question_answer2) If c is the speed of electromagnetic waves in vacuum, its speed in a medium of dielectric constant K and relative permeability\[{{\mu }_{r}}\]is:
question_answer6) The magnification of the image when an object is placed at a distance\[x\]from the principal focus of a mirror of focal length\[f\]is:
question_answer7) In the Youngs double slit experiment, the central maxima is observed to be\[{{I}_{0}}\]. If one of the slits is covered, then the intensity at the central maxima will become:
question_answer10) The number of \[\alpha \]-particles and p-particles respectively emitted in the reaction\[_{88}{{A}^{196}}{{\to }_{78}}{{B}^{164}}\]are:
question_answer11) The counting rate observed from a radioactive source ate = 0 s was 1600 count/s and at\[t=8\]s it was 100 counts/s. The counting rate observed as counts per second at\[t=6\text{ }s,\]will be:
question_answer12) If\[{{D}_{e}},\text{ }{{D}_{b}}\]and\[{{D}_{c}}\]are the doping levels of emitter, base and collector respectively of a transistor, then:
question_answer14) A p-n junction in series with a resistance of\[5\,k\Omega \]is connected across a 50 V DC source. If the forward bias resistance of the junction is\[50\,\Omega ,\], the forward bias current is:
question_answer15) A transistor connected at common-emitter mode contains load resistance of\[5\,k\,\Omega ,\]and an input resistance of\[1\,k\,\Omega \]. If the input peak voltage is 5 mV and the current gain is 50, find the voltage gain:
question_answer19) A TV tower has a height of 100 m. What is the maximum distance up to which the TV transmission can be received\[(R=8\times {{10}^{6}}m)\]?
question_answer21) A physical quantity A is related to four observables a, b, c and d as follows: \[A=\frac{{{a}^{2}}{{b}^{3}}}{c\sqrt{d}}\] The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity A?
question_answer22) A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the 5th second to that covered in 5 s is:
question_answer24) A particle is displaced from a position\[(2\hat{i}-\hat{j}+\hat{k})\]to another position\[(3\hat{i}+2\hat{j}-2\hat{k})\] under the action of the force of\[(2\hat{i}+\hat{j}-\hat{k})\]. The work done by the force in an arbitrary unit is:
question_answer25) From the top of tower, a stone is thrown up. It reaches the ground in\[{{t}_{1}}\]second. A second stone thrown down with the same speed reaches the ground in\[{{t}_{2}}\]second. A third stone released from rest reaches the ground in\[{{t}_{3}}\]second. Then:
question_answer26) An object is projected at an angle of\[45{}^\circ \]with the horizontal. The horizontal range and maximum height reached will be in the ratio:
question_answer28) A player caught a cricket ball of mass 150 g moving at the rate of\[20\text{ }m{{s}^{-1}}\]. If the catching process be completed in 0.1 s, the force of the blow exerted by the ball on the hands of the player is:
question_answer29) A uniform metal chain is placed on a rough table such that one end of it hangs down over the edge of the table. When one-third of its length hangs over the edge, the chain starts sliding. Then, the coefficient of static friction is:
question_answer30) Two masses M and M/2 are joined together by means of light inextensible string passed over a frictionless pulley as shown in the figure. When the bigger mass is released, the small one will ascend with an acceleration of:
question_answer32) A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third second of the motion of the ball is:
question_answer34) Three identical spheres, each of mass 1 kg are kept as shown in figure below, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is:
question_answer35) The moment of inertia of a thin rod of mass M and length L, about an axis perpendicular to the rod at a distance \[\frac{L}{4}\] from one end is:
question_answer36) A body rolls down an inclined plane. If its kinetic energy of rotation is 40% of its kinetic energy of translation, then the body is:
question_answer38) Four particles each of mass M, are located at the vertices of a square with side L. The gravitational potential due to this at the centre of the square is:
question_answer39) Two identical solid copper spheres of radius R are placed in contact with each other. The gravitational attraction between them is proportional to:
question_answer41) Radius of an air bubble at the bottom of the lake is r and it becomes 2 r when the air bubble rises to the top surface of the lake. If P cm of, water be the atmospheric pressure, then the depth of the lake is:
question_answer42) A manometer connected to a closed tap reads\[4.5\times {{10}^{5}}Pa\]. When the tap is opened the reading of the manometer falls to\[4\times {{10}^{5}}Pa\]. Then the velocity of flow of water is:
question_answer43) What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body? (The densities of metal and of liquid are\[\rho \]and\[\sigma \]respectively, and the viscosity. of the liquid is\[\eta \]):
question_answer46) The volume of a metal sphere increases by 0.24% when its temperature is raised by\[40{}^\circ \] C. The coefficient of linear expansion of the metal is...\[/{}^\circ C\].
question_answer47) The temperature of equal masses of three different liquids A, B and C are\[12{}^\circ C,\text{ }19{}^\circ C\]and \[28{}^\circ C\]respectively. The temperature when A and B are mixed is\[16{}^\circ C\]and when B and C are mixed is\[23{}^\circ C\]. The temperature when A and C are mixed is:
question_answer49) A particle starts SHM from the mean position. Its amplitude is a and total energy E. At one instant its kinetic energy is\[3\frac{E}{4}\]. Its displacement at that instant is:
question_answer50) A particle executes linear simple harmonic motion with an amplitude of 2 cm. When the particle is at 1 cm from the mean position the magnitude of its velocity is equal to that of its acceleration. Then its time period in second is:
question_answer53) A set of 24 tuning forks are so arranged that each gives 6 beats/s with the previous one. If the frequency of the last tuning fork is double that of the first, frequency of the second tuning fork is:
question_answer56) Figure below shows four plates each of area A and separated from one another by a distance d. What is the capacitance between P and Q?
question_answer58) A parallel plate capacitor of capacitance\[10\mu F\]is charged to\[1\mu C\]. The charging battery is removed and then the separation between the plates is doubled. Work done during the process is:
question_answer60) For a certain thermocouple, if the temperature of the cold junction is\[0{}^\circ C,\]the neutral temperature and inversion temperatures are\[285{}^\circ C\]and\[570{}^\circ C\] respectively. If the cold junction is brought to \[10{}^\circ C,\]then the new neutral and inversion temperatures are respectively:
question_answer62) Resistors P and Q are connected in the gaps of the meter bridge. The balancing point is obtained\[\frac{1}{3}\]m from the zero end. If a\[6\,\Omega \]resistance is connected in series with P the balance point shifts to\[\frac{2}{3}\]m from the same end. P and Q are:
question_answer63) The currents ii and 13 through the resistors\[{{R}_{1}}(=10\,\Omega )\]and\[{{R}_{2}}(=30\,\Omega )\]in the circuit -diagram with\[{{E}_{1}}=3V\,,{{E}_{2}}=3V\]and\[{{E}_{3}}=2V\]are respectively:
question_answer64) An\[\alpha -\]particle with a specific charge of \[2.5\times {{10}^{7}}C\,k{{g}^{-1}}\] moves with a speed of\[2\times {{10}^{5}}\] \[m{{s}^{-1}}\]in a perpendicular magnetic field of 0.05 T. Then the radius of the circular path described by it is:
question_answer66) The magnitude of the earths magnetic field at a place is\[{{\beta }_{0}}\]and the angle of dip is\[\delta \]. A horizontal conductor of length\[l\]lying magnetic north-south moves eastwards with a velocity v. The emf induced across the conductor is:
question_answer67) A miiliammeter of range 0 - 30 mA has internal resistance of\[20\,\Omega \]. The resistance to be connected in series to convert it into a voltmeter of maximum reading 3V is:
question_answer68) A straight conductor of length I carrying a current 7, is bent in the form of a semicircle. The magnetic field (in tesla) at the centre of the semicircle is:
question_answer69) A coil having an inductance of 0.5 H carries a current which is uniformly varying from 0 to 10 A in 2 s. The emf (in volts) generated in the coil is:
question_answer70) If an alternating voltage is represented as E = 141 sin (628 t), then the rms value of the voltage and the frequency are respectively:
question_answer71) A step-down transformer is used on a 1000 V line to deliver 20 A at 120 V at the secondary coil. If the efficiency of the transformer is 80%, the current drawn from the line is:
question_answer72) For the series LCR circuit shown in the figure, what is the resonance frequency and the amplitude of the current at the resonating frequency?
question_answer73) What would be the heat released when an aqueous solution containing 0.5 mole of\[HN{{O}_{3}}\]is mixed with 0.3 mole of\[O{{H}^{-}}\](enthalpy of neutralization is\[-57.1\text{ }kJ\])?
question_answer74) \[A(g)+3B(g)4C(g)\] Initially concentration of A is equal to that of B. The equilibrium concentrations of A and C are equal.\[{{K}_{c}}\]is:
question_answer75) Two moles of\[PC{{l}_{5}}\]is heated in a closed vessel of 2L capacity. When the equilibrium is attained 40% of it has been found to be dissociated. What is the\[{{K}_{c}}\]in\[mol/d{{m}^{3}}\]?
question_answer76) Dry air is passed through a solution containing 10 g of a solute in 90 g of water and then through pure water. The loss in weight of solution is 2.5 g and that of pure solvent is 0.05 g. Calculate the molecular weight of the solute.
question_answer77) The vant Hoff factor of\[BaC{{l}_{2}}\]at 0.01 M concentration is 1.98. The percentage of dissociation of\[BaC{{l}_{2}}\]at this concentration is:
question_answer78) The standard electrode potentials of\[A{{g}^{+}}/Ag\]is\[+0.80\text{ }V\]and\[C{{u}^{+}}/Cu\]is\[+0.34\text{ }V\]. These electrodes are connected through a salt bridge and if:
A)
copper electrode acts as a cathode then\[E{}^\circ \]cell is\[+0.46\text{ }V\]
doneclear
B)
silver electrode acts as anode then\[E{}^\circ \]cell is\[-0.34\text{ }V\]
doneclear
C)
copper electrode acts as anode then\[E{}^\circ \]cell is\[+0.46V\]
doneclear
D)
silver electrode acts as a cathode then\[E{}^\circ \]cell is\[-0.34\text{ }V\]
doneclear
E)
silver electrode acts as anode and\[E{}^\circ \]cell is \[+1.14V\]
question_answer79) In alkaline medium\[Cl{{O}_{2}}\]oxidizes\[{{H}_{2}}{{O}_{2}}\]to\[{{O}_{2}}\] and itself gets reduced to\[C{{l}^{-}}\]. How many moles ofH^02 are oxidized by 1 mole of\[Cl{{O}_{2}}\]?
question_answer80) For the reaction \[2{{N}_{2}}{{O}_{5}}(g)\xrightarrow[{}]{{}}4N{{O}_{2}}(g)+{{O}_{2}}(g)\] if the concentration of\[N{{O}_{2}}\]increases by \[5.2\times {{10}^{-3}}\]M in 100 s then the rate of the reaction is:
question_answer83) Potassium stearate is obtained by the saponification of an oil or fat. It has the formula\[C{{H}_{3}}-{{(C{{H}_{2}})}_{16}}-CO{{O}^{-}}{{K}^{+}}\]. The molecule has a lyophobic end\[[C{{H}_{3}}]\]and a lyophilic end\[CO{{O}^{-}}{{K}^{+}}\]Potassium stearate is an example for:
question_answer84) (A) \[{{K}_{4}}[Fe{{(CN)}_{6}}]\] (B) \[{{K}_{3}}[Cr{{(CN)}_{6}}]\] (C) \[{{K}_{3}}[Co{{(CN)}_{6}}]\] (D) \[{{K}_{2}}[Ni{{(CN)}_{4}}]\] Select the complexes which are diamagnetic:
question_answer86) The IUPAC name of the compound is: \[HOOC-C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ COOH \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}}-C{{H}_{2}}-COOH\]
question_answer88) An alkene having the molecular formula \[{{C}_{9}}{{H}_{18}}\]on ozonolysis gives 2, 2-dimethyl propanal and 2-butanone. The alkene is:
question_answer94) When 32.25 g of ethyl chloride is subjected to dehydrohalogenation reaction the yield of the alkene formed is 50%. The mass of the product formed is: (atomic mass of chlorine is 35.5)
question_answer98) Identify the product in the following sequence 3, 4, 5-tribromoanilin\[\xrightarrow[(2)\,{{H}_{3}}P{{O}_{2}}]{(1)\,diazotization}\]?
question_answer99) Among the amines\[(A){{C}_{6}}{{H}_{5}}N{{H}_{2}}\]\[(B)C{{H}_{3}}N{{H}_{2}}\]\[(C){{(C{{H}_{3}})}_{2}}NH\]\[(D){{(C{{H}_{3}})}_{3}}N,\]the order of basicity is:
question_answer100) The number average molecular mass and mass average molecular mass of a polymer are respectively 30,000 and 40, 000. The poly dispersity index of the polymer is:
question_answer101) In biological systems, the RNA molecules direct the synthesis of specific proteins which are characteristic of each kind of organism. This process is known is:
question_answer104) \[100\text{ }g\text{ }CaC{{O}_{3}}\]is treated with 1 L of \[1N\text{ }HCl\]. What would be the weight of\[C{{O}_{2}}\]liberated after the completion of the reaction?
question_answer105) The relationship between the energy\[{{E}_{1}}\]of the radiation with a wavelength \[8000\overset{\text{o}}{\mathop{\text{A}}}\,\] and the energy\[{{E}_{2}}\]of the radiation with a wavelength \[16000\overset{\text{o}}{\mathop{\text{A}}}\,\] is:
question_answer106) If the molecule of\[HCl\]were totally polar, the expected value of dipole moment is 6.12 D (debye), but the experimental value of dipole moment was 1.03 D. Calculate the percentage ionic character:
question_answer109) To what temperature must a neon gas sample be heated to double its pressure, if the initial volume of gas at\[75{}^\circ C\]is decreased by 15.0%?
question_answer117) Potassium permanganate acts as an oxidant in alkaline and acidic media. The final products formed from \[KMn{{O}_{4}}\] in the two conditions are respectively:
question_answer118) Calculate the mass loss in the following. \[_{1}^{2}H+_{1}^{3}H\xrightarrow[{}]{{}}_{2}^{4}He+_{0}^{1}n\] [Given the masses: \[^{2}H=2.014{{;}^{3}}H=3.016;\] \[He=4.004;\text{ }n=1.008amu\]]
question_answer120) \[\Delta H\]and\[\Delta S\]for a reaction are\[+30.558\text{ }kJ\] \[mo{{l}^{-1}}\]and\[0.066\,kJ\,{{K}^{-1}}mo{{l}^{-1}}\]at 1 aim pressure. The temperature at which free energy change is equal to zero and the nature of the reaction below this temperature are:
question_answer132) The output s as a Boolean expression in the inputs\[{{x}_{1}},{{x}_{2}}\]and\[{{x}_{3}}\]for the logic circuit in the following figure is:
question_answer133) The. feasible region for the following constraints\[{{L}_{1}}\ge 0,{{L}_{2}}\ge 0,{{L}_{3}}=0,x\ge 0,y\ge 0\]in the diagram shown is:
question_answer145) ABC is a right angled isosceles triangle with\[\angle B=90{}^\circ \]. If D is a point on AB so that\[\angle CDB=15{}^\circ \]and, if\[AD=35\text{ }cm,\]then CD is equal to:
question_answer147) The shadow of a tower is found to be 60 m shorter when the suns altitude changes from \[30{}^\circ \]to\[60{}^\circ \]. The height of the tower from the ground is approximately equal to:
question_answer148) ABCD is a rectangular field. A vertical lamp post of height 12m stands at the corner A. If the angle of elevation of its top from B is\[60{}^\circ \] and from C is\[45{}^\circ \], then the area of the field is:
question_answer150) If\[A(3,5),\text{ }B(-5,-4),C(7,10)\]are the vertices of a parallelogram, taken in the order, then the co-ordinates of the fourth vertex are:
question_answer151) ABC is a triangle with vertices\[A(-1,4),\] \[B(6,-2)\]and\[C(-2,4)\]. D, E and F are the points which divide each AB, BC and CA respectively in the ratio\[3:1\]internally. Then, the centroid of me triangle DEF is:
question_answer152) If the pairs of lines\[{{x}^{2}}-2nxy-{{y}^{2}}=0\]and \[{{x}^{2}}-2mxy-{{y}^{2}}=0\]are such that one of them represents the bisectors of the angles between the other, then:
question_answer153) The angle between the pair of straight lines\[{{y}^{2}}{{\sin }^{2}}\theta -xy{{\sin }^{2}}\theta +{{x}^{2}}({{\cos }^{2}}\theta -1)=0\]is:
question_answer154) If the equation of base of an equilateral triangle is \[2x-y=1\]and the vertex is\[(-1,2),\]then the length of the side of the triangle is:
question_answer158) If the equation of the tangent to the circle \[{{x}^{2}}+{{y}^{2}}-2x+6y-6=0\]parallel to \[3x-4y+7=0\]is\[3x-4y+k=0,\]then the values of k are:
question_answer159) The locus of a point which moves so that the ratio of the length of the tangents to the circles\[{{x}^{2}}+{{y}^{2}}+4x+3=0\]and\[{{x}^{2}}+{{y}^{2}}-6x+5=0\]is\[2:3,\]is:
question_answer160) The foci of Ac ellipse\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]and the hyperbola\[\frac{{{x}^{2}}}{144}-\frac{{{y}^{2}}}{81}=\frac{1}{25}\]coincide. Then, the value of\[{{b}^{2}}\]is:
question_answer162) Suppose S and S are foci of the ellipse\[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1.\]If p is a variable point on the ellipse and if \[\Delta \] is area of the triangle PSS then the maximum value of\[\Delta \]is:
question_answer163) The equation of the hyperbola in the standard from (whit transverse axis along the\[x-\]axis) having the length of the latus rectum = 9 unit and eccentricity\[=\frac{5}{4}\]is:
question_answer164) If \[|\overrightarrow{a}|=|\overrightarrow{b}|=1\]and\[|\overrightarrow{a}+\overrightarrow{b}|=\sqrt{3},\]then the value of \[(3\overrightarrow{a}-4\overrightarrow{b}).(2\overrightarrow{a}+5\overrightarrow{b})\]is:
question_answer165) If\[|\overrightarrow{a}|=3,|\overrightarrow{b}|=4,|\overrightarrow{c}|=5\]and\[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\]are such that each is perpendicular to the sum of other two, then\[|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|\]is:
question_answer166) A unit vector in the plane of\[\hat{i}+2\hat{j}+\hat{k}\]and\[\hat{i}+\hat{j}+2\hat{k}\]hand perpendicular to\[2\hat{i}+\hat{j}+\hat{k}\]is:
question_answer167) If\[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\]are unit coplanar vectors, then\[[2\overrightarrow{a}-\overrightarrow{b},2\overrightarrow{b}-\overrightarrow{c},2\overrightarrow{c}-\overrightarrow{a}]\]is equal to
question_answer168) If\[\overrightarrow{u},\overrightarrow{v},\overrightarrow{w}\]be vectors such that\[\overrightarrow{u}+\overrightarrow{v}+\overrightarrow{w}=\overrightarrow{0},\] and\[|\overrightarrow{u}|=3,|\overrightarrow{v}|=4,|\overrightarrow{w}|=5,\]then \[\overrightarrow{u}.\overrightarrow{v}+\overrightarrow{v}.\overrightarrow{w}+\overrightarrow{w}.\overrightarrow{u}\]equal to:
question_answer169) If \[\vec{a}\] is perpendicular to\[\overrightarrow{b}\]and\[\overrightarrow{c},|\overrightarrow{a}|=2,\]\[|\overrightarrow{b}|=3|\overrightarrow{c}|=4\]and the angle between\[\overrightarrow{b}\]and\[\overrightarrow{c}\]is\[\frac{2\pi }{3},\]then\[[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}]\]is equal to:
question_answer171) If (2, 3, 5) is one end of a diameter of the sphere\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6x-12y-2z+20=0,\]then co-ordinates of the other end of the diameter are:
question_answer172) The equation of the plane through the point \[(2,-1,-3)\]and parallel to the lines\[\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}\]and\[\frac{x}{2}=\frac{y-1}{-3}=\frac{z-2}{2}\]is:
question_answer173) If a line makes angles\[\alpha ,\beta ,\gamma \]with the co-ordinate axes, then\[cos\text{ }2\alpha +cos\text{ }2\beta +cos\text{ }2\gamma \]is:
question_answer174) If for a plane, the intercepts on the co-ordinate axes are 8,4,4, then the length of the perpendicular from the origin on to the plane is:
question_answer176) If a plane meets the co-ordinate axes at A, B and C such that the centroid of the triangle is (1, 2, 4), then the equation of the plane is:
question_answer177) The position vector of the point where the line\[\overrightarrow{r}=\hat{i}-\hat{j}+\hat{k}+t(\hat{i}+\hat{j}-\hat{k})\]meets the plane \[\overrightarrow{r}.(\hat{i}+\hat{j}+\hat{k})=5\]is:
question_answer179) Two persons A and B throw a die alternately till one of them gets a 3 and wins the game, the respective probabilities of winning, if A begins, are:
question_answer181) The average monthly salary of workers in a factory is Rs. 206. If the average monthly salary of males and females are Rs. 210 and Rs. 190 respectively, the percentage of female employed in the factory is:
question_answer183) The function\[f\]satisfies the functional equation\[3f(x)+2f\left( \frac{x+59}{x-1} \right)=10x+30\]for all real\[x\ne 1,\]The value of\[f(7)\]is:
question_answer199) The radius of a cylinder is increasing at the rate of 3 m/s and its altitude is decreasing at the rate of 4 m/s. The rate of change of volume when radius is 4 m and altitude is 6 m, is:
question_answer200) A ladder 10 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of 3 cm/s. The height of the upper end while it is descending at the rate of 4 cm/s, is:
question_answer202) If an antiderivative of\[f(x)\]is\[{{e}^{x}}\]and that of\[g(x)\]is \[\cos x,\]then\[\int{f(x)}\cos x\,dx+\]\[\int{g(x)}\,{{e}^{x}}dx\]is equal to:
question_answer220) Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are:
question_answer221) The number of elements in the set\[\{(a,b):\]\[2{{a}^{2}}+3{{b}^{2}}=35,\text{ }a,b\in Z\},\]where Z is the set of all integers, is:
question_answer224) If\[z=\sqrt{2}-i\sqrt{2}\]is rotated through an angle\[45{}^\circ \]in the anticlockwise direction about the origin, then the co-ordinates of its new position are:
question_answer229) If\[\alpha \]and\[\beta \]are the roots of the equation\[{{x}^{2}}-6x+a=0\]and satisfy the relation \[3\alpha +2\beta =16,\]then the value of a is:
question_answer231) If the roots a, Rot the equation \[\frac{{{x}^{2}}-bx}{ax-c}=\frac{\lambda -1}{\lambda +1}\]are such that\[\alpha +\beta =0,\]then the value of\[\lambda \]is:
question_answer240) A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is: