question_answer1) The length of a simple pendulum is about 100 cm known to an accuracy of 1mm. Its period of oscillation is 2s determined by measuring the time for 100 oscillations using a clock of 0.1 s resolution. What is the accuracy in the determined value of g?
A) 0.2% done clear
B) 0.5% done clear
C) 0.1% done clear
D) 2% done clear
View Answer play_arrowquestion_answer2) Youngs modulus of the material of a wire is V. On pulling the wire by a force F, the increase in its length is x. The potential energy of the stretched wire is:
A) \[\frac{1}{2}Fx\] done clear
B) \[\frac{1}{2}Yx\] done clear
C) \[\frac{1}{2}F{{x}^{2}}\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer3) A charge situated at a certain distance along the axis of an electric dipole experiences a force F. If the distance of the charge from the dipole is doubled, the force acting on it will become:
A) \[2F\] done clear
B) \[\frac{F}{2}\] done clear
C) \[\frac{F}{4}\] done clear
D) \[\frac{F}{8}\] done clear
View Answer play_arrowquestion_answer4) Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non- conducting sphere of radius R?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer5) A certain electrical conductor has a square cross-section, 2.0 mm on side, and is 12 m long. The resistance between its ends is 0.072\[\Omega .\] The resistivity of its material is equal to :
A) \[2.4\times {{10}^{-6}}\Omega m\] done clear
B) \[1.2\times {{10}^{-6}}\Omega m\] done clear
C) \[1.2\times {{10}^{-8}}\Omega m\] done clear
D) \[2.4\times {{10}^{-8}}\Omega m\] done clear
View Answer play_arrowquestion_answer6) Figure shows three points A, B and C in a region of uniform electric field \[\mathbf{\vec{E}}\]. The line AB is perpendicular and BC is parallel to the field lines. Then which of the following holds good?
A) \[{{\text{V}}_{\text{A}}}\text{=}{{\text{V}}_{\text{B}}}\text{=}{{\text{V}}_{\text{C}}}\] done clear
B) \[{{\text{V}}_{\text{A}}}\text{=}{{\text{V}}_{\text{B}}}\text{}{{\text{V}}_{\text{C}}}\] done clear
C) \[{{\text{V}}_{\text{A}}}\text{=}{{\text{V}}_{\text{B}}}\text{}{{\text{V}}_{\text{C}}}\] done clear
D) \[{{\text{V}}_{\text{A}}}\text{}{{\text{V}}_{\text{B}}}\text{=}{{\text{V}}_{\text{C}}}\] done clear
View Answer play_arrowquestion_answer7) The (x, y, z) coordinates of two points A and B are given respectively as (0, 3,-1) and (-2, 6, 4). The displacement vector form A to B may be given by:
A) \[-2\mathbf{\hat{i}}+6\mathbf{\hat{j}}+4\mathbf{\hat{k}}\] done clear
B) \[-2\mathbf{\hat{i}}+3\mathbf{\hat{j}}+3\mathbf{\hat{k}}\] done clear
C) \[-2\mathbf{\hat{i}}+3\mathbf{\hat{j}}+5\mathbf{\hat{k}}\] done clear
D) \[2\mathbf{\hat{i}}-3\mathbf{\hat{j}}-5\mathbf{\hat{k}}\] done clear
View Answer play_arrowquestion_answer8) In the first second of its flight, rocket ejects 1/60 of its mass with a velocity of \[2400\,\,m{{s}^{-1}}\]. The acceleration of the rocket is:
A) \[19.6\,m{{s}^{-2}}\] done clear
B) \[30.2\,m{{s}^{-2}}\] done clear
C) \[40\,m{{s}^{-2}}\] done clear
D) \[49.8\,\,m{{s}^{-2}}\] done clear
View Answer play_arrowquestion_answer9) In the given figure the pulley is assumed massless and frictionless. If the friction force on the object of mass m is \[f\], then its acceleration in terms of the force F will be equal to:
A) \[(F-f)/m\] done clear
B) \[\left( \frac{F}{2}-f \right)/m\] done clear
C) F/m done clear
D) none of these done clear
View Answer play_arrowquestion_answer10) The equivalent resistance between the points P and Q in the network shown in the figure is given by:
A) 2.5 \[\Omega \] done clear
B) 7.5 \[\Omega \] done clear
C) 10 \[\Omega \] done clear
D) 12.5 \[\Omega \] done clear
View Answer play_arrowquestion_answer11) The magnetic field amplitude of an electromagnetic wave is \[2\times {{10}^{-7}}T\], Its electric field amplitude, if the wave is travelling in free space is:
A) \[6\,\,V{{m}^{-1}}\] done clear
B) \[60\,\,V{{m}^{-1}}\] done clear
C) \[\frac{1}{6}\,V{{m}^{-1}}\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer12) A can is moving horizontally along a straight line with constant speed 30 m/s. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 80 m. At what speed (relative to the can) must the projectile be fired? (Takes \[=10\,m/{{s}^{2}}\])
A) 10 m/s done clear
B) \[10\sqrt{8}\]m/s done clear
C) \[\frac{40}{3}\] m/s done clear
D) None of these done clear
View Answer play_arrowquestion_answer13) A boy begins to walk eastward along a street In front of his house, and the graph of his displacement from home is shown in the following figure. His average velocity for the whole time interval is equal to:
A) \[\text{8}\,\text{m/min}\] done clear
B) \[6\,\text{m/min}\] done clear
C) \[\frac{8}{3}\,\text{m/min}\] done clear
D) \[\text{2}\,\text{m/min}\] done clear
View Answer play_arrowquestion_answer14) What is the potential drop between points A and C in the following circuit ? Resistances 1\[\Omega \] and 2\[\Omega \] represent the internal resistances of the respective cells.
A) 1.75V done clear
B) 2.25V done clear
C) \[\frac{\text{5}}{\text{4}}\text{V}\] done clear
D) \[\frac{4}{5}\text{V}\] done clear
View Answer play_arrowquestion_answer15) The escape velocity of a projectile on the earths surface is \[11.2\,\,km{{s}^{-1}}\]. A body is projected out with thrice this speed. The speed of the body far away from the earth will be:
A) \[22.4\,km{{s}^{-1}}\] done clear
B) \[31.7\,km{{s}^{-1}}\] done clear
C) \[33.6\,km{{s}^{-1}}\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer16) A body moves along a circular pa-h of radius 10 m and the coefficient of friction is 0.5. What should be its angular speed in rad/s, if it is not to slip from the surface? \[(g=9.8\,m{{s}^{-2}})\]
A) 5 done clear
B) 10 done clear
C) 0.1 done clear
D) 0.7 done clear
View Answer play_arrowquestion_answer17) One end of a string of length I is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v, the net force on the particle (directed towards the centre) is:
A) \[T\] done clear
B) \[T-\frac{m{{v}^{2}}}{l}\] done clear
C) \[T+\frac{m{{v}^{2}}}{l}\] done clear
D) zero done clear
View Answer play_arrowquestion_answer18) A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to:
A) \[{{t}^{1/2}}\] done clear
B) \[t\] done clear
C) \[{{t}^{3/2}}\] done clear
D) \[{{t}^{2}}\] done clear
View Answer play_arrowquestion_answer19) In the adjacent figure is shown a closed path P. A long straight conductor carrying a current \[I\]passes through O and perpendicular to the plane of the paper. Then which of the following holds good?
A) \[\int_{P}^{{}}{{\mathbf{\vec{B}}}}\,\mathbf{\vec{d}1}=0\] done clear
B) \[\int_{P}^{{}}{{\mathbf{\vec{B}}}}\,\mathbf{\vec{d}1}={{\mu }_{0}}I\] done clear
C) \[\int_{P}^{{}}{{\mathbf{\vec{B}}}}\,\mathbf{\vec{d}1}>{{\mu }_{0}}I\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer20) Two circular, similar, coaxial loops carry equal currents in the same direction, if the loops are brought nearer, what will happen?
A) Current will increase in each loop done clear
B) Current will decrease in each loop done clear
C) Current will remain same in each loop done clear
D) Current will increase in one and decrease in the other done clear
View Answer play_arrowquestion_answer21) The figure below shows the plot of \[\frac{PV}{nT}\] versus P for oxygen gas at two different temperatures. Read the following statements concerning the above curves:
(i) The dotted line corresponds to the ideal gas behaviour. |
(ii) \[{{T}_{1}}>{{T}_{2}}\] |
(iii) The value of \[\frac{PV}{nT}\]at the point where the curves meet on the y-axis is the same for all gases. |
A) (i) only done clear
B) (i) and (ii) only done clear
C) All of these done clear
D) None of these done clear
View Answer play_arrowquestion_answer22) The following figure represents the temperature versus time plot for a given amount of a substance when heat energy is supplied to it at a fixed rate and at a constant pressure. Which parts of the above plot represent a phase change?
A) a to b and e to \[f\] done clear
B) b to c and c to d done clear
C) d to e and e to \[f\] done clear
D) b to c and d to e done clear
View Answer play_arrowquestion_answer23) A bar magnet has a coercivity \[4\times {{10}^{3}}\,A{{m}^{-1}}\]. It is desired to demagnetise it by inserting it inside a solenoid 12 cm long and having 60 turns. The current carried by the solenoid should be:
A) 8 A done clear
B) 6 A done clear
C) 4.5 A done clear
D) 2 A done clear
View Answer play_arrowquestion_answer24) In a series LCR circuit the frequency of a 10 VAC voltage source is adjusted in such a fashion that the reactance of the inductor measures 15 \[\Omega \] and that of capacitor 11\[\Omega \]. If R = 3 \[\Omega \] the potential difference across the series combination of L and C will be:
A) 8 V done clear
B) 10 V done clear
C) 22 V done clear
D) 52 V done clear
View Answer play_arrowquestion_answer25) A circuit draws 330 W from a 110 V, 60 Hz AC line. The power factor is 0.6 and the current lags the voltage. The capacitance of a series capacitor that will result in a power factor of unity is equal to:
A) 31 \[\mu F\] done clear
B) 54 \[\mu F\] done clear
C) 151 \[\mu F\] done clear
D) 201 \[\mu F\] done clear
View Answer play_arrowquestion_answer26) If the focal length of the lens is 20 cm, what is the distance of the image from the lens in the following figure?
A) 5.5 cm done clear
B) 7.5 cm done clear
C) 12.0 cm done clear
D) 20.0 cm done clear
View Answer play_arrowquestion_answer27) An open U-tube contains mercury. When 11.2 cm of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm form its initial level?
A) 0.56 cm done clear
B) 1.35 cm done clear
C) 0.41 cm done clear
D) 2.32 cm done clear
View Answer play_arrowquestion_answer28) The change in the entropy of a 1 mole of an ideal gas which went through an isothermal process from an initial state\[({{P}_{1}},{{V}_{1,}}T)\] to the final state \[({{P}_{2}},{{V}_{2,}}T)\] is equal to:
A) zero done clear
B) \[\text{R}\,\text{In}\,\text{T}\] done clear
C) \[\text{R}\,\text{In}\,\frac{{{\text{V}}_{1}}}{{{\text{V}}_{2}}}\] done clear
D) \[\text{R}\,\text{In}\,\frac{{{\text{V}}_{\text{2}}}}{{{\text{V}}_{\text{1}}}}\] done clear
View Answer play_arrowquestion_answer29) An unpolarized beam of light is incident on a glass surface at an angle of incidence equal to the polarizing angle of the glass. Read the following statements:
(i) The reflected beam is completely polarized. |
(ii) The refracted beam is partially polarized. |
(iii) The angle between the reflected and the refracted beams is \[90{}^\circ \]. |
A) (i) only done clear
B) (ii) only done clear
C) (i) and (iii) done clear
D) All the statements are correct done clear
View Answer play_arrowquestion_answer30) The threshold frequency for certain metal is \[3.3\times {{10}^{14}}Hz\]. If light of frequency \[8.2\,\times {{10}^{14}}Hz\] is incident on the metal, the cut-off voltage of the photoelectric current will be:
A) 4.9 V done clear
B) 3.0 V done clear
C) 2.0 V done clear
D) 1.0 V done clear
View Answer play_arrowquestion_answer31) Frequencies higher than 10 MHz were found not being reflected by the ionosphere on a particular day at a place. The maximum electron density of the ionosphere on the day was near to:
A) \[1.5\times {{10}^{10}}{{m}^{-3}}\] done clear
B) \[1.24\times {{10}^{12}}{{m}^{-3}}\] done clear
C) \[3\times {{10}^{12}}{{m}^{-3}}\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer32) The de-Broglie wavelength of an electron, \[\alpha \]-particle and a proton all having the same kinetic energy is respectively given as \[{{\lambda }_{e,}}{{\lambda }_{\alpha }}\] and \[{{\lambda }_{P.}}\] Then which of the following is not true ?
A) \[{{\lambda }_{e}}>{{\lambda }_{P}}\] done clear
B) \[{{\lambda }_{p}}>{{\lambda }_{\alpha }}\] done clear
C) \[{{\lambda }_{e}}>{{\lambda }_{\alpha }}\] done clear
D) \[{{\lambda }_{\alpha }}<{{\lambda }_{p}}<{{\lambda }_{e}}\] done clear
View Answer play_arrowquestion_answer33) What is the disintegration constant of radon, if the number of its atoms diminishes by 18% in 24 h?
A) \[2.1\times {{10}^{-3}}{{s}^{-1}}\] done clear
B) \[2.1\times {{10}^{-4}}{{s}^{-1}}\] done clear
C) \[2.1\times {{10}^{-5}}{{s}^{-1}}\] done clear
D) \[2.1\times {{10}^{-6}}{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer34) Which of the following statements is true for an n-type semiconductor?
A) The donor level lies closely below the bottom of the conduction band done clear
B) The donor level lies closely above the top of the valence band done clear
C) The donor level lies at the halfway mark of the forbidden energy gap done clear
D) None of the above done clear
View Answer play_arrowquestion_answer35) Carbon, silicon and germanium have four valence electrons each. These are characterized by valence and conduction bands separated by energy band gap respectively equal to \[{{({{E}_{g}})}_{C}}\] \[{{({{E}_{g}})}_{Si}}\]and \[{{({{E}_{g}})}_{Ge.}}\]. Which of the following statements is true?
A) \[{{({{E}_{g}})}_{C}}={{({{E}_{g}})}_{Si}}={{({{E}_{g}})}_{Ge}}\] done clear
B) \[{{({{E}_{g}})}_{C}}>{{({{E}_{g}})}_{Si}}>{{({{E}_{g}})}_{Ge}}\] done clear
C) \[{{({{E}_{g}})}_{C}}<{{({{E}_{g}})}_{Ge}}>{{({{E}_{g}})}_{Si}}\] done clear
D) \[{{({{E}_{g}})}_{Si}}<{{({{E}_{g}})}_{Ge}}>{{({{E}_{g}})}_{C}}\] done clear
View Answer play_arrowquestion_answer36) A particle executes SHM of amplitude 25 cm and time period 3 s. What is the minimum time required for the particle to move between two points 12.5 cm on either side of the mean position?
A) 0.5s done clear
B) 1.0s done clear
C) 1.5s done clear
D) 2.0s done clear
View Answer play_arrowquestion_answer37) The speed of a wave on a string is 150 m/s when the tension is 120 N. The percentage increase the tension in order to raise the wave speed by 20% is:
A) 44% done clear
B) 40% done clear
C) 20% done clear
D) 10% done clear
View Answer play_arrowquestion_answer38) A straight rod of length L has one of its ends at the origin and the other at x - L. If the mass per unit length of the rod is given by A x, where A is constant, where is its mass centre?
A) \[\frac{L}{3}\] done clear
B) \[\frac{L}{2}\] done clear
C) \[\frac{2L}{3}\] done clear
D) \[\frac{3L}{4}\] done clear
View Answer play_arrowquestion_answer39) The image of a small electric bulb fixed on the wall of a room is to be obtained on the oppose wall 4 m away by means of a large convex lens. The maximum possible focal length of the lens required for this purpose will be:
A) 0.5 m done clear
B) 1.0 m done clear
C) 1.5 m done clear
D) 2.0 m done clear
View Answer play_arrowquestion_answer40) The total energy of a satellite moving with an orbital velocity v around the earth is:
A) \[\frac{1}{2}m{{v}^{2}}\] done clear
B) \[-\frac{1}{2}m{{v}^{2}}\] done clear
C) \[m{{v}^{2}}\] done clear
D) \[\frac{3}{2}m{{v}^{2}}\] done clear
View Answer play_arrowquestion_answer41) In hydrogen atom, the electron is moving round the nucleus with velocity \[2.18\,\times {{10}^{6\,}}m/s\] in an orbit of radius \[0.528\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. The acceleration of the electron is:
A) \[9\times {{10}^{18}}m/{{s}^{2}}\] done clear
B) \[9\times {{10}^{22}}m/{{s}^{2}}\] done clear
C) \[9\times {{10}^{-22}}m/{{s}^{2}}\] done clear
D) \[9\times {{10}^{12}}m/{{s}^{2}}\] done clear
View Answer play_arrowquestion_answer42) When a spring is stretched by a distance x, it exerts a force given by \[F=(-5x-16{{x}^{3}})N\]The work done, when the spring is stretched from 0.1 m to 0.2 m is:
A) \[\text{8}\text{.7 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-2}}}\text{J}\] done clear
B) \[\text{12}\text{.2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-2}}}\text{J}\] done clear
C) \[\text{8}\text{.1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-1}}}\text{J}\] done clear
D) \[\text{12}\text{.2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-1}}}\text{J}\] done clear
View Answer play_arrowquestion_answer43) The flow of liquid is laminar or stream line is determined by:
A) rate of flow of liquid done clear
B) density of fluid done clear
C) radius of the tube done clear
D) coefficient of viscosity of liquid done clear
View Answer play_arrowquestion_answer44) If boiling point of water is \[95{}^\circ F\], what will be reduction at Celsius scale?
A) \[7{}^\circ C\] done clear
B) \[65{}^\circ C\] done clear
C) \[63{}^\circ C\] done clear
D) \[35{}^\circ C\] done clear
View Answer play_arrowquestion_answer45) The motion of a particle varies with time according to the relation \[y=a(\sin \,\omega t\,+\cos \,\omega t).\]
A) The motion is oscillatory but not SHM done clear
B) The motion is SHM with amplitude \[a\] done clear
C) The motion is SHM with amplitude \[\alpha \sqrt{2}\] done clear
D) The motion is SHM with amplitude \[2\alpha \] done clear
View Answer play_arrowquestion_answer46) Two closed organ pipes A and B have the same length. A is wider than B. They resonate in the fundamental mode at frequencies \[{{n}_{A}}\] and \[{{n}_{B}}\] respectively, then:
A) \[{{n}_{A}}={{n}_{B}}\] done clear
B) \[{{n}_{A}}>{{n}_{B}}\] done clear
C) \[{{n}_{A}}<{{n}_{B}}\] done clear
D) either (b) or (c) depending on the ratio of their diameters done clear
View Answer play_arrowquestion_answer47) Two waves having sinusoidal waveforms have different wavelengths and different amplitudes. They will be having:
A) same pitch and different intensity done clear
B) same quality and different intensity done clear
C) different quality and different intensity done clear
D) same quality and different pitch done clear
View Answer play_arrowquestion_answer48) In double slit experiment, the distance between two slits is 0.6 mm and these are illuminated with light of wavelength \[4800\overset{\text{o}}{\mathop{\text{A}}}\,\]. The angular width of first dark fringe on the screen distant 120 cm from slits will be:
A) \[\text{8 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\] done clear
B) \[\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\] done clear
C) \[\text{4 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\] done clear
D) \[\text{16 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\,\text{rad}\] done clear
View Answer play_arrowquestion_answer49) If there were no atmosphere, the average temperature on the surface of the earth would be:
A) lower done clear
B) higher done clear
C) same as now done clear
D) \[0{}^\circ \] done clear
View Answer play_arrowquestion_answer50) The ionization energy of 10 times ionized sodium atom is:
A) \[\frac{\text{13}\text{.6}}{\text{11}}\text{eV}\] done clear
B) \[\frac{\text{13}\text{.6}}{\text{112}}\text{eV}\] done clear
C) \[\text{13}\text{.6}\times {{\text{(11)}}^{2}}\,\text{eV}\] done clear
D) \[\text{13}\text{.6}\,\text{eV}\] done clear
View Answer play_arrowquestion_answer51) When \[C{{H}_{3}}COOH\]reacts with \[C{{H}_{3}}-MgX:\]
A) \[C{{H}_{3}}COX\] is formed done clear
B) hydrocarbon is formed done clear
C) acetone is formed done clear
D) alcohol is formed done clear
View Answer play_arrowquestion_answer52) A cyclic hydrocarbon molecule has all the carbon and hydrogen is a single plane. All the carbon-carbon bonds are of same length, less than\[1.54\,\overset{\text{o}}{\mathop{\text{A}}}\,,\] but more than \[1.34\overset{\text{o}}{\mathop{\text{A}}}\,.\] The C-C bond angle will be:
A) \[{{109}^{o}}28\] done clear
B) \[{{100}^{o}}\] done clear
C) \[{{180}^{o}}\] done clear
D) \[{{120}^{o}}\] done clear
View Answer play_arrowquestion_answer53) Which will reduce zinc oxide to zinc?
A) Mg done clear
B) Pb done clear
C) Cu done clear
D) Fe done clear
View Answer play_arrowquestion_answer54) Some chemists at ISRO wished to prepare a saturated solution of a silver compound and they wanted it to have the highest concentration of silver ion possible. Which of the following compounds, would they use? \[{{K}_{sp}}(AgCl)=1.8\times {{10}^{-10}},\] \[{{K}_{sp}}(AgBr)=5.0\times {{10}^{-13}},\] \[{{K}_{sp}}(A{{g}_{2}}Cr{{O}_{4}})=2.4\times {{10}^{-12}}\]
A) \[AgCl\] done clear
B) \[AgBr\] done clear
C) \[A{{g}_{2}}Cr{{O}_{4}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer55) By Wurtz reaction, a mixture of methyl iodide and ethyl iodide gives :
A) butane done clear
B) ethane done clear
C) propane done clear
D) A mixture of the above three done clear
View Answer play_arrowquestion_answer56) Addition of \[SnC{{l}_{2}}\]to \[\text{HgC}{{\text{l}}_{\text{2}}}\] gives precipitate:
A) white turning to red done clear
B) white turning to grey done clear
C) black turning to white done clear
D) none of the above done clear
View Answer play_arrowquestion_answer57) In fermentation by zymase, alcohol and \[C{{O}_{2}}\]are obtained from:
A) invert sugar done clear
B) glucose done clear
C) fructose done clear
D) all of these done clear
View Answer play_arrowquestion_answer58) The stability of ferric ion is due to:
A) half filled \[f-\]orbitals done clear
B) half filled \[d-\]orbitals done clear
C) completely filled \[f-\]orbitals done clear
D) completely filled \[d-\]orbitals done clear
View Answer play_arrowquestion_answer59) Electron affinity is positive, when:
A) O changes into\[{{O}^{-}}\] done clear
B) \[{{O}^{-}}\]changes into \[{{O}^{2-}}\] done clear
C) O changes into \[{{O}^{+}}\] done clear
D) electron affinity is always negative done clear
View Answer play_arrowquestion_answer60) Ionization potential for a noble gas is:
A) maximum in a period done clear
B) minimum in a period done clear
C) either minimum or maximum done clear
D) constant done clear
View Answer play_arrowquestion_answer61) Ethylamine on a acetylation gives:
A) N-ethyl acetamide done clear
B) acetamide done clear
C) methyl acetamide done clear
D) none of the above done clear
View Answer play_arrowquestion_answer62) Strongest oxidizing agent among halogen is:
A) \[{{I}_{2}}\] done clear
B) \[B{{r}_{2}}\] done clear
C) \[C{{I}_{2}}\] done clear
D) \[{{F}_{2}}\] done clear
View Answer play_arrowquestion_answer63) Which reagent can convert acetic acid into ethanol?
A) \[\text{Na + alcohol}\] done clear
B) \[LiAl{{H}_{4}}+\text{ether}\] done clear
C) \[{{H}_{2}}+Pt\] done clear
D) \[Sn+HCl\] done clear
View Answer play_arrowquestion_answer64) In presence of moisture, \[S{{O}_{2}}\]can:
A) act as oxidant done clear
B) act as reductant done clear
C) gain electron done clear
D) not act as reductant done clear
View Answer play_arrowquestion_answer65) Acetals are:
A) ketones done clear
B) diethers done clear
C) aldehyde done clear
D) hydroxy aldehydes done clear
View Answer play_arrowquestion_answer66) The principle involved in the classification of basic radicals, is:
A) common ion effect done clear
B) solubility product done clear
C) valency of radicals done clear
D) strength of salt done clear
View Answer play_arrowquestion_answer67) Formation of diethyl ether from ethanol is based on a:
A) dehydration reaction done clear
B) dehydrogenation reaction done clear
C) hydrogenation reaction done clear
D) homolytic fission reaction done clear
View Answer play_arrowquestion_answer68) Hypo phosphorus acid,\[{{H}_{3}}P{{O}_{2}}\] is:
A) a monobasic acid done clear
B) a tribasic acid done clear
C) a dibasic acid done clear
D) not acidic at all done clear
View Answer play_arrowquestion_answer69) What is obtained when acetyl chloride is heated with benzene in presence of anhydrous\[\text{AlC}{{\text{l}}_{\text{3}}}\]?
A) Acetyl benzoic acid done clear
B) Anisol done clear
C) Acetophenone done clear
D) Chlorobenzene done clear
View Answer play_arrowquestion_answer70) Which gas is used in airated water?
A) \[C{{O}_{2}}\] done clear
B) \[S{{O}_{2}}\] done clear
C) CO done clear
D) Water vapours done clear
View Answer play_arrowquestion_answer71) The refluxing of \[{{(C{{H}_{3}})}_{2}}NCOC{{H}_{3}}\] with acid gives:
A) \[{{(C{{H}_{3}})}_{2}}NH+C{{H}_{3}}COOH\] done clear
B) \[{{(C{{H}_{3}})}_{2}}NCOOH+C{{H}_{4}}\] done clear
C) \[2C{{H}_{3}}OH+C{{H}_{3}}CON{{H}_{2}}\] done clear
D) \[2C{{H}_{3}}N{{H}_{2}}+C{{H}_{3}}COOH\] done clear
View Answer play_arrowquestion_answer72) Which is obtained on treating phenol with dilute\[HN{{O}_{3}}\]?
A) done clear
B) done clear
C) done clear
D) None of these done clear
View Answer play_arrowquestion_answer73) Solder is an alloy of lead with:
A) copper done clear
B) zinc done clear
C) nickel done clear
D) tin done clear
View Answer play_arrowquestion_answer74) Arrange\[NH_{4}^{+},{{H}_{2}}O,{{H}_{3}}{{O}^{+}}.HF\] and \[O{{H}^{-}}\]in increasing order of acidic nature:
A) \[{{H}_{3}}\overset{+}{\mathop{O}}\,<NH_{4}^{+}<HF<O{{H}^{-}}<{{H}_{2}}O\] done clear
B) \[NH_{4}^{+}<HF<{{H}_{3}}{{O}^{+}}<{{H}_{2}}O<O{{H}^{-}}\] done clear
C) \[H{{O}^{-}}<{{H}_{2}}O<NH_{4}^{+}<HF<{{H}_{3}}{{O}^{+}}\] done clear
D) \[{{H}_{3}}O{{\,}^{+}}>HF>{{H}_{2}}O>NH_{4}^{+}>O{{H}^{-}}\] done clear
View Answer play_arrowquestion_answer75) Which of the following radicals gives the apple green flame during flame test?
A) \[B{{a}^{2+}}\] done clear
B) \[S{{r}^{2+}}\] done clear
C) \[C{{a}^{2+}}\] done clear
D) \[C{{r}^{3+}}\] done clear
View Answer play_arrowquestion_answer76) When chlorine is passed through concentrated solution of KOH, the compound formed is:
A) \[KCl{{O}_{4}}\] done clear
B) \[KCl{{O}_{3}}\] done clear
C) \[KCl{{O}_{2}}\] done clear
D) \[KClO\] done clear
View Answer play_arrowquestion_answer77) The equilibrium constant\[{{K}_{p}}\] for the reaction \[{{H}_{2}}(g)+{{I}_{2}}(g)2HI(g)\]is:
A) more than one done clear
B) less than one done clear
C) equal to\[{{K}_{c}}\] done clear
D) zero done clear
View Answer play_arrowquestion_answer78) What is the weight of oxygen that is required the complete combustion of 2.8 kg of ethylene?
A) 9.6 kg done clear
B) 96.0 kg done clear
C) 6.4 kg done clear
D) 2.8 kg done clear
View Answer play_arrowquestion_answer79) The metal that does not displace hydrogen from an acid is:
A) Ca done clear
B) Al done clear
C) Zn done clear
D) Hg done clear
View Answer play_arrowquestion_answer80) The decomposition of \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]occurs as, \[\text{2}{{\text{N}}_{2}}{{O}_{5}}\xrightarrow{{}}4{{N}_{2}}+{{O}_{2}},\] and follows Ist order kinetics, hence:
A) the reaction is unimolecular done clear
B) the reaction is bimolecular done clear
C) \[{{t}_{1/2}}\propto {{a}^{o}}\] done clear
D) none of the above done clear
View Answer play_arrowquestion_answer81) Atomic radii of F and Ne, in \[\overset{\text{o}}{\mathop{\text{A}}}\,,\]are given by:
A) \[0.72,0.71\] done clear
B) \[~0.72,1.6\] done clear
C) \[1.6,\text{ }1.58\] done clear
D) \[~0.71,\text{ }0.72\] done clear
View Answer play_arrowquestion_answer82) Which pair has both members from the same period of periodic table?
A) \[Cl,Br\] done clear
B) \[~Ca,Cl\] done clear
C) \[~Na,Ca\] done clear
D) \[~Na,Cl\] done clear
View Answer play_arrowquestion_answer83) When dilute aqueous solution of \[\text{AgN}{{\text{O}}_{\text{3}}}\](excess) is added to KI solution, positively charged sol of \[\text{AgI}\]is formed due to adsorption of:
A) \[NO_{3}^{-}\] done clear
B) \[O_{2}^{-}\] done clear
C) \[A{{g}^{+}}\] done clear
D) \[{{K}^{+}}\] done clear
View Answer play_arrowquestion_answer84) Which of the following has largest ionic radius?
A) \[C{{s}^{+}}\] done clear
B) \[L{{i}^{+}}\] done clear
C) \[N{{a}^{+}}\] done clear
D) \[{{K}^{+}}\] done clear
View Answer play_arrowquestion_answer85) For \[CaC{{O}_{3}}(s)CaO(s)+C{{O}_{2}}(g)\]at \[927{{\,}^{o}}C,\]\[\Delta H=176\,kJ\,\text{mol}\,;\]then \[\Delta E\]is:
A) 180 kJ done clear
B) 186.4 kJ done clear
C) 166.0 kJ done clear
D) 160 kJ done clear
View Answer play_arrowquestion_answer86) The charge required to liberate one gram equivalent of an element is:
A) 96500 F done clear
B) 1 F done clear
C) 1 C done clear
D) none of these done clear
View Answer play_arrowquestion_answer87) The shape of sulphate ion is:
A) square planar done clear
B) trigonal done clear
C) trigonal planar done clear
D) tetrahedral done clear
View Answer play_arrowquestion_answer88) The H-H bond energy is \[430\text{ }kJ\text{ }mo{{l}^{-1}}\] and \[ClCl\]bond energy is \[240\text{ }kJ\text{ }mo{{l}^{-1}},\]\[\Delta H\] for \[HCl\]is \[-\text{ }90\text{ }kJ.\] The \[HCl\]bond energy is about:
A) \[180\text{ }kJ\text{ }mo{{l}^{-1}}\] done clear
B) \[360\text{ }kJ\text{ }mo{{l}^{-1}}\] done clear
C) \[~213\text{ }kJ\text{ }mo{{l}^{-1}}\] done clear
D) \[425\text{ }kJ\text{ }mo{{l}^{-1}}\] done clear
View Answer play_arrowquestion_answer89) In the equation \[{{H}_{2}}S+2HN{{O}_{3}}\xrightarrow{{}}2{{H}_{2}}O+2N{{O}_{2}}+S.\]The equivalent weight of hydrogen sulphide is:
A) 18 done clear
B) 68 done clear
C) 34 done clear
D) 17 done clear
View Answer play_arrowquestion_answer90) The energy released in an atom bomb explosion is mainly due to:
A) release of neutrons done clear
B) release of electrons done clear
C) greater mass of products than initial material done clear
D) lesser mass of products than initial material done clear
View Answer play_arrowquestion_answer91) Highest entropy is in:
A) hydrogen done clear
B) water done clear
C) graphite done clear
D) mercury done clear
View Answer play_arrowquestion_answer92) Which one will liberate \[B{{r}_{2}}\]from\[KBr\]?
A) \[{{I}_{2}}\] done clear
B) \[S{{O}_{2}}\] done clear
C) \[HI\] done clear
D) \[C{{l}_{2}}\] done clear
View Answer play_arrowquestion_answer93) Nuclides:
A) have specific atomic numbers done clear
B) have same number of protons done clear
C) have specific atomic number and mass numbers done clear
D) are isotopes done clear
View Answer play_arrowquestion_answer94) Arrhenius equation is:
A) \[\Delta H=\Delta E+\Delta {{n}_{g}}RT\] done clear
B) \[\Delta G=\Delta H-T.\Delta S\] done clear
C) \[K=A{{e}^{-{{E}_{a}}/RT}}\] done clear
D) none of the above done clear
View Answer play_arrowquestion_answer95) In which of the following compounds, the oxidation number of iodine is fractional?
A) \[I{{F}_{3}}\] done clear
B) \[I{{F}_{5}}\] done clear
C) \[I_{3}^{-}\] done clear
D) \[I{{F}_{7}}\] done clear
View Answer play_arrowquestion_answer96) Non-directional orbital is:
A) \[4p\] done clear
B) \[4d\] done clear
C) \[4f\] done clear
D) \[3s\] done clear
View Answer play_arrowquestion_answer97) A monoprotic acid in 1.00 M solution is 0.01% ionized. The dissociation constant of this acid is:
A) \[1\times {{10}^{-8}}\] done clear
B) \[1\times {{10}^{-4}}\] done clear
C) \[1\times {{10}^{-6}}\] done clear
D) \[1\times {{10}^{-5}}\] done clear
View Answer play_arrowquestion_answer98) If both oxygen and helium gases are at the same temperature, the rate of diffusion of \[{{O}_{2}}\] is very close to:
A) 4 times that of He done clear
B) 2 times that of He done clear
C) 0.35 times that of He done clear
D) 8 times that of He done clear
View Answer play_arrowquestion_answer99) A white substance having alkaline nature in solution is:
A) \[NaN{{O}_{3}}\] done clear
B) \[N{{H}_{4}}Cl\] done clear
C) \[N{{a}_{2}}C{{O}_{3}}\] done clear
D) \[F{{e}_{2}}{{O}_{3}}\] done clear
View Answer play_arrowquestion_answer100) A solution of \[\text{FeC}{{\text{l}}_{\text{3}}}\]in water acts as acidic solution due to:
A) hydrolysis of \[\text{FeC}{{\text{l}}_{\text{3}}}\] done clear
B) acidic impurities done clear
C) dissociation done clear
D) ionization done clear
View Answer play_arrowquestion_answer101) The units place digit in the number \[{{13}^{25}}+{{11}^{25}}-{{3}^{25}}\]is:
A) 0 done clear
B) 1 done clear
C) 2 done clear
D) 3 done clear
View Answer play_arrowquestion_answer102) The angle of intersection of the curves \[y={{x}^{2}},6y=7-{{x}^{3}}\]at \[(1,1)\]is:
A) \[\frac{\pi }{4}\] done clear
B) \[\frac{\pi }{3}\] done clear
C) \[\frac{\pi }{2}\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer103) The value of \[x\] for which the equation \[1+r+{{r}^{2}}+...+{{r}^{x}}\] \[=(1+r)(1+{{r}^{2}})(1+{{r}^{4}})(1+{{r}^{8}})\] holds is:
A) 12 done clear
B) 13 done clear
C) 14 done clear
D) 15 done clear
View Answer play_arrowquestion_answer104) If \[f(x)=\frac{{{x}^{2}}-1}{{{x}^{2}}+1},\] for every real number \[x;\]then minimum value of \[f(x):\]
A) does not exist done clear
B) is equal to 1 done clear
C) is equal- to 0 done clear
D) is equal to \[-1\] done clear
View Answer play_arrowquestion_answer105) The value of d for which the sum of the squares of the roots of the equation \[{{x}^{2}}-(a-2)x-a-1=0\] assumes the least value is:
A) 0 done clear
B) 1 done clear
C) 2 done clear
D) 3 done clear
View Answer play_arrowquestion_answer106) A particle is dropped under gravity from rest from a height \[h(g=9.8\,m/{{s}^{2}})\]and it travels a distance \[\frac{9h}{25}\] in the last second the height \[h\]is:
A) 100 m done clear
B) 122.5 m done clear
C) 145 m done clear
D) 167.5 m done clear
View Answer play_arrowquestion_answer107) The number of onto mappings from the set A\[A=\{1,2,......,100\}\]to set \[B=\{1,2\}\]is:
A) \[{{2}^{100}}-2\] done clear
B) \[{{2}^{100}}\] done clear
C) \[{{2}^{99}}-2\] done clear
D) \[{{2}^{99}}\] done clear
View Answer play_arrowquestion_answer108) Which of the following functions is inverse of itself?
A) \[f(x)=\frac{1-x}{1+x}\] done clear
B) \[f(x)={{3}^{\log x}}\] done clear
C) \[f(x)={{3}^{x(x+1)}}\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer109) If \[f(x)=\log (x+\sqrt{{{x}^{2}}+1}),\]then \[f(x)\]is:1
A) even function done clear
B) odd function done clear
C) periodic function done clear
D) none of these done clear
View Answer play_arrowquestion_answer110) The solution of \[{{\log }_{99}}\{{{\log }_{2}}({{\log }_{3}}x)\}=0\]is:
A) 4 done clear
B) 9 done clear
C) 44 done clear
D) 99 done clear
View Answer play_arrowquestion_answer111) If \[n=1000!,\]then the value of sum \[\frac{1}{{{\log }_{2}}n}+\frac{1}{{{\log }_{3}}n}+...+\frac{1}{{{\log }_{1000}}n}\]is:
A) 0 done clear
B) 1 done clear
C) 10 done clear
D) \[{{10}^{3}}\] done clear
View Answer play_arrowquestion_answer112) If \[\omega \] and \[{{\omega }^{2}}\]are the two imaginary cube root unity, then the equation whose roots are \[a{{\omega }^{317}}\]and \[a{{\omega }^{382}}\]is:
A) \[{{x}^{2}}+ax-{{a}^{2}}=0\] done clear
B) \[{{x}^{2}}+{{a}^{2}}x+a=0\] done clear
C) \[{{x}^{2}}+ax+{{a}^{2}}=0\] done clear
D) \[{{x}^{2}}-{{a}^{2}}x+a=0\] done clear
View Answer play_arrowquestion_answer113) The value of \[1+\sum\limits_{k=0}^{14}{\left\{ \cos \frac{2k+1}{15}\pi +i\sin \frac{(2k+1)}{15}\pi \right\}}\]is:
A) 0 done clear
B) \[-1\] done clear
C) 1 done clear
D) \[i\] done clear
View Answer play_arrowquestion_answer114) If \[1,{{a}_{1}},{{a}_{2}},....,{{a}_{n-1}}\] are roots of unity, then the value of \[(1-{{a}_{1}})(1-{{a}_{2}})...(1-{{a}_{n-1}})\]is:
A) 0 done clear
B) 1 done clear
C) \[n\] done clear
D) \[{{n}^{2}}\] done clear
View Answer play_arrowquestion_answer115) If \[\alpha ,\beta \]are the roots of \[a{{x}^{2}}+bx+c=0,\alpha +h,\beta +h\] are roots of \[p{{x}^{2}}+qx+r=0;\]and\[{{D}_{1}},{{D}_{2}}\]are the respective discriminants of the equations, then \[{{D}_{1}}:{{D}_{2}}\]is equal to:
A) \[\frac{{{a}^{2}}}{{{p}^{2}}}\] done clear
B) \[\frac{{{b}^{2}}}{{{q}^{2}}}\] done clear
C) \[\frac{{{c}^{2}}}{{{r}^{2}}}\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer116) If a, b, c are three unequal numbers such that b, care in AP and \[b-a,c-b,a\] are in GP, then a: b: c is:
A) 1 : 2 : 3 done clear
B) 1 : 3 : 4 done clear
C) 2 : 3 : 4 done clear
D) 1 : 2 : 4 done clear
View Answer play_arrowquestion_answer117) The number of divisors of \[3\times {{7}^{3}},7\times {{11}^{2}}\]and \[2\times 61\]are in:
A) AP done clear
B) GP done clear
C) HP done clear
D) none of these done clear
View Answer play_arrowquestion_answer118) Suppose a, b, c are in AP and | a|, | b|, | c| < 1. If \[x=1+a+{{a}^{2}}+....\,to\,\infty ,\] \[y=1+b+{{b}^{2}}+....\,\text{to}\,\infty ,\] \[z=-1+c+{{c}^{2}}+...\,\text{to}\,\infty \] then \[x,y,z\]are in
A) AP done clear
B) GP done clear
C) HP done clear
D) none of these done clear
View Answer play_arrowquestion_answer119) \[1+\frac{4}{5}+\frac{7}{{{5}^{3}}}+....to\infty \]is:
A) \[\frac{16}{35}\] done clear
B) \[\frac{11}{8}\] done clear
C) \[\frac{35}{16}\] done clear
D) \[\frac{7}{16}\] done clear
View Answer play_arrowquestion_answer120) If the sum of first \[n\]natural numbers is \[\frac{1}{78}\] times the sum of their cubes, then the value of \[n\] is:
A) 11 done clear
B) 12 done clear
C) 13 done clear
D) 14 done clear
View Answer play_arrowquestion_answer121) If \[p=\cos {{55}^{o}},q=\cos {{65}^{o}}\] and \[r=\cos {{175}^{o}},\] then the value of\[\frac{1}{p}+\frac{1}{q}+\frac{r}{pq}\]is:
A) 0 done clear
B) \[-1\] done clear
C) 1 done clear
D) none of these done clear
View Answer play_arrowquestion_answer122) The value of\[\sin {{20}^{o}}(4+sec{{20}^{o}})\]is:
A) 0 done clear
B) 1 done clear
C) \[\sqrt{2}\] done clear
D) \[\sqrt{3}\] done clear
View Answer play_arrowquestion_answer123) If\[4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,\] then \[x\]is equal to:
A) 0 done clear
B) 1/2 done clear
C) \[-1/2\] done clear
D) 1 done clear
View Answer play_arrowquestion_answer124) If the line \[\frac{x}{a}+\frac{y}{b}=1\] moves such that \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{c}^{2}}},\] where c is a constant, then the locus of the foot of the perpendicular from the origin to the line is:
A) straight line done clear
B) circle done clear
C) parabola done clear
D) ellipse done clear
View Answer play_arrowquestion_answer125) The straight line whose sum of the intercepts on the axes is equal to half of the product of the intercepts, passes through the point:
A) (1, 1) done clear
B) (2, 2) done clear
C) (3, 3) done clear
D) (4, 4) done clear
View Answer play_arrowquestion_answer126) If the circle \[{{x}^{2}}+{{y}^{2}}+4x+22y+c=0\]bisects the circumference of the circle \[{{x}^{2}}+{{y}^{2}}-2x+8y-d=0,\] then \[c+d\]is equal to :
A) 60 done clear
B) 50 done clear
C) 40 done clear
D) 30 done clear
View Answer play_arrowquestion_answer127) The radius of the circle whosc1 tangents at \[x+3y-5=0,\,\,2x+6y+30=0\]is:
A) \[\sqrt{5}\]unit done clear
B) \[\sqrt{10}\]unit done clear
C) \[\sqrt{15}\]unit done clear
D) \[\sqrt{20}\]unit done clear
View Answer play_arrowquestion_answer128) The latusrectum of the parabola \[{{y}^{2}}=4ax\]whose focal chord is \[PSQ\]such that \[SP=3\]and \[SQ=2\]is given by:
A) 24/5 done clear
B) 12/5 done clear
C) 6/5 done clear
D) 1/5 done clear
View Answer play_arrowquestion_answer129) If \[{{M}_{1}}\]and \[{{M}_{2}}\]are the feet of the perpendiculars from the foci \[{{S}_{1}}\]and \[{{S}_{2}}\]of the ellipse\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{16}=1\] on the tangent at a point P on the ellipse, then \[({{S}_{1}}{{M}_{1}})({{S}_{2}}{{M}_{2}})\]is equal to:
A) 16 done clear
B) 9 done clear
C) 4 done clear
D) 3 done clear
View Answer play_arrowquestion_answer130) If the chords of contact of tangents from two points \[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}})\] to the hyperbola \[4{{x}^{2}}-9y-36=0\] are at right angles, then \[\frac{{{x}_{1}}{{x}_{2}}}{{{y}_{1}}{{y}_{2}}}\] is equal to:
A) \[\frac{9}{4}\] done clear
B) \[-\frac{9}{4}\] done clear
C) \[\frac{81}{16}\] done clear
D) \[-\frac{81}{16}\] done clear
View Answer play_arrowquestion_answer131) The solution of \[x\,dy-ydx+{{x}^{2}}{{e}^{x}}dx=0\]is:
A) \[\frac{y}{x}+{{e}^{x}}=c\] done clear
B) \[\frac{x}{y}+{{e}^{x}}=c\] done clear
C) \[x+{{e}^{y}}=c\] done clear
D) \[y+{{e}^{x}}=c\] done clear
View Answer play_arrowquestion_answer132) The coefficient of\[{{x}^{2}}\] in the binomial expansion of \[{{\left( \frac{1}{3}{{x}^{1/2}}+{{x}^{-1/4}} \right)}^{10}}\]is:
A) \[\frac{70}{243}\] done clear
B) \[\frac{60}{423}\] done clear
C) \[\frac{50}{13}\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer133) The solution set of the equation \[{{\left[ 4\left( 1-\frac{1}{3}+\frac{1}{9}-\frac{1}{27}+... \right) \right]}^{{{\log }_{2}}x}}\] \[={{\left[ 54\left( 1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+... \right) \right]}^{{{\log }_{x}}2}}\]is:
A) \[\left\{ 4,\frac{1}{4} \right\}\] done clear
B) \[\left\{ 2,\frac{1}{2} \right\}\] done clear
C) \[\{1,2\}\] done clear
D) \[\left\{ 8,\frac{1}{8} \right\}\] done clear
View Answer play_arrowquestion_answer134) If \[y=x-\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}-\frac{{{x}^{4}}}{4}+....\]and if \[|x|\,<1,\]then:
A) \[x=1-y+\frac{{{y}^{2}}}{2}-\frac{{{y}^{3}}}{3}+....\] done clear
B) \[x=1+y+\frac{{{y}^{2}}}{2}+\frac{{{y}^{3}}}{3}+....\] done clear
C) \[x=y-\frac{{{y}^{2}}}{2!}+\frac{{{y}^{3}}}{3!}-\frac{{{y}^{4}}}{4!}+....\] done clear
D) \[x=y+\frac{{{y}^{2}}}{2!}+\frac{{{y}^{3}}}{3!}+\frac{{{y}^{4}}}{4!}+....\] done clear
View Answer play_arrowquestion_answer135) The length of perpendicular from (1, 6, 3) to the\[\text{line}\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\]is:
A) 3 done clear
B) \[\sqrt{11}\] done clear
C) \[\sqrt{13}\] done clear
D) 5 done clear
View Answer play_arrowquestion_answer136) The plane\[2x+3y+4z=1\]meets the coordinate axes in A, B, C. The centroid of the triangle ABC is:
A) (2, 3, 4) done clear
B) \[\left( \frac{1}{2},\frac{1}{3},\frac{1}{4} \right)\] done clear
C) \[\left( \frac{1}{6},\frac{1}{9},\frac{1}{12} \right)\] done clear
D) \[\left( \frac{1}{2},\frac{3}{3},\frac{3}{4} \right)\] done clear
View Answer play_arrowquestion_answer137) The vector equation of the sphere whose centre is the point (1, 0, 1) and radius is 4, is:
A) \[|\vec{r}-(\hat{i}+\hat{k})|=4\] done clear
B) \[|\vec{r}+(\hat{i}+\hat{k})|={{4}^{2}}\] done clear
C) \[\vec{r}(\hat{i}+\hat{k})=4\] done clear
D) \[\vec{r}(\hat{i}+\hat{k})={{4}^{2}}\] done clear
View Answer play_arrowquestion_answer138) The plane \[2\lambda x-(1+\lambda )y+3z=0\]passes through the intersection of the planes:
A) \[2x-y=0\]and \[y+3z=0\] done clear
B) \[2x-y=0\]and \[y-3z=0\] done clear
C) \[2x+3z=0\]and \[y=0\] done clear
D) none of the above done clear
View Answer play_arrowquestion_answer139) If \[\vec{a}+\vec{b}+\vec{c}=\vec{0}\]and \[|\vec{a}|=\sqrt{37},|\vec{b}|\]\[=3,|\vec{c}|=4,\] then angle between \[\vec{b}\]and \[\vec{c}\] is:
A) \[{{30}^{o}}\] done clear
B) \[{{45}^{o}}\] done clear
C) \[{{60}^{o}}\] done clear
D) \[{{90}^{o}}\] done clear
View Answer play_arrowquestion_answer140) If \[\vec{a}=\hat{i}+\hat{j}-\hat{k},\,\vec{b}=-\hat{i}+\hat{k},\,\vec{c}=2\hat{i}+\hat{j}\]the value of \[\lambda \]such that \[\vec{a}+\lambda \,\vec{c}\]is perpendicular to \[\vec{b}\]is
A) 1 done clear
B) \[-1\] done clear
C) 0 done clear
D) none of these done clear
View Answer play_arrowquestion_answer141) The total work done by two forces \[{{\vec{F}}_{1}}=2\hat{i}-\hat{j}\]at \[{{\vec{F}}_{2}}=3\hat{i}+2\hat{j}-\hat{k}\]acting on a particle when it is displace from the point \[3\hat{i}+2\hat{j}+\hat{k}\]to \[5\hat{i}+5\hat{j}+3\hat{k}\]is:
A) 8 unit done clear
B) 9 unit done clear
C) 10 unit done clear
D) 11 unit done clear
View Answer play_arrowquestion_answer142) Let \[\vec{a},\vec{b}\]and \[\vec{c}\]be three non-coplanar vectors, and let \[\vec{p}\]and \[\vec{r}\]be vectors defined by the relations \[\vec{P}=\frac{\vec{b}\times \vec{c}}{[\vec{a}\vec{b}\vec{c}]}.\vec{q}=\frac{\vec{c}\times \vec{a}}{[\vec{a}\vec{b}\vec{c}]}\]and \[\vec{r}=\frac{\vec{a}\times \vec{b}}{[\vec{a}\vec{b}\vec{c}]}\] Then, the value of the egression \[(\vec{a}+\vec{b}).\vec{p}+(\vec{b}+\vec{c}).\vec{q}+(\vec{c}+\vec{a}).\vec{r}\]is equal to:
A) 0 done clear
B) 1 done clear
C) 2 done clear
D) 3 done clear
View Answer play_arrowquestion_answer143) If \[\left| \begin{matrix} {{x}^{n}} & {{x}^{n+2}} & {{x}^{n+3}} \\ {{y}^{n}} & {{y}^{n+2}} & {{y}^{n+3}} \\ {{z}^{n}} & {{z}^{n+2}} & {{z}^{n+3}} \\ \end{matrix} \right|\]\[=(y-z)(z-x)(x-y)\left( \frac{1}{x}+\frac{1}{y}+\frac{1}{z} \right),\]then \[n\]is equal to:
A) 2 done clear
B) \[-2\] done clear
C) \[-1\] done clear
D) 1 done clear
View Answer play_arrowquestion_answer144) If \[{{a}_{1}},{{a}_{2}},....,{{a}_{n}},...\] are in GP and \[{{a}_{1}}>0\]for each i, then determinant \[\Delta =\left| \begin{matrix} \log \,{{a}_{n}} & \log {{a}_{n+2}} & \log {{a}_{n+4}} \\ \log {{a}_{n+6}} & \log {{a}_{n+8}} & \log {{a}_{n+10}} \\ \log {{a}_{n+12}} & \log {{a}_{n+14}} & \log {{a}_{n+16}} \\ \end{matrix} \right|\] is equal to:
A) 0 done clear
B) 1 done clear
C) 2 done clear
D) \[n\] done clear
View Answer play_arrowquestion_answer145) The values of a for which the system of equation\[x+y+z=0,\]\[x+ay+az=0,\]\[x-ay+z=0,\] possess non-zero solutions, are given by:
A) 1, 2 done clear
B) \[1,-1\] done clear
C) 1, 0 done clear
D) none of these done clear
View Answer play_arrowquestion_answer146) If a square matrix A is such that \[A{{A}^{T}}=I={{A}^{T}}A,\] then \[|A|\] is equal to:
A) 0 done clear
B) \[\pm \,1\] done clear
C) \[\pm \,2\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer147) \[\int_{a}^{b}{\frac{|x|}{x}}dx,a<0<b,\] is equal to:
A) \[|b|-|a|\] done clear
B) \[|b|+|a|\] done clear
C) \[|a-b|\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer148) A and B are two events. Odds against A are 2 to Odds in favour of \[A\cup B\]are 3 to 1. If \[x\le P(B)\le y,\] then ordered pair \[(x,y)\] is:
A) \[\left( \frac{5}{12},\frac{3}{4} \right)\] done clear
B) \[\left( \frac{2}{3},\frac{3}{4} \right)\] done clear
C) \[\left( \frac{1}{3},\frac{3}{4} \right)\] done clear
D) none of these done clear
View Answer play_arrowquestion_answer149) In a series of three trials, the probability of exactly two successes in nine times is as large as the probability of three successes. Then, the probability of success in each trial is :
A) \[\frac{1}{2}\] done clear
B) \[\frac{1}{3}\] done clear
C) \[\frac{1}{4}\] done clear
D) \[\frac{3}{4}\] done clear
View Answer play_arrowquestion_answer150) An integer is chosen at random from first two hundred numbers. Then, the probability that the integer chosen is divisible by 6 or 8 is:
A) \[\frac{1}{4}\] done clear
B) \[\frac{2}{4}\] done clear
C) \[\frac{3}{4}\] done clear
D) None of these done clear
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