B}}}\text{ and W}{{\text{ }\!\!\!\!\text{ }}_{A}}\text{W}{{\text{ }\!\!\!\!\text{ }}_{B}}\]
question_answer12) In the rectangular lamina shown in the figure, \[AB=\frac{BC}{2}.\] The moment of inertia of the lamina is minimum along the axis passing through
question_answer14) Read the following statements \[{{\text{S}}_{1}}\]: An object shall weigh more at pole than at equator when weighed by using a physical balance. \[{{\text{S}}_{2}}\] : It shall weigh the same at pole and equator when weighed by using a physical balance. \[{{\text{S}}_{3}}\]: It shall weigh the same at pole and equator when weighed by using a spring balance. \[{{\text{S}}_{4}}\]: It shall weigh more at the pole than at equator when weighed using a spring balance. Which of the above statements is/are correct?
question_answer15) Two small and heavy spheres, each of mass M, are placed a distance r apart on a horizontal surface. The gravitational potential at the mid-point on the line joining the centre of the spheres is
question_answer16) The temperature coefficient of resistance of the material of a wire is \[0.001/{}^\circ C\]. Its resistance at 300 K is 1\[\Omega \]. At what temperature will the resistance of the wire be \[2\,\Omega \]?
question_answer17) A wire of length L and cross-sectional area A is made of a material of Youngs modulus Y. The work done in stretching the wire by an amount x is given by
question_answer18) When water flows at a rate Q through a tube of radius r placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow is halved, the pressure difference will be
question_answer19) A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of water in the capillary tube is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is
question_answer20) An ideal monoatomic gas is taken thorough the thermodynamic states A \[\to \] B \[\to \] C \[\to \] D via the paths shown in the figure. If \[{{U}_{A}},{{U}_{B}},{{U}_{c}}\] and \[{{\text{U}}_{\text{p}}}\]represent the internal energy of the gas in states A, B, C and D respectively, then which of the following is not true?
question_answer21) A box (thermally insulated) has two chambers separated by a membrane. One of volume V contains an ideal gas at temperature T. The other of volume \[\left( \frac{1}{2}V \right)\]is evacuated. If the membrane breaks down, the gas temperature will be
question_answer23) The van der Waals equation of state for real gases is given as \[\left( p+\frac{a}{{{V}^{2}}} \right)\] (V-b) = \[n\]RT. Which of the following terms has dimensions different from that of energy?
question_answer24) The transverse displacement of a string fixed at both ends is given by \[\text{y}=0.0\text{6 sin}\left( \frac{2\pi x}{3} \right)\text{cos }\left( \text{12}0\text{ }\pi \text{t} \right)\text{y}\]and x are in metres and r in second. The wavelength and frequency of the two superposing waves are
question_answer25) Two bodies A and B of equal masses are suspended from two separate springs of force constants fe, and k respectively. If the two bodies oscillate such that their maximum velocities are equal, the ratio of the amplitudes of oscillation of A and B will be
question_answer26) The adjacent diagram shows a charge + Q held on an insulating support S and enclosed by a hollow spherical conductor. O represents the centre of the spherical conductor and P is a point such that OP = x and SP = r. The electric field at point P will be
question_answer27) An electron is released from the bottom plate A as shown in the figure \[\left( \text{E}=\text{1}{{0}^{\text{4}}}\text{ N}{{\text{C}}^{-\text{1}}} \right).\] The velocity of the electron when it reaches plate B will be nearly equal to
question_answer28) Consider a parallel plate capacitor with plates 20 cm by 20 cm and separated by 2 mm. The dielectric constant of the material between the plates is 5. The plates are connected to a voltage sources of 500 V. The energy density of the field between the plates will be close to
question_answer29) A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved further apart by means of insulating handles, then which of the following is not correct?
A)
The capacitance decreases
doneclear
B)
The charge on the capacitor increases
doneclear
C)
The voltage across the plates increases
doneclear
D)
The electrostatic energy stored in the capacitor increases
question_answer31) An electron is moving on a circle of radius 0.5 A with a frequency .of \[\text{5}\times \text{1}{{0}^{\text{16}}}\] Hz in anti-clockwise direction. The equivalent loop-current is
question_answer32) The external diameter of a 314 m long copper tube is 1.2 cm and the internal diameter is 1 cm. Calculate its resistance if the specific resistance of copper is \[2.2\times {{10}^{-8}}\Omega -m.\]
question_answer33) In the meter bridge experiment shown in the figure, the balance length AC corresponding to null deflection of the galvanometer is x. What would be the balance length if the radius of the wire AB is doubled?
question_answer34) A long, straight wire is turned into a loop of radius 10 cm (see figure). If a current of 8 A is passed through the loop, then the value of the magnetic field and its direction at the centre C of the loop shall be close to
question_answer35) An electron enters into a region of uniform magnetic field of strength \[10\text{ }Wb{{m}^{-2}}\] with a speed of \[3\times {{10}^{7}}m{{s}^{-1}}.\] Which of the following is not possible?
A)
The electron may or may not experience an acceleration
doneclear
B)
The electron may experience an acceleration but can continue to move with same speed
doneclear
C)
The electron may experience an acceleration and continue to move with same velocity
doneclear
D)
The kinetic energy of the electron remains unchanged
question_answer36) A cyclotron is used to accelerate protons, deuterons, a-particles etc. If the energy attained, after acceleration, by the protons is E, the energy attained by a-particles shall be
question_answer38) Two resistances of 10\[\Omega \] and 20\[\Omega \] and an inductor of inductance 5 H are connected to a battery of 2 V through a key K as shown in the figure. At time t = 0, when the key K is closed the initial current through the battery is
question_answer39) An LCR series circuit with \[R=100\Omega \] is connected to a 200 V, 50 Hz AC source. When only the capacitance is removed, the current leads the voltage by 60°. When only the inductance is removed, the current leads the voltage by \[60{}^\circ \]. The current in the circuit is
question_answer40) The magnetic field in the plane electromagnetic field is given by \[By=2\times {{10}^{7}}sin(0.5\times {{10}^{3}}z.+1.5\times {{10}^{11}}t)T\] The expression for the electric field may be given by
question_answer41) Monochromatic light of wavelength 589 nm is incident from air on a water surface. The refractive index of water is 1.33. The wavelength of the refracted light is
question_answer43) A wave travelling in air falls on a glass plate. It is partly reflected and partly refracted. The phase difference between the reflected and refracted waves is
question_answer44) A beam of light of wavelength 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first dark fringes on either side of the central bright fringe is
question_answer45) Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible resulting intensities are
question_answer48) The binding energy of deuteron \[(_{1}^{2}H)\] is 1.15 MeV per nucleon and an alpha particle \[(_{2}^{4}H)\] has binding energy of 7.1 MeV per nucleon. Then in the reaction \[_{1}^{2}H+_{1}^{2}H\to _{2}^{4}He+Q\] the energy Q is
question_answer57) The five d-orbitals are designated as \[{{d}_{xy}},{{d}_{yz}},{{d}_{xz}},{{d}_{{{x}^{2}}-{{y}^{2}}}}\] and \[{{z}^{2}}\]. Choose the correct statement.
A)
The shapes of the first three orbitals are similar but that of the fourth and fifth orbitals are different.
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B)
The shapes of all five d-orbitals are similar
doneclear
C)
The shapes of the first four orbitals are similar but that of the fifth orbital is different
question_answer59) Arrange the following compounds in increasing order of their boiling points \[C{{H}_{3}}CHO,C{{H}_{3}}C{{H}_{2}}OH,C{{H}_{3}}OC{{H}_{3}},\]\[C{{H}_{3}}C{{H}_{2}}C{{H}_{3}}\]
question_answer69) Three elements A, B and C crystallise into a cubic solid lattice. Atoms A occupy the comers, B atoms, the cube centres and C atoms, the edge. The formula of the compound is
question_answer70) When equal volumes of \[AgN{{O}_{3}}\]and NaCI solution are mixed, the precipitation of AgCl \[({{K}_{sp}}=1.81\times {{10}^{-10}})\] will occur with
A)
\[{{10}^{-3}}M\,(A{{g}^{+}})\] and \[{{10}^{-3}}M(C{{l}^{-}})\]
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B)
\[{{10}^{-5}}M\,(A{{g}^{+}})\] and \[{{10}^{-5}}M(C{{l}^{-}})\]
doneclear
C)
\[{{10}^{-6}}M\,(A{{g}^{+}})\] and \[{{10}^{-5}}M(C{{l}^{-}})\]
doneclear
D)
\[{{10}^{-4}}M\,(A{{g}^{+}})\] and \[{{10}^{-4}}M(C{{l}^{-}})\]
question_answer71) Consider the following reactions, I. \[{{H}_{3}}CC{{l}_{3}}\xrightarrow{O{{H}^{\Theta }}}\] II. \[{{H}_{3}}CCHO\xrightarrow{{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}O{{H}^{\Theta }}}\] III. \[{{H}_{3}}CC{{O}_{2}}{{C}_{2}}{{H}_{5}}\xrightarrow{O{{H}^{\Theta }}}\] Carboxylic acid is the final product only in the reaction (s)
question_answer76) Entropy changes for the process,\[{{H}_{2}}O(l)\xrightarrow{{}}{{H}_{2}}O(s)\]at normal pressure and 274 K are given below \[\Delta {{S}_{system}}=-22.13\,\Delta {{S}_{surr}}=+22.05\] The process is non-spontaneous because. (surr stands for surrounding and u stands for universe)
question_answer83) The order of reactivity of the alkenes, (I) \[{{(C{{H}_{3}})}_{2}}C=C{{H}_{2}}\], (II) \[C{{H}_{3}}CH=C{{H}_{2}}\], (III) \[C{{H}_{2}}=C{{H}_{2}}\]when subjected to acid catalyzed hydration is
question_answer85) \[{{K}_{p}}\] and \[K{{}_{p}}\] are the equilibrium constants of the two reactions, given below \[\frac{1}{2}{{N}_{2}}(g)+\frac{3}{2}{{H}_{2}}(g)N{{H}_{3}}(g)\] Therefore, \[{{K}_{p}}\] and \[K{{}_{p}}\] are related by
question_answer86) Critical temperature of \[{{H}_{2}}O,\,N{{H}_{3}}C{{O}_{2}}\] and \[{{O}_{2}}\] are 647 K, 405.6 K, 304.10 K and 154.2 K respectively. If the cooling starts from 500 K to their critical temperature, the gas that liquefies first is
question_answer87) Rate of the given reaction, (1) \[A+B\xrightarrow{{{r}_{1}}=0.05}X\] (2) \[X+B\xrightarrow{{{r}_{2}}=0.89}Y\] (3) \[Y+A\xrightarrow{{{r}_{3}}=0.001}AY\] (4) \[AY+B\xrightarrow{{{r}_{4}}=0.10}AYB\]will be determined by
A)
Step 1 : because the reaction starts with the formation of X
question_answer88) The critical temperature of \[{{O}_{2}},{{N}_{2}},{{H}_{2}}\] and \[C{{O}_{2}}\] are 154.3 K, 126 K, 33.2 K and 304 K. The extent of adsorption on tungsten may be highest in case of
question_answer90) The standard reduction potentials for \[C{{u}^{2+}}/Cu\] and \[C{{u}^{2+}}/C{{u}^{+}}\] are 0.337 and 0.153V respectively. The standard electrode potential of \[C{{u}^{+}}/Cu\] half-cell is
question_answer91) A gas X at 1 atm is bubbled through a solution containing a mixture of 1 M \[{{Y}^{-}}\] and 1 M \[{{Z}^{-}}\]at\[{{25}^{o}}C\]. If the reduction potential order is Z > V > X, then
question_answer126) An institution where valuable plant material-likely to become irretrievably lost in the wild or in cultivation is preserved viable condition is known as
question_answer197) The law of limiting factors was proposed with particular reference to photosynthesis. Identify the scientist who proposed this law?