question_answer2) Two copper spheres having same radii, one solid and other hollow, are charged to the same potential. Which of the following statements is correct?
A)
Hollow sphere will hold more charge
doneclear
B)
Solid sphere will hold more charge
doneclear
C)
Solid sphere will have uniform volume charge density
question_answer3) Two pendula oscillate with a constant phase difference of \[{{45}^{o}}\] and same amplitude. If the maximum velocity of one of them is v and that of other is \['v+x',\] then the value of Y will be
question_answer4) An observer standing near the sea-coast counts 48 waves per min. If the wavelength of the wave is \[10\text{ }m,\] the velocity of the waves will be
question_answer12) In a transformer the number of primary turns is four times that of the secondary turns. Its primary is connected to an AC source of voltage V. Then,
A)
Current through its secondary is about four times that of the current through its primary
doneclear
B)
Voltage across its secondary is about four times that of the voltage across its primary
doneclear
C)
Voltage across its secondary is about two times that of the voltage across its primary
doneclear
D)
Voltage across its secondary is about times that of the voltage across its primary
question_answer13) The path of a charge particle after it enters a region of a uniform electrostatic field with velocity perpendicular to the field will be
question_answer15) A ball is dropped from the top of \[80\text{ }m\]high tower. If after 2 s of fall the gravity \[(g=10\,m/{{s}^{2}})\] disappears, then time taken to reach the ground since the gravity disappeared is
question_answer16) Which of the following is correct statement about the magnitude of the acceleration 'a' of the particle executing simple harmonic motion?
question_answer19) In the fringe pattern of a Young's double slit experiment the ratio of intensities of maxima and minima is\[25:9\]. Then, the ratio of the amplitudes of interfering waves is
question_answer21) Radius of Earth is \[6400\text{ }km\]and that of Mars is \[3200\text{ }km\]. Mass of Mars is \[0.1\] that of Earth's mass. Then, the acceleration due to gravity on Mars is nearly
question_answer23) Smallest division on the main scale of given vernier calipers is \[0.5\text{ }mm\]. Vernier scale has 25 divisions and these coincide with 24 main scale divisions. The least count of vernier calipers is
question_answer32) A person is standing on a weighing-scale and observes that the reading is\[60\text{ }kg\]. He then suddenly jumps up and observes that reading goes to\[70\text{ }kg\]. Then his maximum upward acceleration is
question_answer33) A solid sphere is rolling down an inclined plane. Then, the ratio of its translational kinetic energy to its rotational kinetic energy is
question_answer34) A block of mass 3 kg starts from rest and slides down a curved path in the shape of a quarter-circle of radius \[2\text{ }m\]and reaches the bottom of path with a speed \[1\text{ }m/s\]. If ?g' is \[10\text{ }m/{{s}^{2}},\] the amount of work done against friction is
question_answer36) Consider a bi-convex lens and a plano-convex lens, with radii of curvature of all the curved surfaces being same. If 'f is the focal length of bi-convex lens then, the focal length of the plano-convex lens is
question_answer37) A body is travelling towards East with a speed of \[9\text{ }m/s\]and with an acceleration of \[2\text{ }m/{{s}^{2}}\]acting along West on it. The displacement of the body during the 5th second of its motion is
question_answer39) A bullet fired from a rifle loses \[20%\]of its speed while passing through a wooden plank. Then, minimum number of wooden planks required to completely stop the bullet is
question_answer41) A particle is undergoing uniform circular motion with angular momentum L. While moving on the same path if its kinetic energy becomes four times, then its angular momentum will be
question_answer42) A \[1m\] long solenoid containing 1000 turns produces a flux density of \[3.14\times {{10}^{-3}}\text{ }T\]. The current in the solenoid will be
question_answer45) A person carrying a whistle emitting continuously a note of \[272\text{ }Hz\]is running towards a reflecting surface with a speed of\[18\text{ }km/h\]. If the speed of sound is \[345\text{ }m/s,\]the number of beats heard by him are
question_answer46) Consider the two cells having emf \[{{E}_{1}}\] and \[{{E}_{2}}\] \[({{E}_{1}}>{{E}_{2}})\] connected as shown in the figure. A potentiometer is used to measure potential difference between P and Q and the balancing length of the potentiometer wire is\[0.8m\]. Same potentiometer is then used to measure potential difference between P and R and the balancing length is \[0.2\text{ }m\]. Then, the ratio \[{{E}_{1}}/{{E}_{2}}\] is
question_answer48) Red, blue, green and violet colour lights are one by one made incident on a photocathode. It is observed that only one color light produces photo-electrons.
question_answer50) Consider a region of uniform magnetic field directed along positive X-axis. Now a positive test charge Q, located at origin O \[(0,0)\] inside the field, is released from rest position. The particle will
question_answer51) A charge particle having charge \[1\times {{10}^{-19}}\,C\] revolves in an orbit of radius 1 A such that the frequency of revolution is\[1016\text{ }Hz\]. The resulting magnetic moment in SI units will be
question_answer55) Consider an electric dipole placed in a region of non-uniform electric field. Choose the correct statement out of the following options:
A)
The dipole will experience only a force
doneclear
B)
The dipole will experience only a torque
doneclear
C)
The dipole will experience both the force and torque
doneclear
D)
The dipole will neither experience a force nor a torque
question_answer56) A block of mass 'm' is placed on an inclined plane having coefficient of friction 'm?. The plane is making an angle \[\theta \] with the horizontal. The minimum value of upward force acting along the inclined plane that can just move the block up is
question_answer57) A ball is projected up at an angle 9 with horizontal from the top of a tower with speed V. It hits the ground at point A after time \[{{t}_{A}}\] with speed \[{{v}_{A}}\]. Now, this ball is projected at ' same angle and speed from the base of the tower (located at point P) and it hits ground at point B after time \[{{t}_{B}}\] with speed \[{{v}_{B}}\]. Then
A)
\[PA=PB\]
doneclear
B)
\[{{t}_{A}}<{{t}_{B}}\]
doneclear
C)
\[{{v}_{A}}<{{v}_{B}}\]
doneclear
D)
Ball A hits the ground at an angle \[(-\theta )\] with horizontal
question_answer59) Un-polarised light is travelling from a medium of refractive index 2 to a medium of refractive index 3. The angle of incidence is\[{{60}^{o}}\]. Then
A)
Reflected light will be partially polarized
doneclear
B)
Reflected light will be plane polarised in a plane perpendicular to plane of incidence
doneclear
C)
Refracted light will be plane polarised in a plane perpendicular to plane of incidence
doneclear
D)
Refracted light will be plane polarised in a plane parallel to plane of incidence
question_answer61) If a homogeneous colloid placed in dark is observed in the direction of light, it appears clear and if it is observed from a direction at right angles to the direction of light beam, it appears perfectly dark. This is known as
question_answer64) For a reaction, \[C(s)+C{{O}_{2}}(g)\xrightarrow{{}}2CO(g);\]the partial pressure of \[C{{O}_{2}}\]and CO are 4 and 8 atm, respectively. \[{{K}_{p}}\]for the reaction is
question_answer65) HA is a weak acid. At\[\text{25}{{\,}^{\text{o}}}\text{C,}\]the molar conductivity of 0.02 M HA is \[150\,{{\Omega }^{-1}}c{{m}^{2}}mo{{l}^{-1}}.\]If its\[\text{ }\!\!\Lambda\!\!\text{ }_{\text{m}}^{\text{o}}\] is \[300\,{{\Omega }^{-1}}\,c{{m}^{2}}mo{{l}^{-1}},\]then equilibrium constant of HA dissociation is
question_answer69) In an acidified aqueous solution of\[\text{M}{{\text{n}}^{\text{2+}}}\text{,N}{{\text{i}}^{\text{2+}}}\text{,C}{{\text{u}}^{\text{2+}}}\]and \[\text{H}{{\text{g}}^{\text{2+}}}\,\text{ions,}\,{{\text{H}}_{\text{2}}}\text{S}\]gas was passed. Precipitates are
question_answer80) For a reaction \[\text{2A}\xrightarrow{\text{3B}}\text{3B;}\]if the rate of formation of B is\[x\,\text{mol/L,}\]the rate of consumption of A is
question_answer83) 0.5 molal solution of a solute in benzene shows a depression in freezing point equal to 2 K. Molal depression constant for benzene is \[\text{5}\,\text{K}\,\text{kg}\,\text{mo}{{\text{l}}^{-1}}.\]If the solute forms dimer in benzene, what is the % association?
question_answer86) Molar enthalpy change for melting of ice is 6 kJ/mol. Then the internal energy change (in kJ/mol) when 1 mole of water is converted into ice at 1 atm at \[0{{\,}^{o}}C\]is
question_answer89) For the reaction \[A(s)+2{{B}^{+}}(aq)\to {{A}^{2+}}(aq)+2B(s);\]the \[{{E}^{o}}\]is 1.18 V. Then the equilibrium constant for the reaction is
question_answer92) The ionisation potential of hydrogen atom is 13.6 eV. The energy required to remove an electron from \[n=2\]state of hydrogen atom is
question_answer98) If \[{{E}^{o}}_{{{M}^{+}}/M}=-1.2V,{{E}^{o}}_{{{x}_{2}}/{{x}^{-}}}=-1.1\,V\]and \[{{E}^{o}}_{{{o}_{2}}/{{H}_{2}}O}=1.23\,V,\]then on electrolysis of aqueous solution of salt MX, the products obtained are
question_answer105) The vapour pressure of pure benzene at certain temperature is 1 bar. A non-volatile, non-electrolyte solid weighing 2 g when added to 39 g of benzene (molar mass\[78\,g\,mo{{l}^{-1}}\]) yields solution of vapour pressure of 0.8 bar. The molar mass of solid substance is
question_answer108) Energy of activation of forward reaction for an endothermic process is 90 kJ. If enthalpy change for the reaction is 50 kJ then activation energy for backward reaction will be
question_answer112) When \[{{\text{(C}{{\text{H}}_{\text{3}}}\text{)}}_{\text{3}}}\text{CC}{{\text{H}}_{\text{2}}}\text{Cl}\]is heated at \[\text{300}{{\,}^{o}}\text{C,}\] it gives
question_answer113) If the density of methanol is \[0.8\,\text{kg}\,{{\text{L}}^{-1}},\] what is its volume needed for making 4 L of its 0.25 M solution?
question_answer119) One mole of an ideal gas expands isothermally and reversibly from 2 L to 20 L at 300 K. If the final pressure of the gas is 1 bar, the work done by the gas is
question_answer121) The number of values of \[\alpha \in \,[-\pi ,\pi ]\] for which \[{{\sin }^{2}}\left( \frac{\pi }{8}+\alpha \right)-{{\sin }^{2}}\left( \frac{\pi }{8}-\alpha \right)=\frac{1}{2\sqrt{2}}\], is
question_answer123) The number of values of \[\theta \,\,\in \,(-\pi ,\pi ),\] satisfying \[\sin 5\theta \,\cos 3\theta =\sin \,6\theta \,\cos 2\theta ,\] is
question_answer126) The shortest distance between the lines \[\frac{x}{-1}=\frac{y}{1}=\frac{z}{1}\] and \[\frac{x-3}{0}=\frac{y+3}{1}=\frac{z-3}{-1}\] is
question_answer130) Let P be the set of real numbers and let \[G\subseteq {{R}^{2}}\] be a relation defined by \[G=\{(a,b),\,(c,d)|\,b-a=d-c\}.\]. Then, G is
question_answer132) The sum of lengths of major and minor axes- of an ellipse whose eccentricity is \[\frac{4}{5}\] and length of latuserectum is \[14.4\], is
question_answer134) The number of integer value(s) of A: for which the expression \[{{x}^{2}}-2(4k-1)x+15{{k}^{2}}\] \[-2k-7>0\] for every real number x, is/are
question_answer135) At present, a firm manufactures 1099 items. It is estimated that the rate of change of production P with respect to additional number of workers x is given by \[\frac{dP}{dx}=100-12\sqrt{x}.\]. If the firm empower 25 more workers, then the new level of production of items is
question_answer139) Let A and B be points \[(8,\,\,10)\] and \[(18,\,20),\] respectively. If the point Q divides AB externally in the ratio \[2:3\] and M is the S mid-point of AB, then the length MQ is equal to
question_answer141) A crime is committed by one of two suspects, A and B. Initially, there is equal evidence against both of them. In further investigation at the crime scene, it is found that the guilty party had a blood type found in 20% of the population. If the suspect A does match this blood type, whereas the blood type of suspect B is unknown, then the probability that A is the guilty party, is
question_answer143) Let X be a random variable with its expectation \[E(X)=3\]and its variance \[V(X)=2\]. If V is another random variable defined by \[Y=10X,\]then the ordered pair \[(E(Y),\,V(Y))\] is equal to
question_answer144) The number of values of k for which the following system of equations has at least three solutions \[8x+16y\,\,\,+8z=25,\] \[x+y+z=k\]and \[3x+y+3z={{k}^{2}},\] is
question_answer146) Let the general term of a series be \[(2k-1)\,\,(2k)\]\[(2k+1),\,\,k=1,2,3...,n.\]If the sum of first. N terms is. \[24090,\]then n is equal to
question_answer147) In an isosceles right angled triangle ABC, a value of \[\tan \left( \frac{A}{2} \right)+\tan \left( \frac{B}{2} \right)+\tan \left( \frac{C}{2} \right)\] is
question_answer148) Suppose, 70% of all voters in a city support ,a candidate A. If 40 voters in the city are randomly selected, then the expected number of voters that will support candidate A in this group, is
question_answer155) If a tangent to the hyperbola \[4{{x}^{2}}-9{{y}^{2}}=1\] cuts the ellipse \[4\text{ }{{x}^{2}}+9{{y}^{2}}=1\] in points L and R, then the locus of the mid-point of segment LR is
question_answer156) Let an odd number of terms n of an AP be such that the sum and product of its first and last terms are 10 and 0, respectively. If the common difference is \[\frac{1}{10}\], then the number of terms n is
question_answer158) Let \[G=\{(b,b),\,(b,c),\,(c,c),\,(c,d)\}\] and \[H=\{(b,a),\,(c,b),\,(d,c)\}\] Then, the number of elements in the set \[(G\cup H)\oplus {{(G\cup H)}^{-1}}\] where \[\oplus \] denotes the symmetric difference, is
question_answer159) Let the nth term of a sequence be \[{{t}_{n}}=\frac{1}{2}\{{{(1+\sqrt{3})}^{n}}+{{(1-\sqrt{3})}^{n}}\},\]\[n=3,4,5,.....\]Then, form \[=100\] which of the following is true?
A)
\[\frac{1}{4}{{t}_{m}}\] is the arithmetic mean of \[{{t}_{m-1}}\] and \[{{t}_{m-2}}\]
doneclear
B)
\[\frac{1}{4}{{t}_{m-1}}\] is the arithmetic mean of \[{{t}_{m}}\] and \[{{t}_{m-2}}\]
doneclear
C)
\[\frac{1}{4}{{t}_{m}}\] is the geometric mean of \[{{t}_{m-1}}\] and \[{{t}_{m-2}}\]
doneclear
D)
\[\frac{1}{4}{{t}_{m-1}}\] is the geometric mean of \[{{t}_{m}}\] and \[{{t}_{m-2}}\]
question_answer163) A bag contains one marble which is either green or blue, with equal probability. A green marble is put in the bag (so there are 2 marbles now) and then a marble is picked at random from the bag. If the marble taken out is green, then the probability that the remaining marble is also green, is
question_answer164) If the image of the point \[(1,\,-2,3)\] in the plane \[2x+3y-z=7\]is the point \[(\alpha ,\beta ,\gamma )\] then \[\alpha +\beta +\gamma \] is equal to
question_answer167) An equation of the plane, parallel to the plane passing through the points \[(1,1,1),\,\,(2,3,5)\] and \[(-1,0,2)\] and at a distance 3 from it, is
question_answer169) If getting a number greater than 4 is a success in a throw of a fair die, then the probability of at least 2 successes in six throws of a fair die is
question_answer171) If \[{{z}_{1}}=\cos \alpha +i\,\sin \alpha \]since and \[{{z}_{2}}=\cos \beta +i\,\sin \beta ,\] then \[\frac{({{z}_{1}}-{{z}_{2}})\,({{z}_{1}}{{z}_{2}}+1)}{({{z}_{1}}+{{z}_{2}})({{z}_{1}}{{z}_{2}}-1)}\]is equal to
question_answer174) Out of 64 students in a class, the number of students taking Mathematics is 55 and the number of students taking both Mathematics and Physics is 10. If all the students take either Mathematics or Physics or both, then the number of students taking only Physics is
question_answer178) Length of the segment of the normal at the point \[(1,1)\] to the curve given by \[{{y}^{2}}(2-x)={{x}^{3}}\] between X-axis and the point is
question_answer179) If the direction ratios of a line are \[(\lambda +1,\,1-\lambda ,2)\]and the line makes an angle 60° with the Y-axis, then a value of \[\lambda \] is