question_answer1) Solar spectrum is an example for
A) line emission spectrum
B) continuous emission spectrum
C) band absorption spectrum
D) line absorption spectrum
View Answer play_arrowquestion_answer2) When a piece of metal is illuminated by a monochromatic light of wavelength \[\lambda \], then stopping potential is \[3{{V}_{s}}\]. When same surface is illuminated by light of wavelength \[2\lambda \], then stopping potential becomes \[{{V}_{s}}\]. The value of threshold wavelength for photoelectric emission will be
A) \[4\lambda \]
B) \[8\lambda \]
C) \[\frac{4}{3}\lambda \]
D) \[6\lambda \]
View Answer play_arrowquestion_answer3) The maximum kinetic energy of emitted electrons in a photoelectric effect does not depend upon
A) wavelength
B) frequency
C) intensity
D) work function
View Answer play_arrowquestion_answer4) The ratio of minimum wavelengths of Lyman and Balmer series will be
A) 1.25
B) 0.25
C) 5
D) 10
View Answer play_arrowquestion_answer5) Hydrogen atom does not emit X-rays because
A) it contains only a single electron
B) energy levels in it are far apart
C) its size is very small
D) energy levels in it are very close to each other
View Answer play_arrowquestion_answer6) The potential difference between A and B in the following figure is
A) 32 V
B) 48 V
C) 24 V
D) 14 V
View Answer play_arrowquestion_answer7) The magnetic field at the centre of a circular current carrying conductor of radius r is \[{{B}_{c}}\]. The magnetic field on its axis at a distance r from the centre is \[{{B}_{a}}\]. The value of \[{{B}_{c}}:{{B}_{a}}\] will be
A) \[1:\sqrt{2}\]
B) \[1:2\sqrt{2}\]
C) \[2\sqrt{2}:1\]
D) \[\sqrt{2}:1\]
View Answer play_arrowquestion_answer8) Current \[I\] is flowing in conductor shaped as shown in the figure. The radius of the curved part is r and the length of straight portion is very large. The value of the magnetic field at the centre O will be
A) \[\frac{{{\mu }_{0}}I}{4\pi r}\left( \frac{3\pi }{2}+1 \right)\]
B) \[\frac{{{\mu }_{0}}I}{4\pi r}\left( \frac{3\pi }{2}-1 \right)\]
C) \[\frac{{{\mu }_{0}}I}{4\pi r}\left( \frac{\pi }{2}+1 \right)\]
D) \[\frac{{{\mu }_{0}}I}{4\pi r}\left( \frac{\pi }{2}-1 \right)\]
View Answer play_arrowquestion_answer9) Two tangent galvanometers A and B are identical except in their number of rums. They are connected in series. On passing a current through them, deflections of \[{{60}^{o}}\] and \[{{30}^{o}}\] are produced. The ratio of the number of rums in A and B is
A) \[1:3\]
B) \[3:1\]
C) \[1:2\]
D) \[2:1\]
View Answer play_arrowquestion_answer10) The resultant force on the current loop PQRS due to a long current carrying conductor will be
A) \[{{10}^{-4}}N\]
B) \[3.6\times {{10}^{-4}}N\]
C) \[1.8\times {{10}^{-4}}N\]
D) \[5\times {{10}^{-4}}N\]
View Answer play_arrowquestion_answer11) How many \[6\mu F\], 200 V condensers are needed to make a condenser of \[18\mu F\], 600 V?
A) 9
B) 18
C) 3
D) 27
View Answer play_arrowquestion_answer12) The total energy stored in the condenser system shown in the figure will be
A) \[2\mu J\]
B) \[4\mu J\]
C) \[8\mu J\]
D) \[16\mu J\]
View Answer play_arrowquestion_answer13) A metal wire is subjected to a constant potential difference. When the temperature of the metal wire increases, the drift velocity of the electron in it
A) increases, thermal velocity of the electron decreases
B) decreases, thermal velocity of the electron decreases
C) increases, thermal velocity of the electron increases
D) decreases, thermal velocity of the electron increases
View Answer play_arrowquestion_answer14) The equivalent resistance between the points A and B will be (each resistance is \[10\sqrt{3}\,kgwt\])
A) \[30\,\Omega \]
B) \[8\,\Omega \]
C) \[10\,\Omega \]
D) \[40\,\Omega \]
View Answer play_arrowquestion_answer15) In the Bohr model of hydrogen atom, the electron is pictured to rotate in a circular orbit of radius \[5\times {{10}^{-11}}m\], at a speed \[2.2\times {{10}^{6}}m/s\]. What is the current associated with electron motion?
A) 1.12 mA
B) 3 mA
C) 0.75 mA
D) 2.25 mA
View Answer play_arrowquestion_answer16) A certain current on passing through a galvanometer produces a deflection of 100 divisions. When a shunt of one ohm is connected, the deflection reduces to 1 division. The galvanometer resistance is
A) \[100\,\Omega \]
B) \[99\,\Omega \]
C) \[10\,\Omega \]
D) \[9.9\,\Omega \]
View Answer play_arrowquestion_answer17) Two similar circular loops carry equal current in the same direction. On moving coils further apart, the electric current will
A) increase in both
B) decrease in both
C) remain unaltered
D) increases in one and decreases in the second
View Answer play_arrowquestion_answer18) The value of alternating emf E in the given circuit will be
A) 220 V
B) 140 V
C) 100 V
D) 20 V
View Answer play_arrowquestion_answer19) A current of 5 A is flowing at 220 V in the primary coil of a transformer. If the voltage produced in the secondary coil is 2200 V and 50% of power is lost, then the current secondary will be
A) 2.5 A
B) 5 A
C) 0.25 A
D) 0.5 A
View Answer play_arrowquestion_answer20) For a series LCR circuit at resonance, the statement which is not true is
A) Peak energy stored by a capacitor = peak energy stored by an inductor.
B) Average power = apparent power.
C) Watt less current is zero.
D) Power factor is zero.
View Answer play_arrowquestion_answer21) If \[{{\mu }_{0}}\] is permeability of free space and \[{{\varepsilon }_{0}}\] is permittivity of free space, the speed of light in vacuum is given by
A) \[\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}\]
B) \[\sqrt{\frac{{{\mu }_{0}}}{{{\varepsilon }_{0}}}}\]
C) \[\sqrt{\frac{1}{{{\varepsilon }_{0}}{{\mu }_{0}}}}\]
D) \[\sqrt{\frac{{{\varepsilon }_{0}}}{{{\mu }_{0}}}}\]
View Answer play_arrowquestion_answer22) In Young's double slit experiment, a third slit is made in between the double slits. Then
A) intensity of fringes totally disappears
B) only bright light is observed on the screen
C) fringes of unequal width are formed
D) contrast between bright and dark fringes is reduced
View Answer play_arrowquestion_answer23) In a two slit experiment with monochromatic light fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by \[5\times {{10}^{-2}}m\] towards the slits, the change in fringe width is \[3\times {{10}^{-5}}m\]. If separation between the slits is \[{{10}^{-3}}m\], the wavelength of light used is
A) \[6000\,\,\overset{o}{\mathop{A}}\,\]
B) \[5000\,\,\overset{o}{\mathop{A}}\,\]
C) \[3000\,\,\overset{o}{\mathop{A}}\,\]
D) \[4500\,\,\overset{o}{\mathop{A}}\,\]
View Answer play_arrowquestion_answer24) In a Fraunhofer diffraction experiment at a single slit using a light of wavelength 400 nm, the first minimum is formed at an angle of \[{{30}^{o}}\]. The direction 6 of the first secondary maximum is given by
A) \[{{\sin }^{-1}}\left( \frac{2}{3} \right)\]
B) \[{{\sin }^{-1}}\left( \frac{3}{4} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{1}{4} \right)\]
D) \[ta{{n}^{-1}}\left( \frac{2}{3} \right)\]
View Answer play_arrowquestion_answer25) Maximum diffraction takes place in a given slit for
A) \[\gamma \]-rays
B) ultraviolet light
C) infrared light
D) radio waves
View Answer play_arrowquestion_answer26) If an electron and a proton have the same de Broglie wavelength, then the kinetic energy of the electron is
A) zero
B) less than that of a proton
C) more than that of a proton
D) equal to that of a proton
View Answer play_arrowquestion_answer27) Two protons are kept at a separation of 40 \[{{A}^{o}}\] is the nuclear force and \[{{F}_{e}}\] is the electrostatic force between them. Then
A) \[{{F}_{n}}>>{{F}_{e}}\]
B) \[{{F}_{n}}={{F}_{e}}\]
C) \[{{F}_{n}}<<{{F}_{e}}\]
D) \[{{F}_{n}}\approx {{F}_{e}}\]
View Answer play_arrowquestion_answer28) Blue colour of sea water is due to
A) interference of sunlight reflected from the water surface
B) scattering of sunlight by the water molecules
C) image of sky in water
D) refraction of sunlight
View Answer play_arrowquestion_answer29) The ratio of the nuclear radii of elements with mass numbers 216 and 125 is
A) \[216:125\]
B) \[\sqrt{216}:\sqrt{125}\]
C) \[6:5\]
D) None of these
View Answer play_arrowquestion_answer30) On bombarding \[{{U}^{235}}\] by slow neutron, 200 MeV energy is released, if the power output of atomic reactor is 1.6 MW, then the rate of fission will be
A) \[5\times {{10}^{22}}/s\]
B) \[5\times {{10}^{16}}/s\]
C) \[8\times {{10}^{16}}/s\]
D) \[20\times {{10}^{16}}/s\]
View Answer play_arrowquestion_answer31) A ray of light enters from a rarer to a denser medium. The angle of incidence is \[i\]. Then the reflected and refracted rays are mutually perpendicular to each other. The critical angle for the pair of media is
A) \[{{\sin }^{-1}}(\tan i)\]
B) \[{{\tan }^{-1}}(\sin i)\]
C) \[{{\sin }^{-1}}(\cot i)\]
D) \[{{\cos }^{-1}}(\tan i)\]
View Answer play_arrowquestion_answer32) A fish in water (refractive index n) looks at a bird vertically above in the air. If y is the height of the bird and \[x\] is the depth of the fish from the surface, then the distance of the bird as estimated by the fish is
A) \[x+y\left( 1-\frac{1}{n} \right)\]
B) \[x+ny\]
C) \[x+y\left( 1+\frac{1}{n} \right)\]
D) \[y+x\left( 1-\frac{1}{n} \right)\]
View Answer play_arrowquestion_answer33) Figure shows a mixture of blue, green and red colored rays incident normally on a right angled prism. The critical angles of the material of the prism for red, green and blue are \[{{46}^{o}},{{44}^{o}}\] and \[{{43}^{o}}\] respectively. The arrangement will separate
A) red colour from blue and green
B) blue colour from red and green
C) green colour from red and blue
D) all the three colours
View Answer play_arrowquestion_answer34) A convex and a concave lens separated by distance d are then put in contact. The focal length of the combination
A) decreases
B) increases
C) becomes
D) remains the same
View Answer play_arrowquestion_answer35) A convex lens is made of 3 layers of glass of 3 different materials as in the figures. A point object is placed on its axis. The number of images of the object are
A) 1
B) 2
C) 3
D) 4
View Answer play_arrowquestion_answer36) An unpolarised beam of intensity \[{{I}_{0}}\] falls on a polarold. The intensity of the emergent light is
A) \[\frac{{{I}_{0}}}{2}\]
B) \[{{I}_{0}}\]
C) \[\frac{{{I}_{0}}}{4}\]
D) Zero
View Answer play_arrowquestion_answer37) Which of the following as a dichroic crystal?
A) Quartz
B) Tourmaline
C) Mica
D) Selenite
View Answer play_arrowquestion_answer38) Two identical metal spheres charged with \[+12\mu F\] and \[-8\mu F\] are kept at certain distance in air. They are brought into contact and then kept at the same distance. The ratio of the magnitudes of electrostatic forces between them before and after contact is
A) \[12:1\]
B) \[8:1\]
C) \[24:1\]
D) \[4:1\]
View Answer play_arrowquestion_answer39) A small conducting sphere of radius r is lying concentrically inside a bigger hollow conducting sphere of radius R. The bigger and smaller spheres are charged with Q and \[q\,(Q>q)\] and are insulated from each other. The potential difference between the spheres will be
A) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{r}-\frac{q}{R} \right)\]
B) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{R}-\frac{Q}{r} \right)\]
C) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{r}-\frac{Q}{R} \right)\]
D) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{Q}{R}+\frac{q}{r} \right)\]
View Answer play_arrowquestion_answer40) The charges Q, +q and +q are placed at the vertices of an equilateral triangle of side \[l\]. If the net electrostatic potential energy of the system is zero, then Q is equal to
A) \[-\frac{q}{2}\]
B) \[-q\]
C) \[\frac{+q}{2}\]
D) Zero
View Answer play_arrowquestion_answer41) Dimensional formula for the universal gravitational constant G is
A) \[[{{M}^{-1}}{{L}^{2}}{{T}^{-2}}]\]
B) \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]
C) \[[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]
D) \[[{{M}^{-1}}{{L}^{3}}{{T}^{-1}}]\]
View Answer play_arrowquestion_answer42) A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are \[{{t}_{1}}\] and \[{{t}_{2}}\]respectively Then the velocity of projection is (g is acceleration due to gravity)
A) \[g\sqrt{{{t}_{1}}{{t}_{2}}}\]
B) \[\frac{g{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}\]
C) \[\frac{g\sqrt{{{t}_{1}}{{t}_{2}}}}{2}\]
D) \[\frac{g\,({{t}_{1}}+{{t}_{2}})}{2}\]
View Answer play_arrowquestion_answer43) A mass of 10 kg is suspended from a spring balance. It is pulled aside by a horizontal string so that it makes an angle of \[{{60}^{o}}\] with the vertical The new reading of the balance is
A) 20 kg - wt
B) 10 kg - wt
C) \[10\sqrt{3}\,kgwt\]
D) \[20\sqrt{3}\,kg-wt\]
View Answer play_arrowquestion_answer44) A body weighs 50 gin air and 40 gin water. How much would it weigh in a liquid of specific gravity 1.5?
A) 30 g
B) 35 g
C) 65 g
D) 45 g
View Answer play_arrowquestion_answer45) A body of mass 4 kg is accelerated upon b constant force, travels a distance of 5 m in the first second and a distance of 2 m in the third second. The force acting on the body is
A) 2 N
B) 4 N
C) 6 N
D) 8 N
View Answer play_arrowquestion_answer46) A simple pendulum is suspended from the ceiling of a lift. When the lift is at rest its time period is T. With what acceleration should lift be accelerated upwards in order to reduce its period to T/2? (g is acceleration due to gravity).
A) 2 g
B) 3 g
C) 4 g
D) g
View Answer play_arrowquestion_answer47) If y is the ratio of specific heats and R is the universal gas constant, then the molar specific heat at constant volume C- is given by
A) \[\gamma R\]
B) \[\frac{(\gamma -1)R}{\gamma }\]
C) \[\frac{R}{\gamma -1}\]
D) \[\frac{\gamma R}{\gamma -1}\]
View Answer play_arrowquestion_answer48) An ideal gas is taken via path ABCA as shown in figure. The net work done in the whole cycle is
A) \[3{{p}_{1}}{{V}_{1}}\]
B) \[-3{{p}_{1}}{{V}_{1}}\]
C) \[6{{p}_{1}}{{V}_{1}}\]
D) Zero
View Answer play_arrowquestion_answer49) In which of the processes, does the internal energy of the system remain constant?
A) Adiabatic
B) Isochoric
C) Isobaric
D) Isothermal
View Answer play_arrowquestion_answer50) The coefficient of thermal conductivity of copper is 9 times that of steel. In the composite cylindrical bar shown in the figure, what will be the temperature at the junction of copper and steel?
A) \[{{75}^{o}}C\]
B) \[{{67}^{o}}C\]
C) \[{{25}^{o}}C\]
D) \[{{33}^{o}}C\]
View Answer play_arrowquestion_answer51) The equation of a simple harmonic wave is given by \[y=6\text{ }\sin \text{ }2\pi \,(2t-0.1x)\] where \[x\] and y are in mm and t is in seconds. The phase difference between two particles 2 mm apart at any instant is
A) \[{{18}^{o}}\]
B) \[{{36}^{o}}\]
C) \[{{54}^{o}}\]
D) \[{{72}^{o}}\]
View Answer play_arrowquestion_answer52) With what velocity should an observer approach a stationary sound source, so that the apparent frequency of sound should appear double the actual frequency? (v is velocity of sound).
A) \[\frac{v}{2}\]
B) 3 v
C) 2 v
D) v
View Answer play_arrowquestion_answer53) If a black body emits 0.5 J of energy per second when it is at \[{{27}^{o}}C\], then the amount of energy emitted by it when it is at \[{{627}^{o}}C\] will be
A) 40.5 J
B) 162 J
C) 13.5 J
D) 135 J
View Answer play_arrowquestion_answer54) A string vibrates with a frequency of 200 Hz. When its length is doubled and tension is altered, it begins to vibrate with a frequency of 300 Hz. The ratio of the new tension to the original tension is
A) \[9:1\]
B) \[1:9\]
C) \[3:1\]
D) \[1:3\]
View Answer play_arrowquestion_answer55) How many times more intense is a 60 dB sound than a 30 dB sound?
A) 1000
B) 2
C) 100
D) 4
View Answer play_arrowquestion_answer56) The masses of two radioactive substances are same and their half-lives are 1 yr and 2 yr respectively. The ratio of their activities after 4 yr will be
A) \[1:4\]
B) \[1:2\]
C) \[1:3\]
D) \[1:6\]
View Answer play_arrowquestion_answer57) \[_{92}{{U}^{235}}\] undergoes successive disintegrations with the end product of \[_{82}P{{b}_{203}}\]. The number of \[\alpha \] and \[\beta \] particles emitted are
A) \[\alpha =6,~\beta =4\]
B) \[\alpha =6,~\beta =0\]
C) \[\alpha =8,~\beta =6\]
D) \[\alpha =3,~\beta =3\]
View Answer play_arrowquestion_answer58) The most stable particle in Baryon group is
A) neutron
B) omega-particle
C) proton
D) lambda-particle
View Answer play_arrowquestion_answer59) In an unbiased p-n junction
A) Potential at p is more than that at n
B) Potential at p is less than that at n
C) Potential at p is equal to that at n
D) Potential at p is +ve and that at n is -ve
View Answer play_arrowquestion_answer60) To get an output \[Y=1\] from the circuit shown, the inputs A, B and C must be respectively
A) 0, 1, 0
B) 1, 0, 0
C) 1, 0, 1
D) 1, 1, 0
View Answer play_arrowquestion_answer61) The number of nodal planes present in \[{{\sigma }^{*}}s\] anti bonding orbitals is
A) 1
B) 2
C) 0
D) 3
View Answer play_arrowquestion_answer62) Which of the following electrolytic solutions has the least specific conductance?
A) 0.02 N
B) 0.2 N
C) 2 N
D) 0.002 N
View Answer play_arrowquestion_answer63) The overlapping of orbitals in benzene is of the type
A) \[sp-sp\]
B) \[p-p\]
C) \[s{{p}^{2}}-s{{p}^{2}}\]
D) \[s{{p}^{3}}-s{{p}^{3}}\]
View Answer play_arrowquestion_answer64) The calculated bond order of superoxide ion \[(CO_{2}^{-})\] is
A) 2.5
B) 2
C) 1.5
D) 1
View Answer play_arrowquestion_answer65) Which of the following can be measured by the Ostwald-Walker dynamic method?
A) Relative lowering of vapour pressure
B) Lowering of vapour pressure
C) Vapour pressure of the solvent
D) All of the above
View Answer play_arrowquestion_answer66) Mesomeric effect involves delocalization of
A) pi electrons
B) sigma electrons
C) protons
D) None of these
View Answer play_arrowquestion_answer67) Which of the following has the maximum number of unpaired 'd' electrons?
A) \[Z{{n}^{2+}}\]
B) \[F{{e}^{2+}}\]
C) \[N{{i}^{3+}}\]
D) \[C{{u}^{+}}\]
View Answer play_arrowquestion_answer68) One mole of which of the following has the highest entropy?
A) Liquid nitrogen
B) Hydrogen gas
C) Mercury
D) Diamond
View Answer play_arrowquestion_answer69) Which of the following species does not exert a resonance effect?
A) \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]
B) \[{{C}_{6}}{{H}_{5}}\overset{+}{\mathop{N}}\,{{H}_{3}}\]
C) \[{{C}_{6}}{{H}_{5}}OH\]
D) \[{{C}_{6}}{{H}_{5}}Cl\]
View Answer play_arrowquestion_answer70) A complex compound in which the oxidation number of a metal is zero is
A) \[{{K}_{4}}[Fe{{(CN)}_{6}}]\]
B) \[{{K}_{3}}[Fe{{(CN)}_{6}}]\]
C) \[[Ni{{(CO)}_{4}}]\]
D) \[[Pt{{(N{{H}_{3}})}_{4}}]C{{l}_{2}}\]
View Answer play_arrowquestion_answer71) Catalytic dehydrogenation of a primary alcohol gives a
A) secondary alcohol
B) aldehyde
C) ketone
D) ester
View Answer play_arrowquestion_answer72) Excess of \[PC{{l}_{5}}\] reacts with cone \[{{H}_{2}}S{{O}_{4}}\] giving
A) chlorosulphonic acid
B) thionyl chloride
C) sulphuryl chloride
D) sulphurous acid
View Answer play_arrowquestion_answer73) If one mole of ammonia and one mole of hydrogen chloride are mixed in a closed container to form ammonium chloride gas, then
A) \[\Delta H>\Delta U\]
B) \[\Delta H=\Delta U\]
C) \[\Delta H<\Delta U\]
D) there is no relationship
View Answer play_arrowquestion_answer74) The compound on dehydrogenation gives a ketone. The original compound is
A) primary alcohol
B) secondary alcohol
C) tertiary alcohol
D) carboxylic acid
View Answer play_arrowquestion_answer75) Which is the most easily liquifiable rare gas?
A) Xe
B) Kr
C) Ar
D) Ne
View Answer play_arrowquestion_answer76) Three moles of \[PC{{l}_{5}}\], three moles of \[PC{{l}_{3}}\]and two moles of \[C{{l}_{2}}\] are taken in a closed vessel. If at equilibrium the vessel has 1.5 moles of\[PC{{l}_{5}}\], the number of moles of \[PC{{l}_{3}}\] present in it is
A) 5
B) 3
C) 6
D) 4.5
View Answer play_arrowquestion_answer77) How many optically active stereomers are possible for butan-2,3-diol?
A) 1
B) 2
C) 3
D) 4
View Answer play_arrowquestion_answer78) An octahedral complex is formed when hybrid orbitals of the following type are involved
A) \[s{{p}^{3}}\]
B) \[ds{{p}^{2}}\]
C) \[{{d}^{2}}s{{p}^{3}}\]
D) \[s{{p}^{2}}{{d}^{2}}\]
View Answer play_arrowquestion_answer79) For the reaction\[2HI(g)\rightleftarrows {{H}_{2}}(g)+{{I}_{2}}(g)-Q\,\,kJ\],the equilibrium constant depends upon
A) temperature
B) pressure
C) catalyst
D) volume
View Answer play_arrowquestion_answer80) The angle strain in cyclobutane is
A) \[{{24}^{o}}44'\]
B) \[{{29}^{o}}16'\]
C) \[{{19}^{o}}22'\]
D) \[{{9}^{o}}44'\]
View Answer play_arrowquestion_answer81) Methoxy methane and ethanol are
A) position isomers
B) chain isomers
C) functional isomers
D) optical isomers
View Answer play_arrowquestion_answer82) When the azimuthal quantum number has the value of 2, the number of orbitals possible are
A) 7
B) 5
C) 3
D) 0
View Answer play_arrowquestion_answer83) For the reaction \[F{{e}_{2}}{{O}_{3}}+3CO\xrightarrow{{}}2Fe+3C{{O}_{2}}\] the volume of carbon monoxide required to reduce one mole of ferric oxide is
A) \[22.4\,\,d{{m}^{3}}\]
B) \[44.8\,\,d{{m}^{3}}\]
C) \[67.2\,\,d{{m}^{3}}\]
D) \[11.2\,\,d{{m}^{3}}\]
View Answer play_arrowquestion_answer84) The monomers of buna-S rubber are
A) vinyl chloride and sulphur
B) butadiene
C) styrene and butadiene
D) isoprene and butadiene
View Answer play_arrowquestion_answer85) An element with atomic number 21 is a
A) halogen
B) representative element
C) transition element
D) alkali metal
View Answer play_arrowquestion_answer86) n-propyl bromide on treating with alcoholic KOH produces
A) propane
B) propene
C) propyne
D) propanol
View Answer play_arrowquestion_answer87) Mercury is a liquid metal because
A) it has a completely filled s orbital
B) it has a small atomic size
C) it has a completely filled d orbital that prevents d-d overlapping of orbitals
D) it has a completely filled d orbital that causes d-d overlapping
View Answer play_arrowquestion_answer88) A compound is formed by elements A and B. This crystallizes in the cubic structure where the A atoms are at the corners of the cube and B atoms are at the body centres. The simplest formula of the compound is
A) AB
B) \[{{A}_{6}}B\]
C) \[{{A}_{8}}{{B}_{4}}\]
D) \[A{{B}_{6}}\]
View Answer play_arrowquestion_answer89) Anisole can be prepared by the action of methyl iodide on sodium phenate. The reaction is called
A) Wurtz's reaction
B) Williamson's reaction
C) Fittig's reaction
D) Etard's reaction
View Answer play_arrowquestion_answer90) Malleability and ductility of metals can be accounted due to
A) the presence of electrostatic force
B) -the crystalline structure in metal
C) the capacity of layers of metal ions to slide over the other
D) the interaction of electrons with metal ions in the lattice
View Answer play_arrowquestion_answer91) The correct order in which the first ionization potential increases is
A) Na, K, Be
B) K, Na, Be
C) K, Be, Na
D) Be, Na, K
View Answer play_arrowquestion_answer92) \[10\,\,c{{m}^{3}}\] of 0.1 N monobasic acid requires \[15\,\,c{{m}^{3}}\] of sodium hydroxide solution whose normality is
A) 1.5 N
B) 0.15 N
C) 0.066 N
D) 0.66 N
View Answer play_arrowquestion_answer93) The IUPAC name for tertiary butyl iodide is
A) 4-iodo butane
B) 2-iodo butane
C) 1-iodo-3-methyl propane
D) 2-iodo-2-methyl propane
View Answer play_arrowquestion_answer94) When sulphur dioxide is passed in an acidified\[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\] solution, the oxidation state of sulphur is changed from
A) + 4 to 0
B) + 4 to +2
C) + 4 to +6
D) +6 to +4
View Answer play_arrowquestion_answer95) Mass of 0.1 mole of methane is
A) 1g
B) 16 g
C) 1.6 g
D) 0.1 g
View Answer play_arrowquestion_answer96) The maximum number of hydrogen bonds that a molecule of water can have is
A) 1
B) 2
C) 3
D) 4
View Answer play_arrowquestion_answer97) A gas deviates from ideal behaviour at a high pressure because its molecules
A) attract one another
B) show the Tyndall effect
C) have kinetic energy
D) are bound by covalent bonds
View Answer play_arrowquestion_answer98) The reagent used to convert an alkyne to alkene is
A) \[Zn/HCl\]
B) \[Sn/HCl\]
C) \[Zn-Hg/HCl\]
D) \[Pd-{{H}_{2}}\]
View Answer play_arrowquestion_answer99) When compared to \[\Delta {{G}^{o}}\] for the formation of \[A{{l}_{2}}{{O}_{3}}\], the \[\Delta {{G}^{o}}\] for the formation of \[C{{r}_{2}}{{O}_{3}}\] is
A) higher
B) lower
C) same
D) unpredicted
View Answer play_arrowquestion_answer100) In order to increase the volume of a gas by 10%, the pressure of the gas should be
A) increased by 10%
B) increased by 1%
C) decreased by 10%
D) decreased by 1%
View Answer play_arrowquestion_answer101) Helium is used in balloons in place of hydrogen because it is
A) incombustible
B) lighter than hydrogen
C) radioactive
D) more abundant than hydrogen
View Answer play_arrowquestion_answer102) The basic principle of Cottnell?s precipitator is
A) Le-Chatelier's principle
B) peptisation
C) neutralization of charge on colloidal particles
D) scattering of light'
View Answer play_arrowquestion_answer103) When carbon monoxide is passed over solid caustic soda heated to \[{{200}^{o}}C\], it forms
A) \[N{{a}_{2}}C{{O}_{3}}\]
B) \[NaHC{{O}_{3}}\]
C) \[HCOONa\]
D) \[C{{H}_{3}}COONa\]
View Answer play_arrowquestion_answer104) \[{{N}_{2}}+3{{H}_{2}}\rightleftarrows 2N{{H}_{3}}\]heat. What is the effect of the increase of temperature on the equilibrium of the reaction?
A) Equilibrium is shifted to the left
B) Equilibrium is shifted to the right
C) Equilibrium is unaltered
D) Reaction rate does not change
View Answer play_arrowquestion_answer105) Hydrogen gas is not liberated when the following metal is added to dil \[HCl\]
A) Ag
B) Zn
C) Mg
D) Sn
View Answer play_arrowquestion_answer106) Consider the Bom-Haber cycle for the formation of an ionic compound given below and identify the compound (Z) formed.
A) \[{{M}^{+}}{{X}^{-}}\]
B) \[{{M}^{+}}{{X}^{-}}(s)\]
C) \[MX\]
D) \[{{M}^{+}}{{X}^{-}}(g)\]
View Answer play_arrowquestion_answer107) In the brown ring test, the brown colour of the ring is due to
A) ferrous nitrate
B) ferric nitrate
C) a mixture of NO and \[N{{O}_{2}}\]
D) nitrosoferrous sulphate
View Answer play_arrowquestion_answer108) Amines behave as
A) Lewis acid
B) Lewis base
C) aprotic acid
D) neutral compound
View Answer play_arrowquestion_answer109) Dalda is prepared from oils by
A) oxidation
B) reduction
C) hydrolysis
D) distillation
View Answer play_arrowquestion_answer110) The chemical name of anisole is
A) ethanoic acid
B) methoxy benzene
C) propanone
D) acetone
View Answer play_arrowquestion_answer111) The number of disulphide linkages present in insulin are
A) 1
B) 2
C) 3
D) 4
View Answer play_arrowquestion_answer112) 80 g of oxygen contains as many atoms as in
A) 80 g of hydrogen
B) 1 g of hydrogen
C) 10 g of hydrogen
D) 5 g of hydrogen
View Answer play_arrowquestion_answer113) Which metal has a greater tendency to form metal oxide?
A) Cr
B) Fe
C) Al
D) Ca
View Answer play_arrowquestion_answer114) Identify the reaction that does not take place in a blast furnace.
A) \[CaC{{O}_{3}}\xrightarrow{{}}CaO+C{{O}_{2}}\]
B) \[CaO+Si{{O}_{2}}\xrightarrow{{}}CaSi{{O}_{3}}\]
C) \[2F{{e}_{2}}{{O}_{3}}+3C\xrightarrow{{}}4Fe+3C{{O}_{2}}\]
D) \[C{{O}_{2}}+C\xrightarrow{{}}2CO\]
View Answer play_arrowquestion_answer115) Waxes are esters of
A) glycerol
B) long chain alcohols
C) glycerol and fatty acid
D) long chain alcohols and long chain fatty acids
View Answer play_arrowquestion_answer116) An ionic compound is expected to have tetrahedral structure if \[{{r}_{+}}/{{r}_{-}}\] lies in the range of
A) 0.414 to 0.732
B) 0.225 to 0.414
C) 0.155 to 0.225
D) 0.732 to 1
View Answer play_arrowquestion_answer117) Among the following, which is least acidic?
A) phenol
B) o-cresol
C) p-nitrophenol
D) p-chlorophenol
View Answer play_arrowquestion_answer118) A ligand can also be regarded as
A) Lewis acid
B) Bronstedbase
C) Lewis base
D) Bronsted acid
View Answer play_arrowquestion_answer119) The colour of sky is due to
A) transmission of light
B) wavelength of scattered light
C) absorption of light by atomspheric gases
D) All of the above
View Answer play_arrowquestion_answer120) Which of the following organic compounds answers to both iodoform test and Fehling's test?
A) Ethanol
B) Methanal
C) Ethanal
D) Propanone
View Answer play_arrowquestion_answer121) The locus of a point which moves such that the sum of its distances from two fixed points is a constant, is
A) a circle
B) a parabola
C) an ellipse
D) a hyperbola
View Answer play_arrowquestion_answer122) The centroid of the triangle ABC, where \[A\equiv (2,3),\]\[B\equiv (8,10)\] and \[C\equiv (5,5)\]is
A) \[(5,6)\]
B) \[(6,5)\]
C) \[(6,6)\]
D) \[(15,18)\]
View Answer play_arrowquestion_answer123) If \[3{{x}^{2}}+xy-{{y}^{2}}-3x+6y+k=0\] represents a pair of lines, then k is equal to
A) \[0\]
B) \[9\]
C) \[1\]
D) \[-9\]
View Answer play_arrowquestion_answer124) The equation of the smallest circle passing through the points \[(2,2)\] and \[(3,3)\] is
A) \[{{x}^{2}}+{{y}^{2}}+5x+5y+12=0\]
B) \[{{x}^{2}}+{{y}^{2}}-5x-5y+12=0\]
C) \[{{x}^{2}}+{{y}^{2}}+5x-5y+12=0\]
D) \[{{x}^{2}}+{{y}^{2}}-5x+5y-12=0\]
View Answer play_arrowquestion_answer125) The characteristic roots of the matrix \[\left[ \begin{matrix} 1 & 0 & 0 \\ 2 & 3 & 0 \\ 4 & 5 & 6 \\ \end{matrix} \right]\] are
A) \[1,3,6\]
B) \[1,2,4\]
C) \[4,5,6\]
D) \[2,4,6\]
View Answer play_arrowquestion_answer126) If \[{{e}_{1}}\] and \[{{e}_{2}}\] are the eccentricities of a hyperbola \[3{{x}^{2}}-3{{y}^{2}}=25\] and its conjugate, then
A) \[e_{1}^{2}+e_{2}^{2}=2\]
B) \[e_{1}^{2}+e_{2}^{2}=4\]
C) \[{{e}_{1}}+{{e}_{2}}=4\]
D) \[{{e}_{1}}+{{e}_{2}}=\sqrt{2}\]
View Answer play_arrowquestion_answer127) If p and q are prime numbers satisfying the condition \[{{p}^{2}}-2{{q}^{2}}=1,\] then the value of \[{{p}^{2}}+2{{q}^{2}}\]is
A) \[5\]
B) \[15\]
C) \[16\]
D) \[17\]
View Answer play_arrowquestion_answer128) If \[A(adj\,A)=5I\] where \[I\] is the identity matrix of order 3, then \[|adj\,\,A|\] is equal to
A) \[125\]
B) \[25\]
C) \[5\]
D) \[10\]
View Answer play_arrowquestion_answer129) The number of solutions for the equation \[\sin 2x+\cos 4x=2\] is
A) \[0\]
B) \[1\]
C) \[2\]
D) \[\infty \]
View Answer play_arrowquestion_answer130) \[\int{{{e}^{x}}.{{x}^{5}}\,dx}\] is
A) \[{{e}^{x}}[{{x}^{5}}+5{{x}^{4}}+20{{x}^{3}}+60{{x}^{2}}+120x+120]+C\]
B) \[{{e}^{x}}[{{x}^{5}}-5{{x}^{4}}-20{{x}^{3}}-60{{x}^{2}}-120x-120]+C\]
C) \[{{e}^{x}}[{{x}^{5}}-5{{x}^{4}}+20{{x}^{3}}-60{{x}^{2}}+120x-120]+C\]
D) \[{{e}^{x}}[{{x}^{5}}-5{{x}^{4}}+20{{x}^{3}}-60{{x}^{2}}-120x+120]+C\]
View Answer play_arrowquestion_answer131) The equation \[\frac{{{x}^{2}}}{2-\lambda }-\frac{{{y}^{2}}}{\lambda -5}-1=0\] represents an ellipse, if
A) \[\lambda >5\]
B) \[\lambda <2\]
C) \[2<\lambda <5\]
D) \[2>\lambda >5\]
View Answer play_arrowquestion_answer132) The equation of the normal to the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{9}=1\] at \[(-4,0)\]is
A) \[2x-3y=1\]
B) \[x=0\]
C) \[x=1\]
D) \[y=0\]
View Answer play_arrowquestion_answer133) The converse of the contrapositive of the conditional \[p\to \tilde{\ }q\]is
A) \[p\to q\]
B) \[\tilde{\ }p\to \tilde{\ }q\]
C) \[\tilde{\ }q\to p\]
D) \[\tilde{\ }p\to q\]
View Answer play_arrowquestion_answer134) The perimeter of a certain sector of a circle is equal to the length of the arc of the semicircle. Then, the angle at the centre of the sector in radians is
A) \[\pi -2\]
B) \[\pi +2\]
C) \[\frac{\pi }{3}\]
D) \[\frac{2\pi }{3}\]
View Answer play_arrowquestion_answer135) The value of \[\tan \,67\frac{{{1}^{o}}}{2}+\cos 67\frac{{{1}^{o}}}{2}\] is
A) \[\sqrt{2}\]
B) \[3\sqrt{2}\]
C) \[2\sqrt{2}\]
D) \[2-\sqrt{2}\]
View Answer play_arrowquestion_answer136) If \[f(x)\] is an even function and \[f'(x)\] exists, then \[f'(e)+f'(-e)\]is
A) \[>0\]
B) \[0\]
C) \[\ge 0\]
D) \[<0\]
View Answer play_arrowquestion_answer137) If a is a complex number satisfying the equation \[{{a}^{2}}+a+1=0,\]then \[{{\alpha }^{31}}\]is equal to
A) \[\alpha \]
B) \[{{\alpha }^{2}}\]
C) \[1\]
D) \[i\]
View Answer play_arrowquestion_answer138) The derivative of \[\sin ({{x}^{3}})\] w.r.t. \[cos({{x}^{3}})\] is
A) \[-\tan ({{x}^{3}})\]
B) \[\tan ({{x}^{3}})\]
C) \[-cot({{x}^{3}})\]
D) \[cot({{x}^{3}})\]
View Answer play_arrowquestion_answer139) A unit vector perpendicular to both the vectors \[\hat{i}+\hat{j}\]and \[\hat{j}+\hat{k}\]
A) \[\frac{-\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\]
B) \[\frac{\hat{i}+\hat{j}-\hat{k}}{3}\]
C) \[\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\]
D) \[\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\]
View Answer play_arrowquestion_answer140) If \[A=\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right|\] and \[B=\left| \begin{matrix} {{c}_{1}} & {{c}_{2}} & {{c}_{3}} \\ {{a}_{1}} & {{a}_{2}} & {{a}_{3}} \\ {{b}_{1}} & {{b}_{2}} & {{b}_{3}} \\ \end{matrix} \right|,\] then
A) \[A=-B\]
B) \[A=B\]
C) \[B=0\]
D) \[B={{A}^{2}}\]
View Answer play_arrowquestion_answer141) On the set Z of all integers * is defined by \[a*b=a+b-5,\] if \[2*(x*3)=5,\]then x is equal to
A) \[0\]
B) \[3\]
C) \[5\]
D) \[10\]
View Answer play_arrowquestion_answer142) Which of the following is false?
A) Addition is commutative in N
B) Multiplication is associative in N
C) If \[a*b={{a}^{b}}\] for all a, \[b\in N\] then * is commutative in N
D) Addition is associative in N
View Answer play_arrowquestion_answer143) If \[\vec{a}.\hat{i}=\vec{a}.\left( \hat{i}+\hat{j} \right)=\vec{a}.\left( \hat{i}+\hat{j}+\hat{k} \right)=1\] then \[\vec{a}\] is equal to
A) \[\hat{i}+\hat{j}\]
B) \[\hat{i}-\hat{k}\]
C) \[\hat{i}\]
D) \[\hat{i}+\hat{j}-\hat{k}\]
View Answer play_arrowquestion_answer144) If a and b are unit vectors and \[|\vec{a}+\vec{b}|=1,\] then\[|\vec{a}-\vec{b}|=1,\] is equal to
A) \[\sqrt{2}\]
B) \[1\]
C) \[\sqrt{5}\]
D) \[\sqrt{3}\]
View Answer play_arrowquestion_answer145) The projection of \[\vec{a}=3\hat{i}-\hat{j}+5\hat{k}\] on \[\vec{b}=2\hat{i}+3\hat{j}+\hat{k}\]is
A) \[\frac{8}{\sqrt{35}}\]
B) \[\frac{8}{\sqrt{39}}\]
C) \[\frac{8}{\sqrt{14}}\]
D) \[\sqrt{14}\]
View Answer play_arrowquestion_answer146) If \[A\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ \end{matrix} \right],\]then \[{{A}^{-1}}\] is equal to
A) \[-\frac{1}{2}\left[ \begin{matrix} 4 & -2 \\ -3 & 1 \\ \end{matrix} \right]\]
B) \[\frac{1}{2}\left[ \begin{matrix} 4 & -2 \\ -3 & 1 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} -2 & 4 \\ 1 & 3 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 2 & 4 \\ 1 & 3 \\ \end{matrix} \right]\]
View Answer play_arrowquestion_answer147) The set \[\{-1,0,1\}\] is not a multiplicative group because of the failure of
A) closure law
B) associative law
C) identity law
D) inverse law
View Answer play_arrowquestion_answer148) The angle of elevation of the top of a TV tower from three points A, B and C in a straight line through the foot of the tower are \[\alpha ,2\alpha \] and \[3\alpha \]respectively. If \[AB=a,\] then height of the tower is
A) \[a\text{ }tan\text{ }\alpha \]
B) \[a\text{ }sin\text{ }\alpha \]
C) \[a\text{ }sin\text{ 2}\alpha \]
D) \[a\text{ }sin\text{ 3}\alpha \]
View Answer play_arrowquestion_answer149) The angles A, B and C of a triangle ABC are in AP. If \[b:c=\sqrt{3}:\sqrt{2},\] then the angle A is
A) \[{{30}^{o}}\]
B) \[{{15}^{o}}\]
C) \[{{75}^{o}}\]
D) \[{{45}^{o}}\]
View Answer play_arrowquestion_answer150) \[\sin \left( 2{{\sin }^{-1}}\sqrt{\frac{63}{65}} \right)\] is equal to
A) \[\frac{2\sqrt{126}}{65}\]
B) \[\frac{4\sqrt{65}}{65}\]
C) \[\frac{8\sqrt{63}}{65}\]
D) \[\frac{\sqrt{63}}{65}\]
View Answer play_arrowquestion_answer151) A variable line \[\frac{x}{a}+\frac{y}{b}=1\] is such that \[a+b=4\] The locus of the mid point of the portion of the line intercepted between the axes is
A) \[x+y=4\]
B) \[x+y=8\]
C) \[x+y=1\]
D) \[x+y=2\]
View Answer play_arrowquestion_answer152) The point \[(5,-7)\] lies outside the circle
A) \[{{x}^{2}}+{{y}^{2}}-8x=0\]
B) \[{{x}^{2}}+{{y}^{2}}-5x+7y=0\]
C) \[{{x}^{2}}+{{y}^{2}}-5x+7y-1=0\]
D) \[{{x}^{2}}+{{y}^{2}}-8x+7y-2=0\]
View Answer play_arrowquestion_answer153) If the circles \[{{x}^{2}}+{{y}^{2}}=9\]and \[{{x}^{2}}+{{y}^{2}}+2\alpha x+2y+1=0\]touch each other internally, then a is equal to
A) \[\pm \frac{4}{3}\]
B) \[1\]
C) \[\frac{4}{3}\]
D) \[-\frac{4}{3}\]
View Answer play_arrowquestion_answer154) The locus of the mid point of the line joining the focus and any point on the parabola \[{{y}^{2}}=4ax\] is a parabola with the equation of directrix as
A) \[x+a=0\]
B) \[2x+a=0\]
C) \[x=0\]
D) \[x=\frac{a}{2}\]
View Answer play_arrowquestion_answer155) The tangents drawn at the extremities of a focal chord of the parabola \[{{y}^{2}}=16x\]
A) intersect on \[x=0\]
B) intersect on the line \[x+4=0\]
C) intersect at an angle of \[{{60}^{o}}\]
D) intersect at an angle of \[{{45}^{o}}\]
View Answer play_arrowquestion_answer156) If \[f:R\to R\] is defined by \[f(x)={{x}^{3}},\] then \[{{f}^{-1}}(8)\]is equal to
A) \[\{2\}\]
B) \[\{2,2\omega ,2{{\omega }^{2}}\}\]
C) \[\{2,-2\}\]
D) \[\{2,2\}\]
View Answer play_arrowquestion_answer157) R is a relation on. N given by \[R=\{(x,y):4x+3y=20\}\]. Which of the following belongs to R?
A) \[(-4,12)\]
B) \[(5,0)\]
C) \[(3,4)\]
D) \[(2,4)\]
View Answer play_arrowquestion_answer158) If \[{{\log }_{10}}7=0.8451,\]then the position of the first significant figure of \[{{7}^{-20}}\]is
A) \[16\]
B) \[17\]
C) \[20\]
D) \[15\]
View Answer play_arrowquestion_answer159) \[\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+.....\]upto n terms is equal to
A) \[\frac{n}{4n+6}\]
B) \[\frac{1}{6n+4}\]
C) \[\frac{n}{6n+4}\]
D) \[\frac{n}{3n+7}\]
View Answer play_arrowquestion_answer160) The ten's digit in \[1!4!+7!+10!+12!+13!+15!+16!+17!\]is divisible by
A) \[4\]
B) \[3!\]
C) \[5\]
D) \[7\]
View Answer play_arrowquestion_answer161) The value of \[\int_{-2}^{2}{(a{{x}^{3}}+bx+c)}dx\] depends on the
A) value of b
B) value of c
C) value of a
D) values of a and b
View Answer play_arrowquestion_answer162) The area of the region bounded by \[y=2x-{{x}^{2}}\]and the x -axis is
A) \[\frac{8}{3}sq\,unit\]
B) \[\frac{4}{3}sq\,unit\]
C) \[\frac{7}{3}sq\,unit\]
D) \[\frac{2}{3}sq\,unit\]
View Answer play_arrowquestion_answer163) The differential equation \[y\,\frac{dy}{dx}+x=\]represents
A) a family of hyperbolas
B) a family of circles whose centres are on the y-axis
C) a family of parabolas
D) a family of circles whose centres are on the x-axis
View Answer play_arrowquestion_answer164) If \[f({{x}^{5}})=5{{x}^{3}},\]then \[f'(x)\] is equal to
A) \[\frac{3}{\sqrt[5]{{{x}^{2}}}}\]
B) \[\frac{3}{\sqrt[5]{x}}\]
C) \[\frac{3}{x}\]
D) \[\sqrt[5]{x}\]
View Answer play_arrowquestion_answer165) \[f(x)=\left\{ \begin{matrix} 2a-x & in & -a<x<a \\ 3x-2a & in & a\le x \\ \end{matrix} \right.\] Then, which of the following is true?
A) \[f(x)\] is discontinuous at \[x=a\]
B) \[f(x)\] is not differentiable at \[x=a\]
C) \[f(x)\] is differentiable at \[x\ge a\]
D) \[f(x)\] is continuous at all \[x<a\]
View Answer play_arrowquestion_answer166) The maximum area of a rectangle that can be inscribed in a circle of radius 2 unit is (in square unit)
A) \[4\]
B) \[8\pi \]
C) \[8\]
D) \[5\]
View Answer play_arrowquestion_answer167) If z is a complex number such that \[z=-\bar{z},\] then
A) z is purely real
B) z is purely imaginary
C) z is any complex number
D) real part of z is the same as its imaginary part
View Answer play_arrowquestion_answer168) The value of \[\underset{k=1}{\mathop{\overset{6}{\mathop{\Sigma }}\,}}\,\left( \sin \frac{2k\pi }{7}-i\cos \frac{2k\pi }{7} \right)\]is
A) \[i\]
B) \[0\]
C) \[-i\]
D) \[-1\]
View Answer play_arrowquestion_answer169) \[\underset{x\to \infty }{\mathop{\lim }}\,\,x\,\sin \left( \frac{2}{x} \right)\] is equal to
A) \[\infty \]
B) \[0\]
C) \[2\]
D) \[\frac{1}{2}\]
View Answer play_arrowquestion_answer170) A stone is thrown vertically upwards and the height x ft reached by the stone in t seconds is given by\[x=80t-16{{t}^{2}}\]. The stone reaches the maximum height in
A) \[2s\]
B) \[2.5s\]
C) \[3s\]
D) \[1.5s\]
View Answer play_arrowquestion_answer171) The maximum value of \[\frac{\log x}{x}\] in \[(2,\infty )\] is
A) \[1\]
B) \[\frac{2}{e}\]
C) \[e\]
D) \[\frac{1}{e}\]
View Answer play_arrowquestion_answer172) If \[f(x)=b{{e}^{ax}}+a{{e}^{bx}},\] then \[f'(0)\] is equal to
A) \[0\]
B) \[2ab\]
C) \[ab(a+b)\]
D) \[ab\]
View Answer play_arrowquestion_answer173) If \[\sqrt{\frac{1+\cos A}{1-csoA}}=\frac{x}{y},\] then the value of tan A is is equal is
A) \[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}\]
B) \[\frac{2xy}{{{x}^{2}}+{{y}^{2}}}\]
C) \[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}\]
D) \[\frac{2xy}{{{y}^{2}}-{{x}^{2}}}\]
View Answer play_arrowquestion_answer174) \[\int{\frac{\sec \,x}{\sec \,x+\tan x}}dx\]is equal to
A) \[\tan \,x-\sec x+C\]
B) \[\log (1+\sec x)+C\]
C) \[\sec x+\tan \,x+C\]
D) \[\log \sin x+\log \cos x+C\]
View Answer play_arrowquestion_answer175) If \[\int{f(x)\,dx=g(x),}\] then \[\int{f(x)\,g=g(x)\,dx}\] is equal to
A) \[\frac{1}{2}{{f}^{2}}(x)\]
B) \[\frac{1}{2}{{g}^{2}}(x)\]
C) \[\frac{1}{2}{{[g'(x)]}^{2}}\]
D) \[f'(x)g(x)\]
View Answer play_arrowquestion_answer176) The general solution of \[|\sin x|=\cos x\]is (when\[n\,\in \,I\]) given by
A) \[n\pi +\frac{\pi }{4}\]
B) \[2n\,\,\pi \pm \frac{\pi }{4}\]
C) \[n\,\,\pi \pm \frac{\pi }{4}\]
D) \[n\,\,\pi -\frac{\pi }{4}\]
View Answer play_arrowquestion_answer177) The real root of the equation \[{{x}^{3}}-6x+9=0\] is
A) \[-6\]
B) \[-9\]
C) \[6\]
D) \[-3\]
View Answer play_arrowquestion_answer178) The digit in the unit?s place of \[{{5}^{834}}\] is
A) \[0\]
B) \[1\]
C) \[3\]
D) \[5\]
View Answer play_arrowquestion_answer179) The remainder when \[{{3}^{100}}\times {{2}^{50}}\]is divided by 5 is
A) \[1\]
B) \[2\]
C) \[3\]
D) \[4\]
View Answer play_arrowquestion_answer180) \[\int{\frac{\sin x\,\cos x}{\sqrt{1-{{\sin }^{4}}x}}}dx\] is equal to
A) \[\frac{1}{2}{{\sin }^{-1}}({{\sin }^{2}}x)+C\]
B) \[\frac{1}{2}{{\cos }^{-1}}({{\sin }^{2}}x)+C\]
C) \[{{\tan }^{-1}}({{\sin }^{2}}x)+C\]
D) \[{{\tan }^{-1}}(2{{\sin }^{2}}x)+C\]
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