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 jq is incident on a pair of Nichols making an angle of\[60{}^\circ \]with each other. The intensity of light emerging from the pair is
A) \[{{I}_{0}}\]
B) \[{{I}_{0}}/2\]
C) \[{{I}_{0}}/4\]
D) \[{{I}_{0}}/8\]
View Answer play_arrowquestion_answer4) 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_answer5) The term liquid crystal refers to a state that is intermediate between
A) crystalline solid and amorphous liquid
B) crystalline solid and vapour
C) amorphous liquid and its vapour
D) a crystal immersed in a liquid
View Answer play_arrowquestion_answer6) 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 magenetic flux occuring due to the passage of aircraft
D) vibration created by the passage of aircraft
View Answer play_arrowquestion_answer7) 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 oil 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_answer8) 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_answer9) 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) 1.5V
D) 8.5V
View Answer play_arrowquestion_answer10) A galvanometer coil has a resistance of 150 and gives full scale deflection for a current of 4 mA. To convert it to an ammeter of range 0 to 6 A
A) \[10\text{ }m\text{ }\Omega \]resistance is to be connected in parallel to the galvanometer
B) \[10\text{ }m\text{ }\Omega \]resistance is to be connected in series with the galvanometer
C) \[\text{0}\text{.1 }\Omega \] resistance is to be connected in parallel to the galvanometer
D) \[\text{0}\text{.1 }\Omega \]resistance is to be connected in series with the galvanometer
View Answer play_arrowquestion_answer11) 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_answer12) 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\[g=9.8\text{ }m{{s}^{-2}}\])
A) 2
B) 1.5
C) 0.55
D) 0.65
View Answer play_arrowquestion_answer13) In the circuit shown the value of I in ampere is
A) 1
B) 0.60
C) 0.4
D) 1.5
View Answer play_arrowquestion_answer14) 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_answer15) 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_answer16) A comb run through ones 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 in the paper get polarised by the charged comb
D) the comb possesses magnetic properties
View Answer play_arrowquestion_answer17) The top of the atmosphere is about 400 kV with respect to the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about\[100\text{ }V{{m}^{-1}}\]. Still, we do not get an electric shock as we step out of our house into the open house .because (assume the house to be a steel cage so that there is no field inside)
A) there is a potential difference between our body and the ground
B) \[100\text{ }V{{m}^{-1}}\]is not a high electric field so that we do not feel the shock
C) our body and the ground forms an equipotential surface
D) the dry atmosphere is not a conductor
View Answer play_arrowquestion_answer18) 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) \[2.4\times {{10}^{7}}k{{g}^{-1}}\]
View Answer play_arrowquestion_answer19) 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_answer20) 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_answer21) 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_answer22) 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_answer23) Which of the following figures represents the variation of particle momentum and associated de-Broglle wavelength?
A)
B)
C)
D)
View Answer play_arrowquestion_answer24) 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_answer25) 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_answer26) 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) 0.06m
B) 0.17m
C) 0.05m
D) 0.04m
View Answer play_arrowquestion_answer27) White light is incident on one of the refracting surfaces of a prism of angle\[5{}^\circ \]. If the refractive indices for red and blue colours are 1.641 and 1.659 respectively, the angular separation between these two colours when they emerge out of the prism is
A) \[0.9{}^\circ \]
B) \[0.09{}^\circ \]
C) \[1.8{}^\circ \]
D) \[1.2{}^\circ \]
View Answer play_arrowquestion_answer28) For a given lens, the magnification was found to be twice as large as when the object was 0.15 m distant from It as when the distance was 0.2 m. The focal length of the lens is
A) 1.5m
B) 0.20m
C) 0.10m
D) 0.05m
View Answer play_arrowquestion_answer29) 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_answer30) A thin prism\[{{P}_{1}}\]with angle\[4{}^\circ \]made from a glass of refractive index 1.54 is combined with another thin prism\[{{P}_{2}}\]made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism\[{{P}_{2}}\]is
A) \[5.33{}^\circ \]
B) \[4{}^\circ \]
C) \[3{}^\circ \]
D) \[2.6{}^\circ \]
View Answer play_arrowquestion_answer31) If white light is used in the Newtons 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) \[90{}^\circ \]change of phase in one of the reflected waves
B) \[180{}^\circ \]change of phase in one of the reflected waves
C) \[145{}^\circ \]change of phase in one of the reflected waves
D) \[45{}^\circ \]change of phase in one the reflected Waves
View Answer play_arrowquestion_answer32) Specific rotation of sugar solution is\[~0.5\text{ }deg\text{ }{{m}^{2}}/kg\].\[200\text{ }kg\,{{m}^{-3}}\] of impure sugar solution is taken in a sample polar meter tube of length 20 cm and optical rotation is found to be\[19{}^\circ \]. The percentage of purity of sugar is
A) 20%
B) 80%
C) 95%
D) 89%
View Answer play_arrowquestion_answer33) A simple pendulum has a length? and the mass of the bob is m. The bob is given a charge q coulomb. The pendulum is suspended between the vertical plates of a charged parallel plate capacitor. If? is the electric field strength between the plates, the time period of the pendulum is given by
A) \[2\pi \sqrt{\frac{l}{g}}\]
B) \[2\pi \sqrt{\frac{l}{\sqrt{g+\frac{qE}{m}}}}\]
C) \[2\pi \sqrt{\frac{l}{\sqrt{g-\frac{qE}{m}}}}\]
D) \[2\pi \sqrt{\frac{l}{\sqrt{{{g}^{2}}-{{\left( \frac{qE}{m} \right)}^{2}}}}}\]
View Answer play_arrowquestion_answer34) A gang capacitor is formed by interlocking a number of plates as shown in figure. The distance between the consecutive plates is 0.885 cm and the overlapping area of the plates is\[5\text{ }c{{m}^{2}}\]. The capacity of the unit is
A) 1.06 pF
B) 4 pF
C) 6.36p F
D) 12.72 pF
View Answer play_arrowquestion_answer35) A satellite in a circular orbit of radius R has a period of 4 h. Another satellite with orbital radius 3 R 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_answer36) 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_answer37) The unit of Stefans constant is
A) \[W{{m}^{-2}}{{K}^{-1}}\]
B) \[Wm{{K}^{-4}}\]
C) \[W{{m}^{-2}}{{K}^{-4}}\]
D) \[N{{m}^{-2}}{{K}^{-4}}\]
View Answer play_arrowquestion_answer38) 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_answer39) A Carnot engine takes heat from a reservoir at \[627{}^\circ C\]and rejects heat to a sink at\[27{}^\circ C\]. Its efficiency will be
A) 3/5
B) 1/3
C) 2/3
D) 200/209
View Answer play_arrowquestion_answer40) A 30 y 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_answer41) Maximum velocity of the photoelectrons emitted by a metal surface is\[1.2\times {{10}^{6}}m{{s}^{-1}}\]. Assuming the specific charge of the electron to be\[1.8\times {{10}^{11}}C\text{ }k{{g}^{-1}},\] the value of the stopping potential in volt will be
A) 2
B) 3
C) 4
D) 6
View Answer play_arrowquestion_answer42) 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_answer43) When the length of the vibrating segment of a sonometer wire is increased by 1%, the percentage change in its frequency is
A) \[\frac{100}{101}\]
B) \[\frac{99}{100}\]
C) \[1\]
D) \[2\]
View Answer play_arrowquestion_answer44) 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 vaporization
D) water is a bad conductor of heat
View Answer play_arrowquestion_answer45) 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_answer46) 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_answer47) 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\[200\text{ }km{{h}^{-1}}\]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_answer48) 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_answer49) 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_answer50) In a LCR series circuit, the potential difference between the terminals of the inductance is 60 V between the terminals of the capacitor is 30V 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_answer51) 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_answer52) 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) \[2\pi \times {{10}^{-2}}T\]
D) \[2\pi \times {{10}^{-3}}T\]
View Answer play_arrowquestion_answer53) To a germanium crystal equal number of aluminium and indium atoms are added. Then
A) it remains an intrinsic semiconductor
B) it becomes a n-type semiconductor
C) it becomes a p-type semiconductor
D) it becomes an insulator
View Answer play_arrowquestion_answer54) 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_answer55) A current of 6 A enters one corner P of an equilateral triangle PQR having 3 wires of resistances\[2\,\Omega \]each and leaves by the corner R. Then the current\[{{I}_{1}}\]and\[{{I}_{2}}\]are
A) 2 A, 4 A
B) 4 A, 2 A
C) 1A, 2A
D) 2A, 3A
View Answer play_arrowquestion_answer56) Which of the following is not an ore of magnesium?
A) Carnal lite
B) Dolomite
C) Calamine
D) Sea water
View Answer play_arrowquestion_answer57) The atomic number of Ni and Cu are 28 and 29 respectively. The electronic configuration. \[1{{s}^{2}}\text{ }2{{s}^{2}}\text{ }2{{p}^{6}}\text{ }3{{s}^{2}}\text{ }3{{p}^{6}}\text{ }3{{d}^{10}}\]represents
A) \[C{{u}^{+}}\]
B) \[C{{u}^{2+}}\]
C) \[N{{i}^{2+}}\]
D) \[Ni\]
View Answer play_arrowquestion_answer58) In the following, the element with the highest ionlsatlon 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_answer59) 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_answer60) 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_answer61) Which of the following represents the Lewis structure of \[{{N}_{3}}\] molecule?
A) \[_{\times }^{\times }N\equiv N_{\times }^{\times }\]
B) \[_{\times }^{\times }\overset{\times \,\,\,\,\,\times }{\mathop{N}}\,\equiv \overset{\times \,\,\,\,\,\times }{\mathop{N}}\,\,_{\times }^{\times }\]
C) \[_{\times }^{\times }\overset{\times \,\,\,\,\,\times }{\mathop{N}}\,\,_{\times }^{\times }-\underset{\times \,\,\,\,\,\,\,\times }{\overset{\times \,\,\,\,\,\,\times }{\mathop{N}}}\,\,_{\times }^{\times }\]
D) \[_{\times }^{\times }\underset{\times \,\,\,\,\,\,\,\times }{\overset{\times \,\,\,\,\,\,\times }{\mathop{N}}}\,=\underset{\times \,\,\,\,\,\,\,\times }{\overset{\times \,\,\,\,\,\,\times }{\mathop{N}}}\,\,_{\times }^{\times }\]
View Answer play_arrowquestion_answer62) Hydrogen bond is strongest in
A) \[S-H...O\]
B) \[O-H...S\]
C) \[F-H...F\]
D) \[O-H...N\]
View Answer play_arrowquestion_answer63) The decomposition of a certain mass of\[CaC{{O}_{3}}\] gave\[11.2\text{ }d{{m}^{3}}\]of\[C{{O}_{2}}\]gas at STR The mass of \[KOH\]required to completely neutralise the gas is
A) 56 g
B) 28 g
C) 42 g
D) 20 g
View Answer play_arrowquestion_answer64) The density of a gas is\[1.964\text{ }g\text{ }d{{m}^{-3}}\]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_answer65) 0.06 mole of\[KN{{O}_{3}}\]solid is added to\[100\text{ }c{{m}^{3}}\]of water at 298K. The enthalpy of \[KN{{O}_{3}}\]aqueous solution is\[35.8\text{ }kJ\text{ }mo{{l}^{-1}}\]. After the solute is dissolved die temperature of die solution will be
A) 293 K
B) 298 K
C) 301 K
D) 304 K
View Answer play_arrowquestion_answer66) 4 moles each of\[S{{O}_{2}}\]and\[{{O}_{2}}\]gases are allowed to react to form\[S{{O}_{2}}\]in a closed vessel. At equilibrium 25% of\[{{O}_{2}}\]is used up. The total number of moles of all the gases at equilibrium is
A) 6.5
B) 7.0
C) 8.0
D) 2.0
View Answer play_arrowquestion_answer67) An example for autocatalysis is
A) oxidation of\[NO\]to\[N{{O}_{2}}\]
B) oxidation of\[S{{O}_{2}}\]to\[S{{O}_{3}}\]
C) decomposition of\[KCl{{O}_{3}}\]to\[KCl\]and\[{{O}_{2}}\]
D) oxidation of oxalic acid by acidified\[KMn{{O}_{4}}\]
View Answer play_arrowquestion_answer68) During the fusion of an organic compound with sodium metal, nitrogen of the compound is converted into
A) \[NaN{{O}_{2}}\]
B) \[NaN{{H}_{2}}\]
C) \[NaCN\]
D) \[NaNC\]
View Answer play_arrowquestion_answer69) Identify the product Y in the following reaction sequence \[\underset{C{{H}_{2}}-C{{H}_{2}}-COO}{\overset{C{{H}_{2}}-C{{H}_{2}}-COO}{\mathop{|}}}\,Ca\xrightarrow[{}]{heat}X\xrightarrow[HCl,heat]{Zn-Hg}Y\]
A) pentane
B) cyclobutane
C) cyclopentane
D) cyclopentanone
View Answer play_arrowquestion_answer70) The reaction\[{{C}_{2}}{{H}_{5}}ONa+{{C}_{2}}{{H}_{5}}I\to {{C}_{2}}{{H}_{5}}O{{C}_{2}}{{H}_{5}}\]\[+NaI\]is known as
A) Kolbes synthesis
B) Wurtzs synthesis
C) Williamsons synthesis
D) Grignards synthesis
View Answer play_arrowquestion_answer71) \[\Delta G{}^\circ vsT\] plot in the Ellinghams diagram slopes downwards for the reactions
A) \[Mg+\frac{1}{2}{{O}_{2}}\xrightarrow[{}]{{}}MgO\]
B) \[2Ag+\frac{1}{2}{{O}_{2}}\xrightarrow[{}]{{}}A{{g}_{2}}O\]
C) \[CO+\frac{1}{2}{{O}_{2}}\xrightarrow[{}]{{}}C{{O}_{2}}\]
D) All of the above
View Answer play_arrowquestion_answer72) Which of the following taking place in the blast furnace is endothermic?
A) \[CaC{{O}_{3}}\xrightarrow[{}]{{}}CaO+C{{O}_{2}}\]
B) \[2C+{{O}_{2}}\xrightarrow[{}]{{}}2CO\]
C) \[C+{{O}_{2}}\xrightarrow[{}]{{}}C{{O}_{2}}\]
D) \[F{{e}_{2}}{{O}_{3}}+CO\xrightarrow[{}]{{}}2Fe+3C{{O}_{2}}\]
View Answer play_arrowquestion_answer73) Liquor ammonia bottles are opened only after cooling. This is because
A) it is a mild explosive
B) it generates high vapour pressure
C) Both (a) and (b)
D) it is a lachrymatory
View Answer play_arrowquestion_answer74) The formation of\[O_{2}^{+}{{[Pt{{F}_{6}}]}^{-}}\]is the basis for the formation of xenon fluorides. This is because
A) \[{{O}_{2}}\]and\[Xe\]have comparable sizes
B) Both\[{{O}_{2}}\]and\[Xe\]are gases
C) \[{{O}_{2}}\]and\[Xe\] have comparable lonisation energies
D) Both (a) and (c)
View Answer play_arrowquestion_answer75) The highest magnetic moment is shown by the transition metal ion with the configuration
A) \[3{{d}^{2}}\]
B) \[3{{d}^{5}}\]
C) \[3{{d}^{7}}\]
D) \[3{{d}^{9}}\]
View Answer play_arrowquestion_answer76) A transition metal ion exists in its highest oxidation state. It is expected to behave as
A) a chelating agent
B) a central metal in a coordination compound
C) an oxidising agent
D) a reducing agent
View Answer play_arrowquestion_answer77) In which of the following complex ion, the central metal ion is in a state of\[s{{p}^{3}}{{d}^{2}}\] hybridisation?
A) \[{{[Co{{F}_{6}}]}^{3-}}\]
B) \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
C) \[{{[Fe{{(CN)}_{6}}]}^{3-}}\]
D) \[{{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}\]
View Answer play_arrowquestion_answer78) Which of the following can participate in linkage isomerism?
A) \[NO_{2}^{-}\]
B) \[{{H}_{2}}\overset{\bullet \,\bullet }{\mathop{N}}\,C{{H}_{2}}C{{H}_{2}}\overset{\bullet \,\bullet }{\mathop{N}}\,{{H}_{2}}\]
C) \[H{{e}_{2}}\]
D) \[{}_{\bullet }^{\bullet }N{{H}_{3}}\]
View Answer play_arrowquestion_answer79) Which of the following has the highest bond order?
A) \[{{N}_{3}}\]
B) \[{{O}_{2}}\]
C) \[H{{e}_{2}}\]
D) \[{{H}_{2}}\]
View Answer play_arrowquestion_answer80) Which of the following is diamagnetic?
A) \[{{H}_{2}}\]
B) \[{{O}_{2}}\]
C) \[L{{i}_{2}}\]
D) \[H{{e}_{2}}\]
View Answer play_arrowquestion_answer81) The concentration of a reactant\[X\]decreases from 0.1 M to 0.005 M in 40 minute. If the reaction follows 1 order kinetics, the rate of the reaction when the concentration of\[X\]is M will be
A) \[1.73\times {{10}^{-4}}M\,mi{{n}^{-1}}\]
B) \[3.47\times {{10}^{-4}}M\text{ }mi{{n}^{-1}}\]
C) \[3.47\times 10\,M\,{{\min }^{-1}}\]
D) \[7.5\times {{10}^{-4}}M\,{{\min }^{-1}}\]
View Answer play_arrowquestion_answer82) Chemical reactions with very high\[{{E}_{a}}\]values are generally
A) very fast
B) very slow
C) moderately fast
D) spontaneous
View Answer play_arrowquestion_answer83) Which of the following does not conduct electricity?
A) Fused\[NaCl\]
B) Solid\[NaCl\]
C) Brine solution
D) Copper
View Answer play_arrowquestion_answer84) When a quantity of electricity is passed through\[CuS{{O}_{4}}\]solution, 0.16 g of copper gets deposited. If the same quantity of electricity is passed through acidulated water, then the volume of\[{{H}_{2}}\]liberated at STP will be [given: atomic weight of\[Cu=64\]]
A) \[4.0\,c{{m}^{3}}\]
B) \[56\,c{{m}^{3}}\]
C) \[604\,c{{m}^{3}}\]
D) \[8.0\,c{{m}^{3}}\]
View Answer play_arrowquestion_answer85) 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_answer86) Which one of the following condition will increase the voltage of the cell represented by the equation? \[Cu(s)+2A{{g}^{+}}(aq)C{{u}^{2+}}(aq)+2Ag(s)\]
A) Increase in the dimension of\[Cu\]electrode
B) Increase in the dimension of\[Ag\]electrode
C) Increase in the concentration of\[C{{u}^{2+}}\]ions
D) Increase in the concentration of\[A{{g}^{+}}\]ions
View Answer play_arrowquestion_answer87) The pH of\[{{10}^{-8}}M\text{ }HCl\]solution is
A) 8
B) more than 8
C) between 6 and 7
D) slightly more than 7
View Answer play_arrowquestion_answer88) The mass of glucose that should be dissolved in 50 g of water in order to produce the same lowering of vapour pressure as is produced by dissolving 1 g of urea in the same quantity of water is
A) \[1\,g\]
B) \[3\,g\]
C) \[6\,g\]
D) \[18\,g\]
View Answer play_arrowquestion_answer89) Osmotic pressure observed when benzoic acid is dissolved in benzene is less than that expected from theoretical considerations. This is because
A) benzoic acid is an organic solute
B) benzoic acid has higher molar mass than benzene
C) benzoic acid gets associated in benzene
D) benzoic acid gets dfesefciated in benzene
View Answer play_arrowquestion_answer90) 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_answer91) Which of the following electrolyte 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_answer92) For a reversible reaction: \[X(g)+3Y(g)2Z(g);\]\[\Delta H=-40\,kJ,\]the standard entropies of\[X,Y\]and Z are 60, 40 and \[50~J{{K}^{-1}}mo{{l}^{-1}}\] respectively The temperature at which the above reaction attains equilibrium is about
A) 400 K
B) 500 K
C) 273 K
D) 373 K
View Answer play_arrowquestion_answer93) The radii of\[N{{a}^{+}}\]and\[C{{l}^{-}}\]ions are 95 pm and 181 pm respectively. The edge length of\[NaCl\]unit cell is
A) 276pm
B) 138pm
C) 552 pm
D) 415 pm
View Answer play_arrowquestion_answer94) 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_answer95) The basicity of aniline is less than that of cyclohexylamine. This is due to
A) \[+R-\]effect of\[-N{{H}_{2}}\] group
B) \[-I\]effect of\[-N{{H}_{2}}\]group
C) \[-R\]effect of\[-N{{H}_{2}}\]group
D) hyper conjugation effect
View Answer play_arrowquestion_answer96) Mefthyl bromide is converted into ethane by heating it in ether medium with
A) \[Al\]
B) \[Zn\]
C) \[Na\]
D) \[Cu\]
View Answer play_arrowquestion_answer97) 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_answer98) Which cycloalkane has the lowest heat of combustion per\[C{{H}_{2}}\]group?
A) Cyclopropane
B) Cyclobutane
C) Cyclopentane
D) Cyclohexane
View Answer play_arrowquestion_answer99) The catalyst used in the preparation of an alkyl chloride by the action of dry\[HCl\]on an alcohol is
A) anhydrous \[AlC{{l}_{3}}\]
B) \[FeC{{l}_{3}}\]
C) anyhydrous \[ZnC{{l}_{2}}\]
D) \[Cu\]
View Answer play_arrowquestion_answer100) In the reaction,\[R-X\xrightarrow[{}]{alcoholic\text{ }KCN}A\xrightarrow[{}]{dilute\text{ }HCl}B\] The product B is
A) alkyl chloride
B) aldehyde
C) carboxylic acid
D) ketone
View Answer play_arrowquestion_answer101) Which of the following compound would not evolve\[C{{O}_{2}}\]when treated with\[NaHC{{O}_{3}}\] solution?
A) Salicylic acid
B) Phenol
C) Benzoic acid
D) 4-nitrobenzoic acid
View Answer play_arrowquestion_answer102) 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_answer103) When a mixture of calcium benzoate and calcium acetate is dry distilled, the resulting compound is
A) acetophenone
B) benzaldehyde
C) benzophenone
D) acetaldehyde
View Answer play_arrowquestion_answer104) 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_answer105) Which of the following would undergo Hofmann reaction to give a primary amine?
A) \[R-\overset{\begin{smallmatrix} O \\ |\,| \end{smallmatrix}}{\mathop{C}}\,-Cl\]
B) \[RCONHC{{H}_{3}}\]
C) \[RCON{{H}_{2}}\]
D) \[RCOOR\]
View Answer play_arrowquestion_answer106) 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_answer107) A distinctive and characteristic functional group of fats is
A) a peptide group
B) an ester group
C) an alcoholic group
D) a ketonic group
View Answer play_arrowquestion_answer108) At\[pH=4,\]glycine exists as
A) \[{{H}_{3}}\overset{+}{\mathop{N}}\,C{{H}_{2}}CO{{O}^{-}}\]
B) \[{{H}_{3}}\overset{+}{\mathop{N}}\,C{{H}_{2}}COOH\]
C) \[{{H}_{2}}NC{{H}_{2}}COOH\]
D) \[{{H}_{2}}NC{{H}_{2}}CO{{O}^{-}}\]
View Answer play_arrowquestion_answer109) Insulin regulates the metabolism of
A) minerals
B) amino acids
C) glucose
D) vitamins
View Answer play_arrowquestion_answer110) The formula mass of Mohrs salt is 392. The. iron present in it is oxidised by\[KMn{{O}_{4}}\]in acid medium. The equivalent mass of Mohrs salt is
A) 392
B) 31.6
C) 278
D) 156
View Answer play_arrowquestion_answer111) If\[\alpha ,\beta \]and\[\gamma \]are the roots of the equation \[{{x}^{3}}-8x+8=0,\]then\[\Sigma {{\alpha }^{2}}\]and\[\Sigma \frac{1}{\alpha \beta }\]are respectively
A) 0 and\[-16\]
B) 16 and 18
C) \[-16\]and 0
D) 16 and 0
View Answer play_arrowquestion_answer112) \[x=4(1+\cos \theta )\]and\[y=3(1+\sin \theta )\]are the parametric equations of
A) \[\frac{{{(x-3)}^{2}}}{9}+\frac{{{(y-4)}^{2}}}{16}=1\]
B) \[\frac{{{(x+4)}^{2}}}{16}+\frac{{{(y-3)}^{2}}}{9}=1\]
C) \[\frac{{{(x-4)}^{2}}}{16}-\frac{{{(y-3)}^{2}}}{9}=1\]
D) \[\frac{{{(x-4)}^{2}}}{16}+\frac{{{(y-3)}^{2}}}{9}=1\]
View Answer play_arrowquestion_answer113) If the distance between the foci and the distance between the directrices of the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]are in the ratio\[3:2,\] then\[a:b\]is
A) \[\sqrt{2}:1\]
B) \[\sqrt{3}:\sqrt{2}\]
C) \[1:2\]
D) \[2:1\]
View Answer play_arrowquestion_answer114) The ellipse\[\sec \theta =m\]and\[\tan \theta =n,\]the hyperbola\[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{16}=1\]have in common
A) centre only
B) centre, foci and directrices
C) centre, foci and vertices
D) centre and vertices only
View Answer play_arrowquestion_answer115) If\[\sec \theta =m\]and\[\tan \theta =n,\]then \[\frac{1}{m}\left[ (m+n)+\frac{1}{(m+n)} \right]\]is
A) \[2\]
B) \[2m\]
C) \[2n\]
D) \[mn\]
View Answer play_arrowquestion_answer116) The value of\[\frac{\sin 85{}^\circ -\sin 35{}^\circ }{\cos 65{}^\circ }\]is
A) 2
B) \[-1\]
C) 1
D) \[0\]
View Answer play_arrowquestion_answer117) If the length of the tangent from any point on the circle\[{{(x-3)}^{2}}+{{(y+2)}^{2}}=5{{r}^{2}}\]to the circle \[{{(x-3)}^{2}}+{{(y+2)}^{2}}={{r}^{2}}\]is 16 unit, then the area between the two circles in sq unit is
A) \[32\pi \]
B) \[4\pi \]
C) \[8\pi \]
D) \[256\pi \]
View Answer play_arrowquestion_answer118) The circles\[a{{x}^{2}}+a{{y}^{2}}+2{{g}_{1}}x+2{{f}_{1}}y+{{c}_{1}}=0\] and \[b{{x}^{2}}+b{{y}^{2}}+2{{g}_{2}}x+2{{f}_{2}}y+{{c}_{2}}=0\] (\[a\ne 0\]and\[b\ne 0\])cut orthogonally if
A) \[{{g}_{1}}{{g}_{2}}+{{f}_{1}}{{f}_{2}}=a{{c}_{1}}+b{{c}_{1}}\]
B) \[2({{g}_{1}}{{g}_{2}}+{{f}_{1}}{{f}_{2}})=b{{c}_{1}}+a{{c}_{1}}\]
C) \[b{{g}_{1}}{{g}_{2}}+a{{f}_{1}}{{f}_{2}}=b{{c}_{1}}+a{{c}_{1}}\]
D) \[{{g}_{1}}{{g}_{2}}+{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\]
View Answer play_arrowquestion_answer119) The equation of the common tangent of the two touching circles,\[{{y}^{2}}+{{x}^{2}}-6x-12y+37=0\]and\[{{x}^{2}}+{{y}^{2}}-6y+7=0\]is
A) \[x-y-5=0\]
B) \[x-y+5=0\]
C) \[x-y-5=0\]
D) \[x+y+5=0\]
View Answer play_arrowquestion_answer120) The equation of the parabola with vertex at \[(-1,1)\]and focus (2, 1) is
A) \[{{y}^{2}}-2y-12x-11=0\]
B) \[{{x}^{2}}+2x-12y+13=0\]
C) \[{{y}^{2}}-2y+12x+11=0\]
D) \[{{y}^{2}}-2y-12x+13=0\]
View Answer play_arrowquestion_answer121) The equation of the line which is tangent to both the circle\[{{x}^{2}}+{{y}^{2}}=5\]and the parabola \[{{y}^{2}}=40x\]is
A) \[2x-y\pm 5=0\]
B) \[2x-y+5=0\]
C) \[2x-y-5=0\]
D) \[2x+y+5=0\]
View Answer play_arrowquestion_answer122) If\[2A+3B=\left[ \begin{matrix} 2 & -1 & 4 \\ 3 & 2 & 5 \\ \end{matrix} \right]\]and\[A+2B=\left[ \begin{matrix} 5 & 0 & 3 \\ 1 & 6 & 2 \\ \end{matrix} \right],\]then B is
A) \[\left[ \begin{matrix} 8 & -1 & 2 \\ -1 & 10 & -1 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 8 & 1 & 2 \\ -1 & 10 & -1 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 8 & 1 & -2 \\ -1 & 10 & -1 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 8 & 1 & 2 \\ 1 & 10 & 1 \\ \end{matrix} \right]\]
View Answer play_arrowquestion_answer123) If\[O(A)=2\times 3,O(B)=3\times 2,\]and\[O(C)=3\times 3,\]which one of the following is not defined?
A) \[CB+A\]
B) \[BAC\]
C) \[C(A+B)\]
D) \[C(A+B)\]
View Answer play_arrowquestion_answer124) If\[A=\left[ \begin{matrix} 1 & -3 \\ 2 & k \\ \end{matrix} \right]\]and\[{{A}^{2}}-4A+10I=A,\]then k is equal to
A) 0
B) \[-4\]
C) 4 and not 1
D) 1 or 4
View Answer play_arrowquestion_answer125) The value of \[\left| \begin{matrix} x+y & y+z & z+x \\ x & y & z \\ x-y & y-z & z-x \\ \end{matrix} \right|\]is equal to:
A) \[2{{(x+y+z)}^{2}}\]
B) \[2{{(x+y+z)}^{3}}\]
C) \[{{(x+y+z)}^{3}}\]
D) \[0\]
View Answer play_arrowquestion_answer126) From an aeroplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the sameside of the aeroplane are observed to be\[30{}^\circ \]and\[60{}^\circ \]respectively The height at which the aeroplane is flying in km is
A) \[\frac{4}{\sqrt{3}}\]
B) \[\frac{\sqrt{3}}{2}\]
C) \[\frac{2}{\sqrt{3}}\]
D) \[2\]
View Answer play_arrowquestion_answer127) If the angles of a triangle are in the ratio\[3:4:5,\]then the sides are in the ratio ,
A) \[2:\sqrt{6}:\sqrt{3}+1\]
B) \[\sqrt{2}:\sqrt{6}:\sqrt{3}+1\]
C) \[2:\sqrt{3}:\sqrt{3}+1\]
D) \[3:4:5\]
View Answer play_arrowquestion_answer128) If\[{{\cos }^{-1}}x=\alpha ,(0<x<1)\]and\[{{\sin }^{-1}}(2x\sqrt{1-{{x}^{2}}})+{{\sec }^{-1}}\left( \frac{1}{2{{x}^{2}}-1} \right)=\frac{2\pi }{3},\] then \[{{\tan }^{-1}}(2x)\]equals
A) \[\pi /6\]
B) \[\pi /4\]
C) \[\pi /3\]
D) \[\pi /2\]
View Answer play_arrowquestion_answer129) If\[a>b>0,\]then the value of\[{{\tan }^{-1}}\left( \frac{a}{b} \right)+{{\tan }^{-1}}\left( \frac{a+b}{a-b} \right)\]depends on
A) both a and b
B) band not a
C) a and not b
D) neither a nor b
View Answer play_arrowquestion_answer130) Which one of the following equations has no solution?
A) (a) \[\cos ec\theta -\sec \theta =\cos ec\theta .\sec \theta \]
B) (b)\[\cos ec\theta .\sec \theta =1\]
C) \[\cos \theta +\sin \theta =\sqrt{2}\]
D) \[\sqrt{3}\sin \theta -\cos \theta =2\]
View Answer play_arrowquestion_answer131) If A = {a, b, c}, B = {b, c, d} and C = {a, d, c}, then \[(A-B)\times (B\cap C)\]is equal to
A) {(a, c), (a, d)}
B) {(a, b), fc d)}
C) {(c a), (d, a)}
D) {(a, c), (a, d). (b, d)}
View Answer play_arrowquestion_answer132) The function\[f:X\to Y\]defined by \[f(x)=\sin x\]is one-one but not onto, if\[X\]and Y are respectively equal to
A) R and R
B) \[[0,\pi ]\]and [0,1]
C) \[\left[ 0,\frac{\pi }{2} \right]\]and \[[-1,1]\]
D) \[\left[ \frac{-\pi }{2},\frac{\pi }{2} \right]\]and \[[-1,1]\]
View Answer play_arrowquestion_answer133) If\[lo{{g}_{4}}2+lo{{g}_{4}}4+lo{{g}_{4}}x+lo{{g}_{4}}16=6,\]then value of\[x\]is
A) 64
B) 4
C) 8
D) 32
View Answer play_arrowquestion_answer134) If \[{{S}_{n}}=\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+....\]to\[n\]terms, then\[6{{S}_{n}}\]equals
A) \[\frac{5n-4}{5n+6}\]
B) \[\frac{n}{(5n+6)}\]
C) \[\frac{2n-1}{5n+6}\]
D) \[\frac{1}{(5n+6)}\]
View Answer play_arrowquestion_answer135) If\[\overrightarrow{p}=\hat{i}+\hat{j},\overrightarrow{q}=4\hat{k}-\hat{j}\]and\[\overrightarrow{r}=\hat{i}+\hat{k}\]then the unit vector in the direction of\[3\overrightarrow{p}+\overrightarrow{q}-2\overrightarrow{r}\]is
A) \[\frac{1}{3}(\hat{i}+2\hat{j}+2\hat{k})\]
B) \[\frac{1}{3}(\hat{i}-2\hat{j}-2\hat{k})\]
C) \[\frac{1}{3}(\hat{i}-2\hat{j}+2\hat{k})\]
D) \[\hat{i}+2\hat{j}+2\hat{k}\]
View Answer play_arrowquestion_answer136) If a and b are the two vectors such that\[|\overrightarrow{a}|=3\sqrt{3},|\overrightarrow{b}|=4\]and\[|\overrightarrow{a}+\overrightarrow{b}|=\sqrt{7},\]then the angle between a and b is
A) \[120{}^\circ \]
B) \[60{}^\circ \]
C) \[30{}^\circ \]
D) \[150{}^\circ \]
View Answer play_arrowquestion_answer137) If the area of the parallelogram with\[\overrightarrow{a}\]and\[\overrightarrow{b}\]as two adjacent sides is 15 sq unit, then the area of the parallelogram having,\[3\overrightarrow{a}+2\overrightarrow{b}\]and\[\overrightarrow{a}+3\overrightarrow{b}\] as two adjacent sides in sq unit is
A) 120
B) 105
C) 75
D) 45
View Answer play_arrowquestion_answer138) The locus of the point which moves such that the ratio of its distance from two fixed point in the plane is always a constant\[k(<1)\]is
A) hyperbola
B) ellipse
C) straight line
D) circle
View Answer play_arrowquestion_answer139) If the lines\[x+3y-9=0,4x+by-2=0\]and\[2x-y-4=0\]are concurrent, then b equals
A) \[-5\]
B) 5
C) 1
D) 0
View Answer play_arrowquestion_answer140) The lines represented by\[a{{x}^{2}}+2gxy+b{{y}^{2}}=0\] are perpendicular to each other, if
A) \[{{h}^{2}}=a+b\]
B) \[a+b=0\]
C) \[{{h}^{2}}=ab\]
D) \[h=0\]
View Answer play_arrowquestion_answer141) The equation of the circle having\[x-y-2=0\]and\[x-y+2=0\]as two tangents and\[x-y=0\]as a diameter is
A) \[{{x}^{2}}+{{y}^{2}}+2x-2y+1=0\]
B) \[{{x}^{2}}+{{y}^{2}}-2x+2y-1=0\]
C) \[{{x}^{2}}+{{y}^{2}}=2\]
D) \[{{x}^{2}}+{{y}^{2}}=1\]
View Answer play_arrowquestion_answer142) If the curve\[y=2{{x}^{3}}+a{{x}^{2}}+bx+c\]passes through the origin and the tangents drawn to it at\[x=-1\]and\[x=2\]are parallel to the\[x-\]axis, then the values of a, b and c are respectively
A) \[12,-3\]and 0
B) \[-3,-12\]and 0
C) \[-3,12\]and 0
D) \[3,-12\]and 0
View Answer play_arrowquestion_answer143) A circular sector of perimeter 60 m with maximum area is to be constructed. The radius of the circular arc in metre must be
A) 20
B) 5
C) 15
D) 10
View Answer play_arrowquestion_answer144) The tangent and the normal drawn to the curve\[y={{x}^{2}}-x+4\]at P(1, 4) tut the\[x-\]axis at A and B respectively. If the length of the subtangent drawn to the curve at P is equal to the length of the subnormal, then the area of the triangle PAB in sq unit is
A) 4
B) 32
C) 8
D) 16
View Answer play_arrowquestion_answer145) \[\int{\frac{({{x}^{3}}+3{{x}^{2}}+3x+1)}{{{(x+1)}^{5}}}}dx\]is equal to
A) \[-\frac{1}{(x+1)}+c\]
B) \[\frac{1}{5}\log (x+1)+c\]
C) \[\log (x+1)+c\]
D) \[{{\tan }^{-1}}x+c\]
View Answer play_arrowquestion_answer146) \[\int{\frac{\cos ecx}{{{\cos }^{2}}\left( 1+\log \tan \frac{x}{2} \right)}}dx\]is equal to
A) \[{{\sin }^{2}}\left[ 1+\log \tan \frac{x}{2} \right]+c\]
B) \[\tan \left[ 1+\log \tan \frac{x}{2} \right]+c\]
C) \[{{\sec }^{2}}\left[ 1+\log \tan \frac{x}{2} \right]+c\]
D) \[-\tan \left[ 1+\log \tan \frac{x}{2} \right]+c\]
View Answer play_arrowquestion_answer147) The complex number\[\frac{(-\sqrt{3}+3i)(1-i)}{(3+\sqrt{3}i)(i)(\sqrt{3}+\sqrt{3}i)}\]when represented in the Argand diagram is
A) in the second quadrant
B) in the first quadrant
C) on the y-axis (imaginary axis)
D) on the x-axis (real axis).
View Answer play_arrowquestion_answer148) If\[2x=-1+\sqrt{3}i,\]then the value of\[{{(1-{{x}^{2}}+x)}^{6}}-{{(1-x+{{x}^{2}})}^{6}}\]is equal to
A) 32
B) \[-64\]
C) 64
D) 0
View Answer play_arrowquestion_answer149) The modulus and amplitude of\[{{(1+i\sqrt{3})}^{8}}\]are respectively
A) 256 and\[\frac{\pi }{3}\]
B) 256 and\[\frac{2\pi }{3}\]
C) 2 and\[\frac{2\pi }{3}\]
D) 256 and\[\frac{8\pi }{3}\]
View Answer play_arrowquestion_answer150) The value of\[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{5}^{x}}-{{5}^{-x}}}{2x}\]is
A) log 5
B) 0
C) 1
D) \[2\text{ }log\text{ }5\]
View Answer play_arrowquestion_answer151) Which one of the following is not true always?
A) If\[f(x)\]is not continuous at\[x=a,\]then it is not differentiable at \[x=a\]
B) If\[f(x)\]is continuous at x = a, then it is differentiable at\[x=a\]
C) If\[f(x)\]and\[g(x)\]are differentiable at\[x=a\], then\[f(x)+g(x)\]is also differentiable at\[x=a\]
D) If a function\[f(x)\]is continuous at\[x=a\], then\[\underset{x\to a}{\mathop{\lim }}\,f(x)\]exists
View Answer play_arrowquestion_answer152) \[\int{\frac{dx}{x\sqrt{{{x}^{6}}-16}}}\]is equal to
A) \[\frac{1}{3}{{\sec }^{-1}}\left( \frac{{{x}^{3}}}{4} \right)+c\]
B) \[{{\cos }^{-1}}\left( \frac{{{x}^{3}}}{4} \right)+c\]
C) \[\frac{1}{12}{{\sec }^{-1}}\left( \frac{{{x}^{3}}}{4} \right)+c\]
D) \[{{\sec }^{-1}}\left( \frac{{{x}^{3}}}{4} \right)+c\]
View Answer play_arrowquestion_answer153) If\[{{I}_{1}}=\int_{0}^{\pi /2}{x\sin xdx}\]and\[{{I}_{2}}=\int_{0}^{\pi /2}{x\cos xdx},\]then which one of the following is true?
A) \[{{I}_{1}}+{{I}_{2}}=\frac{\pi }{2}\]
B) \[{{I}_{2}}-{{I}_{1}}=\frac{\pi }{2}\]
C) \[{{I}_{1}}+{{I}_{2}}=0\]
D) \[{{I}_{1}}={{I}_{2}}\]
View Answer play_arrowquestion_answer154) If\[f(x)\]is defined\[[-2,2]\]by\[f(x)=4{{x}^{2}}-3x+1\] and\[g(x)=\frac{f(-x)-f(x)}{{{x}^{2}}+3},\]then\[\int_{-2}^{2}{g(x)}dx\]is equal to
A) 64
B) \[-48\]
C) 0
D) 24
View Answer play_arrowquestion_answer155) The area enclosed between the parabola \[y={{x}^{2}}-x+2\]and the line\[y=x+2\]in sq unit equals
A) 8/3
B) 1/3
C) 2/3
D) 4/3
View Answer play_arrowquestion_answer156) The solution of the differential equation. \[{{e}^{-x}}(y+1)dy+({{\cos }^{2}}x+\sin 2x)y\,dx=0\] subjected to the condition that\[y=1\]when \[x=0\]is
A) \[y+log\text{ }y+{{e}^{x}}co{{s}^{2}}x=2\]
B) \[\log (y+1)+{{e}^{x}}{{\cos }^{2}}x=1\]
C) \[y+\log y={{e}^{x}}{{\cos }^{2}}x\]
D) \[(y+1)+{{e}^{x}}{{\cos }^{2}}x=2\]
View Answer play_arrowquestion_answer157) If\[y=\frac{1}{x}+\frac{1}{{{x}^{2}}}+\frac{1}{{{x}^{3}}}+....\]with\[|x|>1,\]then\[\frac{dy}{dx}\]is
A) \[\frac{{{x}^{2}}}{{{y}^{2}}}\]
B) \[{{x}^{2}}{{y}^{2}}\]
C) \[\frac{{{y}^{2}}}{{{x}^{2}}}\]
D) \[\frac{-{{y}^{2}}}{{{x}^{2}}}\]
View Answer play_arrowquestion_answer158) If\[f(x)\]and\[g(x)\]are two functions with \[g(x)=x-\frac{1}{x}\]and\[fog(x)={{x}^{3}}-\frac{1}{{{x}^{3}}},\]then\[f(x)\]is
A) \[3{{x}^{2}}+3\]
B) \[{{x}^{2}}-\frac{1}{{{x}^{2}}}\]
C) \[1+\frac{1}{{{x}^{2}}}\]
D) \[3{{x}^{2}}+\frac{3}{{{x}^{4}}}\]
View Answer play_arrowquestion_answer159) The derivative of\[{{a}^{\sec x}}\]w.r.t.\[{{a}^{\tan x}}(a>0)\]is
A) \[\sec x{{a}^{\sec x-\tan x}}\]
B) \[\sin x{{a}^{\tan x-\sec x}}\]
C) \[\sin x{{a}^{\sec x-\tan x}}\]
D) \[{{a}^{\sec x-\tan x}}\]
View Answer play_arrowquestion_answer160) For the given data, the calculation corresponding to all values of varis\[(x,\text{ }y)\]is following \[\Sigma {{(x-\overline{x})}^{2}}=36,\Sigma {{(y-\overline{y})}^{2}}=25,\]\[\Sigma (x-\overline{x})(y-\overline{y})=20\] The Karl Pearsons correlation coefficient is
A) 0.2
B) 0.5
C) 0.66
D) 0.33
View Answer play_arrowquestion_answer161) If the variance of\[x=9\]and regression equations are\[4x-5y+33=0\]and \[20x-9y-10=0,\]then the coefficient of correlation between x and y and the variance of y respectively are
A) \[0.6;\text{ }16\]
B) \[0.16;\text{ }16\]
C) \[0.3;\text{ }4\]
D) \[0.6;\text{ }4\]
View Answer play_arrowquestion_answer162) The value of mean, median and made coincides, then the distribution is
A) positive skew ness
B) symmetrical distribution
C) negative skew ness
D) all of the above
View Answer play_arrowquestion_answer163) The volume of the solid generated by revolving the region bounded by\[y={{x}^{2}}+1\]and\[y=2x+1\]about\[x-\]axis is
A) \[\frac{104}{15}\pi \]cu unit
B) \[\frac{42\pi }{15}\]cu unit
C) \[\frac{52\pi }{15}\]cu unit
D) None of these
View Answer play_arrowquestion_answer164) The function \[x\sqrt{1-{{x}^{2}}},(x>0)\]has
A) a local maxima
B) a local minima
C) neither a local maxima nor a local minima
D) None of the above
View Answer play_arrowquestion_answer165) For the curve\[xy={{c}^{2}},\]the subnormal at any point varies as
A) \[\frac{{{x}^{2}}}{{{c}^{2}}}\]
B) \[\frac{{{x}^{3}}}{c}\]
C) \[\frac{{{y}^{2}}}{{{c}^{2}}}\]
D) \[\frac{-{{y}^{3}}}{{{c}^{2}}}\]
View Answer play_arrowquestion_answer166) The acute angle between the line joining the points\[(2,1,-3),(-3,1,7)\]and a line parallel to\[\frac{x-1}{3}=\frac{y}{4}=\frac{z+3}{5}\]through die point\[(-1,0,4)\]is
A) \[{{\cos }^{-1}}\left( \frac{1}{\sqrt{10}} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{1}{5\sqrt{10}} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{7}{5\sqrt{10}} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{3}{5\sqrt{10}} \right)\]
View Answer play_arrowquestion_answer167) The centre of sphere passes through four points (0, 0, 0). (0, 2, 2), (1, 0, 0) and (0, 0, 4) is
A) \[\left( -\frac{1}{2},1,2 \right)\]
B) \[\left( 1,\frac{1}{2},2 \right)\]
C) \[\left( \frac{1}{2},1,2 \right)\]
D) \[\left( \frac{1}{2},1,-2 \right)\]
View Answer play_arrowquestion_answer168) If\[f(x)\]is an odd periodic function with period 2, then\[f(4)\]equals
A) 0
B) 2
C) 4
D) \[-4\]
View Answer play_arrowquestion_answer169) If\[A=\left[ \begin{matrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{matrix} \right],\]then which of the following statement is not correct?
A) A is orthogonal matrix
B) \[A\]is orthogonal matrix
C) Determinant\[A\equiv 1\]
D) A is not invertible
View Answer play_arrowquestion_answer170) \[R\]is a relation from {11,12,13} to {8,10,12} defined by\[y=x-3\]. Then\[{{R}^{-1}}\]is
A) {(8,11), (10,13)}
B) {(11,18), (13,10)}
C) {(10,13), (8,11)}
D) None of the above
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