question_answer2) A transmitting antenna of height \[h\] and the receiving antenna of height \[\frac{3}{4}h\] are separated by a distance of d for satisfactory communication in line-of-sight mode. Then, the value of \[h\] is [Given, radius of the earth is\[R\]]
question_answer4) With a standard rectangular bar magnet of length\[(L)\], breadth \[(b;\,\,b<<l)\] and magnetic moment\[M\], the time period of the magnet in a vibration magnetometer is\[8\,\,s\]. If the magnet is cut normal to its length into 8 equal pieces, then the time period (in second) with one of the pieces is
question_answer5) A disc of radius \[a\] and mass \[m\] is pivoted at the rim and is set in small oscillation. If a simple pendulum have the same period as that of the disc, then the length of the simple pendulum should be
question_answer7) A physical quantity \[X\] is represented by\[X=[{{M}^{n}}{{L}^{-\theta }}{{T}^{-\phi }}]\]. The maximum percentage errors in the measurement of \[M,\,\,L\] and\[T\], respectively are \[\alpha %,\,\,\beta %\] and\[\gamma %\]. The maximum percentage error in the measurement of\[X\]will be
question_answer8) A Galilean telescope has an objective of focal length \[200\,\,cm\] and magnifying power\[100\]. What is the distance between the two lenses in normal?
question_answer9) An elliptically shaped ring of dimensions shown in figure just touches, the horizontal surface of a liquid of surface tension 5. The force required to pull the ring away from the liquid surface is
question_answer10) A \[50\Omega \] galvanometer is shunted by a resistance of\[5\Omega \]. The percentage of the total current, which passes through the galvanometer is
question_answer11) An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy\[\frac{{{E}_{0}}}{4}\]. Its potential energy is
question_answer12) A plano-convex glass lens \[({{\mu }_{g}}=3/2)\] of radius of curvature \[R=20\,\,cm\] is placed at a distance \['a'\] from a concave lens of focal length\[40\,\,cm\]. What should be the distance \['b'\] of a point object \[O\] from plano-convex lens so that the position of final image is independent of\[a\]?
question_answer13) In the figure, the ball \[P\] is released from rest, when the spring is at its natural length. For the block \[Q\] of mass \[2{{m}_{0}}\] to leave contact with ground at some stage, the minimum mass of P must be
question_answer15) The potential energy of a particle varies with height \[h\] from a fixed point as \[E=\left( \frac{\operatorname{P}\sqrt{h}}{h+Q} \right)\] where, \[P\] and \[Q\] are constants. The dimensions of \[PQ\] are
question_answer16) Figure shows two convex lenses \[P\] and\[Q\], each made up of three different transparent materials. The number of images formed of an object kept on the principal axis of lenses \[P\] and \[Q\] respectively
question_answer17) What is the minimum acceleration \[({{a}_{0}})\] of the cart in the given figure so that block \[P\] will not fall? (Assume coefficient of friction as\[\mu \]).
question_answer18) The output resistance of a common emitter transistor amplifier, if the input resistance is\[200\,\,\Omega \](\[\alpha =0.98\] and power gain is\[5\times {{10}^{6}}\], is)
question_answer19) In the shown figure, length of the rod is\[L\], area of cross-section\[A\], Young's modulus of the material of the rod is\[Y\]. Then, \[B\] and \[A\] is subjected to a tensile force \[{{F}_{A}}\] while force applied at end\[B\], \[{{F}_{B}}\] is lesser than\[{{F}_{A}}\]. Total change in length of the rod will be
question_answer20) A long insulated copper wire is closely wound as a spiral of \[{{N}_{0}}\] turn. The spiral lies in the \[y-z\] plane and a steady current \[{{I}_{0}}\] flows through the wire. The \[X-\]component of the magnetic field at the centre of the spiral is (assume inner radius as \[{{R}_{1}}\] and outer radius as\[{{R}_{2}}\]).
question_answer21) A cable in the form of a spiral roll (shown in the figure) has a linear density\[\rho \]. It is uncoiled at a uniform speed\[v\]. If the total length of the cable is\[L\]. The work done in uncoiling the cable is
question_answer22) A person can see objects clearly only upto a maximum distance of 60 cm. His eye defect, nature of the corrective lens and its focal length are respectively
question_answer23) Consider two identical iron spheres \[P\] and\[Q\], one which lie on a thermally insulating plate, while the other hangs from an insulated thread. Equal amount of heat \[(\Delta Q)\] is supplied to the two spheres. Then,
question_answer24) A plane electromagnetic wave of frequency \[50\,\,MHz\] travels in free space along the \[X-\]direction. At a particular point in space\[E=7.2\widehat{\mathbf{j}}\,\,V/m\]. At this point, B is equal to
question_answer25) Two tuning forks \[P\] and \[Q\] sounded together and 6 beats per second are heard. \[P\] is in unison with a \[30\,\,cm\] air column open at both ends and \[Q\] is in resonance when length of air column is increased by\[2\,\,cm\]. The frequencies of forks \[P\] and \[Q\] are
question_answer26) An electrical cable having a resistance of\[0.4\,\,\Omega \]delivers \[20\,\,kW\] at \[400\,\,V\,\,DC\] to a factory. What is the efficiency of transformer?
question_answer27) Consider a track having frictional coefficient\[\mu \]. A block of mass \[m\] is released from point\[P\] situated at height\[h\]. Which of the following is correct?
A)
It can reach at\[V\]
doneclear
B)
It cannot reach at\[V\]
doneclear
C)
It can reach at\[V\], if \[\mu \] is reduced to\[\mu /2\]
doneclear
D)
It can reach at\[V\], if \[\mu \] is increased to\[2\mu \]
question_answer28) Suppose, we split a spherical surface into two parts by a circular loop. Now, a bar magnet is placed near the spherical system as shown in the figure. Through which of the two parts is the magnitude of the magnetic flux larger?
A)
Part I
doneclear
B)
Part II
doneclear
C)
The magnitude of the flux is same for both
doneclear
D)
Cannot be predicted without more information about magnetic field
question_answer29) A partition divides a container having insulated walls into two compartments. The same gas fills the two compartments (see figure). The ratio of the number of molecules is compartments I and II is
question_answer30) In the circuit shown in the figure, the \[AC\] source gives a voltage\[V=10\sin (1000t)\]. Neglecting source resistance, the voltmeter and ammeter reading will be
question_answer31) The amplitude of a wave disturbance propagating in the positive \[X-\]direction is given by \[y=\frac{1}{2+{{x}^{2}}}\]at\[t=0\]and\[y=\frac{1}{[2+{{(x-1)}^{2}}]}\]at \[t=3s\], where x and y are in metre. If the shape of the wave disturbance does not change during the propagation, the velocity of the wave is
question_answer32) Assume an YDSE that has different slits width, as a result, amplitude of waves from two slits are \[2A\] and \[4A\] respectively. If \[4{{I}_{0}}\] be the maximum intensity of the interference pattern, then intensity of the pattern of a point, where phase difference between waves is \[2\phi \], is
question_answer33) A sphere of mass \[m\] moving with a constant velocity \[u\] hits another stationary sphere of the same mass and of coefficient of restitution\[(e)\]. The ratio of velocities of the two spheres, after collision will be
question_answer35) A particle of mass m is located in a one-dimensional potential field, where the potential energy of the particle depends on the coordinates as\[U(x)={{U}_{0}}(1-\sin bx)\]; where \[{{U}_{0}}\] and \[b\] are constant. Find the period of small oscillations that the particle performs about the equilibrium position.
question_answer36) A square loop of side length \[a\] having \[m\] turns is kept in a horizontal plane. A uniform magnetic field \[B\] exists in vertical direction as shown in figure. Now, the loop is rotated with constant angular speed \[\omega \] as shown below. Which of the following statement is correct?
question_answer37) Two blocks are resting on ground with masses \[{{m}_{1}}\] and \[{{m}_{2}}\]. A string connects them which goes over a mass less pulley\[P\]. There is no friction between pulley and string. A force \[F\] is applied on pulley\[P\]. The acceleration of centre of mass of blocks is (Given that\[T=2{{m}_{1}}g\]and\[{{m}_{2}}=3{{m}_{1}}\])
question_answer38) The binding energy per nucleon of \[{{C}^{12}}\] is \[{{E}_{1}}\] and that of \[{{C}^{13}}\] is\[{{E}_{2}}\]. The energy required to remove one neutron from \[{{C}^{13}}\] is
question_answer39) One mole of an ideal gas is taken from state \[P\] to state \[Q\] by three different processes (i)\[PRQ\], (ii) \[PSQ\] and (iii) \[PTQ\] as shown in the \[p-V\] diagram. The heat absorbed by the gas is
question_answer40) \[_{87}^{221}Ra\] undergoes radioactive decay with a half-life of 4 days. The probability that a Ra nucleus will disintegrate in 8 days is
question_answer41) A uniform rod of mass m and length\[L\]is rotated about an axis passing through the point \[P\] as shown in figure. The magnitude of angular momentum of the rod about the rotational axis\[yy'\] passing through the point \[P\]is
question_answer42) A stationary hydrogen atom emits photon corresponding to the first line of Lyman series. If \[R\] is the Rydberg's constant and m is the mass of the atom, then the velocity acquired by the atom is (neglect energy absorbed by the photon)
question_answer43) Three metal rods of same length and area of cross-section are arranged to form an equilateral triangle as shown in figure.\[S\] is the middle point of side\[QR\]. If \[PS\] is independent of temperature, then \[[{{\alpha }_{1}}\]is coefficient of linear expansion for rod \[QR\] and \[{{\alpha }_{2}}\] is that for \[PQ\] and\[PR]\]
question_answer44) A graph regarding photoelectric effect is shown between the maximum kinetic energy of electrons and the frequency of the incident light. On the basis of the data as shown in the graph, calculate the work function.
question_answer45) A tetrahedral is consisting of 6 identical wires as shown in the figure. Each wire is having a resistance of\[4\Omega \]. When an ideal cell of \[emf\,5\,\,V\] is connected across \[AB\] as shown, then current through \[OR\] is
question_answer46) A stone is projected from the point on the ground in such a direction so as to hit a bird on the top of a telegraph post of height and then attain the maximum height \[3h/2\] above the ground. If at the instant of projection, the bird were to fly away horizontally with uniform speed. Find the ratio between horizontal velocities of the bird and stone, if the stone still hits the bird while decreasing
question_answer48) Three charges\[{{q}_{1}}=2\times {{10}^{6}}C\],\[{{q}_{2}}=3\times {{10}^{-6}}C\] and \[{{q}_{3}}=6\times {{10}^{-6}}C\]have been placed as shown in figure. Then, the net electric flux will be minimum for the surface
question_answer49) Find the electric field vector at \[P(b,\,\,b,\,\,b)\] due to three infinitely long lines of charges along \[x,\,\,y\] and \[z-\]axes, respectively. The charge density, \[i.e.\] charge per unit length of each wire is\[\sigma \].
question_answer50) A 2 m wide truck is moving with a uniform speed \[{{v}_{0}}=8\,\,m{{s}^{-1}}\] along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed\[v\], when the truck is \[4\,\,m\] away from him. The minimum value of \[v\] so that he can cross the road safely is
question_answer66) \[12\,\,g\] of a non-volatile solute dissolved in \[108\,\,g\] of water produces the relative lowering of vapour pressure of\[0.1\]. The molecular mass of the solute is
question_answer79) Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with\[{{t}_{1/2}}=3.00\,\,h\].What fraction of sample of sucrose remains after\[8\,\,h\]?
question_answer81) An alloy of \[Cu,\,\,Ag,\,\,Au\] is found to have a simple cubic close packed lattice. If the \[Ag\] atoms occupy the face centres and \[Au\] is present at the body centre, the formula of the alloy will be
question_answer83) An in saturated hydrocarbon \['A'\] adds two molecules of H^ and on reductive ozonolysis gives butane-1, 4-dial, ethanol and propanone. Give the \[IUPAC\] name of\[A\].
question_answer87) The solubility product of \[A{{g}_{2}}Cr{{O}_{4}}\] is\[32\times {{10}^{-12}}\]. What is the concentration of \[CrO_{4}^{-}\] ions in that solution?
question_answer90) The heat of neutralisation of a strong acid and a strong alkali is\[57.0\,\,kJ\,\,mo{{l}^{-1}}\]. The heat released when \[0.5\] mole of \[HN{{O}_{3}}\] solution is mixed with \[0.2\] mole of \[KOH\] is
question_answer92) A weak acid HA after treatment with \[1.2\,\,ml\] of \[0.1\,\,M\] strong base has \[\text{a}\]\[pH\]of\[5\]. At the end point, the volume of same base required is\[26.6\,\,mL\]. The value of \[{{K}_{a}}\] is
question_answer97) A person was using water supplied by municipality. Due to shortage of water, he started using underground water. He felt laxative effect. Its cause due to high concentration of
question_answer100) The radius of divalent cation \[{{M}^{2+}}\] is \[94\,\,pm\] and that of divalent anion \[{{X}^{2-}}\] is\[146\,\,pm\]. Thus \[{{M}^{2+}}{{X}^{2-}}\] has
question_answer105) If the tangent at any point \[P\] on the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]meets the tangents at the vertices \[A\] and \[A'\] in \[L\] and \[L'\] respectively, then \[AL\cdot \text{ }A'L'\]is equal to
question_answer107) In a test, there are \[n\] questions in which \[{{2}^{n-i}}\] students gave wrong answers to atleast \[i\] questions, where\[i=1,\,\,2,\,\,...n\]. If the total number of wrong answers given is \[2047\], then \[n\]is equal to
question_answer112) If \[m\] and \[n\] are the order and degree of the differential equation\[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{5}}+4\frac{{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}}{\frac{{{d}^{3}}y}{d{{x}^{3}}}}+\frac{{{d}^{3}}y}{d{{x}^{3}}}={{x}^{2}}-1\], then
question_answer118) Equation of plane passing through the points\[(2,\,\,2,\,\,1)\],\[(9,\,\,3,\,\,6)\] and perpendicular to the plane \[2x+6y+6z-1=0\], is
question_answer119) The length of the shadows of a vertical pole of height\[h\], thrown by the sun's rays at three different moments are \[h,\,\,2h\] and\[3h\]. The sum of the angles of elevation of the rays at these three moments is equal to
question_answer124) Locus of the middle points of all chords of\[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{9}=1\], which are at a distance of\[2\] units from the vertex of parabola\[{{y}^{2}}=-8ax\],
question_answer128) The values of x for which the angle between \[\mathbf{a}=2{{x}^{2}}\widehat{\mathbf{i}}+4x\widehat{\mathbf{j}}+\widehat{\mathbf{k}}\]and\[\mathbf{b}=7\widehat{\mathbf{i}}-2\widehat{\mathbf{j}}+x\widehat{\mathbf{k}}\]is obtuse and the angle between b and the \[Z-axis\] is acute and less than\[\pi /6\], are
question_answer129) The value of a for which the function \[f(x)=\left\{ \begin{matrix} {{\tan }^{-1}}a-3{{x}^{2}} & ,0<x<1 \\ -6x & ,x\ge 1 \\ \end{matrix} \right.\]has a maximum at\[x=1\], is
question_answer131) If a is perpendicular to b and r is non-zero vector such that\[p\mathbf{r}+(\mathbf{r}\cdot \mathbf{b})=\mathbf{a}=\mathbf{c}\], then r is equal to
question_answer133) A person is to count \[4500\] currency notes. Let \[{{a}_{n}}\] denotes the number of notes he counts in the nth minute. If \[{{a}_{1}}={{a}_{2}}=...={{a}_{10}}=150\] and \[{{a}_{10}},\,\,{{a}_{11}}...\] are in AP with common difference\[-2\], then the time taken by him to count all notes is
question_answer134) The number of points with integral coordinates that lie in the interior of the region common to the circle \[{{x}^{2}}+{{y}^{2}}=16\] and the parabola \[{{y}^{2}}=4x\], is
question_answer135) In a \[GP\] with alternatively positive and negative terms and any term is the \[AM\] of the next two terms: Then, the common ratio of the \[GP\] is
question_answer136) If a curve is given by\[x=a\cos t+\frac{b}{2}\cos 2t\] and \[y=\sin t+\frac{b}{2}\sin 2t\], then the points for which\[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\], are given by
question_answer138) The area of the region bounded by the parabola\[{{(y-2)}^{2}}=(x-1)\], the tangent to the parabola at the point \[(2,\,\,3)\] and the \[X-axis\] is
question_answer140) Total number of words that can be formed using all letters of the word BRIJESH that neither begins with I nor ends with B is equal to
question_answer141) Let \[A\] and \[B\] be two sets defined as given below: \[A=\{(x,\,\,y):|x-3|\,\,<1\,\,and|y-3|<1\}\] \[B=\{(x,\,\,y):4{{x}^{2}}+9{{y}^{2}}-32x-54y+109\le 0\}\] Then,
question_answer142) A variable plane\[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\]at a unit distance from the origin cuts the coordinate axes \[A,\,\,B\] and\[C\]. Centroid \[(x,\,\,y,\,\,z)\] of \[\Delta ABC\] satisfies the equation\[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}+\frac{1}{{{z}^{2}}}=k\]. The value of\[k\]is
question_answer146) A plane passes through \[(1,\,\,-2,\,\,1)\] and is perpendicular to two planes \[2x-2y+z=0\] and\[x-y+2z=4\]. The distance of the plane from the point \[(1,\,\,2,\,\,2)\] is
question_answer149) If the axes are rotated through an angle of \[{{30}^{o}}\] in the clockwise direction, the point \[(4,\,\,2\sqrt{3})\] in the new system is
question_answer150) The range of values of a for which the points \[(\alpha ,\,\,2+\alpha )\] and\[\left( \frac{3\alpha }{2},\,\,{{\alpha }^{2}} \right)\]lie on opposite sides of the line\[2x+3y=6\], is