question_answer1) A vector of magnitude \[|\psi |\] is turned through angle\[\frac{\phi }{2}\]. The magnitude of change in the vector is given by
A) \[2|\psi ||\cos \phi /4|\] done clear
B) \[|\psi ||\sin \phi /4|\] done clear
C) \[|\psi {{|}^{2}}|\sin \phi /4{{|}^{2}}\] done clear
D) \[2|\psi ||\sin \phi /4|\] done clear
View Answer play_arrowquestion_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\[R\]]
A) \[\frac{{{d}^{2}}}{2R}{{(2\sqrt{2}-\sqrt{6})}^{2}}\] done clear
B) \[\frac{{{d}^{2}}}{4R}{{(2\sqrt{2}-\sqrt{6})}^{2}}\] done clear
C) \[\frac{{{d}^{2}}}{R}{{(2\sqrt{2}-\sqrt{6})}^{2}}\] done clear
D) \[\frac{{{d}^{2}}}{8R}{{(2\sqrt{2}-\sqrt{6})}^{2}}\] done clear
View Answer play_arrowquestion_answer3) The difference of sound levels between two points is\[40\,\,dB\]. What is the ratio of pressure amplitudes between the two points?
A) \[10\] done clear
B) \[200\] done clear
C) \[100\] done clear
D) \[400\] done clear
View Answer play_arrowquestion_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
A) \[8\,\,s\] done clear
B) \[2\,\,s\] done clear
C) \[1\,\,s\] done clear
D) \[4\,\,s\] done clear
View Answer play_arrowquestion_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
A) \[\frac{5}{2}a\] done clear
B) \[\frac{3}{2}a\] done clear
C) \[\frac{7}{2}a\] done clear
D) \[\frac{1}{2}a\] done clear
View Answer play_arrowquestion_answer6) The effective resistance across the points\[P\] and \[Q\] is
A) \[\frac{r}{4}\] done clear
B) \[\frac{r}{2}\] done clear
C) \[\frac{r}{8}\] done clear
D) \[\frac{r}{16}\] done clear
View Answer play_arrowquestion_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
A) \[(\eta \alpha -\theta \beta -\phi \gamma )%\] done clear
B) \[(\theta \beta +\phi \gamma -\eta \alpha )%\] done clear
C) \[\left( \frac{\alpha }{\eta }-\frac{\beta }{\theta }-\frac{\gamma }{\theta } \right)%\] done clear
D) \[(\eta \alpha +\theta \beta +\phi \gamma )%\] done clear
View Answer play_arrowquestion_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?
A) \[98\,\,cm\] done clear
B) \[198\,\,cm\] done clear
C) \[298\,\,cm\] done clear
D) \[3\,\,m\] done clear
View Answer play_arrowquestion_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
A) \[2\pi (\sqrt{{{a}_{1}}{{b}_{1}}}+\sqrt{{{a}_{2}}{{b}_{2}}})S\] done clear
B) \[\pi ({{a}_{1}}+{{b}_{1}}+{{a}_{2}}+{{b}_{2}})S\] done clear
C) \[\pi \left( \frac{{{a}_{1}}+{{a}_{2}}}{2}+\frac{{{b}_{1}}+{{b}_{2}}}{2} \right)S\] done clear
D) \[\sqrt{2}\pi (\sqrt{{{a}_{1}}{{b}_{1}}}+\sqrt{{{a}_{2}}{{b}_{2}}})S\] done clear
View Answer play_arrowquestion_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
A) \[8.1%\] done clear
B) \[10.1%\] done clear
C) \[11.1%\] done clear
D) \[9.1%\] done clear
View Answer play_arrowquestion_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
A) \[\frac{{{E}_{0}}}{4}\] done clear
B) \[\frac{{{E}_{0}}}{2}\] done clear
C) \[\frac{{{E}_{0}}}{8}\] done clear
D) \[{{E}_{0}}\] done clear
View Answer play_arrowquestion_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\[a\]?
A) \[20\,\,cm\] done clear
B) \[60\,\,cm\] done clear
C) \[40\,\,cm\] done clear
D) \[30\,\,cm\] done clear
View Answer play_arrowquestion_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
A) \[{{m}_{0}}\] done clear
B) \[2{{m}_{0}}\] done clear
C) \[{{m}_{0}}/2\] done clear
D) \[{{m}_{0}}/4\] done clear
View Answer play_arrowquestion_answer14) Consider the circuit, the current through the Zener diode is
A) \[20\,\,mA\] done clear
B) \[10\,\,mA\] done clear
C) \[15\,\,mA\] done clear
D) \[40\,\,mA\] done clear
View Answer play_arrowquestion_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
A) \[[M{{L}^{2}}{{T}^{-2}}]\] done clear
B) \[[{{M}^{3/2}}{{L}^{3/2}}{{T}^{-2}}]\] done clear
C) \[[M{{L}^{7/2}}{{T}^{-2}}]\] done clear
D) \[[M{{L}^{3/2}}{{T}^{-2}}]\] done clear
View Answer play_arrowquestion_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
A) 3 and 1 done clear
B) 3 and 3 done clear
C) 3 and 2 done clear
D) 1 and 3 done clear
View Answer play_arrowquestion_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\[\mu \]).
A) \[g/\sqrt{\mu }\] done clear
B) \[g/\mu \] done clear
C) \[2\mu g\] done clear
D) \[{{\mu }^{2}}g\] done clear
View Answer play_arrowquestion_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)
A) \[516\,\,k\Omega \] done clear
B) \[216\,\,k\Omega \] done clear
C) \[300\,\,k\Omega \] done clear
D) \[416\,\,k\Omega \] done clear
View Answer play_arrowquestion_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
A) \[{{F}_{A}}\times \frac{L}{2AY}\] done clear
B) \[{{F}_{B}}\times \frac{L}{2AY}\] done clear
C) \[\frac{({{F}_{A}}+{{F}_{B}})L}{2AY}\] done clear
D) \[\frac{({{F}_{A}}-{{F}_{B}})L}{2AY}\] done clear
View Answer play_arrowquestion_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\[{{R}_{2}}\]).
A) \[\frac{{{\mu }_{0}}{{N}_{0}}{{I}_{0}}}{4({{R}_{2}}-{{R}_{1}})}\ln ({{R}_{2}}/{{R}_{1}})\] done clear
B) \[\frac{2{{\mu }_{0}}{{N}_{0}}{{I}_{0}}}{{{R}_{2}}-{{R}_{1}}}\ln ({{R}_{2}}/{{R}_{1}})\] done clear
C) \[\frac{{{\mu }_{0}}{{N}_{0}}{{I}_{0}}}{2({{R}_{2}}-{{R}_{1}})}\ln {{({{R}_{2}}/{{R}_{1}})}^{2}}\] done clear
D) \[\frac{{{\mu }_{0}}{{N}_{0}}{{I}_{0}}}{2({{R}_{2}}-{{R}_{1}})}\ln ({{R}_{2}}/{{R}_{1}})\] done clear
View Answer play_arrowquestion_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
A) \[\rho L{{v}^{2}}/4\] done clear
B) \[\rho L{{v}^{2}}/2\] done clear
C) \[\rho L{{v}^{2}}/3\] done clear
D) \[\rho L{{v}^{2}}\] done clear
View Answer play_arrowquestion_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
A) myopia, convex,\[60\,\,cm\] done clear
B) myopia, concave,\[60\,\,cm\] done clear
C) hypermetropia, concave,\[60\,\,cm\] done clear
D) contract, convex,\[60\,\,cm\] done clear
View Answer play_arrowquestion_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,
A) the temperature of Q will be greater than P done clear
B) the temperature of P will be greater than Q done clear
C) their temperature will be equal done clear
D) can't be predicted done clear
View Answer play_arrowquestion_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
A) \[8.4\times {{10}^{-8}}\widehat{\mathbf{k}}T\] done clear
B) \[2.4\times {{10}^{-8}}\widehat{\mathbf{k}}T\] done clear
C) \[7.4\times {{10}^{-6}}\widehat{\mathbf{i}}T\] done clear
D) \[2.4\times {{10}^{-8}}\widehat{\mathbf{j}}T\] done clear
View Answer play_arrowquestion_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
A) \[90\,\,Hz\]and\[84\,\,Hz\] done clear
B) \[100\,\,Hz\]and\[106\,\,Hz\] done clear
C) \[96\,\,Hz\] and\[90\,\,Hz\] done clear
D) \[206\,\,Hz\] and\[200\,\,Hz\] done clear
View Answer play_arrowquestion_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?
A) \[89.5%\] done clear
B) \[99.5%\] done clear
C) \[79.5%\] done clear
D) \[90.5%\] done clear
View Answer play_arrowquestion_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\[V\] done clear
B) It cannot reach at\[V\] done clear
C) It can reach at\[V\], if \[\mu \] is reduced to\[\mu /2\] done clear
D) It can reach at\[V\], if \[\mu \] is increased to\[2\mu \] done clear
View Answer play_arrowquestion_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 done clear
B) Part II done clear
C) The magnitude of the flux is same for both done clear
D) Cannot be predicted without more information about magnetic field done clear
View Answer play_arrowquestion_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
A) \[6:1\] done clear
B) \[1:6\] done clear
C) \[4:1\] done clear
D) \[1:4\] done clear
View Answer play_arrowquestion_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
A) \[20\sqrt{\frac{125}{538}}V\]and\[\frac{10}{\sqrt{538}}A\] done clear
B) \[10\sqrt{\frac{250}{538}}V\]and\[\frac{10}{\sqrt{538}}A\] done clear
C) \[\sqrt{\frac{250}{538}}V\]and\[\frac{1}{\sqrt{538}}A\] done clear
D) \[\sqrt{\frac{125}{539}}V\]and\[\frac{1}{\sqrt{538}}A\] done clear
View Answer play_arrowquestion_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
A) \[\frac{1}{2}m{{s}^{-1}}\] done clear
B) \[\frac{1}{3}m{{s}^{-1}}\] done clear
C) \[\frac{1}{4}m{{s}^{-1}}\] done clear
D) \[\frac{1}{5}m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_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
A) \[4{{I}_{0}}{{\cos }^{2}}\phi /2\] done clear
B) \[\frac{4{{I}_{0}}}{3}{{\sin }^{2}}\phi \] done clear
C) \[\frac{4{{I}_{0}}}{9}[5+4\cos 2\phi ]\] done clear
D) \[\frac{4{{I}_{0}}}{9}[5+8\cos 2\phi ]\] done clear
View Answer play_arrowquestion_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
A) \[\frac{1-e}{1+e}\] done clear
B) \[\frac{e}{e+1}\] done clear
C) \[2/e\] done clear
D) \[\frac{e+1}{2e}\] done clear
View Answer play_arrowquestion_answer34) The circuit is equivalent to
A) NOR gate done clear
B) AND gate done clear
C) NAND gate done clear
D) OR gate done clear
View Answer play_arrowquestion_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.
A) \[\frac{2\pi }{{{b}^{2}}}\sqrt{\frac{m}{{{U}_{0}}}}\] done clear
B) \[\frac{\pi }{b}\sqrt{\frac{m}{{{U}_{0}}}}\] done clear
C) \[\frac{{{\pi }^{2}}}{2b}\sqrt{\frac{m}{{{U}_{0}}}}\] done clear
D) \[\frac{2\pi }{b}\sqrt{\frac{m}{{{U}_{0}}}}\] done clear
View Answer play_arrowquestion_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?
A) Same emf is induced in both cases (i) and (ii) done clear
B) Maximum emf is induced in case (i) done clear
C) Emf induced in case (ii) is more than (i) done clear
D) No emf induced in case (ii) done clear
View Answer play_arrowquestion_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\[{{m}_{2}}=3{{m}_{1}}\])
A) \[g/8\] done clear
B) \[g/4\] done clear
C) \[\frac{g}{2}\] done clear
D) \[g\] done clear
View Answer play_arrowquestion_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
A) \[12{{E}_{1}}+12{{E}_{2}}\] done clear
B) \[13{{E}_{2}}-12{{E}_{1}}\] done clear
C) \[12{{E}_{2}}-13{{E}_{1}}\] done clear
D) \[13{{E}_{2}}+12{{E}_{1}}\] done clear
View Answer play_arrowquestion_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
A) the least in process (ii) done clear
B) greater in process (ii) than in process (i) done clear
C) the same in the processes (i) and (iii) done clear
D) less in process (iii) than in process (ii) done clear
View Answer play_arrowquestion_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
A) \[\frac{1}{2}\] done clear
B) \[\frac{3}{8}\] done clear
C) \[\frac{1}{4}\] done clear
D) \[\frac{3}{4}\] done clear
View Answer play_arrowquestion_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
A) \[\frac{M{{L}^{2}}}{18}\] done clear
B) \[\frac{M{{(x+y)}^{2}}}{9}\] done clear
C) \[\frac{M({{L}^{2}}+{{x}^{2}})}{9}\] done clear
D) \[\frac{M({{L}^{2}}+2{{y}^{2}})}{18}\] done clear
View Answer play_arrowquestion_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)
A) \[\frac{4m}{Rh}\] done clear
B) \[\frac{Rh}{4m}\] done clear
C) \[\frac{3Rh}{4m}\] done clear
D) \[\frac{4m}{3Rh}\] done clear
View Answer play_arrowquestion_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\[PR]\]
A) \[{{\alpha }_{1}}=2{{\alpha }_{2}}\] done clear
B) \[{{\alpha }_{1}}={{\alpha }_{2}}/2\] done clear
C) \[{{\alpha }_{1}}={{\alpha }_{2}}\] done clear
D) \[{{\alpha }_{1}}=4{{\alpha }_{2}}\] done clear
View Answer play_arrowquestion_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.
A) \[4\,\,eV\] done clear
B) \[2\,\,eV\] done clear
C) \[4.2\,\,eV\] done clear
D) \[2.5\,\,eV\] done clear
View Answer play_arrowquestion_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
A) \[4\,\,A\] done clear
B) \[\frac{6}{19}A\] done clear
C) \[zero\] done clear
D) \[1\,\,A\] done clear
View Answer play_arrowquestion_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
A) \[\sqrt{3}-1\] done clear
B) \[1/\sqrt{3}-1\] done clear
C) \[\sqrt{3}+1\] done clear
D) \[1/\sqrt{3}+1\] done clear
View Answer play_arrowquestion_answer47) Four equal capacitors are connected to a battery as shown in the adjoining figure. The potentials of \[P\] and \[Q\] are
A) \[5V\]and\[5V\] done clear
B) \[10V\]and\[5V\] done clear
C) \[10V\]and\[-10V\] done clear
D) \[5V\]and\[-5V\] done clear
View Answer play_arrowquestion_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
A) \[{{S}_{1}}\] done clear
B) \[{{S}_{2}}\] done clear
C) \[{{S}_{3}}\] done clear
D) same for all done clear
View Answer play_arrowquestion_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\[\sigma \].
A) \[\frac{\sigma }{\pi {{\varepsilon }_{0}}b}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}})\] done clear
B) \[\frac{\sigma }{2\pi {{\varepsilon }_{0}}b}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}})\] done clear
C) \[\frac{\sigma }{\pi {{\varepsilon }_{0}}b}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\widehat{\mathbf{k}})\] done clear
D) \[\frac{\sigma }{2\pi {{\varepsilon }_{0}}b}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\widehat{\mathbf{k}})\] done clear
View Answer play_arrowquestion_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
A) \[2.62\,\,m{{s}^{-1}}\] done clear
B) \[4.6\,\,m{{s}^{-1}}\] done clear
C) \[0.89\,\,m{{s}^{-1}}\] done clear
D) \[1.414\,\,m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer51) In the following reaction, product formed is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer52) Which of the following compounds has same oxidation state of the central metal atom in the cationic and anionic part?
A) \[[Pt{{(N{{H}_{3}})}_{4}}][PtC{{l}_{6}}]\] done clear
B) \[[Pt{{(py)}_{4}}][PtC{{l}_{4}}]\] done clear
C) \[[Pt{{(N{{H}_{3}})}_{4}}C{{l}_{2}}][PtC{{l}_{4}}]\] done clear
D) \[{{K}_{4}}[Ni{{(CN)}_{6}}]\] done clear
View Answer play_arrowquestion_answer53) Which of the following calcium salt will : give cyclopentanone on heating?
A) Calcium succinate done clear
B) Calcium adipate done clear
C) Calcium glucarate done clear
D) Calcium oxalate done clear
View Answer play_arrowquestion_answer54) In the reaction,\[C{{H}_{3}}COOH\xrightarrow{LiAl{{H}_{4}}}A\xrightarrow{PC{{l}_{5}}}B\xrightarrow{Alc.\,\,KOH}C\]the product is
A) acetaldehyde done clear
B) acetylene done clear
C) ethylene done clear
D) acetylchloride done clear
View Answer play_arrowquestion_answer55) Complete hydrolysis of cellulose gives
A) D-fructose done clear
B) D-ribose done clear
C) D-glucose done clear
D) L-glucose done clear
View Answer play_arrowquestion_answer56) Bakelite is obtained from phenol by reacting with
A) \[{{(C{{H}_{2}}OH)}_{2}}\] done clear
B) \[C{{H}_{3}}CHO\] done clear
C) \[C{{H}_{3}}COC{{H}_{3}}\] done clear
D) \[HCHO\] done clear
View Answer play_arrowquestion_answer57) Phosgene can be obtained when
A) white phophorus reacts with alkali done clear
B) calcium phosphide reacts with water done clear
C) chloroform reacts with air done clear
D) bone comes in contact with water done clear
View Answer play_arrowquestion_answer58) Select the coloured and paramagnetic ions
A) \[C{{u}^{+}},\,\,Z{{n}^{2+}},\,\,C{{a}^{2+}}\] done clear
B) \[S{{c}^{3+}},\,\,T{{i}^{4+}},\,\,{{V}^{5+}}\] done clear
C) \[C{{u}^{2+}},\,\,C{{r}^{+}},\,\,M{{n}^{2+}}\] done clear
D) \[N{{i}^{2+}},\,\,C{{u}^{+}},\,\,H{{g}^{2+}}\] done clear
View Answer play_arrowquestion_answer59) Which of the following process is used in extractive metallurgy of magnesium?
A) Fused salt electrolysis done clear
B) Self reduction done clear
C) Aqueous solution electrolysis done clear
D) Thermite reduction done clear
View Answer play_arrowquestion_answer60) Which of the following alkaline earth metal sulphates has hydration enthalpy higher than the lattice enthalpy?
A) \[SrS{{O}_{4}}\] done clear
B) \[CaS{{O}_{4}}\] done clear
C) \[BeS{{O}_{4}}\] done clear
D) \[BaS{{O}_{4}}\] done clear
View Answer play_arrowquestion_answer61) Which of the following statements is true?
A) \[{{H}_{3}}P{{O}_{4}}\] is stronger acid, than\[{{H}_{2}}S{{O}_{3}}\] done clear
B) In aqueous medium, \[HF\] is a stronger acid than\[HCl\] done clear
C) \[HCl{{O}_{4}}\] is a weaker acid than\[HCl{{O}_{3}}\] done clear
D) \[HN{{O}_{3}}\] is a stronger acid than\[HN{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer62) The orbital angular momentum of an electron is \[2s\] orbital is
A) \[+\frac{1}{2}.\frac{h}{2\pi }\] done clear
B) \[zero\] done clear
C) \[\frac{h}{2\pi }\] done clear
D) \[\sqrt{2}\cdot \frac{h}{2\pi }\] done clear
View Answer play_arrowquestion_answer63) The enthalpy change for a reaction does not depend upon the
A) physical state of reactants and products done clear
B) use of different reactants for the same product done clear
C) nature of intermediate reaction steps done clear
D) difference in initial or final temperature of involved substances done clear
View Answer play_arrowquestion_answer64) The role of a catalyst is to change......
A) Gibbs energy of reaction done clear
B) enthalpy of reaction done clear
C) activation energy of reaction done clear
D) equilibrium constant done clear
View Answer play_arrowquestion_answer65) When ortho boric acid \[({{H}_{3}}B{{O}_{3}})\] is heated, the residue is
A) boron done clear
B) metaboric acid done clear
C) boric anhydride done clear
D) borax done clear
View Answer play_arrowquestion_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
A) \[80\] done clear
B) \[60\] done clear
C) \[20\] done clear
D) \[40\] done clear
View Answer play_arrowquestion_answer67) Electron gain enthalpy with negative sign of fluorine is less than that of chlorine due to
A) high ionisation enthalpy of fluorine done clear
B) smaller size of chlorine atom done clear
C) smaller size of fluorine atom done clear
D) bigger size of 2p orbital of fluorine done clear
View Answer play_arrowquestion_answer68) Fog is a colloidal solution of
A) liquid particles dispersed in a gas done clear
B) gaseous particles dispersed in a liquid done clear
C) solid particles dispersed in a liquid done clear
D) solid particles dispersed in a gas done clear
View Answer play_arrowquestion_answer69) In the reaction sequence, is
A) cyclohexanone done clear
B) caprolactum done clear
C) \[HO{{(C{{H}_{2}})}_{6}}N{{H}_{2}}\] done clear
D) hexamethylene diisocyanate done clear
View Answer play_arrowquestion_answer70) The highest calorific value is found in
A) proteins done clear
B) fats done clear
C) vitamins done clear
D) carbohydrates done clear
View Answer play_arrowquestion_answer71) In an electric field, if an amino acid migrate towards cathode, the pH of solution is said to be
A) less than\[Pl\] done clear
B) More than\[Pl\] done clear
C) equal to\[Pl\] done clear
D) \[7\] done clear
View Answer play_arrowquestion_answer72) Acid anhydrides on reaction with primary amines gives
A) amide done clear
B) imide done clear
C) secondary amine done clear
D) imine done clear
View Answer play_arrowquestion_answer73) Benzene diazonium chloride on reaction with phenol in weakly basic medium gives
A) diphenyl ether done clear
B) p-hydroxyazobenzene done clear
C) chlorobenzene done clear
D) benzene done clear
View Answer play_arrowquestion_answer74) Reagent used for the oxidation of allyl alcohol to acrolein is
A) \[KMn{{O}_{4}}\] done clear
B) \[{{H}_{2}}{{O}_{2}}\] done clear
C) active\[Mn{{O}_{2}}\] done clear
D) \[Os{{O}_{4}}\] done clear
View Answer play_arrowquestion_answer75) The enol form of acetone, after treatment with \[{{D}_{2}}O\] gives
A) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OD \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}\] done clear
B) \[C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{3}}\] done clear
C) \[C{{H}_{2}}=\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}D\] done clear
D) \[C{{D}_{2}}=\underset{\begin{smallmatrix} | \\ OD \end{smallmatrix}}{\mathop{C}}\,-C{{D}_{3}}\] done clear
View Answer play_arrowquestion_answer76) The compounds \[[Co(S{{O}_{4}}){{(N{{H}_{3}})}_{5}}]Br\] and \[[CO(S{{O}_{4}}){{(N{{H}_{3}})}_{5}}]Cl\]represent
A) linkage isomerism done clear
B) ionisation isomerism done clear
C) coordination isomerism done clear
D) no isomerism done clear
View Answer play_arrowquestion_answer77) \[Xe{{F}_{2}}\] on hydrolysis gives
A) \[Xe{{O}_{3}}\] done clear
B) \[XeO\] done clear
C) \[Xe\] done clear
D) \[Xe{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer78) Sulphur in \[+3\] oxidation state is present in
A) dithionous acid done clear
B) sulphurous acid done clear
C) thionous acid done clear
D) phyrosulphuric acid done clear
View Answer play_arrowquestion_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\[8\,\,h\]?
A) \[1.023\,\,M\] done clear
B) \[0.8725\,\,M\] done clear
C) \[0.023\,\,M\] done clear
D) \[0.1576\,\,M\] done clear
View Answer play_arrowquestion_answer80) The osmotic pressure of a \[5%(wt./vol)\] solution of cane sugar at \[{{150}^{o}}C\] is
A) \[3.078\,\,atm\] done clear
B) \[4.078\,\,atm\] done clear
C) \[5.078\,\,atm\] done clear
D) \[2.45\,\,atm\] done clear
View Answer play_arrowquestion_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
A) \[C{{u}_{4}}A{{g}_{4}}Au\] done clear
B) \[CuA{{g}_{3}}Au\] done clear
C) \[CuAgCu\] done clear
D) \[C{{u}_{4}}A{{g}_{2}}Cu\] done clear
View Answer play_arrowquestion_answer82) Ozone layer of stratosphere requires protection from indiscriminate use of
A) pesticides done clear
B) atomic explosions done clear
C) aerosols and high flying jets done clear
D) balloons done clear
View Answer play_arrowquestion_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\[A\].
A) 3-methyl octa-2, 6-diene done clear
B) 2-methyl octa-2, 5-diene done clear
C) 2-methyl octa-2, 6-diene done clear
D) 2-methyl octa-3, 5-diene done clear
View Answer play_arrowquestion_answer84) Carborundum is obtained when silica is heated at high temperature with
A) carbon done clear
B) carbon monoxide done clear
C) carbon dioxide done clear
D) calcium carbonate done clear
View Answer play_arrowquestion_answer85) The difference of water molecules in gypsum and plaster of Paris is
A) \[\frac{5}{2}\] done clear
B) \[2\] done clear
C) \[\frac{1}{2}\] done clear
D) \[1\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer86) Identify disproportionation reaction.
A) \[C{{H}_{3}}+2{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}+2{{H}_{2}}O\] done clear
B) \[C{{H}_{4}}+4C{{l}_{2}}\xrightarrow{{}}CC{{l}_{4}}+4HCl\] done clear
C) \[2{{F}_{2}}+2O{{H}^{-}}\xrightarrow{{}}2{{F}^{-}}+O{{F}_{2}}+{{H}_{2}}O\] done clear
D) \[2N{{O}_{2}}+2O{{H}^{-}}\xrightarrow{{}}NO_{2}^{-}+NO_{3}^{-}+{{H}_{2}}O\] done clear
View Answer play_arrowquestion_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?
A) \[2\times {{10}^{-4}}M\] done clear
B) \[16\times {{10}^{-4}}M\] done clear
C) \[8\times {{10}^{-4}}M\] done clear
D) \[8\times {{10}^{-8}}M\] done clear
View Answer play_arrowquestion_answer88) The structure of \[I{{F}_{5}}\] can be described as
A) done clear
B) done clear
C) done clear
D) None of these done clear
View Answer play_arrowquestion_answer89) \[pH\]of \[{{10}^{-8}}N\]\[NaOH\] is
A) \[8.0\] done clear
B) \[6.0\] done clear
C) \[6.98\] done clear
D) \[7.04\] done clear
View Answer play_arrowquestion_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
A) \[57.0\,\,kJ\] done clear
B) \[11.4\,\,kJ\] done clear
C) \[28.5\,\,kJ\] done clear
D) \[34.9\,\,kJ\] done clear
View Answer play_arrowquestion_answer91) The unit and value of rate constant and that of rate of reaction are same for
A) zero order done clear
B) first order done clear
C) second order done clear
D) third order done clear
View Answer play_arrowquestion_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
A) \[8.2\times {{10}^{-6}}\] done clear
B) \[6.4\times {{10}^{-6}}\] done clear
C) \[5.3\times {{10}^{-5}}\] done clear
D) \[2.4\times {{10}^{-6}}\] done clear
View Answer play_arrowquestion_answer93) \[A\]and \[B\] are respectively.
A) \[{{H}_{2}}/Pt;\,\,LiAl{{H}_{4}}/{{H}_{2}}O\] done clear
B) \[{{H}_{2}}/Pt;\,\,{{H}_{2}}/Pt\] done clear
C) \[LiAl{{H}_{4}}/{{H}_{2}}O;\,\,LiAl{{H}_{4}}/{{H}_{2}}O\] done clear
D) \[LiAl{{H}_{4}}/{{H}_{2}}O;\,\,{{H}_{2}}/Pt\] done clear
View Answer play_arrowquestion_answer94) The \[IUPAC\] name of
A) 3, 4-dimethylpentanoyl chloride done clear
B) 1-chloro-1 -oxo-2, 3-dimethylpentane done clear
C) 2-ethyl-3-methylbutanoyl chloride done clear
D) 2, 3-dimethylpentanoyl chloride done clear
View Answer play_arrowquestion_answer95) \[F{{e}^{2+}}\] reduces \[N{{H}_{4}}OH\] to
A) \[N{{H}_{3}}\] done clear
B) \[{{N}_{3}}H\] done clear
C) \[{{N}_{2}}{{H}_{4}}\] done clear
D) \[{{N}_{2}}\] done clear
View Answer play_arrowquestion_answer96) Proteins when heated with conc.\[HN{{O}_{3}}\]give yellow colour. This is known as
A) Hoppe's test done clear
B) acid-base test done clear
C) Biuret's test done clear
D) Xanthoprotic test done clear
View Answer play_arrowquestion_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
A) \[C{{O}_{2}}\] done clear
B) \[SO_{4}^{2-}\] done clear
C) \[CO_{3}^{2-}\] done clear
D) \[{{S}^{2-}}\] done clear
View Answer play_arrowquestion_answer98) The order of acidic strength of boron dialyses is
A) \[B{{F}_{3}}<BC{{l}_{3}}<BB{{r}_{3}}<B{{l}_{3}}\] done clear
B) \[B{{l}_{3}}<BB{{r}_{3}}<BC{{l}_{3}}<B{{F}_{3}}\] done clear
C) \[BC{{l}_{3}}<BB{{r}_{3}}<B{{l}_{3}}<B{{F}_{3}}\] done clear
D) \[BB{{r}_{3}}<BC{{l}_{3}}<B{{F}_{3}}<B{{l}_{3}}\] done clear
View Answer play_arrowquestion_answer99) The hardest substance amongst the following is
A) \[B{{e}_{2}}C\] done clear
B) tritonium done clear
C) \[{{B}_{4}}C\] done clear
D) graphite done clear
View Answer play_arrowquestion_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
A) \[NaCl\] structure done clear
B) linear structure done clear
C) \[CsCl\] structure done clear
D) \[ZnS\] structure done clear
View Answer play_arrowquestion_answer101) If \[p,\,\,q,\,\,r\] have truth values \[T,\,\,F,\,\,T\] respectively, then which of the following is true?
A) \[(p\to q)\wedge r\] done clear
B) \[(p\to q)\wedge \tilde{\ }r\] done clear
C) \[(p\wedge q)\wedge (p\vee r)\] done clear
D) \[q\to (p\wedge r)\] done clear
View Answer play_arrowquestion_answer102) If one root of the equation\[{{z}^{2}}+(a+i)z+b+ic=0\] = 0 is real, when\[a,\,\,b\in R\], R, then\[{{c}^{2}}+b-ac\]is equal to
A) \[0\] done clear
B) \[-1\] done clear
C) \[1\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer103) If the slopes of the lines given by\[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]are in the ratio \[3:1\], then\[{{h}^{2}}\] is equal to
A) \[\frac{ab}{3}\] done clear
B) \[\frac{4ab}{3}\] done clear
C) \[\frac{4a}{3b}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer104) If \[a\in Z\] and the equation\[(x-a)(x-10)+1=0\]has integral roots, then the values of a are
A) \[10,\,\,8\] done clear
B) \[12,\,\,10\] done clear
C) \[12,\,\,8\] done clear
D) \[18,\,\,10\] done clear
View Answer play_arrowquestion_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
A) \[a+b\] done clear
B) \[{{a}^{2}}+{{b}^{2}}\] done clear
C) \[{{a}^{2}}\] done clear
D) \[{{b}^{2}}\] done clear
View Answer play_arrowquestion_answer106) If \[z\] is any complex number satisfying\[|z-1|\,\,=1\], then which of the following is correct?
A) \[\arg (z-1)=2\arg (z)\] done clear
B) \[2\arg (z)=\frac{2}{3}\arg ({{z}^{2}}-z)\] done clear
C) \[\arg (z-1)=\arg (z+1)\] done clear
D) \[\arg (z)=2\arg (z+1)\] done clear
View Answer play_arrowquestion_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
A) \[12\] done clear
B) \[11\] done clear
C) \[10\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer108) The period of the function\[f(x)=\frac{|\sin x|-|\cos x|}{|\sin x+\cos x|}\]is
A) \[\frac{\pi }{2}\] done clear
B) \[2\pi \] done clear
C) \[\pi \] done clear
D) None of these done clear
View Answer play_arrowquestion_answer109) Let \[[x]\] denotes the greatest integer less than or equal to \[x\]and\[f[x]=[{{\tan }^{2}}x]\]. Then,
A) \[\underset{x\to 0}{\mathop{\lim }}\,f(x)\] does not exist done clear
B) \[f(x)\]is continuous at\[x=0\] done clear
C) \[f(x)\] is not differentiate at\[x=0\] done clear
D) \[f'(0)=1\] done clear
View Answer play_arrowquestion_answer110) The value of\[\underset{x\to 0}{\mathop{\lim }}\,\frac{1-{{\cos }^{3}}x}{x\sin x\cos x}\]is
A) \[\frac{2}{5}\] done clear
B) \[\frac{3}{5}\] done clear
C) \[\frac{3}{2}\] done clear
D) \[\frac{3}{4}\] done clear
View Answer play_arrowquestion_answer111) If\[f(x)=\]\[\left| \begin{matrix} \sin x+\sin 2x+\sin 3x & \sin 2x & \sin 3x \\ 3+4\sin x & 3 & 4\sin x \\ 1+\sin x & \sin x & 1 \\ \end{matrix} \right|\], then the value of\[\int_{0}^{\pi /2}{f(x)}dx\]is
A) \[3\] done clear
B) \[2/3\] done clear
C) \[1/3\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_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
A) \[m=3,\,\,n=3\] done clear
B) \[m=3,\,\,n=2\] done clear
C) \[m=3,\,\,n=5\] done clear
D) \[m=3,\,\,n=1\] done clear
View Answer play_arrowquestion_answer113) \[\int{\frac{{{\sin }^{3}}x}{({{\cos }^{4}}x+3{{\cos }^{2}}x+1){{\tan }^{-1}}(\sec x+\cos x)}dx}\]is equal to
A) \[{{\tan }^{-1}}(\sec x+\cos x)+C\] done clear
B) \[{{\log }_{e}}|{{\tan }^{-1}}(\sec x+\cos x)|+C\] done clear
C) \[\frac{1}{{{(\sec x+\cos x)}^{2}}}+C\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer114) The solution of the differential equation\[({{x}^{2}}-y{{x}^{2}})\frac{dy}{dx}+{{y}^{2}}+x{{y}^{2}}=0\]is
A) \[\log \left( \frac{x}{y} \right)=\frac{1}{x}+\frac{1}{y}+C\] done clear
B) \[\log \left( \frac{y}{x} \right)=\frac{1}{x}+\frac{1}{y}+C\] done clear
C) \[\log \,(xy)=\frac{1}{x}+\frac{1}{y}+C\] done clear
D) \[\log \,(xy)+\frac{1}{x}+\frac{1}{y}=C\] done clear
View Answer play_arrowquestion_answer115) The coefficient of \[{{x}^{5}}\] in the expansion of\[{{(1+x)}^{21}}+{{(1+x)}^{22}}+...+{{(1+x)}^{30}}\]is
A) \[^{51}{{C}_{5}}\] done clear
B) \[^{9}{{C}_{5}}\] done clear
C) \[^{31}{{C}_{6}}{{-}^{21}}{{C}_{6}}\] done clear
D) \[^{30}{{C}_{5}}{{+}^{20}}{{C}_{5}}\] done clear
View Answer play_arrowquestion_answer116) If the direction cosines of line are\[\frac{1}{c},\,\,\frac{1}{c},\,\,\frac{1}{c},\] then
A) \[0<c<1\] done clear
B) \[c>2\] done clear
C) \[c>0\] done clear
D) \[c=\pm \sqrt{3}\] done clear
View Answer play_arrowquestion_answer117) If\[0\le x<1\], then\[\sin \left\{ {{\tan }^{-1}}\frac{1-{{x}^{2}}}{2x}+{{\cos }^{-1}}\frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right\}\]is equal to
A) \[1\] done clear
B) \[-1\] done clear
C) \[0\] done clear
D) None of the above done clear
View Answer play_arrowquestion_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
A) \[3x+4y+5z=9\] done clear
B) \[3x+4y-5z+9=0\] done clear
C) \[3x+4y-5z-9=0\] done clear
D) None of these done clear
View Answer play_arrowquestion_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
A) \[\frac{\pi }{2}\] done clear
B) \[\frac{\pi }{3}\] done clear
C) \[\frac{\pi }{4}\] done clear
D) \[\frac{\pi }{6}\] done clear
View Answer play_arrowquestion_answer120) If\[{{(1-x+{{x}^{2}})}^{n}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...\]\[+{{a}_{2n}}{{x}^{2n}}\], then\[{{a}_{0}}+{{a}_{2}}+{{a}_{4}}+...+{{a}_{2n}}\]is equal
A) \[\frac{{{3}^{n}}+1}{2}\] done clear
B) \[\frac{{{3}^{n}}-1}{2}\] done clear
C) \[\frac{{{3}^{n-1}}+1}{2}\] done clear
D) \[\frac{{{3}^{n-1}}-1}{2}\] done clear
View Answer play_arrowquestion_answer121) If\[f:[1,\,\,\infty )\to [2,\,\,\infty )\]is given by\[f(x)=x+\frac{1}{x}\], then \[{{f}^{-1}}(x)\] equals
A) \[\frac{x+\sqrt{{{x}^{2}}-4}}{2}\] done clear
B) \[\frac{x}{1+{{x}^{2}}}\] done clear
C) \[\frac{x-\sqrt{{{x}^{2}}-4}}{2}\] done clear
D) \[1+\sqrt{{{x}^{2}}-4}\] done clear
View Answer play_arrowquestion_answer122) If\[A=\left[ \begin{matrix} 1 & 2 & -1 \\ -1 & 1 & 2 \\ 2 & -1 & 1 \\ \end{matrix} \right]\],then \[\det (adj(adjA))\]is equal to
A) \[{{14}^{4}}\] done clear
B) \[{{14}^{3}}\] done clear
C) \[{{14}^{2}}\] done clear
D) \[14\] done clear
View Answer play_arrowquestion_answer123) The sum of n terms of the series \[1.4+3.04+5.004+7.0004+...\]is
A) \[{{n}^{2}}+\frac{4}{9}\left( 1+\frac{1}{{{10}^{n}}} \right)\] done clear
B) \[{{n}^{2}}+\frac{4}{9}\left( 1-\frac{1}{{{10}^{n}}} \right)\] done clear
C) \[n+\frac{4}{9}\left( 1-\frac{1}{{{10}^{n}}} \right)\] done clear
D) None of these done clear
View Answer play_arrowquestion_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\[{{y}^{2}}=-8ax\],
A) \[{{\left( \frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{9} \right)}^{2}}=\frac{xy}{6}\] done clear
B) \[{{\left( \frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{9} \right)}^{2}}=\left( \frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{81} \right)\] done clear
C) \[\left( \frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{9} \right)=\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer125) The solution set of the in equation\[\frac{|x+3|+x}{x+2}>1\], is
A) \[(-5,\,\,-2)\cup (-1,\,\,\infty )\] done clear
B) \[(-5,\,\,-2)\] done clear
C) \[(-1,\,\,\infty )\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer126) If\[f(x)=\frac{1-x}{1+x},\,\,x\ne 0,\,\,-1\]and\[\alpha =f(f(x))+f(f(1/x))\], then
A) \[\alpha >2\] done clear
B) \[\alpha <-2\] done clear
C) \[|\alpha |\,\,>2\] done clear
D) \[\alpha =2\] done clear
View Answer play_arrowquestion_answer127) The perimeter of a sector is constant. If its area is to be maximum, then sectorial angle is
A) \[\frac{\pi }{6}\] done clear
B) \[\frac{\pi }{4}\] done clear
C) \[{{4}^{C}}\] done clear
D) \[{{2}^{C}}\] done clear
View Answer play_arrowquestion_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
A) \[a<x<1/2\] done clear
B) \[1/2<x<15\] done clear
C) \[x>1/2\]or\[x<0\] done clear
D) None of these done clear
View Answer play_arrowquestion_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
A) \[0\] done clear
B) \[1\] done clear
C) \[2\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer130) The subtangent at any point on the curve \[{{x}^{m}}{{y}^{n}}={{a}^{m+n}}\]varies as
A) \[{{(abscissa)}^{2}}\] done clear
B) \[{{(ordinate)}^{2}}\] done clear
C) \[abscissa\] done clear
D) \[ordinate\] done clear
View Answer play_arrowquestion_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
A) \[\frac{\mathbf{c}}{p}-\frac{(\mathbf{b}\cdot \mathbf{c})\mathbf{a}}{{{p}^{2}}}\] done clear
B) \[\frac{\mathbf{a}}{p}-\frac{(\mathbf{c}\cdot \mathbf{a})\mathbf{b}}{{{p}^{2}}}\] done clear
C) \[\frac{\mathbf{b}}{p}-\frac{(\mathbf{a}\cdot \mathbf{b})\mathbf{c}}{{{p}^{2}}}\] done clear
D) \[\frac{\mathbf{c}}{{{p}^{2}}}-\frac{(\mathbf{b}\cdot \mathbf{c})\mathbf{a}}{p}\] done clear
View Answer play_arrowquestion_answer132) If \[A\] satisfies the equation\[{{x}^{3}}-5{{x}^{2}}+4x\]\[+\lambda =O\], then \[{{A}^{-1}}\] exists if
A) \[\lambda \ne 1\] done clear
B) \[\lambda \ne 2\] done clear
C) \[\lambda \ne -1\] done clear
D) \[\lambda \ne 0\] done clear
View Answer play_arrowquestion_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
A) \[12.5\,\,\min \] done clear
B) \[135\,\,\min \] done clear
C) \[34\,\,\min \] done clear
D) \[24\,\,\min \] done clear
View Answer play_arrowquestion_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
A) \[8\] done clear
B) \[10\] done clear
C) \[16\] done clear
D) None of these done clear
View Answer play_arrowquestion_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
A) \[-1\] done clear
B) \[-3\] done clear
C) \[-2\] done clear
D) \[-1/2\] done clear
View Answer play_arrowquestion_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
A) \[\sin t=\frac{2{{a}^{2}}+{{b}^{2}}}{3ab}\] done clear
B) \[\cos t=\frac{{{a}^{2}}+2{{b}^{2}}}{3ab}\] done clear
C) \[\tan t=a/b\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer137) The weighted mean of first n natural numbers whose weights are equal, is given by
A) \[\frac{n+1}{2}\] done clear
B) \[\frac{2n+1}{2}\] done clear
C) \[\frac{2n+1}{3}\] done clear
D) \[\frac{(2n+1)(n+1)}{6}\] done clear
View Answer play_arrowquestion_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
A) \[3\] done clear
B) \[6\] done clear
C) \[9\] done clear
D) \[12\] done clear
View Answer play_arrowquestion_answer139) \[\frac{d}{dx}\left\{ {{\sin }^{2}}x\left( {{\cot }^{-1}}\sqrt{\frac{1-x}{1+x}} \right) \right\}\]equals
A) \[-1\] done clear
B) \[1/2\] done clear
C) \[-1/2\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_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
A) 4920 done clear
B) 3720 done clear
C) 3600 done clear
D) 4800 done clear
View Answer play_arrowquestion_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,
A) \[A\subset B\] done clear
B) \[B\subset A\] done clear
C) \[A=B\] done clear
D) None of these done clear
View Answer play_arrowquestion_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
A) \[9\] done clear
B) \[3\] done clear
C) \[1/9\] done clear
D) \[1/3\] done clear
View Answer play_arrowquestion_answer143) The set of values of a for which the equation \[\sin x(\sin x+\cos x)=a\]has real solutions, is
A) \[[1-\sqrt{2},\,\,1+\sqrt{2}]\] done clear
B) \[[2-\sqrt{3},\,\,2+\sqrt{3}]\] done clear
C) \[[0,\,\,2+\sqrt{3}]\] done clear
D) \[\left[ \frac{1-\sqrt{2}}{2},\,\,\frac{1+\sqrt{2}}{2} \right]\] done clear
View Answer play_arrowquestion_answer144) If\[x\sin \theta =y\sin \left( \theta +\frac{2\pi }{3} \right)=z\sin \left( \theta +\frac{4\pi }{3} \right)\] then
A) \[x+y+z=0\] done clear
B) \[xy+yz+zx=0\] done clear
C) \[xyz+x+y+z=1\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer145) Let\[f(x)=2{{\tan }^{-1}}x+{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\]. Then,
A) \[f'(2)=f'(3)\] done clear
B) \[f'(2)=0\] done clear
C) \[f'(1/2)=16/5\] done clear
D) All of these done clear
View Answer play_arrowquestion_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
A) \[0\] done clear
B) \[1\] done clear
C) \[\sqrt{2}\] done clear
D) \[2\sqrt{2}\] done clear
View Answer play_arrowquestion_answer147) The number of integral triplets \[(a,\,\,b,\,\,c)\] such that\[a+b\cos 2x+c{{\sin }^{2}}x=0\]for all\[x,\]is
A) \[0\] done clear
B) \[1\] done clear
C) \[3\] done clear
D) infinitely many done clear
View Answer play_arrowquestion_answer148) The point on the line \[\frac{x-2}{1}=\frac{y+3}{-2}=\frac{z+5}{-2}\] at a distance of 6 from the point \[(2,\,\,-3,\,\,-5)\] is
A) \[(3,\,\,-5,\,\,-3)\] done clear
B) \[(4,\,\,-7,\,\,-9)\] done clear
C) \[(0,\,\,2,\,\,-1)\] done clear
D) \[(-3,\,\,5,\,\,3)\] done clear
View Answer play_arrowquestion_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
A) \[(2,\,\,3)\] done clear
B) \[(2,\,\,\sqrt{3})\] done clear
C) \[(\sqrt{3},\,\,2)\] done clear
D) \[(\sqrt{3},\,\,5)\] done clear
View Answer play_arrowquestion_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
A) \[(-2,\,\,1)\] done clear
B) \[(-\infty ,\,\,-2)\cup (0,\,\,1)\] done clear
C) \[(-2,\,\,0)\cup (1,\,\,\infty )\] done clear
D) \[(-1,\,\,0)\cup (2,\,\,\infty )\] done clear
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