question_answer1) The twinkling effect of star light is due to
A) total internal reflection
B) high dense matter of star
C) constant burning of hydrogen in the star
D) the fluctuating apparent position of the star being slightly different from the actual position of the star
View Answer play_arrowquestion_answer2) The width of the diffraction band varies
A) inversely as the wavelength
B) directly as the width of the slit
C) directly as the distance between the slit and the screen
D) inversely as the size of the source from which the slit is illuminated
View Answer play_arrowquestion_answer3) An unpolarised beam of intensity \[{{I}_{0}}\] is incident on a pair of Nichols making an angle of \[{{60}^{o}}\] with each other. The intensity of light emerging from the pair is
A) \[{{I}_{0}}\]
B) \[\frac{{{I}_{0}}}{2}\]
C) \[\frac{{{I}_{0}}}{4}\]
D) \[\frac{{{I}_{0}}}{8}\]
View Answer play_arrowquestion_answer4) When a low flying aircraft passes over head, we sometimes notice a slight shaking of the picture on our TV screen. This is due to
A) diffraction of the signal received from the antenna
B) interference of the direct signal received by the antenna with the weak signal reflected by the passing aircraft
C) change of magnetic flux occurring due to the passage of aircraft
D) vibration created by the, passage of aircraft,
View Answer play_arrowquestion_answer5) A beam of light of wavelength \[600\,\,nm\] from a distant source falls on a single slit \[1\,\,mm\] wide and the resulting diffraction pattern is observed on a screen \[2\,\,m\] away. The distance between the first dark fringes on either side of the central bright fringe is
A) \[1.2\,\,cm\]
B) \[1.2\,\,mm\]
C) \[2.4\,\,cm\]
D) \[2.4\,\,mm\]
View Answer play_arrowquestion_answer6) The physical quantity having the dimensions \[[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{A}^{2}}]\]is
A) resistance
B) resistivity
C) electrical conductivity
D) electromotive force
View Answer play_arrowquestion_answer7) A battery of emf \[10\,\,V\] and internal resistance \[3\Omega \] is connected to a resistor. The current in the circuit is\[0.5\,\,A\] The terminal voltage of the battery when the circuit is closed is
A) \[10\,\,V\]
B) \[0\,\,V\]
C) \[1.5\,\,V\]
D) \[8.5\,\,V\]
View Answer play_arrowquestion_answer8) A galvanometer coil has a resistance of \[15\Omega \] and gives full scale deflection for a current of\[4\,\,mA\]. To convert it to an am metal of range \[0\] to\[6\,\,A\]
A) \[10\,\,m\Omega \] resistance is to be connected in parallel to the galvanometer
B) \[10\,\,m\Omega \] resistance is to be connected in series with the galvanometer
C) \[0.1\,\,\Omega \] resistance is to be connected in parallel to the galvanometer
D) \[0.1\,\,\Omega \] resistance is to be connected in series with the galvanometer
View Answer play_arrowquestion_answer9) The electron drift speed is small and the charge of the electron is also small but still, we obtain large current in a conductor. This is due to
A) the conducting property of the conductor
B) the resistance of the conductor is small
C) the electron number density of the conductor is small
D) the electron number density of the conductor is enormous
View Answer play_arrowquestion_answer10) A straight wire of mass \[200\,\,g\] and length \[1.5\,\,m\] carries a current of\[2\,\,A\]. It is suspended in mid- air by a uniform horizontal magnetic field\[B\]. The magnitude of \[B\] (in tesla) is (assume\[g=9.8\,\,m{{s}^{-2}})\]
A) \[2\]
B) \[1.5\]
C) \[0.55\]
D) \[0.65\]
View Answer play_arrowquestion_answer11) A Gaussian sphere encloses an electric dipole within it. The total flux across the sphere is
A) zero
B) half that due to a single charge
C) double that due to a single charge
D) dependent on the position of the dipole
View Answer play_arrowquestion_answer12) A parallel plate air capacitor has a capacitance\[C\]. When it is half filled with a dielectric of dielectric constant\[5\], the percentage increase in the capacitance will be
A) \[400%\]
B) \[66.6%\]
C) \[33.3%\]
D) \[200%\]
View Answer play_arrowquestion_answer13) A comb run through one's dry hair attracts small bits of paper. This is due to
A) comb is a good conductor
B) paper is a good conductor
C) the atoms is the paper get polarised by the charged comb
D) the comb possesses magnetic properties
View Answer play_arrowquestion_answer14) The specific charge of a proton is\[9.6\times {{10}^{7}}C\,\,k{{g}^{-1}}\]. The specific charge of an alpha particle will be
A) \[9.6\times {{10}^{7}}C\,\,k{{g}^{-1}}\]
B) \[19.2\times {{10}^{7}}C\,\,k{{g}^{-1}}\]
C) \[4.8\times {{10}^{7}}C\,\,k{{g}^{-1}}\]
D) \[2.4\times {{10}^{7}}C\,\,k{{g}^{-1}}\]
View Answer play_arrowquestion_answer15) When light of wavelength \[300\,\,nm\] falls on a photoelectric emitter, photoelectrons are liberated. For another emitter, light of wavelength \[600\,\,nm\] is sufficient for liberating photoelectrons. The ratio of the work function of the two emitters is
A) \[1:2\]
B) \[2:1\]
C) \[4:1\]
D) \[1:4\]
View Answer play_arrowquestion_answer16) White light is passed through a dilute solution of potassium permanganate. The spectrum produced by the emergent light is
A) band emission spectrum
B) line emission spectrum
C) band absorption spectrum
D) line absorption spectrum
View Answer play_arrowquestion_answer17) If \[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\] are the wavelengths of the first members of the Lyman and Paschen series respectively, then \[{{\lambda }_{1}}:{{\lambda }_{2}}\] is
A) \[1:3\]
B) \[1:30\]
C) \[7:50\]
D) \[7:108\]
View Answer play_arrowquestion_answer18) Activity of a radioactive sample decreases to \[{{(1/3)}^{rd}}\] of its original value in \[3\] days. Then, in \[9\] days its activity will become
A) \[(1/27)\] of the original value
B) \[(1/9)\] of the original value
C) \[(1/18)\] of the original value
D) \[(1/3)\]of the original value
View Answer play_arrowquestion_answer19) The working of which of the following is similar to that of a slide projector?
A) Electron microscope
B) Scanning electron microscope
C) Transmission electron microscope
D) Atomic force microscope
View Answer play_arrowquestion_answer20) In a transistor the collector current is always less than the emitter current because
A) collector side is reverse biased and the emitter side is forward biased
B) a few electrons are lost in the base and only remaining ones reach the collector
C) collector being reverse biased, attracts less electrons
D) collector side is forward biased and emitter side is reverse biased
View Answer play_arrowquestion_answer21) A transparent cube of \[0.21\,\,m\] edge contains a small air bubble. Its apparent distance when viewed through one face of the cube is \[0.10\,\,m\] and when viewed from the opposite face is\[0.04\,\,m\]. The actual distance of the bubble from the second face of the cube is
A) \[0.06\,\,m\]
B) \[0.17\,\,m\]
C) \[0.05\,\,m\]
D) \[0.04\,\,m\]
View Answer play_arrowquestion_answer22) To a fish under water, viewing obliquely a fisherman standing on the bank of a lake, the man looks
A) taller than what he actually is
B) shorter that what he actually is
C) the same height as he actually is
D) depends on the obliquity
View Answer play_arrowquestion_answer23) If white light is used in the Newton's rings experiment, the colour observed in the reflected light is complementary to that observed in the transmitted light through the same point. This is due to
A) \[{{90}^{o}}\] change of phase in one of the reflected waves
B) \[{{180}^{o}}\] change of phase in one of the reflected waves
C) \[{{145}^{o}}\] change of phase in one of the reflected waves
D) \[{{45}^{o}}\] change of phase in one the reflected waves
View Answer play_arrowquestion_answer24) A satellite in a circular orbit of radius \[R\] has a period of\[4\,\,h\]. Another satellite with orbital radius \[3R\] around the same planet will have a period (in hours)
A) \[16\]
B) \[4\]
C) \[4\sqrt{27}\]
D) \[4\sqrt{8}\]
View Answer play_arrowquestion_answer25) The freezer in a refrigerator is located at the top section so that
A) the entire chamber of the refrigerator is cooled quickly due to convection
B) the motor is not heated
C) the heat gained from the environment is high
D) the heat gained from the environment is low
View Answer play_arrowquestion_answer26) A monoatomic gas is suddenly compressed to \[{{(1/8)}^{th}}\] of its initial volume adiabatically. The ratio of its final pressure to the initial pressure is (Given the ratio of the specific heats of the given gas to be\[5/3)\]
A) \[32\]
B) \[40/3\]
C) \[24/5\]
D) \[8\]
View Answer play_arrowquestion_answer27) A Carnot engine takes heat from a reservoir at \[{{627}^{o}}C\] and rejects heat to a sink at\[{{27}^{o}}C\]. Its efficiency will be
A) \[3/5\]
B) \[1/3\]
C) \[2/3\]
D) \[200/209\]
View Answer play_arrowquestion_answer28) A \[30\,\,V,\,\,90\,\,W\] lamp is to be operated on a \[120\,\,V\]\[DC\] line. For proper glow, a resistor, of\[...\Omega \] should be connected in series with the lamp.
A) \[40\]
B) \[10\]
C) \[20\]
D) \[30\]
View Answer play_arrowquestion_answer29) A tuning fork \[A\] produces \[4\] beats/s with another tuning fork \[B\] of frequency\[320\,\,Hz\]. On filing one of the prongs of \[A,\,\,4\] beats/s are again heard when sounded with the same fork\[B\]. Then, the frequency of the fork \[A\] before filing is
A) \[328\,\,Hz\]
B) \[316\,\,Hz\]
C) \[324\,\,Hz\]
D) \[320\,\,Hz\]
View Answer play_arrowquestion_answer30) The sprinkling of water reduces slightly the temperature of a closed room because
A) temperature of water is less than that of the room
B) specific heat of water is high
C) water has large latent heat of vaporisation
D) water is a bad conductor of heat
View Answer play_arrowquestion_answer31) The equation of a simple harmonic wave is given by\[y=5\sin \frac{\pi }{2}(100t-x)\], where \[x\] and \[y\] are in metre and time is in second. The period of the wave in second will be
A) \[0.04\]
B) \[0.01\]
C) \[1\]
D) \[5\]
View Answer play_arrowquestion_answer32) The loudness and pitch of a sound note depends on
A) intensity and frequency
B) frequency and number of harmonics
C) intensity and velocity
D) frequency and velocity
View Answer play_arrowquestion_answer33) For ordinary terrestrial experiments, the observer in an inertial frame in the following cases is
A) a child revolving in a giant wheel
B) a driver in a sports car moving with a constant high speed of \[200\,\,km{{h}^{-1}}\] on a straight rod
C) the pilot of an aeroplane which is taking off
D) a cyclist negotiating a sharp curve
View Answer play_arrowquestion_answer34) A rectangular vessel when full of water, takes \[10\,\,\min \] to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water?
A) \[9\,\,\min \]
B) \[7\,\,\min \]
C) \[5\,\,\min \]
D) \[3\,\,\min \]
View Answer play_arrowquestion_answer35) If there were no gravity, which of the following will not be there for a fluid?
A) Viscosity
B) Surface tension
C) Pressure
D) Archimedes' upward thrust
View Answer play_arrowquestion_answer36) In a \[LCR\] series circuit, the potential difference between the terminals of the inductance is\[60\,\,V\], between the terminals of the capacitor is\[30\,\,V\] and that across the resistance is\[40\,\,V\]. Then, supply voltage will be equal to
A) \[50\,\,V\]
B) \[70\,\,V\]
C) \[130\,\,V\]
D) \[10\,\,V\]
View Answer play_arrowquestion_answer37) When deuterium and helium are subjected to an accelerating field simultaneously then
A) both acquire same energy
B) deuterium accelerates faster
C) helium accelerates faster
D) neither of them is accelerated
View Answer play_arrowquestion_answer38) A solenoid \[1.5\,\,m\] long and \[0.4\,\,cm\] in diameter possesses \[10\] turns per \[cm\] length. A current of \[5\,\,A\] falls through it. The magnetic field at the axis inside the solenoid is
A) \[2\pi \times {{10}^{-3}}T\]
B) \[2\pi \times {{10}^{-5}}T\]
C) \[4\pi \times {{10}^{-2}}T\]
D) \[4\pi \times {{10}^{-3}}T\]
View Answer play_arrowquestion_answer39) A wire \[PQR\] is bent as shown in figure and is placed in a region of uniform magnetic field\[B\]. The length of \[PQ=QR=l\,\,A\] current \[l\] ampere flows through the wire as shown. The magnitude of the force on \[PQ\] and \[QR\] will be
A) \[BIl,\,\,0\]
B) \[BIl,\,\,0\]
C) \[0,\,\,BIl\]
D) \[0,\,\,0\]
View Answer play_arrowquestion_answer40) A choke is preferred to a resistance for limiting current in \[AC\] circuit because
A) choke is cheap
B) there is no wastage of power
C) choke is compact in size
D) choke is a good absorber of heat
View Answer play_arrowquestion_answer41) If \[{{r}_{1}}\] and \[{{r}_{2}}\] are the radii of the atomic nuclei of mass numbers 64 and 125 respectively, then the ratio \[({{r}_{1}}/{{r}_{2}})\] is
A) \[\frac{64}{125}\]
B) \[\sqrt{\frac{64}{125}}\]
C) \[\frac{5}{4}\]
D) \[\frac{4}{5}\]
View Answer play_arrowquestion_answer42) A motor is used to deliver water at a certain rate through a given horizontal pipe. To deliver \[n-\]times the water through the same pipe in the same time the power of the motor must be increased as follows
A) \[n-\]times
B) \[{{n}^{2}}-\]times
C) \[{{n}^{3}}-\]times
D) \[{{n}^{4}}-\]times
View Answer play_arrowquestion_answer43) For a system to follow the law of conservation of linear momentum during a collision, the condition is (i) total external force acting on the system is zero. (ii) total external force acting on the system is finite and time of collision is negligible. (iii) total internal force acting on the system is zero.
A) (i) only
B) (ii) only
C) (iii) only
D) (i) or (ii)
View Answer play_arrowquestion_answer44) An air bubble of radius \[1\,\,cm\] rises from the bottom portion through a liquid of density \[1.5\,\,g/cc\] at a constant speed of\[0.25\,\,cm\,\,{{s}^{-1}}\]. If the density of air is neglected, the coefficient of viscosity of the liquid is approximately, (In\[Pa)\]
A) \[13000\]
B) \[1300\]
C) \[130\]
D) \[13\]
View Answer play_arrowquestion_answer45) A given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored and its pressure is then found to be \[0.75\] of its initial pressure. The ratio of the specific heats of the gas is approximately
A) \[1.2\]
B) \[1.41\]
C) \[1.67\]
D) \[1.83\]
View Answer play_arrowquestion_answer46) Two solid spheres \[A\] and \[B\] made of the same material have radii \[{{r}_{A}}\] and \[{{r}_{B}}\] respectively. Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling. The ratio of the rate of change of temperature \[A\] and \[B\] is
A) \[\frac{{{r}_{A}}}{{{r}_{B}}}\]
B) \[\frac{{{r}_{B}}}{{{r}_{A}}}\]
C) \[\frac{r_{A}^{2}}{r_{B}^{2}}\]
D) \[\frac{r_{B}^{2}}{r_{A}^{2}}\]
View Answer play_arrowquestion_answer47) The effect due to uniform magnetic field on a freely suspended magnetic needle is as follows
A) both torque and net force are present
B) torque is present but no net force
C) both torque and net force are absent
D) net force is present but not torque
View Answer play_arrowquestion_answer48) When a positively charged particle enters a uniform magnetic field with uniform velocity, its trajectory can be (i) a straight line (ii) a circle (iii) a helix
A) (i) only
B) (i) or (ii)
C) (i) or (iii)
D) any one of (i), (ii) and (iii)
View Answer play_arrowquestion_answer49) An oil drop having a mass \[4.8\times {{10}^{-10}}g\] and charge \[24\times {{10}^{-18}}C\] stands still between two charged horizontal plates separated by a distance of\[1\,\,cm\]. If now the polarity of the plates is changed, instantaneous acceleration of the drop is\[(g=10\,\,m{{s}^{-2}})\]
A) \[5\,\,m{{s}^{-2}}\]
B) \[10\,\,m{{s}^{-2}}\]
C) \[15\,\,m{{s}^{-2}}\]
D) \[20\,\,m{{s}^{-2}}\]
View Answer play_arrowquestion_answer50) A free neutron decays spontaneously into
A) a proton, an electron and anti-neutrino
B) a proton, an electron and a neutrino
C) a proton and electron
D) a proton, and electron, a neutrino and an anti-neutrino
View Answer play_arrowquestion_answer51) What is the correct order of spin only magnetic moment (in\[BM)\]of\[M{{n}^{2+}},\,\,\,C{{r}^{2+}}\]and\[{{V}^{2+}}\]?
A) \[M{{n}^{2+}}>{{V}^{2+}}>C{{r}^{2+}}\]
B) \[{{V}^{2+}}>C{{r}^{2+}}>M{{n}^{2+}}\]
C) \[M{{n}^{2+}}>C{{r}^{2+}}>{{V}^{2+}}\]
D) \[C{{r}^{2+}}>{{V}^{2+}}>M{{n}^{2+}}\]
View Answer play_arrowquestion_answer52) Which of the following is used for making optical instruments?
A) \[Si{{O}_{2}}\]
B) \[Si\]
C) \[Si{{H}_{4}}\]
D) \[SiC\]
View Answer play_arrowquestion_answer53) Which of the following is not correct?
A) \[3{{O}_{2}}\underset{\text{discharge}}{\overset{\text{Silent}\,\,\text{electric}}{\longleftrightarrow}}2{{O}_{3}};\,\,\Delta H=-284.5\,\,kJ\]
B) Ozone undergoes addition reaction with unsaturated carbon compounds
C) Sodium thio sulphate reacts with \[{{I}_{2}}\] to form sodium tetrathionate and sodium iodide
D) Ozone oxidises lead sulphide to lead sulphate
View Answer play_arrowquestion_answer54) Which of the following reactions can produce aniline as main product?
A) \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}+Zn/KOH\]
B) \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}+Zn/N{{H}_{4}}Cl\]
C) \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}+LiAl{{H}_{4}}\]
D) \[{{C}_{6}}{{H}_{5}}N{{O}_{2}}+Zn/HCl\]
View Answer play_arrowquestion_answer55) Which of the following reagents when heated with ethyl chloride, forms ethylene?
A) Aqueous\[KOH\]
B) \[Zn/HCl\]
C) Alcoholic\[KOH\]
D) \[HI\]
View Answer play_arrowquestion_answer56) The energy of a photon is\[3\times {{10}^{-12}}erg\]. What is its wavelength in\[nm\]? \[(h=6.62\times {{10}^{-27}}erg-s;\,\,c=3\times {{10}^{10}}cm/s)\]
A) \[66.2\]
B) \[1324\]
C) \[66.2\]
D) \[6.62\]
View Answer play_arrowquestion_answer57) What is the time (in sec) required for depositing all the Silver present in \[125\,\,mL\] of \[1\,\,M\,\,AgN{{O}_{3}}\] solution by passing a current of\[241.25\,\,A\]? \[(1F=96500\,\,C)\]
A) \[10\]
B) \[50\]
C) \[1000\]
D) \[100\]
View Answer play_arrowquestion_answer58) The disperse phase, dispersion medium and nature of colloidal solution (lyophilic or lyophobic) of ?gold sol? respectively, are
A) solid, solid, lyophobic
B) liquid, liquid, lyophobic
C) solid, liquid, lyophobic
D) solid, liquid, lyophilic
View Answer play_arrowquestion_answer59) The rate constant of a first order reaction at \[{{27}^{o}}C\] is \[{{10}^{-3}}{{\min }^{-1}}\]. The temperature coefficient of this reaction is\[2\]. What is the rate constant (in\[{{\min }^{-1}})\] at \[{{17}^{o}}C\] for this reaction?
A) \[{{10}^{-3}}\]
B) \[5\times {{10}^{-4}}\]
C) \[2\times {{10}^{-3}}\]
D) \[{{10}^{-2}}\]
View Answer play_arrowquestion_answer60) A solution of an acid has\[[{{H}^{+}}]=2\times {{10}^{-5}}\]. Find out the concentration of \[O{{H}^{-}}\] ions.
A) \[5\times {{10}^{-10}}N\]
B) \[4\times {{10}^{-10}}N\]
C) \[2\times {{10}^{-5}}N\]
D) \[9\times {{10}^{-4}}N\]
View Answer play_arrowquestion_answer61) Which of the following is added to chloroform to slow down its aerial oxidation in presence of light?
A) Carbonyl chloride
B) Ethyl alcohol
C) Sodium hydroxide
D) Nitric acid
View Answer play_arrowquestion_answer62) Which of the products is formed when acetone is reacted with barium hydroxide solution?
A) \[C{{H}_{3}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]
B) \[C{{H}_{3}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\]
C) \[C{{H}_{3}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\]
D) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{C}}}\,-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]
View Answer play_arrowquestion_answer63) When acetaldehyde is heated with Fehling solution, a red precipitate is formed. Which of the following is that?
A) \[C{{u}_{2}}O\]
B) \[Cu\]
C) \[CuO\]
D) \[CuS{{O}_{4}}\]
View Answer play_arrowquestion_answer64) What is the correct order of occurrence \[(%\] by weight) in air of\[Ne,\,\,\,Ar\]and\[Kr\]?
A) \[Ne>Ar>Kr\]
B) \[Ar>Ne>Kr\]
C) \[Ar>Kr>Ne\]
D) \[Ne>Kr>Ar\]
View Answer play_arrowquestion_answer65) Which of the following compounds when heated with \[CO\] at \[{{150}^{o}}C\] and \[500\,\,atm\] pressure in presence of \[B{{F}_{3}}\] forms ethyl propionate?
A) \[{{C}_{2}}{{H}_{5}}OH\]
B) \[C{{H}_{3}}OC{{H}_{3}}\]
C) \[{{C}_{2}}{{H}_{5}}O{{C}_{2}}{{H}_{5}}\]
D) \[C{{H}_{3}}O{{C}_{2}}{{H}_{5}}\]
View Answer play_arrowquestion_answer66) Identify the reaction for which\[\Delta H\ne \Delta E\].
A) \[S(\text{rhombic})+{{O}_{2}}(g)\xrightarrow{{}}S{{O}_{2}}(g)\]
B) \[{{N}_{2}}(g)+{{O}_{2}}(g)\xrightarrow{{}}2NO(g)\]
C) \[{{H}_{2}}(g)+C{{l}_{2}}(g)\xrightarrow{{}}2HCl(g)\]
D) \[CO(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}C{{O}_{2}}(g)\]
View Answer play_arrowquestion_answer67) Hydrolysis of \[N{{O}_{3}}\] gives \[N{{H}_{3}}\] and\[X\]. Which of the following is\[X\]?
A) \[HClO\]
B) \[HCl{{O}_{3}}\]
C) \[HOCl\]
D) \[HCl{{O}_{2}}\]
View Answer play_arrowquestion_answer68) What are the metal ions present in carnallite?
A) \[Mg,\,\,K\]
B) \[Al,\,\,Na\]
C) \[Na,\,\,Mg\]
D) \[Zn,\,\,Mg\]
View Answer play_arrowquestion_answer69) Ethyl chloride reacts with sodium ethoxide to form a compound\[A\]. Which of the following reactions also yields\[A?\]
A) \[{{C}_{2}}{{H}_{5}}Cl,\,\,KOH(alc.),\,\,\Delta \]
B) \[2{{C}_{2}}{{H}_{5}}OH,\,\,conc.{{H}_{2}}S{{O}_{4}},\,\,{{140}^{o}}C\]
C) \[{{C}_{2}}{{H}_{5}}Cl,\,\,Mg\](dry ether)
D) \[{{C}_{2}}{{H}_{2}}dil.\,\,{{H}_{2}}S{{O}_{4}},\,\,HgS{{O}_{4}}\]
View Answer play_arrowquestion_answer70) The number of sigma and \[pi(\pi )\] bonds present in benzene respectively are
A) \[12,\,\,6\]
B) \[6,\,\,6\]
C) \[6,\,\,12\]
D) \[12,\,\,3\]
View Answer play_arrowquestion_answer71) Edge length of a cube is \[400\,\,pm\], its body diagonal would be
A) \[566\,\,pm\]
B) \[600\,\,pm\]
C) \[500\,\,pm\]
D) \[693\,\,pm\]
View Answer play_arrowquestion_answer72) The number of \[\alpha -\]particles emitted by\[_{84}R{{a}^{218}}{{\xrightarrow{{}}}_{82}}P{{b}^{206}}\]
A) \[3\]
B) \[4\]
C) \[6\]
D) \[2\]
View Answer play_arrowquestion_answer73) The \[IUPAC\] name of the following compound is\[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ {{C}_{6}}{{H}_{5}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{2}}-C{{H}_{3}}\]
A) \[2-\]cyclohexylbutane
B) \[\sec -\]butylbenzene
C) \[3-\]cyclohexylbutane
D) \[2-\]phenylbutane
View Answer play_arrowquestion_answer74) The reaction of primary amine with chloroform and ethanolic solution of \[KOH\] is called
A) Hermann's reaction
B) Reimer-Tiemann's reaction
C) Carbylamine reaction
D) Kolbe's reaction
View Answer play_arrowquestion_answer75) \[0.01\]mole of a non-electrolyte is dissolved in \[10\,\,g\] of water. The molality of the solution is
A) \[0.1\,\,m\]
B) \[0.5\,\,m\]
C) \[1.0\,\,m\]
D) \[0.18\,\,m\]
View Answer play_arrowquestion_answer76) Atoms with same atomic number and different mass numbers are called
A) isobars
B) isomers
C) isotones
D) isotopes
View Answer play_arrowquestion_answer77) The shape of the orbital with the value of\[l=2\] and \[m=0\]is
A) spherical
B) dumb-bell
C) trigonal planar
D) square-planar
View Answer play_arrowquestion_answer78) In the following, the element with the highest ionisation energy is
A) \[[Ne]3{{s}^{2}}3{{p}^{1}}\]
B) \[[Ne]3{{s}^{2}}3{{p}^{3}}\]
C) \[[Ne]3{{s}^{2}}3{{p}^{2}}\]
D) \[[Ne]3{{s}^{2}}3{{p}^{4}}\]
View Answer play_arrowquestion_answer79) In the conversion of \[B{{r}_{2}}\] to\[BrO_{3}^{-}\], the oxidation number of \[Br\] changes from
A) zero to\[+5\]
B) \[+1\]to\[+5\]
C) zero to\[-3\]
D) \[+2\]to\[+5\]
View Answer play_arrowquestion_answer80) Among the alkali metals cesium is the most reactive because
A) its incomplete shell is nearest to the nucleus
B) it has a single electron in-the valence shell
C) it is the heaviest alkali metal
D) the outermost electron is more loosely bound than the outermost electron of the other alkali metals
View Answer play_arrowquestion_answer81) Which of the following represents the Lewis structure of \[{{N}_{3}}\] molecule?
A) \[_{\text{X}}^{\text{X}}N\equiv N_{\text{X}}^{\text{X}}\]
B) \[_{\text{X}}^{\text{X}}\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,\equiv \overset{\text{X}\,\,\text{X}}{\mathop{N}}\,_{\text{X}}^{\text{X}}\]
C) \[_{\text{X}}^{\text{X}}\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,_{\text{X}}^{\text{X}}-\underset{\text{X}\,\,\text{X}}{\mathop{\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,_{\text{X}}^{\text{X}}}}\,\]
D) \[\underset{\text{X}\,\,\text{X}}{\mathop{_{\text{X}}^{\text{X}}\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,}}\,_{\text{X}}^{\text{X}}-\underset{\text{X}\,\,\text{X}}{\mathop{\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,_{\text{X}}^{\text{X}}}}\,\]
View Answer play_arrowquestion_answer82) Hydrogen bond is strongest in
A) \[S-H\cdot \cdot \cdot O\]
B) \[O-H\cdot \cdot \cdot S\]
C) \[F-H\cdot \cdot \cdot F\]
D) \[O-H\cdot \cdot \cdot N\]
View Answer play_arrowquestion_answer83) The density of a gas is \[1.964\,\,d{{m}^{-3}}\] at \[273\,\,K\]and\[76\,\,cm\]\[Hg\]. The gas is
A) \[C{{H}_{4}}\]
B) \[{{C}_{2}}{{H}_{6}}\]
C) \[C{{O}_{2}}\]
D) \[Xe\]
View Answer play_arrowquestion_answer84) The shape of \[PC{{l}_{3}}\] molecule is
A) trigonal bipyramidal
B) tetrahedral
C) pyramidal
D) square planar
View Answer play_arrowquestion_answer85) The concentration of a reactant \[X\] decreases from \[0.1\,\,M\] to \[0.005\,\,M\] in\[40\,\,\min \]. If the reaction follows first order kinetics, the rate of the reaction when the concentration of \[X\] is \[0.01\,\,M\] will be
A) \[1.73\times {{10}^{-4}}M\,\,{{\min }^{-1}}\]
B) \[3.47\times {{10}^{-4}}M\,\,{{\min }^{-1}}\]
C) \[3.47\times {{10}^{-5}}M\,\,{{\min }^{-1}}\]
D) \[7.5\times {{10}^{-4}}M\,\,{{\min }^{-1}}\]
View Answer play_arrowquestion_answer86) Which of the following does not conduct electricity?
A) Fused\[NaCl\]
B) Solid\[NaCl\]
C) Brine solution
D) Copper
View Answer play_arrowquestion_answer87) Solubility product of a salt \[AB\] is \[1\times {{10}^{-8}}{{M}^{2}}\] in a solution in which the concentration of \[{{A}^{+}}\] ions is\[{{10}^{-3}}M\]. The salt will precipitate when the concentration of \[{{B}^{-}}\] ions is kept
A) between\[{{10}^{-8}}M\]to\[{{10}^{-7}}M\]
B) between\[{{10}^{-7}}M\]to\[{{10}^{-8}}M\]
C) \[>{{10}^{-5}}M\]
D) \[<{{10}^{-8}}M\]
View Answer play_arrowquestion_answer88) The \[pH\] of \[{{10}^{-8}}M\,\,HCl\] Solution is
A) \[8\]
B) more than\[8\]
C) between \[6\] and \[7\]
D) slightly more than\[7\]
View Answer play_arrowquestion_answer89) For a reaction to be spontaneous, at all temperatures
A) \[\Delta G\] and \[\Delta H\] should be negative
B) \[\Delta G\] and \[\Delta H\] should be positive
C) \[\Delta G=\Delta S=0\]
D) \[\Delta H<\Delta G\]
View Answer play_arrowquestion_answer90) Which of the following electrolytes will have maximum flocculation value for\[Fe{{(OH)}_{3}}\]sol?
A) \[NaCl\]
B) \[N{{a}_{2}}S\]
C) \[{{(N{{H}_{4}})}_{3}}P{{O}_{4}}\]
D) \[{{K}_{2}}S{{O}_{4}}\]
View Answer play_arrowquestion_answer91) What is the order of a reaction which has a rate expression\[rate=k{{[A]}^{3/2}}{{[B]}^{-1}}\]?
A) \[\frac{3}{2}\]
B) \[\frac{1}{2}\]
C) \[0\]
D) \[\frac{4}{2}\]
View Answer play_arrowquestion_answer92) Inductive effect involves
A) displacement of \[\sigma -\]electrons
B) delocalisation of \[\pi -\]electrons
C) delocalisation of \[\sigma -\]electrons
D) displacement of \[\pi -\]electrons
View Answer play_arrowquestion_answer93) Which of the following compound is expected to be optically active?
A) \[{{(C{{H}_{3}})}_{2}}CHCHO\]
B) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}CHO\]
C) \[C{{H}_{3}}C{{H}_{2}}CHBrCHO\]
D) \[C{{H}_{3}}C{{H}_{2}}CB{{r}_{2}}CHO\]
View Answer play_arrowquestion_answer94) The catalyst used in the preparation of an alkyl chloride by the action of dry HC1 on an alcohol is
A) anhydrous\[AlC{{l}_{3}}\]
B) \[FeC{{l}_{3}}\]
C) anhydrous\[ZnC{{l}_{2}}\]
D) \[Cu\]
View Answer play_arrowquestion_answer95) By heating phenol with chloroform in alkali, it is converted into
A) salicylic acid
B) salicylaldehyde
C) anisole
D) phenyl benzoate
View Answer play_arrowquestion_answer96) Which of the following does not give benzoic acid on hydrolysis?
A) Phenyl cyanide
B) Benzoyl chloride
C) Benzyl chloride
D) Methyl benzoate
View Answer play_arrowquestion_answer97) Glucose contains in addition to aldehyde group
A) one secondary \[-OH\] and four primary\[-OH\] groups
B) one primary \[-OH\] and four secondary \[-OH\] groups
C) two primary \[-OH\] and three secondary\[-OH\] groups
D) three primary \[-OH\] and two secondary \[-OH\] groups
View Answer play_arrowquestion_answer98) The formula mass of Mohr's salt is\[392\]. The iron present in it is oxidised by \[KMn{{O}_{4}}\] in acid medium. The equivalent mass of Mohr's salt is
A) \[392\]
B) \[31.6\]
C) \[278\]
D) \[156\]
View Answer play_arrowquestion_answer99) The brown ring test for nitrates depends on
A) the reduction of nitrate to nitric oxide
B) oxidation of nitric oxide to nitrogen dioxide
C) reduction of ferrous sulphate to iron
D) oxidising action of sulphuric acid
View Answer play_arrowquestion_answer100) Which of the following solutions will exhibit highest boiling point?
A) \[0.01\,\,M\,\,N{{a}_{2}}S{{O}_{4}}(aq)\]
B) \[0.01\,\,M\,\,KN{{O}_{3}}(aq)\]
C) \[0.015\,\,M\,\,urea(aq)\]
D) \[0.015\,\,M\,\,glucose(aq)\]
View Answer play_arrowquestion_answer101) \[\int_{0}^{\pi /2}{\frac{x\sin x\cdot \cos x}{{{\cos }^{4}}x+{{\sin }^{4}}x}}dx\]is equal to
A) \[\frac{{{\pi }^{2}}}{8}\]
B) \[\frac{{{\pi }^{2}}}{16}\]
C) \[1\]
D) \[0\]
View Answer play_arrowquestion_answer102) Equation of the tangent to the hyperbola\[2{{x}^{2}}-3{{y}^{2}}=6\]. Which is parallel to the line \[y-3x-4=0\]is
A) \[y=3x+8\]
B) \[y=3x-8\]
C) \[y=3x+2\]
D) None of these
View Answer play_arrowquestion_answer103) If the coefficient of correlation between two variables is\[0.32\], covariance is \[8\] and variance of \[x\] is\[25\], then variance of \[y\] is
A) \[36\]
B) \[25\]
C) \[64\]
D) None of these
View Answer play_arrowquestion_answer104) Ten coins are thrown simultaneously, the probability of getting at least \[7\] heads is
A) \[\frac{63}{256}\]
B) \[\frac{121}{172}\]
C) \[\frac{113}{512}\]
D) \[\frac{11}{64}\]
View Answer play_arrowquestion_answer105) When \[{{b}_{yx}}=0.03\] and\[{{b}_{xy}}=0.3\], then \[r\] is equal to approximately
A) \[0.003\]
B) \[0.095\]
C) \[0.3\]
D) \[-0.3\]
View Answer play_arrowquestion_answer106) Use Simpson's\[\frac{1}{3}\]rule to find the value of \[\int_{1}^{5}{f(x)}\,\,dx\]given
\[x\] | \[1\] | \[2\] | \[3\] | \[4\] | \[4\] |
\[y\] | \[10\] | \[50\] | \[70\] | \[80\] | \[100\] |
A) \[140.88\]
B) \[256.66\]
C) \[160.26\]
D) None of these
View Answer play_arrowquestion_answer107) The feasible region represented by\[{{x}_{1}}+{{x}_{2}}\le 1\],\[-3{{x}_{1}}+{{x}_{2}}\ge 3,\,\,({{x}_{1}},\,\,{{x}_{2}}\ge 0)\]is
A) a polygon
B) a singleton set
C) empty set
D) None of these
View Answer play_arrowquestion_answer108) The points on the curve \[{{x}^{2}}=2y\] which are closest to the point \[(0,\,\,5)\] are
A) \[(2,\,\,2),\,\,(-2,\,\,2)\]
B) \[(2\sqrt{2},\,\,4),\,\,(-2\sqrt{2},\,\,4)\]
C) \[(\sqrt{6},\,\,3),\,\,(-\sqrt{6},\,\,3)\]
D) \[(2\sqrt{3},\,\,6),\,\,(-2\sqrt{3},\,\,6)\]
View Answer play_arrowquestion_answer109) Solve\[\left( \frac{dy}{dx} \right)\tan y=\sin (x+y)+\sin (x-y)\]
A) \[\sec x-\frac{1}{2}\tan y=c\]
B) \[\log \sin (x+y)=c\]
C) \[\sec x+\tan y=c\]
D) \[\sec y+2\cos x=c\]
View Answer play_arrowquestion_answer110) \[\overset{\to }{\mathop{\mathbf{A}}}\,\cdot \{(\overset{\to }{\mathop{\mathbf{B}}}\,+\overset{\to }{\mathop{\mathbf{C}}}\,)\times (\overset{\to }{\mathop{\mathbf{A}}}\,+\overset{\to }{\mathop{\mathbf{B}}}\,+\overset{\to }{\mathop{\mathbf{C}}}\,)\}\]equals
A) \[[\overset{\to }{\mathop{\mathbf{A}}}\,\overset{\to }{\mathop{\mathbf{B}}}\,\overset{\to }{\mathop{\mathbf{C}}}\,]\]
B) \[[\overset{\to }{\mathop{\mathbf{B}}}\,\overset{\to }{\mathop{\mathbf{A}}}\,\overset{\to }{\mathop{\mathbf{C}}}\,]\]
C) \[0\]
D) \[1\]
View Answer play_arrowquestion_answer111) If\[y=\frac{{{y}^{3}}}{3}+\frac{{{y}^{5}}}{5}+...\infty =2\left[ x+\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5}+...\infty \right]\] then value of \[y\] is
A) \[\frac{x}{1-{{x}^{2}}}\]
B) \[\frac{2x}{1+{{x}^{2}}}\]
C) \[\frac{1-{{x}^{2}}}{2x}\]
D) None of these
View Answer play_arrowquestion_answer112) If\[x=\frac{1}{2}(\sqrt{3}+i)\], then \[{{x}^{3}}\] is equal to
A) \[1\]
B) \[-1\]
C) \[i\]
D) \[-i\]
View Answer play_arrowquestion_answer113) if the complex numbers \[\sin x+i\cos 2x\] and \[\cos x-i\sin 2x\] are complex conjugate to each other, then the value of \[x\] is
A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{8}\]
C) \[\frac{3\pi }{4}\]
D) None of these
View Answer play_arrowquestion_answer114) \[\underset{x\to {{2}^{+}}}{\mathop{\lim }}\,\frac{|x-2|}{x-2}\]is equal to
A) \[-1\]
B) \[1\]
C) \[2\]
D) \[-2\]
View Answer play_arrowquestion_answer115) If\[\left| \begin{matrix} x & {{x}^{2}} & 1+{{x}^{3}} \\ y & {{y}^{2}} & 1+{{y}^{3}} \\ z & {{z}^{2}} & 1+{{z}^{3}} \\ \end{matrix} \right|=0\], then
A) \[z=xy\]
B) \[z=\frac{1}{xy}\]
C) \[z=-\frac{1}{xy}\]
D) None of these
View Answer play_arrowquestion_answer116) \[{{\cos }^{4}}\frac{\pi }{8}+{{\cos }^{4}}\frac{3\pi }{8}+{{\cos }^{4}}\frac{5\pi }{8}+{{\cos }^{4}}\frac{7\pi }{8}\]is equal to
A) \[\frac{3}{2}\]
B) \[-\frac{2}{3}\]
C) \[-1\]
D) \[1\]
View Answer play_arrowquestion_answer117) In a triangle\[ABC\], if\[\tan \frac{A}{2}=\frac{5}{6}\]and\[\tan \frac{B}{2}=\frac{20}{37}\], then \[a+c\]is equal to
A) \[b\]
B) \[2b\]
C) \[3b\]
D) \[4b\]
View Answer play_arrowquestion_answer118) Number of solutions of the equation \[\tan x+\sec x=2\cos x\] lying in the interval\[[0,\,\,2\pi ]\]is
A) \[0\]
B) \[1\]
C) \[2\]
D) \[3\]
View Answer play_arrowquestion_answer119) Equation of the pair of straight lines bisecting the angles between the lines represented by \[a{{x}^{2}}+hxy+b{{y}^{2}}=0\]is
A) \[\frac{{{x}^{2}}-{{y}^{2}}}{a-b}=\frac{2xy}{h}\]
B) \[\frac{{{x}^{2}}+{{y}^{2}}}{a+b}=\frac{xy}{2h}\]
C) \[\frac{{{x}^{2}}-{{y}^{2}}}{a-b}=\frac{xy}{h}\]
D) None of these
View Answer play_arrowquestion_answer120) The equation of circle which touches the axes and the line \[\frac{x}{3}+\frac{y}{4}=1\] and whose centre lies in the first quadrant is\[{{x}^{2}}+{{y}^{2}}-2cx-2cy+{{c}^{2}}=0\]. Then, \[c\] is equal to
A) \[1\]
B) \[2\]
C) \[3\]
D) .\[6\]
View Answer play_arrowquestion_answer121) Angle between any two diagonals of a cube is
A) \[\frac{\pi }{3}\]
B) \[{{\cos }^{-1}}\left( \frac{1}{3} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]
D) None of these
View Answer play_arrowquestion_answer122) If`\[{{a}_{1}},\,\,{{a}_{2}},\,\,{{a}_{3}},...,{{a}_{n}}\]are in\[AP\]. Where\[{{a}_{i}}>0\]for all\[i\]. Find the sum of series \[\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{1}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+\frac{1}{\sqrt{{{a}_{3}}+{{a}_{4}}}}+...\]\[+\frac{1}{\sqrt{{{a}_{n-1}}}+\sqrt{{{a}_{n}}}}\]
A) \[\frac{n+1}{\sqrt{{{a}_{1}}+{{a}_{n}}}}\]
B) \[\frac{n-1}{\sqrt{{{a}_{1}}}-\sqrt{{{a}_{n}}}}\]
C) \[\frac{n+1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\]
D) \[\frac{n-1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\]
View Answer play_arrowquestion_answer123) The ratio in which the \[xy-\]plane meets the line joining the points \[(-3,\,\,4,\,\,-8)\] and \[(5,\,\,-6,\,\,4)\]is
A) \[2:3\]
B) \[2:1\]
C) \[4:5\]
D) None of these
View Answer play_arrowquestion_answer124) The unit vector perpendicular to each of the vectors\[3\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+2\widehat{\mathbf{k}}\], and\[2\widehat{\mathbf{i}}-2\widehat{\mathbf{j}}+4\widehat{\mathbf{k}}\]
A) \[\frac{\widehat{\mathbf{i}}-\widehat{\mathbf{j}}-\widehat{\mathbf{k}}}{\sqrt{3}}\]
B) \[\frac{\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}}}{\sqrt{3}}\]
C) \[\frac{\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\widehat{\mathbf{k}}}{\sqrt{3}}\]
D) None of these
View Answer play_arrowquestion_answer125) \[y={{\tan }^{-1}}\frac{\sqrt{(1+{{x}^{2}})}+\sqrt{(1-{{x}^{2}})}}{\sqrt{(1+{{x}^{2}})}-\sqrt{(1-{{x}^{2}})}}\], then\[\frac{dy}{dx}\]is equal to
A) \[\frac{1}{\sqrt{1+{{x}^{2}}}}\]
B) \[-\frac{1}{2}\]
C) \[-\frac{x}{\sqrt{(1-{{x}^{4}})}}\]
D) \[\frac{x\sqrt{1+{{x}^{2}}}}{1-{{x}^{4}}}\]
View Answer play_arrowquestion_answer126) \[\overrightarrow{\mathbf{a}},\,\,\overrightarrow{\mathbf{b}},\,\,\overrightarrow{\mathbf{c}}\] are coplanar vectors, then which of the following is not correct?
A) \[\overrightarrow{\mathbf{a}}\cdot (\overrightarrow{\mathbf{b}}\times \overrightarrow{\mathbf{c}})=0\]
B) \[\overrightarrow{\mathbf{a}}\times (\overrightarrow{\mathbf{b}}\times \overrightarrow{\mathbf{c}})=0\]
C) \[[\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}},\,\,\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}},\,\,\overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{a}}]=0\]
D) \[\overrightarrow{\mathbf{a}}=p\overrightarrow{\mathbf{b}}+q\overrightarrow{\mathbf{c}}\]
View Answer play_arrowquestion_answer127) If\[|A|\ne 0\]and \[A\] is of order n, then\[adj\,\,(adj\,\,A)\]is equal to
A) \[|A{{|}^{n}}\]
B) \[|A{{|}^{2}}\]
C) \[|A{{|}^{n-1}}I\]
D) \[|A{{|}^{n-2}}\cdot A\]
View Answer play_arrowquestion_answer128) \[\int{\frac{x+\sin x}{1+\cos x}}dx\]is equal to
A) \[x\log (1+\cos x)+c\]
B) \[\frac{1}{x}\log (1+\cos x)+c\]
C) \[x\tan \frac{x}{2}+c\]
D) \[{{x}^{2}}{{\tan }^{-1}}\frac{x}{2}+c\]
View Answer play_arrowquestion_answer129) Find the differential equation of curves \[y=A{{e}^{x}}+B{{e}^{-x}}\] for different values of \[A\] and \[B\]
A) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-2y=0\]
B) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=y\]
C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=4y+3\]
D) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\]
View Answer play_arrowquestion_answer130) Solve\[\frac{dy}{dx}=\frac{{{y}^{2}}}{xy-{{x}^{2}}}\]
A) \[y=c{{e}^{x/y}}\]
B) \[y=c{{e}^{-y/x}}+x\]
C) \[y=c{{e}^{y/x}}\]
D) \[xy=c{{e}^{y/x}}\]
View Answer play_arrowquestion_answer131) If\[\underset{x\to a}{\mathop{\lim }}\,\frac{{{a}^{x}}-{{x}^{a}}}{{{x}^{x}}-{{a}^{a}}}=-1\], then
A) \[a=1\]
B) \[a=0\]
C) \[a=e\]
D) \[a=\frac{1}{e}\]
View Answer play_arrowquestion_answer132) If four digits are taken from the digits \[1,\,\,2,\,\,3,\,\,4,\] \[5,\,\,6,\,\,7\]. The probability that the sum of digits is less than\[12\], is
A) \[\frac{3}{25}\]
B) \[\frac{4}{35}\]
C) \[\frac{2}{35}\]
D) \[\frac{1}{35}\]
View Answer play_arrowquestion_answer133) The probability of happening exactly one of a two events \[A\] and \[B\] is
A) \[P(A)+P(B)-2P(A\cap B)\]
B) \[P(A)+P(B)-P(A\cap B)\]
C) \[P(A)-P(B)\]
D) None of the above
View Answer play_arrowquestion_answer134) Solve\[x\cos x\left( \frac{dy}{dx} \right)+y(x\sin x+\cos x)=1\]
A) \[y=x\tan x+\sin x+c\]
B) \[x=y\tan x+c\]
C) \[yx\sec x=\tan x+c\]
D) \[xy\cos x=x+c\]
View Answer play_arrowquestion_answer135) If the equation\[({{a}^{2}}+4a+3){{x}^{2}}+({{a}^{2}}-a-2)x\]\[+a(a+1)=0\]has more than two roots, then value of \[a\] is
A) \[0\]
B) \[1\]
C) \[-1\]
D) None of these
View Answer play_arrowquestion_answer136) \[{{S}_{1}},\,\,{{S}_{2}}\]and \[{{S}_{3}}\] are the sums of\[n,\,\,2n\] and \[3n\]terms of an arithmetic progression respectively, then
A) \[{{S}_{2}}=3{{S}_{3}}-2{{S}_{1}}\]
B) \[{{S}_{3}}=4({{S}_{1}}+{{S}_{2}})\]
C) \[{{S}_{3}}=3({{S}_{2}}-{{S}_{1}})\]
D) \[{{S}_{3}}=2({{S}_{2}}+{{S}_{1}})\]
View Answer play_arrowquestion_answer137) If\[^{n}{{C}_{r-1}}=36,\,{{\,}^{n}}{{C}_{r}}=84\]and\[^{n}{{C}_{r+1}}=126\], then \[n\] is equal to
A) \[8\]
B) \[9\]
C) \[10\]
D) \[11\]
View Answer play_arrowquestion_answer138) The sides \[AB,\,\,BC,\,\,CA\] of triangle \[ABC\] have \[3,\,\,\,4\] and \[5\] interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices
A) \[201\]
B) \[120\]
C) \[205\]
D) \[435\]
View Answer play_arrowquestion_answer139) Coefficient of \[{{x}^{n}}\] in the expansion of\[1+\frac{a+bx}{1!}+\frac{{{(a+bx)}^{2}}}{2!}+\frac{{{(a+bx)}^{3}}}{3!}+...\]is
A) \[\frac{{{e}^{a}}{{b}^{n}}}{n!}\]
B) \[\frac{{{(b\cdot a)}^{n}}}{n}\]
C) \[\frac{{{e}^{b}}\cdot {{b}^{n}}}{(n-1)!}\]
D) \[\frac{{{a}^{n}}\cdot {{b}^{n-1}}}{n!}\]
View Answer play_arrowquestion_answer140) \[\frac{{{C}_{0}}}{1}+\frac{{{C}_{2}}}{3}+\frac{{{C}_{4}}}{5}+\frac{{{C}_{6}}}{7}+...\]is equal to
A) \[\frac{{{2}^{n-1}}}{n-1}\]
B) \[\frac{{{2}^{n+1}}}{n+3}\]
C) \[\frac{{{2}^{n}}}{n+1}\]
D) \[\frac{{{2}^{n-2}}}{n}\]
View Answer play_arrowquestion_answer141) The equation of the parabola having the focus at the point \[(3,\,\,-1)\] and the vertex at \[(2,\,\,-1)\] is
A) \[{{y}^{2}}-4x-2y+9=0\]
B) \[{{y}^{2}}+4x+2y-9=0\]
C) \[{{y}^{2}}-4x+2y+9=0\]
D) \[{{y}^{2}}+4x-2y+9=0\]
View Answer play_arrowquestion_answer142) The equation of lines joining the origin to the points of intersection of \[y=x+3\] and \[4{{x}^{2}}+4{{y}^{2}}=1\] is
A) \[36({{x}^{2}}+{{y}^{2}})={{(x-y)}^{2}}\]
B) \[12({{x}^{2}}+{{y}^{2}})={{(x+y)}^{2}}\]
C) \[9({{x}^{2}}+{{y}^{2}})=4{{(x+y)}^{2}}\]
D) None of the above
View Answer play_arrowquestion_answer143) The angle of elevation of a jet fighter from a point \[A\] on the ground is\[{{60}^{o}}\]. After a flight of\[10\,\,s\], the angle of elevation changes to\[{{30}^{o}}\]. If the jet is flying at a speed of\[432\,\,km/h\]. Find the constant height at which the jet is flying.
A) \[200\sqrt{3}m\]
B) \[400\sqrt{3}m\]
C) \[600\sqrt{3}m\]
D) \[800\sqrt{3}m\]
View Answer play_arrowquestion_answer144) Which is incorrect?
A) \[(AB)'=B'A'\]
B) \[{{(AB)}^{\theta }}={{B}^{\theta }}{{A}^{\theta }}\]
C) \[\overline{AB}=\bar{B}\bar{A}\]
D) \[{{(AB)}^{-1}}={{B}^{-1}}{{A}^{-1}}\]
View Answer play_arrowquestion_answer145) Find the equation of plane through the line\[\frac{x-2}{2}=\frac{y-3}{3}=\frac{z-4}{5}\]and parallel to \[x-\]axis.
A) \[2x+3y+5z=1\]
B) \[2x-5y=4\]
C) \[5y-3z-3=0\]
D) \[3y+4z=0\]
View Answer play_arrowquestion_answer146) Find the moment of the force\[5\widehat{\mathbf{i}}+10\widehat{\mathbf{j}}+16\widehat{\mathbf{k}}\] acting at the point\[2\widehat{\mathbf{i}}-7\widehat{\mathbf{j}}+10\widehat{\mathbf{k}}\], about the point \[-5\widehat{\mathbf{i}}+6\widehat{\mathbf{j}}-10\widehat{\mathbf{k}}\]
A) \[41\widehat{\mathbf{i}}-8\widehat{\mathbf{j}}+55\widehat{\mathbf{k}}\]
B) \[-408\widehat{\mathbf{i}}-12\widehat{\mathbf{j}}+135\widehat{\mathbf{k}}\]
C) \[-36\widehat{\mathbf{i}}+14\widehat{\mathbf{j}}-35\widehat{\mathbf{k}}\]
D) None of the above
View Answer play_arrowquestion_answer147) Find the equation of tangents to the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\], which cut off equal intercepts or the axes.
A) \[y=\sqrt{3}x\pm \sqrt{3{{a}^{2}}+{{b}^{2}}}\]
B) \[y=\pm x\mp \sqrt{{{a}^{2}}+{{b}^{2}}}\]
C) \[y=\sqrt{3}\pm \sqrt{{{a}^{2}}+3{{b}^{2}}}\]
D) None of the above
View Answer play_arrowquestion_answer148) A square matrix \[A\] is called an orthogonal matrix if
A) \[A\bar{A}=I\]
B) \[AA'=I\]
C) \[A{{A}^{\theta }}=I\]
D) \[{{A}^{2}}=I\]
View Answer play_arrowquestion_answer149) The value of \['c'\] Rolle's theorem for \[f(x)={{e}^{x}}\sin x\]in\[[0,\,\,\pi ]\]is given by
A) \[\frac{\pi }{4}\]
B) \[\frac{3\pi }{4}\]
C) \[\frac{5\pi }{6}\]
D) \[\frac{\pi }{2}\]
View Answer play_arrowquestion_answer150) \[\int_{-a}^{a}{x\sqrt{({{a}^{2}}-{{x}^{2}})}}dx\]is equal to
A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{8}\]
D) \[0\]
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