question_answer1) Two springs of spring constants \[{{k}_{1}}\] and \[{{k}_{2}}\] are joined in series and a mass m is attached to them as shown in figure. The time-period of oscillations of the springs is
A) \[T=\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}{{k}_{2}}}}\]
B) \[T=2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}{{k}_{2}}}}\]
C) \[T=2\pi \sqrt{\frac{m}{{{k}_{1}}+{{k}_{2}}}}\]
D) \[T=2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{2{{k}_{1}}{{k}_{2}}}}\]
View Answer play_arrowquestion_answer2) A hot body at temperature T losses heat to the surrounding temperature \[{{T}_{S}}\] by radiation. If the difference in temperature is small then, the rate of loss of heat by the hot body is proportional to
A) \[(T-{{T}_{S}})\]
B) \[{{(T-{{T}_{S}})}^{2}}\]
C) \[{{(T-{{T}_{S}})}^{1/2}}\]
D) \[{{(T-{{T}_{S}})}^{4}}\]
View Answer play_arrowquestion_answer3) Which one of the following statement is not correct in the case of light emitting diodes?
A) It is a heavily doped p-n junction
B) It emits light only when it is forward biased
C) It emits light only when it is reverse biased
D) The energy of the light emitted is less than the energy of the semiconductor used
View Answer play_arrowquestion_answer4) Which one of the following cannot be used as a moderator in a nuclear reactor?
A) Water
B) Heavy water
C) Molten sodium
D) Graphite
View Answer play_arrowquestion_answer5) The fraction of a sample of radioactive nuclei that remains undecayed after one mean life is
A) \[\frac{1}{e}\]
B) \[1-\frac{1}{e}\]
C) \[\frac{1}{{{e}^{2}}}\]
D) \[1-\frac{1}{{{e}^{2}}}\]
View Answer play_arrowquestion_answer6) If the radius of a nucleus of mass number 3 is R, ,then the radius of a nucleus of mass number 81 is
A) \[3\,R\]
B) \[9\,R\]
C) \[{{(27)}^{1/2}}\,R\]
D) \[27\text{ }R\]
View Answer play_arrowquestion_answer7) In hydrogen atom, which one of the following transitions is most energetic?
A) \[{{n}_{1}}=2\to {{n}_{2}}=1\]
B) \[{{n}_{1}}=3\to {{n}_{2}}=1\]
C) \[{{n}_{1}}=10\to {{n}_{2}}=2\]
D) \[{{n}_{1}}=100\to {{n}_{2}}=3\]
View Answer play_arrowquestion_answer8) A common example of \[{{\beta }^{-}}\] decay is \[_{15}{{P}^{32}}{{\to }_{17}}{{S}^{32}}+x+y\]. Then x and y stand for
A) electron and neutrino
B) positron and neutrino
C) electron and antineutrino
D) positron and antineutrino
View Answer play_arrowquestion_answer9) Based on the energy band description, a solid can be classified as insulator the energy gap between the valance band and conduction band is
A) \[3\,\,eV<{{E}_{g}}<6\,eV\]
B) \[{{E}_{g}}>6\,eV\]
C) \[{{E}_{g}}<3\,eV\]
D) \[{{E}_{g}}=0\,eV\]
View Answer play_arrowquestion_answer10) In the diagram, a system of two metals of equal lengths and of same cross-sectional area are joined together. The coefficient of thermal conductivities of the metals are K and \[2K\]respectively. If the furnace temperature at one end is \[{{300}^{o}}C\]and ice box temperature at the other end is \[{{0}^{o}}C,\] then the junction temperature is
A) \[{{100}^{o}}C\]
B) \[{{125}^{o}}C\]
C) \[{{150}^{o}}C\]
D) \[{{200}^{o}}C\]
View Answer play_arrowquestion_answer11) A Carnot cycle has the reversible processes in the following order
A) isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression
B) isothermal compression, adiabatic expansion, isothermal expansion and adiabatic compression
C) isothermal expansion, adiabatic compression, isothermal compression and adiabatic expansion
D) adiabatic expansion, isothermal expansion, adiabatic compression and isothermal compression
View Answer play_arrowquestion_answer12) Through which mode of propagation, the radio waves can be sent from one place to another
A) ground wave propagation
B) sky wave propagation
C) space wave propagation
D) All of them
View Answer play_arrowquestion_answer13) The logic operation carried out by the circuit below is that of
A) AND gate
B) OR gate
C) NOT gate
D) NAND gate
View Answer play_arrowquestion_answer14) If \[\beta ,{{R}_{L}}\] and r are the AC current gain, load resistance and the input resistance of a transistor respectively in CE configuration, the voltage and the power gains respectively are
A) \[\beta \frac{{{R}_{L}}}{r}\] and \[{{\beta }^{3}}\frac{{{R}_{L}}}{r}\]
B) \[\beta \frac{r}{{{R}_{L}}}\] and \[{{\beta }^{2}}\frac{r}{{{R}_{L}}}\]
C) \[\beta \frac{{{R}_{L}}}{r}\] and \[\beta {{\left( \frac{{{R}_{L}}}{r} \right)}^{2}}\]
D) \[\beta \frac{r}{{{R}_{L}}}\] and \[\beta {{\left( \frac{r}{{{R}_{L}}} \right)}^{2}}\]
View Answer play_arrowquestion_answer15) A message signal of frequency \[5\text{ }kHz\]and peak voltage \[10\text{ }V\]is used to amplify modulate a carrier wave with frequency \[1\text{ }MHz\]and peak voltage 20 V. The side bands produced are
A) \[(1000\pm 5)kHz\]
B) \[(1000\pm 7.5)kHz\]
C) \[(1000\pm 10)kHz\]
D) \[(1000\pm 15)kHz\]
View Answer play_arrowquestion_answer16) The volume of one mole of an ideal gas changes from V to \[2\text{ }V\]at temperature\[{{327}^{o}}C\] If R is the universal gas constant, then the work done in this process is
A) \[300\text{ }R\]In 2
B) \[600\text{ }R\]In 2
C) \[300\]In 2
D) \[600\] In 2
View Answer play_arrowquestion_answer17) A wooden piece can float both in mercury (of density\[13.6\text{ }g/cc\]) and in water (of density\[1\text{ }g/cc\]). The ratio of mass of mercury displaced to the mass of water displaced is
A) \[1\]
B) \[13.6\]
C) \[\frac{1}{13.6}\]
D) \[\frac{12.6}{13.6}\]
View Answer play_arrowquestion_answer18) A container of height 10 m which is open at the top, has water to its full height. Two small openings are made on the wall of the container .one exactly at the middle and the other at the bottom. The ratio of the velocities with which water comes out from the middle and the bottom region respectively is
A) \[2\]
B) \[\frac{1}{2}\]
C) \[\sqrt{2}\]
D) \[\frac{1}{\sqrt{2}}\]
View Answer play_arrowquestion_answer19) If the radius of a spherical liquid (of surface tension S) drop increases from r to \[r+Ar,\]the corresponding increase in the surface energy is
A) \[8\pi \,r\,\Delta rS\]
B) \[4\pi \,r\,\Delta rS\]
C) \[16\pi \,r\,\Delta rS\]
D) \[2\pi \,r\,\Delta rS\]
View Answer play_arrowquestion_answer20) Which one of the following is not an assumption in the kinetic theory of gases?
A) The volume occupied by the molecules of the gas is negligible
B) The force of attraction between the molecules is negligible
C) The collision between molecules are elastic
D) All molecules have some speed
View Answer play_arrowquestion_answer21) The crystal structure can be studied using
A) UV rays
B) X-rays
C) IR radiation
D) Microwave
View Answer play_arrowquestion_answer22) The number of turns of the primary and the secondary coils of a transformer are 10 and 100 respectively. The primary voltage and the current are given as \[2\text{ }V\]and\[1\text{ }A\]. Assuming the efficiency of the transformer as \[90%,\] the secondary voltage and the current respectively are
A) \[20\text{ }V\]and\[0.1\text{ }A\]
B) \[0.2\text{ }V\]and \[1\text{ }A\]
C) \[20\,\,V\]and \[0.09\text{ }A\]
D) \[0.2\,\,V\]and \[0.9\text{ }A\]
View Answer play_arrowquestion_answer23) Which one of the following units is not that of mutual inductance?
A) Henry
B) Weber
C) Ohm-second
D) Volt-second-\[{{(ampere)}^{-1}}\]
View Answer play_arrowquestion_answer24) In an L-C-R series AC circuit at resonance
A) the capacitive reactance is more than the inductive reactance
B) the capacitive reactance equals the inductive reactance
C) the capacitive reactance is less than the inductive reactance
D) the power dissipated is minimum
View Answer play_arrowquestion_answer25) In an L-C-R serries resonant circuit which one of the following cannot be the expression for the Q-factor
A) \[\frac{\omega L}{R}\]
B) \[\frac{1}{\omega \,\,CR}\]
C) \[\sqrt{\frac{L}{C}}\frac{1}{R}\]
D) \[\frac{R}{LC}\]
View Answer play_arrowquestion_answer26) If the eighth bright band due to light of wavelength \[{{\lambda }_{1}}\] coincides with ninth bright band from light of wavelength \[{{\lambda }_{2}}\]in Young's double slit experiment, then the possible wavelengths of visible light are
A) \[400\,\,nm\]and \[450\,\,nm\]
B) \[425\text{ }nm\] and \[400\text{ }nm\]
C) \[400\,\,nm\] and \[425\text{ }nm\]
D) \[450\,\,nm\] and \[400\,\,nm\]
View Answer play_arrowquestion_answer27) The elastic energy stored per unit volume in a stretched wire is
A) \[\frac{1}{2}\] (Young modulus) \[{{(Strain)}^{2}}\]
B) \[\frac{1}{2}\] (Stress) \[{{(Strain)}^{2}}\]
C) \[\frac{1}{2}\frac{Stress}{Strain}\]
D) \[\frac{1}{2}\] (Young modulus) (Stress)
View Answer play_arrowquestion_answer28) The electromagnetic waves of frequency \[~2\text{ }MHz\]to \[30\text{ }MHz\]are used
A) in ground wave propagation
B) in sky wave propagation
C) in microwave propagation
D) in satellite communication
View Answer play_arrowquestion_answer29) Assuming that the earth is a sphere of radius \[{{R}_{E}}\]with uniform density, the distance from its centre at which the acceleration due to gravity is equal to \[\frac{g}{3}\] (g = the acceleration due to gravity on the surface of earth) is
A) \[\frac{{{R}_{E}}}{3}\]
B) \[2\,\,\frac{{{R}_{E}}}{3}\]
C) \[\frac{{{R}_{E}}}{3}\]
D) \[\frac{{{R}_{E}}}{4}\]
View Answer play_arrowquestion_answer30) The terminal velocity of a rain drop of radius r Is \[2\text{ }cm\,\,\,{{s}^{-1}}\]. If eight such identical drops combine to form a single large drop, the terminal velocity would be
A) \[1\,cm\,\,\,{{s}^{-1}}\]
B) \[2\,cm\,\,\,{{s}^{-1}}\]
C) \[4\,cm\,\,\,{{s}^{-1}}\]
D) \[8\,cm\,\,\,{{s}^{-1}}\]
View Answer play_arrowquestion_answer31) The maximum kinetic energy of photoelectrons
A) varies linearly with the frequency of the incident radiation
B) , varies linearly with the wavelength of incident light
C) proportional to the frequency of the incident radiation
D) proportional to the square of the frequency of incident radiation
View Answer play_arrowquestion_answer32) Which one of the following is not associated with the total internal reflection?
A) The mirage formation
B) Optical fibre communication
C) The glittering of diamond
D) Dispersion of light
View Answer play_arrowquestion_answer33) The angular width of the central maximum of the diffraction pattern in a single slit (of width a) experiment, with \[\lambda \] as the wavelength of light, is
A) \[\frac{3\lambda }{2a}\]
B) \[\frac{\lambda }{2a}\]
C) \[\frac{2\lambda }{a}\]
D) \[\frac{\lambda }{a}\]
View Answer play_arrowquestion_answer34) The Brewster angle for the glass-air interface is \[{{54.74}^{o}}\]. if a ray of light going from air to glass strikes at an angle of incidence \[{{45}^{o}},\] then the angle of refraction is (Given, tan\[{{54.74}^{o}}=\sqrt{2}\])
A) \[{{60}^{o}}\]
B) \[{{30}^{o}}\]
C) \[{{25}^{o}}\]
D) \[{{54.74}^{o}}\]
View Answer play_arrowquestion_answer35) When sun light is scattered by minute particles of atmosphere, the intensity of light scattered away is proportional to
A) \[{{(wavelength\text{ }of\text{ }light)}^{4}}\]
B) \[{{(frequency\text{ }of\text{ }light)}^{4}}\]
C) \[{{(wavelength\text{ }of\text{ }light)}^{2}}\]
D) \[{{(frequency\text{ }of\text{ }light)}^{2}}\]
View Answer play_arrowquestion_answer36) If K be the kinetic energy and m the mass of a moving particle, then the de-Broglie wavelength of the particle is
A) \[\lambda =\frac{h}{\sqrt{mK}}\]
B) \[\lambda =\frac{2h}{\sqrt{mK}}\]
C) \[\lambda =\frac{h}{2\sqrt{mK}}\]
D) \[\lambda =\frac{h}{\sqrt{2\,mK}}\]
View Answer play_arrowquestion_answer37) The radius of gyration of a thin uniform circular disc (of radius R) about an axis passing through its centre and lying in its plane is
A) \[R\]
B) \[\frac{R}{\sqrt{2}}\]
C) \[\frac{R}{4}\]
D) \[\frac{R}{2}\]
View Answer play_arrowquestion_answer38) Two particles of masses \[1\text{ }kg\]and \[\text{2 }kg\] are located at \[{{x}_{1}}=0,\] \[{{y}_{1}}=0\] and \[{{x}_{2}}=1,\]\[{{y}_{2}}=0\] respectively. The centre of mass of the system is at.
A) \[x=1;\,\,y=2\]
B) \[x=2;\,\,y=1\]
C) \[x=\frac{1}{3};\,\,y=\frac{2}{3}\]
D) \[x=\frac{2}{3};\,\,y=\frac{1}{3}\]
E) None of these
View Answer play_arrowquestion_answer39) The energy that is associated with one gram of mass is
A) \[9\times {{10}^{-13}}\,J\]
B) \[9\times {{10}^{-16}}\,J\]
C) \[9\times {{10}^{13}}\,J\]
D) \[9\times {{10}^{16}}\,J\]
View Answer play_arrowquestion_answer40) If the polar ice caps were to -melt suddenly
A) the length of the day will be more than \[24\text{ }h\]
B) the length of the day will be less than \[24\text{ }h\]
C) the length of the day will remain as \[24\text{ }h\] the length of the day will become more
D) than \[24\text{ }h\] initially and then becomes equal to \[24\text{ }h\]
View Answer play_arrowquestion_answer41) The work done in taking an object of mass m from the surface of earth to a height \[h=R,\] where R is the radius of the earth, is
A) \[mgR\]
B) \[\frac{1}{2}mgR\]
C) \[\frac{1}{3}mgR\]
D) \[\frac{2}{3}mgR\]
View Answer play_arrowquestion_answer42) The inversion temperature of a copper-iron thermocouple is \[{{540}^{o}}C\]when the cold junction temperature is \[{{0}^{o}}C\]. If the cold junction temperature is increased by\[{{10}^{o}}C,\] then the inversion temperature and the neutral temperature of the thermocouple respectively are
A) \[{{270}^{o}}C\]and \[{{530}^{o}}C\]
B) \[{{270}^{o}}C\] and \[{{550}^{o}}C\]
C) \[{{280}^{o}}C\]and \[{{530}^{o}}C\]
D) \[{{280}^{o}}C\]and \[{{550}^{o}}C\]
View Answer play_arrowquestion_answer43) Two bulbs marked \[60\text{ }W,\] \[220\text{ }V\] and \[100\text{ }W\]\[220\text{ }V\] are connected in series and the series combination is now connected across a \[220\text{ }V\] mains supply. The power dissipated in the circuit is
A) \[37.5\text{ }W\]
B) \[75\text{ }W\]
C) \[80\text{ }W\]
D) \[40\text{ }W\]
View Answer play_arrowquestion_answer44) The steady state current through the battery in the circuit given below is
A) \[17\,A\]
B) \[7\,A\]
C) zero
D) \[\frac{10}{7}A\]
View Answer play_arrowquestion_answer45) Two concentric circular loops of radii R and 2R carry currents of 2i and i respectively in opposite sense (ie, clockwise in one coil and counter-clockwise in the other coil). The resultant magnetic field at their common centre is
A) \[{{\mu }_{0}}\frac{i}{4R}\]
B) \[{{\mu }_{0}}\frac{5i}{4R}\]
C) \[{{\mu }_{0}}\frac{3i}{4R}\]
D) \[{{\mu }_{0}}\frac{i}{2R}\]
View Answer play_arrowquestion_answer46) Three identical spherical balls A, B and C are placed on a table as shown in the figure along a straight line. B and C are at rest initially. The ball A hits B head on with a speed of \[10\,m{{s}^{-1}}\]. Then after all collisions (assumed to be elastic) A and B are brought to rest and C takes off with a velocity of
A) \[5\,m{{s}^{-1}}\]
B) \[10\,m{{s}^{-1}}\]
C) \[2.5\,m{{s}^{-1}}\]
D) \[7.5\,m{{s}^{-1}}\]
View Answer play_arrowquestion_answer47) An object placed on an inclined plane starts sliding when the angle of incline becomes\[{{30}^{o}}\]. The coefficient of static friction between the object and the plane is
A) \[\frac{1}{\sqrt{3}}\]
B) \[\sqrt{3}\]
C) \[\frac{1}{2}\]
D) \[\frac{\sqrt{3}}{2}\]
View Answer play_arrowquestion_answer48) Given below is a graph between a variable force (F) (along y-axis) and the displacement (x) (along x-axis) of a particle in one dimension. The work done by the force in the displacement interval between \[0\text{ }m\]and \[30\text{ }m\]is
A) \[275\text{ }J\]
B) \[375\text{ }J\]
C) \[400\text{ }J\]
D) \[300\text{ }J\]
View Answer play_arrowquestion_answer49) The mobility of free electrons (charge = e, mass = -m and relaxation time = \[\tau \].) in a metal is proportional to
A) \[\frac{e}{m}\tau \]
B) \[\frac{m}{e}\tau \]
C) \[\frac{e}{m\tau }\]
D) \[\frac{m}{e\tau }\]
View Answer play_arrowquestion_answer50) n identical capacitors each of capacitance C when connected in parallel give the effective capacitance \[90\text{ }\mu F\]and when connected in series give \[\text{2}\text{.5 }\mu F\]. Then the values of n and C respectively are
A) \[6\] and \[15\,\mu F\]
B) \[5\] and \[18\,\mu F\]
C) \[15\] and \[6\,\mu ,F\]
D) \[18\] and \[5\,\mu ,F\]
View Answer play_arrowquestion_answer51) A capacitor is charged by a battery and the energy stored is U. The battery is now removed and the separation distance between the plates. is doubled. The energy stored now is
A) \[\frac{U}{2}\]
B) \[U\]
C) \[2\,\,U\]
D) \[4\,\,U\]
View Answer play_arrowquestion_answer52) The number of ways one can arrange three identical capacitors to obtain distinct effective capacitances is
A) \[8\]
B) \[6\]
C) \[4\]
D) \[3\]
View Answer play_arrowquestion_answer53) When a uniform wire of resistance R is stretched uniformly to increase its length by \[10%,\]the new resistance value would
A) remain as R
B) become \[1.21R\]
C) become \[1.10\text{ }R\]
D) become \[1.20\text{ }R\]
View Answer play_arrowquestion_answer54) Rocket propulsion is associated with
A) the conservation of angular momentum
B) the conservation of mass
C) the conservation of mechanical energy
D) Newton's third law of motion
View Answer play_arrowquestion_answer55) Which one of the following statements is not correct in uniform circular motion?
A) The speed of the particle remains constant
B) The acceleration always points towards the centre
C) The angular speed remains constant
D) The velocity remains constant
View Answer play_arrowquestion_answer56) If a car is to travel with a speed v along a frictionless, banked circular track of radius r, the required angle of banking so that the car does skid, is
A) \[\theta ={{\tan }^{-1}}\,\left( \frac{{{v}^{2}}}{rg} \right)\]
B) \[\theta ={{\tan }^{-1}}\,\left( \frac{v}{rg} \right)\]
C) \[\theta ={{\tan }^{-1}}\,\left( \frac{{{r}^{2}}}{vg} \right)\]
D) \[\theta <{{\tan }^{-1}}\,\left( \frac{{{v}^{2}}}{rg} \right)\]
View Answer play_arrowquestion_answer57) Three forces \[{{F}_{1}},{{F}_{2}}\] and \[{{F}_{3}}\] together keep a body in equilibrium. If \[{{F}_{1}}=3N\]along the positive x-axis, \[{{F}_{2}}=4N\] along the positive y-axis, then the third force \[{{F}_{3}}\] is
A) \[5\text{ }N\]making an angle \[\theta ={{\tan }^{-1}}\left( \frac{3}{4} \right)\] with the negative y-axis
B) \[5\text{ }N\]making an angle \[\theta ={{\tan }^{-1}}\left( \frac{4}{3} \right)\] with the negative y-axis
C) \[7\text{ }N\]making an angle \[\theta ={{\tan }^{-1}}\left( \frac{3}{4} \right)\] with the negative y-axis
D) \[7\text{ }N\] making an angle \[\theta ={{\tan }^{-1}}\left( \frac{4}{3} \right)\] with the negative y-axis
View Answer play_arrowquestion_answer58) The electrostatic potential of a uniformly charged thin spherical shell of charge Q and radius R at a distance r from the centre is
A) \[\frac{Q}{4\,\pi \,{{\varepsilon }_{0}}r}\]for points outside and \[\frac{Q}{4\,\pi \,{{\varepsilon }_{0}}R}\] for points inside the shell
B) \[\frac{Q}{4\,\pi \,{{\varepsilon }_{0}}r}\] for both points inside and outside the shell
C) zero for points outside and \[\frac{Q}{4\,\pi \,{{\varepsilon }_{0}}r}\] for points inside the shell
D) zero for both points inside and outside the shell
View Answer play_arrowquestion_answer59) The electric field and the potential of an electric dipole vary with distance r as
A) \[\frac{1}{r}\]and \[\frac{1}{{{r}^{2}}}\]
B) \[\frac{1}{{{r}^{2}}}\] and \[\frac{1}{r}\]
C) \[\frac{1}{{{r}^{2}}}\] and \[\frac{1}{{{r}^{3}}}\]
D) \[\frac{1}{{{r}^{3}}}\] and \[\frac{1}{{{r}^{2}}}\]
View Answer play_arrowquestion_answer60) A point charge Q is placed at one of the vertices of a cubical block. The electric flux flowing through this cube is
A) \[\frac{Q}{6{{\varepsilon }_{0}}}\]
B) \[\frac{Q}{4{{\varepsilon }_{0}}}\]
C) \[\frac{Q}{8{{\varepsilon }_{0}}}\]
D) \[\frac{Q}{{{\varepsilon }_{0}}}\]
View Answer play_arrowquestion_answer61) Two parallel infinite line charges \[+\lambda \] and \[-\lambda \] are placed with a separation distance R in free space. The net electric field exactly mid-way between the two line charges is
A) \[\frac{Q}{6\,{{\varepsilon }_{0}}}\]
B) \[\frac{Q}{4\,{{\varepsilon }_{0}}}\]
C) \[\frac{Q}{8\,{{\varepsilon }_{0}}}\]
D) \[\frac{Q}{\,{{\varepsilon }_{0}}}\]
View Answer play_arrowquestion_answer62) A particle is thrown vertically up with a certain velocity. Assuming the air resistance to be negligible, which one of the following represents the velocity (along y-axis) time (along x-axis) graph for the entire motion of the particle till it reaches back to the ground
A)
B)
C)
D)
View Answer play_arrowquestion_answer63) The dimensions of .the coefficient of viscosity are
A) \[[M{{L}^{-1}}{{T}^{-3}}]\]
B) \[[M{{L}^{-1}}{{T}^{-1}}]\]
C) \[[M{{L}^{-2}}{{T}^{-1}}]\]
D) \[[ML{{T}^{-1}}]\]
View Answer play_arrowquestion_answer64) The components of the sum of two vectors \[2\hat{i}+3\hat{j}\] and \[2\hat{j}+3\hat{k}\]along x and y directions respectively are
A) \[2\] and \[5\]
B) \[4\]and \[6\]
C) \[2\] and \[6\]
D) \[4\]and \[3\]
View Answer play_arrowquestion_answer65) An object is projected so that its horizontal range R is maximum. If the maximum height attained by the object is H, then the ratio of R/H is
A) \[4\]
B) \[1/4\]
C) \[2\]
D) \[1/2\]
View Answer play_arrowquestion_answer66) Which one of the following is not a characteristics of diamagnetism?
A) The diamagnetic materials are repelled by a bar magnet
B) The magnetic susceptibility of the materials is small and negative
C) The origin of diamagnetism is the spin of electrons
D) The material move from a region of strong magnetic field to weak magnetic field
View Answer play_arrowquestion_answer67) When the number of turns of the coil is doubled, the current sensitivity of a moving coil galvanometer is doubled whereas, the voltage sensitivity of the galvanometer
A) remains the same
B) is halved
C) is doubled
D) is quadrupled
View Answer play_arrowquestion_answer68) Ampere's circuital law is equivalent to
A) Biot-Savart law
B) Coulomb's law
C) Faraday's law
D) Kirchhoff?s law
View Answer play_arrowquestion_answer69) A proton, a deuteron and an alpha particle all having same momenta enter a uniform magnetic field and describe circular paths. The respective radii of their paths are in the ratio
A) \[4:2:1\]
B) \[2:2:1\]
C) \[1:2:4\]
D) \[1:1:1\]
View Answer play_arrowquestion_answer70) If the horizontal component of the earth's magnetic field is \[0.30\text{ }G,\] and the dip angle is \[60{}^\circ \] at a given place, then the value of earth's total magnetic field is
A) \[0.15\text{ }G\]
B) \[0.15\,\sqrt{3}G\]
C) \[0.15\,\sqrt{2}G\]
D) \[~0.60\text{ }G\]
View Answer play_arrowquestion_answer71) If a current of \[5\text{ }A\]in a coil of self inductance \[2\text{ }mH\]is cut-off in time \[0.1\text{ }s,\]the induced emf in the coil is
A) \[0.1\,\,V\]
B) \[0.01\text{ }V\]
C) \[0.2V\]
D) \[0.02V\]
View Answer play_arrowquestion_answer72) A source of sound is approaching an observer with speed of \[30\text{ }m{{s}^{-1}}\]and the observer is approaching the source with a speed of\[60\,\,m{{s}^{-1}}\]. Then the fractional change in the frequency of sound (speed of sound in air \[=330\,\,m{{s}^{-1}}\]) is
A) \[\frac{1}{3}\]
B) \[\frac{3}{10}\]
C) \[\frac{2}{5}\]
D) \[\frac{2}{3}\]
View Answer play_arrowquestion_answer73) A wave motion is described by \[y(x,t)=a\,\sin (kx-\omega t)\]. Then the ratio of the maximum particle velocity to the wave velocity is
A) \[\omega a\]
B) \[\frac{1}{ka}\]
C) \[\frac{\omega }{k}\]
D) \[ka\]
View Answer play_arrowquestion_answer74) The equation of a damped simple harmonic motion is \[m\frac{{{d}^{2}}x}{d{{t}^{2}}}+\frac{dx}{dt}+kx=0\]. Then the angular frequency of oscillation is
A) \[\omega ={{\left( \frac{k}{m}-\frac{{{b}^{2}}}{4{{m}^{2}}} \right)}^{1/2}}\]
B) \[\omega ={{\left( \frac{k}{m}-\frac{b}{4m} \right)}^{1/2}}\]
C) \[\omega ={{\left( \frac{k}{m}-\frac{{{b}^{2}}}{4m} \right)}^{1/2}}\]
D) \[\omega ={{\left( \frac{k}{m}-\frac{{{b}^{2}}}{4{{m}^{2}}} \right)}^{1/2}}\]
View Answer play_arrowquestion_answer75) The fundamental frequencies of an open and a closed tube, each of same length L with v as the speed of sound in air, respectively are
A) \[\frac{v}{2L}\] and \[\frac{v}{L}\]
B) \[\frac{v}{L}\] and \[\frac{v}{2L}\]
C) \[\frac{v}{2L}\] and \[\frac{v}{4L}\]
D) \[\frac{v}{4L}\] and \[\frac{v}{2L}\]
View Answer play_arrowquestion_answer76) For the reaction, \[{{N}_{2}}(g)+3{{H}_{2}}(g)\rightleftharpoons 2N{{H}_{3}}(g)\] at \[400\text{ }K,{{K}_{p}}=41.\] Find the value for the following reaction \[\frac{1}{2}{{N}_{2}}(g)+\frac{3}{2}{{H}_{2}}(g)\rightleftharpoons N{{H}_{3}}(g)\]
A) 6.4
B) 0.02
C) 50
D) 4.6
View Answer play_arrowquestion_answer77) What will be the resultant pH when 200 mL of, an aqueous solution of \[HCl(pH=2.0)\]is mixed with 300 mL of an aqueous solution of \[NaOH(pH=12)?\]
A) 2.699
B) 13.30
C) 11.3010
D) 1.330
View Answer play_arrowquestion_answer78) Why do most chemical reaction rates increases rapidly as the temperature rises?
A) The fraction of the molecules with kinetic energy greater than the activation energy increases rapidly with temperature
B) The average kinetic energy increases as temperature rises
C) The activation energy decreases as the temperature rises
D) More collision take place between particles so that the reaction can occur
View Answer play_arrowquestion_answer79) To an equilibrium mixture of \[2S{{O}_{2}}(g)+{{O}_{2}}(g)\rightleftharpoons 2S{{O}_{3}}(g),\] some helium, an inert gas, is added at constant volume. The addition of helium causes the total pressure to double, which of the following is true?
A) The concentration of all three gases is unchanged
B) The concentration of sulphur trioxide increases
C) The number of moles of sulphur trioxide increases
D) The concentration of sulphur dioxide increases
View Answer play_arrowquestion_answer80) Identify the substance whose 0.1 M solution is basic?
A) Ammonium chloride
B) Ammonium acetate
C) Ammonium sulphate
D) Sodium acetate
View Answer play_arrowquestion_answer81) The vapour pressure of pure liquid solvent is 0.80 arm. When a non-volatile substance B is added to the solvent, its vapour pressure drops to 0.6 arm. What is the mole fraction of component B in this solution?
A) 0.75
B) 0.25
C) 0.48
D) 0.3
View Answer play_arrowquestion_answer82) The standard enthalpy of formation of\[{{\text{H}}_{\text{2}}}\text{(g)}\] and\[C{{l}_{2}}(g)\]and\[HCl(g)\]are \[218\text{ }kJ/mol,\]\[\text{ }121.68\text{ }kJ/mol\]and\[92.31\text{ }kJ/mol\]respectively. Calculate standard enthalpy change in kJ for \[\frac{1}{2}{{H}_{2}}(g)\frac{1}{2}C{{l}_{2}}(g)\xrightarrow{{}}HCl(g)\]
A) \[+\,\,431.99\]
B) \[-246.37\]
C) \[-431.99\]
D) \[+\,247.37\]
E) None of these
View Answer play_arrowquestion_answer83) In which of the following pair the enthalpy of neutralization does not remain constant?
A) \[\text{HN}{{\text{O}}_{\text{3}}}\]and\[\text{ }\!\!~\!\!\text{ NaOH}\]
B) \[HCl\]and \[NaOH\]
C) \[HCN\]and \[NaOH\]
D) \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\] and \[NaOH\]
View Answer play_arrowquestion_answer84) A system is changed from an initial state to a final state by a manner such that \[\Delta H=q.\]If the change from the initial state to the final state were made by a different manner then \[\Delta H\]remains same but q changes because
A) \[\Delta H\] is a path function and q is a state function
B) \[\Delta H\]is a state function and q is a path function
C) Both \[\Delta H\]and q are state function
D) Both \[\Delta H\]and q are path function
View Answer play_arrowquestion_answer85) When water is cooled to ice, its entropy
A) increases
B) decreases
C) remains same
D) becomes zero
View Answer play_arrowquestion_answer86) The charge on \[\text{Fe(OH}{{\text{)}}_{\text{3}}}\]sol is due to
A) adsorption of hydroxyl ion
B) adsorption of hydrogen ion
C) adsorption of ferric ion
D) absorption of ferric ion
View Answer play_arrowquestion_answer87) Which of the following statement is true?
A) Chemisorption forms multimolecular layer
B) Chemisorption is a reversible process
C) Chemisorption is independent of the pressure
D) Chemisorption has low enthalpy change
View Answer play_arrowquestion_answer88) Identify the incorrect statement out of the following.
A) Isoelectronic species have dissimilar ionic radii
B) Be and Al does not show diagonal relationship
C) Outer electronic configuration of halogen is \[n{{s}^{2}}.n{{p}^{7}}\]
D) In any period atomic radius of noble gas is the highest
View Answer play_arrowquestion_answer89) According to VSEPR theory, the molecule that has T-shape is
A) \[Cl{{F}_{3}}\]
B) \[N{{H}_{3}}\]
C) \[B{{F}_{3}}\]
D) \[{{H}_{2}}O\]
View Answer play_arrowquestion_answer90) Bakelite is the polymer of
A) benzaldehyde and phenol
B) formaldehyde and phenol
C) formaldehyde and benzyl alcohol
D) acetaldehyde and phenol
View Answer play_arrowquestion_answer91) Which of these elements is expected to have the lowest first ionisation potential?
A) Sr
B) As
C) Xe
D) S
View Answer play_arrowquestion_answer92) Which is false statement about LCAO?
A) Addition of atomic orbital results in molecular orbital
B) Atomic orbital of nearly same energy combine to molecular orbital
C) Bonding molecular orbital occupies higher energy than the atomic orbitals
D) Each molecular orbital accommodate maximum of two electrons
View Answer play_arrowquestion_answer93) Which one among the following statement about transition elements is incorrect?
A) They show variable oxidation state
B) All the ions are coloured
C) They exhibit diamagnetic and paramagnetic properties
D) They exhibit catalytic properties
View Answer play_arrowquestion_answer94) German silver is an alloy of
A) copper, zinc and silver
B) copper, zinc and nickel
C) copper, zinc and tin
D) manganese, chromium and nickel
View Answer play_arrowquestion_answer95) The metal-carbon bond in metal carbonyls possess
A) only s character
B) only p character
C) both s and p character
D) only d character
View Answer play_arrowquestion_answer96) Irregular trend in the standard reduction potential value of first row transition elements is due to
A) regular variation of first and second ionisation enthalpies
B) irregular variation of sublimation enthalpies
C) regular variation of sublimation enthalpies
D) increase in the number of unpaired electrons
View Answer play_arrowquestion_answer97) Which of the following lanthanoid ion is paramagnetic?
A) \[C{{e}^{4+}}\]
B) \[Y{{b}^{2+}}\]
C) \[L{{u}^{3+}}\]
D) \[E{{u}^{2+}}\]
View Answer play_arrowquestion_answer98) The complex \[{{[Co{{F}_{6}}]}^{4-}}\] is
A) outer orbital and diamagnetic
B) inner orbital and paramagnetic
C) inner orbital and diamagnetic
D) outer orbital and paramagnetic
View Answer play_arrowquestion_answer99) The oxidation number, d-orbital occupation and coordination number of Cr in the complex \[cis[Cr{{(en)}_{2}}C{{l}_{2}}]Cl\]are respectively
A) \[+\,3,\text{ }3d\]and 4
B) \[~+\,3,\text{ }4d\] and 6
C) \[+\,3,\text{ }3d\]and 6
D) \[~+\,2,\text{ }3d\] and 6
View Answer play_arrowquestion_answer100) Which is a non-aromatic compound?
A)
B)
C)
D)
View Answer play_arrowquestion_answer101) The number of isomers including stereoisomers possible for the compound having molecular formula \[{{\text{C}}_{\text{4}}}{{\text{H}}_{\text{8}}}\]is
A) one
B) two
C) three
D) four
View Answer play_arrowquestion_answer102) The correct order of decreasing acidic nature of \[Hp,\text{ }ROH,CH\equiv CH\]and\[N{{H}_{3}}\] is
A) \[CH\equiv CH>{{H}_{2}}O>ROH>N{{H}_{3}}\]
B) \[{{H}_{2}}O\,>ROH>CH\equiv CH>N{{H}_{3}}\]
C) \[ROH>N{{H}_{3}}>CH\equiv CH>{{H}_{2}}O\]
D) \[{{H}_{2}}O>ROH>N{{H}_{3}}>CH\equiv CH\]
View Answer play_arrowquestion_answer103) Reaction between propene and hydrochloric acid to form \[iso-\]propyl chloride takes place through
A) nucleophilic addition reaction
B) electrophilic substitution reaction
C) nucleophilic substitution reaction
D) electrophilic addition reaction
View Answer play_arrowquestion_answer104) Stability of\[iso-\]butylene can be best explained by
A) inductive effect
B) mesomeric effect
C) hyperconjugative effect
D) steric effect
View Answer play_arrowquestion_answer105) The d and I enantiomers of an optically active compound differ in
A) their boiling and melting point
B) their rotation of plane polarized light
C) their solubility
D) their refractive index
View Answer play_arrowquestion_answer106) Cannizaro reaction is not given by
A) methanal
B) phenyl methanal
C) 2, 2-dimethyl butanal
D) phenyl ethanol
View Answer play_arrowquestion_answer107) Which of the following compound will have the smallest \[\text{p}{{\text{K}}_{\text{a}}}\]value?
A) Benzoic acid
B) Formic acid
C) Acetic acid
D) Phenyl acetic acid
View Answer play_arrowquestion_answer108) Ethyl alcohol cannot be used as a solvent for methyl magnesium iodide because
A) methyl magnesium iodide reacts with alcohol-giving methane
B) the reaction between them is explosive in nature
C) methyl magnesium iodide is converted to ethyl magnesium iodide
D) alcohol is immiscible with methyl magnesium iodide
View Answer play_arrowquestion_answer109) Which is not true about acetophenone?
A) It reacts with alkaline potassium permanganate followed by acid hydrolysis and forms benzoic acid
B) It reacts with iodine and sodium hydroxide to form tri-iodomethane
C) It is prepared by the reaction of benzene with benzoyl chloride in presence of anhydrous aluminium chloride
D) It does not react with freshly prepared ammoniacal silver nitrate solution
View Answer play_arrowquestion_answer110) Formation of methyl tertiary butyl ether by the reaction of sodium tertiary butoxide and methyl bromide involves
A) elimination reaction
B) electrophilic addition reaction
C) nucleophilic substitution unimolecular reaction
D) nucleophilic substitution bimolecular reaction
View Answer play_arrowquestion_answer111) 10 g of a radioisotope is reduced to 1.25 g of . active material after 12 yr. Therefore, the half-life of the isotope (in yr) is
A) 24
B) 4
C) 2
D) 8
View Answer play_arrowquestion_answer112) Out of the following, which is the correct set of quantum number for the outermost electron of potassium atom (Z = 19)?
A) \[n-4\] \[l-3\] \[m-2\] \[s-\,\,\,\,\,\text{-1/2}\]
B) \[n-4\] \[l-2\] \[m-0\] \[s-\,\,\,\,\,\text{-1/2}\]
C) \[n-4\] \[l-1\] \[m-0\] \[s-\,\,\,\,\,+\text{1/2}\]
D) \[n-4\] \[l-0\] \[m-0\] \[s-\,\,\,\,\,\text{-1/2}\]
View Answer play_arrowquestion_answer113) The molecules present in 5.6 L of sulphur dioxide at STP is
A) \[1.5\times {{10}^{23}}\]
B) \[1.5\times {{10}^{-23}}\]
C) \[4\times {{10}^{23}}\]
D) \[0.15\times {{10}^{23}}\]
View Answer play_arrowquestion_answer114) What is the relationship between the parent and daughter nuclei, when a nucleus of an atom undergoes beta emission?
A) Isobars
B) Isotopes
C) Isotones
D) Isomers
View Answer play_arrowquestion_answer115) In photoelectric effect, the kinetic energy of the photoelectron increases linearly with the
A) wavelength of the incident light
B) frequency of the incident light
C) velocity of the incident light
D) atomic mass of an element
View Answer play_arrowquestion_answer116) Dual behaviour of matter was proposed by
A) Niels Bohr
B) Erwin Schrodinger
C) Louis de-Broglie
D) Max Planck
View Answer play_arrowquestion_answer117) What is the maximum number of emission lines obtained when the excited electron of a hydrogen atom in \[n=5\]drops to the ground state?
A) 10
B) 5
C) 12
D) 15
View Answer play_arrowquestion_answer118) For a reaction\[[R]\xrightarrow{{}}P\]a graph of [R] against time is found to be a straight line. What is the order of this reaction?
A) Second order
B) Third order
C) First order
D) Zero order
View Answer play_arrowquestion_answer119) For getting accurate value of molar mass of a solute by osmotic pressure measurement
A) the solute must be volatile
B) the solution concentration must be high
C) the solute should undergo dissociation
D) the solute must be non-volatile
View Answer play_arrowquestion_answer120) In a catalytic experiment involving the Haber process, \[{{N}_{2}}(g)+3{{H}_{2}}(g)\xrightarrow{{}}2N{{H}_{3}}(g),\] the rate of reaction was measured as Rate \[=[N{{H}_{3}}]=2.0\times {{10}^{-4}}M{{s}^{-1}}\] If there were no side reactions what was the rate of reaction expressed in terms of \[{{N}_{2}}?\]
A) \[1\times {{10}^{-4}}M{{s}^{-1}}\]
B) \[4\times {{10}^{-4}}M{{s}^{-1}}\]
C) \[5\times {{10}^{-3}}M{{s}^{-1}}\]
D) \[1\times {{10}^{-3}}M{{s}^{-1}}\]
View Answer play_arrowquestion_answer121) For a dilute solution, Raoulfs law states that
A) lowering of vapour pressure is equal to the mole fraction of the solute
B) relative lowering of vapour pressure is equal to the mole fraction of the solvent
C) relative lowering of vapour pressure of the solvent is equal to the mole fraction of the solute
D) vapour pressure of the solution is equal to the vapour pressure of the solvent
View Answer play_arrowquestion_answer122) 36 g of glucose (molar mass\[=180\text{ }g/mol\]) if present in 500 g of water, the molality of the solution is
A) 0.2
B) 0.4
C) 0.8
D) 1.0
View Answer play_arrowquestion_answer123) A certain current liberates 0.504 g hydrogen is 2 h. How many gram of oxygen can be liberated by the same current in the same time?
A) 2.0 g
B) 0.4 g
C) 4.0 g
D) 8.0 g
View Answer play_arrowquestion_answer124) The reduction potential values of X, Y and Z are \[-3.05\,V,-0.44\,V\]and\[~-0.83\,V\] respectively. Which of the following order is correct with respect to their reducing property?
A) \[X>Y>Z\]
B) \[X>Z>Y\]
C) \[Y>Z>X\]
D) \[~Z>Y>X\]
View Answer play_arrowquestion_answer125) Relationship between atomic radius r and the edge length a of a body centred cubic unit cell is
A) \[r=\frac{a}{2}\]
B) \[r=\sqrt{\frac{a}{2}}\]
C) \[r=\frac{\sqrt{3}}{4}a\]
D) \[r=\frac{3a}{2}\]
View Answer play_arrowquestion_answer126) Calculate the reduction potential of a half-cell containing of platinum electrode immersed in \[\text{2}\text{.0}\,\text{M}\,\text{F}{{\text{e}}^{\text{2+}}}\]and \[\text{0}\text{.02 M F}{{\text{e}}^{\text{3+}}}\text{.}\] Given \[\text{E}_{F{{e}^{3+}}/F{{e}^{2+}}}^{o}=0.771\,V,\] \[F{{e}^{3+}}+{{e}^{-}}\xrightarrow{{}}F{{e}^{2+}}\]
A) 0.653 V
B) 0.889 V
C) 0.0653V
D) 2.771V
View Answer play_arrowquestion_answer127) Faraday constant is defined as
A) charge carried by one electron
B) charge carried by one mole of electron
C) charge required depositing one mole of substance
D) charge carried by two moles of electron
View Answer play_arrowquestion_answer128) If 300mL of a gas weighs 0.368 g at STP. What is its molecular weight?
A) 30.16
B) 2.55
C) 27.5
D) 37.5
View Answer play_arrowquestion_answer129) Which one of the following compound exhibit both Schottky and Frenkel defects?
A) \[~NaCl\]
B) \[~AgCl\]
C) \[AgBr\]
D) \[Agl\]
View Answer play_arrowquestion_answer130) Identify the molecule that has zero dipole moment.
A) \[C{{H}_{3}}Cl\]
B) \[CHC{{l}_{3}}\]
C) \[C{{H}_{2}}C{{l}_{2}}\]
D) \[CC{{l}_{4}}\]
View Answer play_arrowquestion_answer131) Which one statement about sulphur dioxide gas is incorrect?
A) It has an angular shape
B) lt decolourises acidified potassium permanganate solution
C) Two S?O bonds are equal
D) It is a dehydrating agent
View Answer play_arrowquestion_answer132) In which of the following arrangement, the order is not according to the property indicated against it?
A) \[{{F}_{2}}>C{{l}_{2}}>B{{r}_{2}}>{{I}_{2}}-\]Oxidising agent
B) \[N{{H}_{3}}>P{{H}_{3}}>As{{H}_{3}}>Sb{{H}_{3}}>Bi{{H}_{3}}-\]Basic property
C) \[F>Cl>Br>I-\]Electron gain enthalpy
D) \[C>Si>Ge>Sn-\]Ability to form p-p bond
View Answer play_arrowquestion_answer133) In \[\text{C}{{\text{O}}_{\text{2}}}\text{,C}{{\text{H}}_{\text{4}}}\]and\[\text{CH}_{\text{3}}^{\text{+}}\]the hybridisation of carbon atom are
A) \[s{{p}^{2}},s{{p}^{3}}\]and \[s{{p}^{2}}\]respectively
B) \[~sp,s{{p}^{3}}\] and \[s{{p}^{2}}\]respectively
C) \[~sp,\text{ }s{{p}^{3}}\] and \[sp\]respectively
D) \[s{{p}^{2}},\text{ }s{{p}^{3}}\]and \[sp\]respectively
View Answer play_arrowquestion_answer134) Why calcium ion makes water hard but sodium ion does not?
A) Calcium forms insoluble compound with stearate ion present in soap
B) Sodium forms insoluble compound with stearate ion present in soap
C) Calcium forms soluble compound with stearate ion present in soap
D) Both calcium and sodium forms insoluble compound with stearate ion present in soap
View Answer play_arrowquestion_answer135) The colourless gas that turns brown in air is
A) \[NO\]
B) \[N{{O}_{2}}\]
C) \[{{N}_{2}}{{O}_{4}}\]
D) \[{{N}_{2}}{{O}_{5}}\]
View Answer play_arrowquestion_answer136) IUPAC name of the complex \[{{K}_{3}}[Al{{({{C}_{2}}{{O}_{4}})}_{3}}]\]is
A) potassium tris(oxalato)aluminate(III)
B) potassium tri(oxalato)aluminate(III)
C) potassium tris(oxalato)aluminium(III)
D) potassium tri(oxalato)alumimum(III)
View Answer play_arrowquestion_answer137) The depressant used to separate lead sulphide and zinc sulphide ores is
A) potassium cyanide
B) sodium cyanide
C) silver cyanide
D) sodium sulphide
View Answer play_arrowquestion_answer138) IUPAC name of the compound
A) 1-fluoro-4-methyl-2-nitrobenzene
B) 4-fluoro-1-methyl-3-nitrobenzene
C) 4-methyl-1-fluoro-2-nitrobenzene
D) 5-methyl-2-fluoro-1-nitrobenzene
View Answer play_arrowquestion_answer139) In the extraction of copper, the copper matte is a mixture of
A) copper(II) sulphide and iron(II) sulphide
B) copperd (II) sulphide and iron(III) sulphide
C) copper(I) sulphide and iron(II) sulphide
D) copper(I) sulphide and iron(III) sulphide
View Answer play_arrowquestion_answer140) Silver halide which is readily soluble m ammonium chloride is
A) silver chloride
B) silver bromide
C) silver fluoride
D) silver iodide
View Answer play_arrowquestion_answer141) Which of the following reagent can be used to convert ethanamide to methanamme?
A) \[{{P}_{2}}{{O}_{5}}\]
B) \[NaOBr\]
C) \[LiAl{{H}_{4}}/{{H}_{2}}O\]
D) \[Na(Hg)/{{C}_{2}}{{H}_{5}}OH\]
View Answer play_arrowquestion_answer142) Identify the product ?C? in the series \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}\xrightarrow{Fe/HCl}A\xrightarrow[273\,K]{NaN{{O}_{2}}+HCl}\]\[B\xrightarrow[283\,K]{{{H}_{2}}O}C\]
A) \[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{OH}\]
B) \[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{C}{{\text{H}}_{\text{2}}}\text{OH}\]
C) \[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{CHO}\]
D) \[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{N}{{\text{H}}_{\text{2}}}\]
View Answer play_arrowquestion_answer143) The class of drug used for the treatment of stress is
A) analgesics
B) antiseptic
C) antihistamine
D) tranquilizers
View Answer play_arrowquestion_answer144) Compound that has smell of bitter almonds is
A) aniline
B) benzonitnie
C) phenylisocyanide
D) nitrobenzene
View Answer play_arrowquestion_answer145) Which of the following is the correct increasing order of basicity of amines in gaseous phase?
A) \[{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{3}}N>N{{H}_{3}}\]
B) \[{{(C{{H}_{3}})}_{3}}N>{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}>N{{H}_{3}}\]
C) \[{{(C{{H}_{3}})}_{2}}NH>{{(C{{H}_{3}})}_{3}}N>C{{H}_{3}}N{{H}_{2}}>N{{H}_{3}}\]
D) \[{{(C{{H}_{3}})}_{3}}N>C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{2}}NH>N{{H}_{3}}\]
View Answer play_arrowquestion_answer146) Nitrogenous base that found in RNA but absent in DNA is
A) uracil
B) thymine
C) cytosine
D) adenine
View Answer play_arrowquestion_answer147) Glycerol when reacts with potassium hydrogen sulphate at \[473\text{ }K-503\text{ }K\]forms
A) allyl iodide
B) allyl alcohol
C) glycericacid
D) acrolein
View Answer play_arrowquestion_answer148) Phenol reacts with bromine in chloroform at low temperature to give
A) \[m-\]bromophenol
B) mixture of ortho and para bromophenol
C) \[~p-\] bromophenol
D) 2, 4, 6-tribromophenol
View Answer play_arrowquestion_answer149) Identify the compound 'X' in the following reaction
A)
B)
C)
D)
View Answer play_arrowquestion_answer150) Alkyl halides undergoing substitution nucleophilic bimolecular reaction involves
A) formation of carbocation
B) racemic mixture
C) inversion of configuration
D) retention of configuration
View Answer play_arrowquestion_answer151) The radius of the sphere \[|\,3\,\vec{r}+2\hat{i}-\hat{j}-4\hat{k}|=3\] is
A) \[2\]
B) \[3\]
C) \[1\]
D) \[9\]
View Answer play_arrowquestion_answer152) The foot of the perpendicular drawn from the origin to a plane is \[(1,-1,5)\]. The equation of the plane is
A) \[\vec{r}.(\hat{i}-\hat{j}+5\hat{k})=27\]
B) \[\vec{r}.(\hat{i}-\hat{j}+5\hat{k})=\sqrt{27}\]
C) \[\vec{r}.(5\hat{i}-\hat{j}+\hat{k})=\frac{1}{\sqrt{27}}\]
D) \[x-y-5z-27=0\]
View Answer play_arrowquestion_answer153) The dual of the statement \[(\tilde{\ }p)\wedge [(\tilde{\ }q)\wedge (p\vee q)\wedge (\tilde{\ }r)]\]is
A) \[p\wedge [q\vee (p\wedge q)\vee r]\]
B) \[(\tilde{\ }p)\vee [(\tilde{\ }q)\vee (p\wedge q)\vee (\tilde{\ }r)]\]
C) \[(\tilde{\ }p)\wedge [(\tilde{\ }q)\vee (p\vee q)\vee r]\]
D) \[(\tilde{\ }p)\vee [(\tilde{\ }q)\vee (p\wedge q)\vee r]\]
View Answer play_arrowquestion_answer154) The vector equation of the straight line \[6x-8=2y-7=3z\]is
A) \[\vec{r}=\left( \frac{8}{6}\hat{i}+\frac{7}{2}\hat{j} \right)+t\left( \frac{1}{6}\hat{i}+\frac{1}{2}\hat{j}-\frac{1}{3}\hat{k} \right)\]
B) \[\vec{r}=\left( \frac{8}{6}\hat{i}+\frac{7}{2}\hat{j} \right)+s\left( \frac{1}{6}\hat{i}+\frac{1}{2}\hat{j}-\frac{1}{3}\hat{k} \right)\]
C) \[\vec{r}=\left( -\frac{8}{6}\hat{i}-\frac{7}{2}\hat{j} \right)+t\left( \frac{1}{6}\hat{i}+\frac{1}{2}\hat{j}-\frac{1}{3}\hat{k} \right)\]
D) \[\vec{r}=\left( -\frac{8}{6}\hat{i}-\frac{7}{2}\hat{j} \right)+s\left( \frac{1}{6}\hat{i}-\frac{1}{2}\hat{j}-\frac{1}{3}\hat{k} \right)\]
View Answer play_arrowquestion_answer155) The unit normal vector to the plane \[3x+2y-2z=8\sqrt{17}\] is
A) \[\frac{1}{\sqrt{3}}\,(\hat{i}+\hat{j}-\hat{k})\]
B) \[\frac{1}{\sqrt{17}}\,(3\hat{i}+2\hat{j}-2\hat{k})\]
C) \[\frac{1}{\sqrt{13}}\,(3\hat{i}+2\hat{j}+2\hat{k})\]
D) \[\frac{1}{\sqrt{11}}\,(3\hat{i}+\hat{j}+\hat{k})\]
View Answer play_arrowquestion_answer156) The centroid of the triangle formed by joining the mid points of the sides of a triangle with vertices \[(-1,-1),(2,4)\] and \[(-5,-6)\] is
A) \[\left( -\frac{2}{3},1 \right)\]
B) \[\left( -\frac{4}{3},-1 \right)\]
C) \[\left( -\frac{1}{3},\frac{1}{2} \right)\]
D) \[\left( -\frac{1}{4},\frac{1}{4} \right)\]
View Answer play_arrowquestion_answer157) if the straight lines \[2x+5ay-1=0\] and \[3x+7y+7=0\] are mutually perpendicular, then value of \[\alpha \] is
A) \[\frac{6}{37}\]
B) \[\frac{-6}{31}\]
C) \[\frac{-6}{37}\]
D) \[\frac{-6}{35}\]
View Answer play_arrowquestion_answer158) The pair of straight lines \[{{x}^{2}}-3{{y}^{2}}=0\]and the line \[x=1\]form a triangle which is
A) right angled
B) isosceles
C) scalene
D) equilateral
View Answer play_arrowquestion_answer159) If the straight lines \[2x-3y+1=0\] and \[4x-6y+5=0\] are tangents to the same circle, then the radius of the circle is
A) \[\frac{3}{2\sqrt{13}}\]
B) \[\frac{3}{4\sqrt{13}}\]
C) \[\frac{3}{8\sqrt{13}}\]
D) \[2\]
View Answer play_arrowquestion_answer160) If \[A\,(5,-1)\] and \[B\,(-3,7)\] are two points on a circle and if \[P(x,y)\] is any point on the circle such that s\[\angle APB=\frac{\pi }{2},\] then the equation of the circle is
A) \[{{x}^{2}}+{{y}^{2}}-2x+6y-22=0\]
B) \[{{x}^{2}}+{{y}^{2}}+2x+6y-11=0\]
C) \[{{x}^{2}}+{{y}^{2}}-2x+6y+22=0\]
D) \[{{x}^{2}}+{{y}^{2}}-2x-6y-22=0\]
View Answer play_arrowquestion_answer161) The angle between the pair of straight lines represented by the equation \[12{{x}^{2}}+7xy-12{{y}^{2}}-x-7y-1=0\]is
A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{2}\]
D) \[\frac{\pi }{6}\]
View Answer play_arrowquestion_answer162) The equation of a straight line which is parallel to \[x-2y+8=0\]and passes through \[(0,4)\] is
A) \[x-2y+8=0~~~\]
B) \[x-2y+7=0\]
C) \[x-2y+4=0\]
D) \[2x+2y-13=0\]
View Answer play_arrowquestion_answer163) The algebraic sum of the moments of the forces, forming a couple, about any point in their plane is
A) proportional to the sum of the magnitudes of the forces
B) inversely proportional to the magnitudes of the forces
C) constant and is equal to the moment of the couple
D) constant and is equal to one-third of the moment of the couple
View Answer play_arrowquestion_answer164) At time t, the distance x cm of a moving particle in a horizontal line is given by\[x=12\,{{t}^{3}}-7\,{{t}^{2}}+14t+2.\]. The acceleration when \[t=1\text{ }s\]is
A) \[48\,\,cm/{{s}^{2}}\]
B) \[68\text{ }cm/{{s}^{2}}\]
C) \[58\text{ }cm/{{s}^{2}}\]
D) \[56\text{ }cm/{{s}^{2}}\]
View Answer play_arrowquestion_answer165) The horizontal range of a projectile is \[\frac{4}{\sqrt{3}}\] times its maximum height. The angle of projection is
A) \[{{30}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{45}^{o}}\]
D) \[{{\tan }^{-1}}\,(2)\]
View Answer play_arrowquestion_answer166) A particle with uniform acceleration reaches \[100\text{ }m\]in the 5th second and \[151\text{ }m\]in the 8th second. The acceleration is
A) \[15m/{{s}^{2}}\]
B) \[~16m/{{s}^{2}}\]
C) \[17\text{ }m/{{s}^{2}}\]
D) \[20\text{ }m/{{s}^{2}}\]
View Answer play_arrowquestion_answer167) Let \[\vec{u}\] and \[\vec{v}\] be the velocity vectors of a particle at a point O. If \[\vec{u}\] and \[\vec{v}\] are in opposite directions and if \[u>v,\] then the magnitude of the resultant velocity vector \[\vec{v}\] is
A) \[u+v\]
B) \[2\,u+v\]
C) \[u-v\]
D) \[u-\frac{1}{2}v\]
View Answer play_arrowquestion_answer168) The forces of magnitude \[9\text{ }N\]and \[11\text{ }N\]act at a point and are inclined to each other at an angle of\[{{45}^{o}}\]. The magnitude of the resultant force is
A) \[\sqrt{301}\,N\]
B) \[\sqrt{202+99\sqrt{2}}\,N\]
C) \[\sqrt{{{9}^{2}}+{{11}^{2}}}\,\,N\]
D) \[202\,N\]
View Answer play_arrowquestion_answer169) If X and Y are two non-singular matrices such that \[XY{{X}^{-1}}=\left( \begin{matrix} 3 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & -7 \\ \end{matrix} \right),\] then \[X{{Y}^{-1}}{{X}^{-1}}\] is equal to
A) \[\left( \begin{matrix} \frac{1}{3} & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & -\frac{1}{7} \\ \end{matrix} \right)\]
B) \[\left( \begin{matrix} -\frac{1}{3} & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & -7 \\ \end{matrix} \right)\]
C) \[\left( \begin{matrix} \frac{1}{3} & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & 7 \\ \end{matrix} \right)\]
D) \[\left( \begin{matrix} \frac{1}{3} & 0 & 0 \\ 0 & -\frac{1}{2} & 0 \\ 0 & 0 & 7 \\ \end{matrix} \right)\]
View Answer play_arrowquestion_answer170) Let \[\vec{a}\,-\,2\vec{b}\] and \[2\vec{a}\,-\vec{b}\] be position vectors of the points A and B respectively. The position vector of the point which divides AB in the ratio \[3:2\]externally is
A) \[\frac{8}{5}\,\vec{a}-\frac{7}{5}\vec{b}\]
B) \[4\,\vec{a}+\vec{b}\]
C) \[\,\vec{a}+4\vec{b}\]
D) \[\frac{7}{5}\vec{b}-\frac{8}{5}\vec{a}\]
View Answer play_arrowquestion_answer171) If \[|\vec{a}|=2,\,|\vec{b}|=5,\] and \[\vec{a}\,.\,\vec{b}=5\sqrt{2},\]then \[|\vec{a}\times \vec{b}|\] is equal to
A) \[5\sqrt{2}\]
B) \[\sqrt{2}\]
C) \[4\sqrt{2}\]
D) \[2\]
View Answer play_arrowquestion_answer172) Let \[\vec{a}-2\vec{b}+3\vec{c},\,\,\,\,\,-2\vec{a}+3\vec{b}-\vec{c}\]and \[4\vec{a}-7\vec{b}+7\vec{c}\]be position vectors of the points A, B and C respectively. Then, the points A, B and Care
A) vertices of an equilateral triangle
B) vertices of a right angled triangle
C) vertices of an isosceles triangle
D) collinear points
View Answer play_arrowquestion_answer173) If \[\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right|=3,\] then \[\left| \begin{matrix} 3\,{{a}_{1}} & 9\,{{b}_{1}} & 3\,{{c}_{1}} \\ {{a}_{2}} & 3\,{{b}_{2}} & {{c}_{2}} \\ 3\,{{a}_{3}} & 9\,{{b}_{3}} & 3\,{{c}_{3}} \\ \end{matrix} \right|\] is equal to
A) \[51\]
B) \[27\]
C) \[81\]
D) \[91\]
View Answer play_arrowquestion_answer174) The domain of the function \[f(x)=\frac{1}{{{\log }_{10}}\,(1-x)}\]is
A) \[(-\infty ,\,1]\,-\{0\}\]
B) \[(-\infty ,\,1)\,-\{0\}\]
C) \[(-\infty ,\,\,2)\,\]
D) \[(0,\,-\infty )\,\]
View Answer play_arrowquestion_answer175) If \[\omega \] is a complex cube root of unity, then \[\frac{a+b\omega +c{{\omega }^{2}}}{a{{\omega }^{2}}+b+c\omega }+\frac{a{{\omega }^{2}}+b\omega +c}{a+b{{\omega }^{2}}+c\omega }\] is equal to
A) \[1\]
B) \[2\,\omega \]
C) \[2\,{{\omega }^{2}}\]
D) \[-1\]
View Answer play_arrowquestion_answer176) If 19 times 12th term of an AP and 18 times 11 th term of an AP are equal, then the 30th term of the AP is
A) \[0\]
B) \[2\]
C) \[11\]
D) \[29\]
View Answer play_arrowquestion_answer177) Sum ton terms of the series \[1+11+111+....\]is
A) \[\frac{10}{81}\,\,({{10}^{n}}-1)-\frac{n}{81}\]
B) \[\frac{10}{81}\,\,({{10}^{n}}-1)-\frac{n}{9}\]
C) \[\frac{10}{81}\,\,({{10}^{n}}-1)+\frac{n}{9}\]
D) \[\frac{10}{81}\,\,({{10}^{n}}-1)+\frac{n}{81}\]
View Answer play_arrowquestion_answer178) If one root of the equation \[{{x}^{2}}-(3\sqrt{2}-2i)\,x-6\,\sqrt{2}i=0\] is \[-2i,\] then the other root of the equation is
A) \[2i\]
B) \[3\,\sqrt{2}\]
C) \[-3\,\sqrt{2}\]
D) \[5\,\sqrt{2}\]
View Answer play_arrowquestion_answer179) If \[{{z}_{1}}\] and \[{{z}_{2}}\] are non-zero complex numbers such that arg \[\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)=\frac{\pi }{2},\] then \[\left| \frac{3{{z}_{1}}-5{{z}_{2}}}{3{{z}_{1}}+5{{z}_{2}}} \right|\] equal to
A) \[\sqrt{2}\]
B) \[\sqrt{34}\]
C) \[1\]
D) \[\frac{2}{\sqrt{34}}\]
View Answer play_arrowquestion_answer180) Which one of the following is not true for the function \[f(x)={{x}^{2}}-x+1,\,0\le x\le 1\]?
A) Increases on \[\left[ \frac{1}{2},1 \right]\]
B) Decreases on \[\left[ 0,\frac{1}{2} \right]\]
C) Increases on \[\left[ 0,\frac{1}{2} \right]\]
D) Neither increases nor decreases on \[[0,\,\,1]\]
View Answer play_arrowquestion_answer181) The value of the integral \[\int{{{({{x}^{4}}+3{{x}^{3}}+9{{x}^{2}}+8x-6)}^{12}}}\] \[(4{{x}^{3}}+9{{x}^{2}}+18x+8)\,dx\] is equal to
A) \[\frac{{{({{x}^{4}}+3{{x}^{3}}+9{{x}^{2}}+8x-6)}^{12}}}{12}+c\]
B) \[\frac{{{(4{{x}^{3}}+9{{x}^{2}}+18x+8)}^{13}}}{13}+c\]
C) \[\frac{{{({{x}^{4}}+3{{x}^{2}}+9{{x}^{2}}+8x-6)}^{13}}}{13}+c\]
D) \[\frac{{{({{x}^{4}}+3{{x}^{2}}+9{{x}^{2}}+8x-6)}^{11}}}{11}+c\]
View Answer play_arrowquestion_answer182) \[\int{{{x}^{2}}\,{{7}^{x}}\,\,dx}\] is equal to
A) \[\frac{{{x}^{2}}{{7}^{x}}}{\log \,7}+2x\frac{{{7}^{x}}}{{{(\log \,7)}^{2}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+c\]
B) \[\frac{{{x}^{2}}{{7}^{x}}}{\log \,7}-2x\frac{{{7}^{x}}}{{{(\log \,7)}^{2}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+c\]
C) \[{{x}^{2}}{{7}^{x}}-2x\,\frac{7x}{\log \,7}+2\,\frac{7x}{{{(\log \,7)}^{2}}}+c\]
D) \[\frac{{{x}^{2}}{{7}^{x}}}{{{(\log \,7)}^{2}}}-2x\,\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{4}}}+c\]
View Answer play_arrowquestion_answer183) If \[y=\cos \,(m\,\,{{\sin }^{-1}}\,x),\] then \[(1-{{x}^{2}})\,\frac{{{d}^{2}}y}{d{{x}^{2}}}-x\frac{dy}{dx}+{{m}^{2}}y\] is equal to
A) \[1\]
B) \[7\]
C) \[-1\]
D) \[0\]
View Answer play_arrowquestion_answer184) \[{{\cos }^{2}}\,B+{{\cos }^{2}}\,(A-B)\,-2\cos \,A\,\cos \,B\,\cos \,(A-B)\]is equal to
A) \[co{{s}^{2}}\text{ }A\]
B) \[co{{s}^{2}}\text{ }A-1\]
C) \[si{{n}^{2}}\text{ }A\]
D) \[1\]
View Answer play_arrowquestion_answer185) If \[A+B+C=\pi ,\]then \[\tan \frac{A}{2}.\tan \frac{B}{2}+\tan \frac{B}{2}.\tan \frac{C}{2}+\tan \frac{C}{2}+\tan \frac{C}{2}.\tan \frac{A}{2}\]is equal to
A) \[3\]
B) \[2\]
C) \[1\]
D) \[0\]
View Answer play_arrowquestion_answer186) If \[{{\tan }^{-1}}\,(1-x),\,\,{{\tan }^{-1}}\,(x)\] and \[{{\tan }^{-1}}\,(1+x)\] are in AP, then the value of \[{{x}^{3}}+{{x}^{2}}\]is equal to
A) \[2\]
B) \[-1\]
C) \[1\]
D) \[-2\]
View Answer play_arrowquestion_answer187) \[{{\sin }^{-1}}x+{{\sec }^{-1}}x+{{\cot }^{-1}}x+{{\cos }^{-1}}x\]\[+\text{cose}{{\text{c}}^{-1}}\,x+{{\tan }^{-1}}x\] is equal to
A) \[\pi \]
B) \[2\pi \]
C) \[\frac{\pi }{2}\]
D) \[\frac{3\pi }{2}\]
View Answer play_arrowquestion_answer188) The general solution of the equation\[sin\text{ }x+cos\text{ }x=2\]is
A) \[x=n\pi \,+{{(-1)}^{n}}\,\frac{\pi }{4},\,n=....,-3,\,-2,\,\] \[-1,\,0,1,\,2,\,3,...\]
B) \[x=n\pi +{{(-1)}^{n}}\frac{\pi }{6},n=....,-3,-2,-1,\] \[0,\,1,\,2,\,3,....\]
C) \[x=n\pi +{{(-1)}^{n+1}}\frac{\pi }{4},n=...,-3,-2,\] \[-1,0,1,2,3,...\]
D) does not exist
View Answer play_arrowquestion_answer189) If a \[\sin \theta +b\,\cos \theta =4\] and a \[\sin \theta -b\,\cos \theta =3,\]then the value of \[\sin 2\,\theta \] is
A) \[\frac{7}{{{a}^{2}}+{{b}^{2}}}\]
B) \[\frac{5}{{{a}^{2}}+{{b}^{2}}}\]
C) \[\frac{7}{{{a}^{2}}-{{b}^{2}}}\]
D) \[\frac{7}{2ab}\]
View Answer play_arrowquestion_answer190) \[(1-\tan A)\,(\cot \,A+1)\] is equal to
A) \[(1-\tan A)\,(1+tanA)\]
B) \[(1+\tan A)\,(cot\,A-1)\]
C) \[(1+\tan A)\,(1-cot\,A)\]
D) \[(\tan \,A-1)\,(\cot \,A-1)\]
View Answer play_arrowquestion_answer191) \[\int{{{\sec }^{2}}x\,\,\text{cose}{{\text{c}}^{2}}x\,\,dx}\]is equal to
A) \[\tan x-\cot \,x+c\]
B) \[\tan x+\cot \,x+c\]
C) \[\tan x+\operatorname{cosec}\,x+c\]
D) \[\cot x+\operatorname{cosec}\,+c\]
View Answer play_arrowquestion_answer192) The area of the region bounded by the curve \[x=2\,\cos \,\theta ,\,\,y=2\,\sin \theta ,\,x=0,\,x=2\] and the x-axis is (in sq unit)
A) \[4\pi \]
B) \[2\pi \]
C) \[\pi \]
D) \[\frac{\pi }{2}\]
View Answer play_arrowquestion_answer193) The solution of the differential equation \[\frac{dy}{dx}=5+5x+10y+10xy\]is
A) \[\log \,(5+10y)=x+\frac{{{x}^{2}}}{2}+c\]
B) \[\frac{1}{10}\log \,(5+10y)=x+\frac{{{x}^{2}}}{2}+c\]
C) \[\frac{1}{5}\log \,(5+10y)=x+\frac{{{x}^{2}}}{2}+c\]
D) \[\frac{1}{10}\log \,(5+10y)=x+{{x}^{2}}+c\]
View Answer play_arrowquestion_answer194) The order and degree of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y+{{\left( \frac{dy}{dx}+\frac{{{d}^{3}}y}{d{{x}^{3}}} \right)}^{5/2}}=0\] are respectively
A) \[3,\,\,\,2\]
B) \[2,\,\,3\]
C) \[3,\,\,1\]
D) \[3,\,\,5\]
View Answer play_arrowquestion_answer195) \[\int_{0}^{\pi /2}{\frac{{{\sin }^{100}}x}{{{\sin }^{100}}x+{{\cos }^{100}}x}\,\,dx}\]is equal to
A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{12}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{\pi }{8}\]
View Answer play_arrowquestion_answer196) If \[(\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c})\]and \[\vec{a},\vec{b}\] and \[\vec{c}\] are not mutually perpendicular vectors, then
A) \[\vec{a}\] and \[\vec{c}\] are parallel
B) \[\vec{a}\] and \[\vec{b}\] are parallel
C) \[\vec{b}\]and \[\vec{c}\] are parallel
D) \[\vec{a}\] and \[\vec{c}\]are perpendicular
View Answer play_arrowquestion_answer197) Which me of the following is a point on the straight line \[\vec{r}=(-5\hat{i}+2\hat{j}+3\hat{k})\,+\,t\,(9\hat{i}-5\hat{j}+3\hat{k})\]?
A) \[(13,-8,\,7)\]
B) \[(4,-3,\,5)\]
C) \[(-14,7,\,6)\]
D) \[(22,-13,12)\]
View Answer play_arrowquestion_answer198) \[\vec{r}=(1-t)\,(3\hat{i}-4\hat{j}+7\hat{k})+t(\hat{i}+\hat{j}-\hat{k})\]\[+s(-2\hat{i}+\hat{j}-\hat{k})\] is the equation of a plane in vector form when it
A) passes through three given non-collinear points
B) passes through one point and parallel to two vectors
C) passes through two points and parallel to one vector
D) passes through one point and perpendicular to one vector
View Answer play_arrowquestion_answer199) The point of intersection of the lines \[\frac{x-1}{3}=\frac{y-1}{-1}=\frac{z+1}{0}\] and \[\frac{x-4}{2}=\frac{y}{0}=\frac{z+1}{3}\]is
A) \[(4,0,1)\]
B) \[(4,0,-1)\]
C) \[(1,1,1)\]
D) \[(1,1,-1)\]
View Answer play_arrowquestion_answer200) If \[3\hat{i}+\hat{j}-2\hat{k}\]and \[\hat{i}-3\hat{j}+4\hat{k}\] are the diagonals of a parallelogram, then the area of the parallelogram is
A) \[10\sqrt{3}\] sq unit
B) \[5\sqrt{3}\] sq unit
C) \[5\sqrt{2}\]sq unit
D) \[10\sqrt{2}\]sq unit
View Answer play_arrowquestion_answer201) \[\vec{a}=\hat{i}+2\hat{j}+3\hat{k},\,\,\,\,\,\vec{b}=-\hat{i}+2\hat{j}+3\hat{k}\] and \[\vec{c}=2\hat{i}-2\hat{j}-3\hat{k},\]then \[(\vec{b}+\vec{c}).\vec{a}\times \{(\vec{b}+\vec{c})\times \vec{a}\}\] is equal to
A) \[9\]
B) \[21\]
C) \[13\]
D) \[7\]
View Answer play_arrowquestion_answer202) The coefficient of \[{{x}^{4}}\]in the expansion of \[{{(1+x)}^{-2}},\]where \[|x|<1,\] is
A) \[-5\]
B) \[5\]
C) \[4\]
D) \[-3\]
View Answer play_arrowquestion_answer203) If \[m{{=}^{n}}{{C}_{2}},\] then \[^{m}{{C}_{2}}\] is equal to
A) \[^{n+1}{{C}_{4}}\]
B) \[{{2}^{n+1}}{{C}_{4}}\]
C) \[{{3}^{n+1}}{{C}_{4}}\]
D) \[{{4}^{n+1}}{{C}_{4}}\]
View Answer play_arrowquestion_answer204) \[\frac{1+\frac{1}{2!}+\frac{1}{4!}+\frac{1}{6!}+...}{\frac{1}{1!}+\frac{1}{3!}+\frac{1}{5!}+....}\] is equal to
A) \[\frac{{{e}^{2}}-1}{{{e}^{2}}+1}\]
B) \[\frac{{{e}^{2}}+1}{{{e}^{2}}-1}\]
C) \[\frac{e+1}{e-1}\]
D) \[\frac{1-{{e}^{2}}}{e+{{e}^{2}}}\]
View Answer play_arrowquestion_answer205) Four arithmetic means between -10 and 25 are inserted. Then, the 5th term in the series is
A) \[11\]
B) \[19\]
C) \[17\]
D) \[18\]
View Answer play_arrowquestion_answer206) The mean deviation about the mean for the values 18, 20, 12, 14, 19, 22, 26, 16, 19, 24 is
A) \[3.1\]
B) \[3.4\]
C) \[3.2\]
D) \[3.3\]
View Answer play_arrowquestion_answer207) \[3\,{{\log }_{e}}2+\frac{1}{4}-\frac{1}{2}.\frac{1}{{{4}^{2}}}+\frac{1}{3}.\frac{1}{{{4}^{3}}}-....\]is equal to
A) \[{{\log }_{e}}10\]
B) \[3\,\,{{\log }_{e}}4\]
C) \[2\,{{\log }_{e}}5\]
D) \[{{\log }_{e}}\,8\]
View Answer play_arrowquestion_answer208) The number of ways of selecting a boy and a girl from a class consisting of 20 boys and 30 girls is
A) \[50\]
B) \[10\]
C) \[600\]
D) \[1300\]
View Answer play_arrowquestion_answer209) The sum of the coefficients in the expansion of \[{{(1+x-3x)}^{143}}\] is
A) \[-1\]
B) \[1\]
C) \[-3\]
D) \[-7\]
View Answer play_arrowquestion_answer210) If \[f(x)={{\cot }^{-1}}\left[ \sqrt{\frac{1+\sin x}{1-\sin x}} \right],\,0\le x\le \frac{\pi }{4},\]then \[f'\left( \frac{\pi }{4} \right)\] is equal to
A) \[\frac{1}{2}\]
B) \[\frac{-1}{2}\]
C) \[\frac{1-{{x}^{2}}}{1+{{x}^{2}}}\]
D) \[\frac{x}{1-{{x}^{2}}}\]
View Answer play_arrowquestion_answer211) For the function \[f(x)=|x-8|,\,0\le x\le 16,\] the Rollers theorem is not applicable as
A) the function is not continuous at\[x=8\]
B) \[f(0)\ne f(16)\]
C) the function is not differentiable at \[x=8\]
D) the function is not differentiable at all points in \[(0,\,16)\]
View Answer play_arrowquestion_answer212) If the tangent at \[x=c\] to the curve \[y={{x}^{3}}-5{{x}^{2}}-3x,\,1\le x\le 3,\]is parallel to the chord joining the points \[(1,-7)\] and \[(3,-27),\] then the value of c is equal to
A) \[1\]
B) \[\frac{5}{3}\]
C) \[\frac{7}{3}\]
D) \[\frac{2}{3}\]
View Answer play_arrowquestion_answer213) If \[x=2\,\left[ \cos \theta +\log \,\left( \tan \frac{\theta }{2} \right) \right],y=2\,\,\sin \theta ,\]then \[\frac{dy}{dx}\]is
A) \[\cot \theta \]
B) \[\cos \theta \]
C) \[\tan \theta \]
D) \[\sin \theta \]
View Answer play_arrowquestion_answer214) If \[y=6\,\,\sin x\,{{\log }_{10}}x+{{e}^{{{x}^{2}}}},\] then \[\frac{dy}{dx}\] is equal to
A) \[\frac{6\,\,\sin x}{x}+6\,\cos \,x\,{{\log }_{10}}\,x+2x{{e}^{{{x}^{2}}}}\]
B) \[\frac{6\,\,\sin x}{x}\,{{\log }_{10}}\,e+6\,\cos \,x\,{{\log }_{10}}x+2x{{e}^{{{x}^{2}}}}\]
C) \[6\,\cos \,x\,{{\log }_{10}}x+6\,\sin x.\frac{10}{x}+2x{{e}^{{{x}^{2}}}}\]
D) \[\frac{6\,\sin \,x}{x}+6\,\cos \,x\,{{\log }_{10}}x+x{{e}^{{{x}^{2}}}}\]
View Answer play_arrowquestion_answer215) Two events A and 5 have probabilities \[0.3\] and \[0.4\] respectively. The probability that both A and B occur simultaneously is \[0.1\]. The probability that neither A nor B occur is
A) \[0.2\]
B) \[0.3\]
C) \[0.4\]
D) \[0.1\]
View Answer play_arrowquestion_answer216) \[\underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{{{2}^{n+1}}+{{3}^{n+1}}}{{{2}^{n}}+{{3}^{n}}}\]is equal to
A) \[0\]
B) \[1\]
C) \[2\]
D) \[3\]
View Answer play_arrowquestion_answer217) The value of n such that \[\underset{x\to 3}{\mathop{\lim }}\,\,\frac{{{x}^{n}}-{{3}^{n}}}{x-3}=108\]is
A) \[3\]
B) \[7\]
C) \[6\]
D) \[4\]
View Answer play_arrowquestion_answer218) If the function \[f(x)=\left\{ \begin{matrix} \frac{{{x}^{3}}-8}{{{x}^{2}}-4}, & if & x\ne 2 \\ k, & if & x=2 \\ \end{matrix} \right.\] is continuous at \[x=2,\]then the value of k is
A) \[2\]
B) \[0\]
C) \[3\]
D) \[4\]
View Answer play_arrowquestion_answer219) The probability distribution of a random variable X is
\[x=x\] | \[-1\] | \[0\] | \[1\] | \[2\] |
\[P(X=X)\] | \[0.2\] | \[0.1\] | \[0.4\] | \[\lambda \] |
A) \[0.8\]
B) \[0.6\]
C) \[0.5\]
D) \[0.7\]
View Answer play_arrowquestion_answer220) The general solution of \[{{\cot }^{2}}\theta =3\] is
A) \[2n\pi \pm \frac{\pi }{3},n\in Z\]
B) \[n\pi \pm \frac{\pi }{6},n\in Z\]
C) \[n\pi \pm \frac{\pi }{2},n\in Z\]
D) \[2n\pi \pm \frac{\pi }{6},n\in Z\]
View Answer play_arrowquestion_answer221) If A and B are square matrices such that \[AB\text{ }=A\]and \[BA=B,\]then \[{{A}^{2}}+{{B}^{2}}\]is equal to
A) \[AB\]
B) \[A+B\]
C) \[BA+B\]
D) \[AB+A\]
View Answer play_arrowquestion_answer222) If A is a square matrix of order 3 and if \[\det \,(A)=3,\] then \[\det \,[adj\,\,\{adj\,(adj\,A)\}]\] is equal to
A) \[{{81}^{2}}\]
B) \[81\]
C) \[729\]
D) \[27\]
View Answer play_arrowquestion_answer223) The value of the determinant \[\left| \begin{matrix} 1+\log \,a & \log \,b & \log \,c \\ \log \,a & 1+\log \,b & \log \,c \\ \log \,a & \log \,b & 1+\log \,c \\ \end{matrix} \right|\]is equal to
A) \[\log \,(abc)\]
B) \[1-\log \,\,abc\]
C) \[\log \,(a+b+c)\]
D) \[1+\,\log \,abc\]
View Answer play_arrowquestion_answer224) If A and Bare square matrices of order 3 such that \[det\text{ }A=1\] and \[det\text{ }B=-1~\]then \[det\text{ (-10}\,\text{AB)}\] is equal to
A) \[10\]
B) \[-10\]
C) \[-1000\]
D) \[1000\]
View Answer play_arrowquestion_answer225) \[{{\sin }^{2}}\,\frac{\pi }{8}+{{\sin }^{2}}\,\frac{3\pi }{8}+{{\sin }^{2}}\frac{5\pi }{8}+{{\sin }^{2}}\frac{7\pi }{8}\]is equal to
A) \[1\]
B) \[\frac{3}{2}\]
C) 2
D) \[\frac{5}{2}\]
View Answer play_arrow
You need to login to perform this action.
You will be redirected in
3 sec