question_answer1) One drop of soap bubble of diameter D breakes into 27 drops having surface tension T. The change in surface energy is
A) \[2\pi T{{D}^{2}}\] done clear
B) \[4\pi T{{D}^{2}}\] done clear
C) \[\pi T{{D}^{2}}\] done clear
D) \[8\pi T{{D}^{2}}\] done clear
View Answer play_arrowquestion_answer2) The period of a planet around sun is 27 times that of earth. The ratio of radius of planets orbit to the radius of earths orbit is
A) 4 done clear
B) 9 done clear
C) 64 done clear
D) 27 done clear
View Answer play_arrowquestion_answer3) Three particles each of mass m are kept at vertices of an equilateral triangle of side L. The gravitational field at centre due to these particles is
A) zero done clear
B) \[\frac{3GM}{{{L}^{2}}}\] done clear
C) \[\frac{9GM}{{{L}^{2}}}\] done clear
D) \[\frac{12}{\sqrt{3}}\frac{GM}{{{L}^{2}}}\] done clear
View Answer play_arrowquestion_answer4) In a turbulent flow, the velocity of the liquid in contact with the walls of the tube is
A) zero done clear
B) maximum done clear
C) in between zero and maximum done clear
D) equal to critical velocity done clear
View Answer play_arrowquestion_answer5) A charge q is fixed. Another charge Q is brought near it and rotated in a circle of radius r around it. Work done during rotation is
A) zero done clear
B) \[\frac{Qq}{4\pi G{{\varepsilon }_{0}}r}\] done clear
C) \[\frac{Qq}{2\pi G{{\varepsilon }_{0}}r}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer6) A diode having potential difference 0.5 V across its junction which does not depend on current, is connected in series with resistance of 20 \[\Omega \] across source. If 0.1 A current passes through resistance then what is the voltage of the source?
A) 1.5V done clear
B) 2.0V done clear
C) 2.5 V done clear
D) 5 V done clear
View Answer play_arrowquestion_answer7) Dipole is placed parallel to the electric field. If Q is the work done in rotating the dipole by 60?, then work done in rotating it by 180? is
A) 2W done clear
B) 3W done clear
C) 4W done clear
D) W/2 done clear
View Answer play_arrowquestion_answer8) An electron of charge e moves in a circular orbit of radius r around the nucleus at a frequency v. The magnetic moment associated with the orbital motion of the electron is
A) \[\pi ve{{r}^{2}}\] done clear
B) \[\frac{\pi v{{r}^{2}}}{e}\] done clear
C) \[\frac{\pi v\,e}{r}\] done clear
D) \[\frac{\pi v{{r}^{2}}}{v}\] done clear
View Answer play_arrowquestion_answer9) A and B are two identical spherical charged bodies which repel each other with force F, kept at a finite distance. A third uncharged sphere of the same size is brought in contact with sphere B and removed. It is then kept at mid-point of A and B. Find the magnitude of force on C.
A) F/2 done clear
B) F/8 done clear
C) F done clear
D) Zero done clear
View Answer play_arrowquestion_answer10) A wave equation is \[y=0.1\sin [100\pi t-kx]\]and wave velocity is 100 m/s, its wave number is equal to
A) \[1{{m}^{-1}}\] done clear
B) \[2{{m}^{-1}}\] done clear
C) \[\pi {{m}^{-1}}\] done clear
D) \[2\pi {{m}^{-1}}\] done clear
View Answer play_arrowquestion_answer11) Volume-temperature graph at atmospheric pressure for a monoatomic gas \[\left( V\text{ }in\text{ }{{m}^{3}},\text{ }T\text{ }in\text{ }{}^\circ C \right)\] is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer12) An optically active compound
A) rotates the plane polarized light done clear
B) changing the direction of polarized light done clear
C) do not allow plane polarized light to pass through done clear
D) None of the above done clear
View Answer play_arrowquestion_answer13) Power applied to a particle varies with time as \[P=(3{{t}^{2}}-2t+1)\] W, where t is in second. Find the change in its kinetic energy between t = 1 s and t = 4 s.
A) 32 J done clear
B) 46 J done clear
C) 61 J done clear
D) 102 J done clear
View Answer play_arrowquestion_answer14) A hockey player receives a corner shot at a speed of 15 m/s at an angle of 30? with the y-axis and then shoots the ball of mass 100 g along the negative x-axis with a speed of 30 m/s. If it remains in contact with the hockey stick for 0.01 s, the force imparted to the ball in the x-direction is
A) 281.25 N done clear
B) 187.5N done clear
C) 562.5 N done clear
D) 375 N done clear
View Answer play_arrowquestion_answer15) Two equal charges are separated by a distance d. A third charge placed on a perpendicular bisector at x distance from centre will experience maximum coulomb force, when
A) \[x=d/\sqrt{2}\] done clear
B) \[x=d/2\] done clear
C) \[x=d/2\sqrt{2}\] done clear
D) \[x=d/2\sqrt{3}\] done clear
View Answer play_arrowquestion_answer16) The equivalent resistance between points A and B of an infinite network of resistance s each of \[1\,\Omega ,\] connected as shown, is
A) infinite done clear
B) 2\[\Omega \] done clear
C) \[\frac{1+\sqrt{5}}{2}\Omega \] done clear
D) zero done clear
View Answer play_arrowquestion_answer17) A circular current carrying coil has a radius R The distance from the centre of the coil off the axis of the coil, where the magnetic induction is I/8th of its value at the centre of the coil is
A) \[\sqrt{3}R\] done clear
B) \[R/\sqrt{3}\] done clear
C) \[\left( \frac{2}{\sqrt{3}} \right)R\] done clear
D) \[\frac{R}{2\sqrt{3}}\] done clear
View Answer play_arrowquestion_answer18) A point source of light is placed 4m below he surface of water of refractive index 5/ 3. The minimum diameter of a disc, which should be placed over the source, on the surface of water to cut-off all light coming out of water is
A) infinite done clear
B) 6 m done clear
C) 4m done clear
D) 3m done clear
View Answer play_arrowquestion_answer19) A ray falls on a prism ABC (AB =BC) and travels as shown in figure. The minimum refractive index of the prism material should be
A) \[\frac{4}{3}\] done clear
B) \[\sqrt{2}\] done clear
C) 1.5 done clear
D) \[\sqrt{3}\] done clear
View Answer play_arrowquestion_answer20) The plane face of a planoconvex lens is silvered. If u be the refractive index and R, the radius of curvature of curved surface, then the system will behave like a concave mirror of radius of curvature
A) \[\mu R\] done clear
B) \[\frac{R}{(\mu -1)}\] done clear
C) \[\frac{{{R}^{2}}}{\mu }\] done clear
D) \[\left[ \frac{(\mu +1)}{(\mu -1)} \right]R\] done clear
View Answer play_arrowquestion_answer21) Two similar accumulators each of emf E and internal resistance r are connected as shown in the following figure. Then, the potential difference between x and y is
A) 2E done clear
B) E done clear
C) zero done clear
D) None of these done clear
View Answer play_arrowquestion_answer22) A conducting circular loop is placed in a uniform magnetic field of induction B tesla with its plane normal to the field. Now, the radius of the loop starts shrinking at the rate\[\left( \frac{dr}{dt} \right)\]. Then, the induced emf at the instant when the radius is r, is
A) \[\pi rB\left( \frac{dr}{dt} \right)\] done clear
B) \[2\pi rB\left( \frac{dr}{dt} \right)\] done clear
C) \[\pi {{r}^{2}}\left( \frac{dr}{dt} \right)\] done clear
D) \[{{\left( \frac{\pi {{r}^{2}}}{2} \right)}^{2}}B\left( \frac{dr}{dt} \right)\] done clear
View Answer play_arrowquestion_answer23) The first excitation potential of a given atom is 10.2V. Then, ionization potential must be
A) 20.4V done clear
B) 13.6V done clear
C) 30.6V done clear
D) 40.8V done clear
View Answer play_arrowquestion_answer24) A train is approaching with velocity 25 m/s towards a pedestrian standing on the track, frequency of horn of train is 1 kHz. Frequency heard by the pedestrain is (v= 350 m/s)
A) 1077 Hz done clear
B) 1167 Hz done clear
C) 985 Hz done clear
D) 954 Hz done clear
View Answer play_arrowquestion_answer25) Intensity of wave A is 91, while of wave B is 7. What is maximum and minimum intensity in YDSE?
A) 82\[I\], 80\[I\] done clear
B) 8\[I\], 10\[I\] done clear
C) 16\[I\], 4\[I\] done clear
D) 4\[I\],\[I\] done clear
View Answer play_arrowquestion_answer26) What happens inside optical fibre?
A) Diffraction done clear
B) Polarization done clear
C) Interference done clear
D) Total internal reflection done clear
View Answer play_arrowquestion_answer27) A manometer connected to a closed tap reads\[3.5\times {{10}^{5}}\,N/{{m}^{2}}\]. When the valve is opened, the reading of manometer falls to \[3.0\times {{10}^{5}}\,N/{{m}^{2}}\], then velocity of flow of water is
A) 100 m/s done clear
B) 10 m/s done clear
C) 1m/s done clear
D) \[10\sqrt{10}\]m/s done clear
View Answer play_arrowquestion_answer28) Water is moving with a speed of 5.18 \[m{{s}^{-1}}\] through a pipe with a cross-sectional area of 4.20\[c{{m}^{2}}\]. The water gradually descends 9.66 m as the pipe increase in area to 7.60\[c{{m}^{2}}\]. The speed of flow at the lower level is
A) 3.0\[m{{s}^{-1}}\] done clear
B) 5.7\[m{{s}^{-1}}\] done clear
C) 3.82\[m{{s}^{-1}}\] done clear
D) 2.86\[m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer29) What is de-Broglie wavelength of electron having energy 10 keV?
A) \[0.12\overset{\text{o}}{\mathop{\text{A}}}\,\] done clear
B) \[1.2\overset{\text{o}}{\mathop{\text{A}}}\,\] done clear
C) \[12.2\,\overset{\text{o}}{\mathop{\text{A}}}\,\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer30) Find beat frequency? Motion of two particles is given by \[{{y}_{1}}=0.25\sin (310t)\] \[{{y}_{2}}=0.25\sin (316t)\]
A) 3 done clear
B) \[\frac{3}{\pi }\] done clear
C) \[\frac{6}{\pi }\] done clear
D) 6 done clear
View Answer play_arrowquestion_answer31) Half-life of radioactive substance is 3.20 h. What is the time taken for a 75% of substance to be used?
A) 6.38 h done clear
B) 12 h done clear
C) 4.18 day done clear
D) 1.2day done clear
View Answer play_arrowquestion_answer32) A capacitor of capacitance 1 \[\mu F\] is filled with two dielectrics of dielectric constants 4 and 6. What is the new capacitance?
A) 10\[\mu F\] done clear
B) 5\[\mu F\] done clear
C) 4\[\mu F\] done clear
D) 7\[\mu F\] done clear
View Answer play_arrowquestion_answer33) The given combination represents the following gate
A) OR done clear
B) XOR done clear
C) NAND done clear
D) NOR done clear
View Answer play_arrowquestion_answer34) In BJT, maximum current flows in which of the following?
A) Emitter region done clear
B) Base region done clear
C) Collector region done clear
D) Equal in all the regions done clear
View Answer play_arrowquestion_answer35) In semiconductors at a room temperature
A) the valence band is partially empty and the conduction band is partially filled done clear
B) the valence band is completely filled and the conduction band is partially filled done clear
C) the valence band is completely filled done clear
D) the conduction band is completely empty done clear
View Answer play_arrowquestion_answer36) If coil is open then L and R become
A) \[\infty ,0\] done clear
B) \[0,\infty \] done clear
C) \[\infty ,\infty \] done clear
D) 0, 0 done clear
View Answer play_arrowquestion_answer37) In a coil when current changes from 10A to 2A in time 0.1 s, induced emf is 3.28V. What is self-inductance of coil?
A) 4H done clear
B) 0.4H done clear
C) 0.04H done clear
D) 5H done clear
View Answer play_arrowquestion_answer38) Resistance of rod is 1\[\Omega \]. It is bent in form of square. What is resistance across adjoint corners?
A) 1\[\Omega \] done clear
B) 3\[\Omega \] done clear
C) \[\frac{3}{16}\Omega \] done clear
D) \[\frac{3}{4}\Omega \] done clear
View Answer play_arrowquestion_answer39) In a circuit L, C and R are connected in series with an alternating voltage source of frequency \[f\]. The current leads the voltage by \[45{}^\circ \]. The value of C is
A) \[\frac{1}{2\pi f(2\pi fL+R)}\] done clear
B) \[\frac{1}{\pi f(2\pi fL+R)}\] done clear
C) \[\frac{1}{2\pi f(2\pi fL-R)}\] done clear
D) \[\frac{1}{\pi f(2\pi fL-R)}\] done clear
View Answer play_arrowquestion_answer40) What is angle between electric field and equipotential surface?
A) \[90{}^\circ \text{ }always\] done clear
B) \[0{}^\circ \text{ }always\] done clear
C) \[0{}^\circ \text{ }to\text{ }90{}^\circ \] done clear
D) \[0{}^\circ \text{ }to\text{ }180{}^\circ \] done clear
View Answer play_arrowquestion_answer41) A ball falls from 20 m height on floor and rebounds to 5m. Time of contact is 0.02s. Find acceleration during impact.
A) \[1200\,m/{{s}^{2}}\] done clear
B) \[1000\,m/{{s}^{2}}\] done clear
C) \[2000\,m/{{s}^{2}}\] done clear
D) \[1500\,m/{{s}^{2}}\] done clear
View Answer play_arrowquestion_answer42) Two drops of equal radius coalesce to form a bigger drop. What is ratio of surface energy of bigger drop to smaller one?
A) \[{{2}^{1/2}}:1\] done clear
B) \[1:1\] done clear
C) \[{{2}^{2/3}}:1\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer43) In any fission process the ratio \[\frac{mass\,of\,fission\,products}{mass\,of\,parent\,nucleus}is\]
A) less than 1 done clear
B) greater than 1 done clear
C) equal to 1 done clear
D) depends on the mass of parent nucleus done clear
View Answer play_arrowquestion_answer44) In the phenomenon of diffraction of light. when blue light is used in the experiment instead of red light, then
A) fringes will become narrower done clear
B) fringes will become broader done clear
C) no change in fringe width done clear
D) None of the above done clear
View Answer play_arrowquestion_answer45) A glass slab \[(\mu =1.5)\] of thickness 6 cm is placed over a paper. What is the shift in the letters?
A) 4 cm done clear
B) 2 cm done clear
C) 1 cm done clear
D) None of these done clear
View Answer play_arrowquestion_answer46) Two capacitors of capacitance C are connected in series. If one of them is filled with dielectric substance K, what is the effective capacitance?
A) \[\frac{KC}{(1+K)}\] done clear
B) C (K + 1) done clear
C) \[\frac{2KC}{K+1}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer47) A person is sitting in a lift accelerating upwards. Measured weight of person will be
A) less than actual weight done clear
B) equal to actual weight done clear
C) more than actual weight done clear
D) None of the above done clear
View Answer play_arrowquestion_answer48) By mistake a voltmeter is connected in series and an ammeter is connected in parallel with a resistance in an electrical circuit. What will happen to the instruments?
A) Voltmeter is damaged done clear
B) Ammeter is damaged done clear
C) Both are damaged done clear
D) None is damaged done clear
View Answer play_arrowquestion_answer49) The half-life of \[A{{t}^{215}}\]is 100 \[\mu s\]. If a sample contains 215 mg of \[A{{t}^{215}}\], the activity of the sample initially is
A) \[{{10}^{2}}Bq\] done clear
B) \[3\times {{10}^{10}}Bq\] done clear
C) \[4.17\times {{10}^{24}}Bq\] done clear
D) \[1.16\times {{10}^{5}}Bq\] done clear
View Answer play_arrowquestion_answer50) The ratio of minimum to maximum wavelength in Balmer series is
A) 5 : 9 done clear
B) 5 : 36 done clear
C) 1 : 4 done clear
D) 3 : 4 done clear
View Answer play_arrowquestion_answer51) A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third second of the motion of the ball is
A) 1 : 2 : 3 done clear
B) 1 : 4 : 9 done clear
C) 1 : 3 : 5 done clear
D) 1 : 5 : 3 done clear
View Answer play_arrowquestion_answer52) A body of mass 2 kg moving with a velocity of 3 m/s collides head on with a body of mass 1 kg moving in opposite direction with a velocity of 4 m/s. After collision two bodies stick together and move with a common velocity which in m/s is equal to
A) 1/4 done clear
B) 1/3 done clear
C) 2/3 done clear
D) 3/4 done clear
View Answer play_arrowquestion_answer53) Two spheres P and Q, of same colour having radii 8 cm and 2 cm are maintained at temperatures \[127{}^\circ C\] and \[527{}^\circ C\] respectively. The energy radiated by P and Q is
A) 0.054 done clear
B) 0.0034 done clear
C) 1 done clear
D) 2 done clear
View Answer play_arrowquestion_answer54) A cane is taken out from a refrigerator at \[0{}^\circ C\]. The atmospheric temperature is \[25{}^\circ C\]. If \[{{t}_{1}}\] is the time taken to heat from \[0{}^\circ C\] to \[5{}^\circ C\] and \[{{t}_{2}}\] is the time taken from \[10{}^\circ C\] to \[15{}^\circ C\], then
A) \[{{t}_{1}}>{{t}_{2}}\] done clear
B) \[{{t}_{1}}<{{t}_{2}}\] done clear
C) \[{{t}_{1}}={{t}_{2}}\] done clear
D) there is no relation done clear
View Answer play_arrowquestion_answer55) If an electron and a photon propagate in the form of waves having the same wavelength, it implies that they have the same
A) energy done clear
B) momentum done clear
C) velocity done clear
D) angular momentum done clear
View Answer play_arrowquestion_answer56) The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately
A) 540 nm done clear
B) 400 nm done clear
C) 310nm done clear
D) 220 nm done clear
View Answer play_arrowquestion_answer57) Work function of a metal is 2.1 eV. Which of the waves of the following wavelengths will be able to emit photoelectrons from its surface?
A) \[4000\overset{\text{o}}{\mathop{\text{A}}}\,,\,\,7500\overset{\text{o}}{\mathop{\text{A}}}\,\] done clear
B) \[5500\overset{\text{o}}{\mathop{\text{A}}}\,,\,6000\overset{\text{o}}{\mathop{\text{A}}}\,\] done clear
C) \[4000\overset{\text{o}}{\mathop{\text{A}}}\,,\,6000\overset{\text{o}}{\mathop{\text{A}}}\,\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer58) A laser beam of pulse power \[{{10}^{12}}\]W is focused on an object of area\[{{10}^{-4}}c{{m}^{2}}\]. The energy flux in watt/\[c{{m}^{2}}\] at the point of focus is
A) \[{{10}^{20}}\] done clear
B) \[{{10}^{16}}\] done clear
C) \[{{10}^{8}}\] done clear
D) \[{{10}^{4}}\] done clear
View Answer play_arrowquestion_answer59) A laser device produces amplification in the
A) microwave region done clear
B) ultraviolet or visible region done clear
C) infrared region done clear
D) None of the above done clear
View Answer play_arrowquestion_answer60) Which of the following circular rods. (given radius r and length 0 each made of the same material as whose ends are maintained at the same temperature will conduct most heat?
A) \[r=2{{r}_{0}};l=2{{l}_{0}}\] done clear
B) \[r=2{{r}_{0}};l={{l}_{0}}\] done clear
C) \[r={{r}_{0}};l={{l}_{0}}\] done clear
D) \[r={{r}_{0}};l=2{{l}_{0}}\] done clear
View Answer play_arrowquestion_answer61) Which of the following is diamagnetic?
A) \[H_{2}^{+}\] done clear
B) \[{{O}_{2}}\] done clear
C) \[L{{i}_{2}}\] done clear
D) \[He_{2}^{+}\] done clear
View Answer play_arrowquestion_answer62) Which of the following can participate in linkage isomerism?
A) \[NO_{2}^{-}\] done clear
B) \[{{H}_{2}}\overset{\centerdot \,\,\,\centerdot }{\mathop{N}}\,C{{H}_{2}}C{{H}_{2}}\overset{\centerdot \,\,\,\centerdot }{\mathop{N}}\,{{H}_{2}}\] done clear
C) \[{{H}_{2}}O\] done clear
D) \[:N{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer63) By heating phenol with chloroform in alkali, it is converted into
A) salicylic acid done clear
B) salicylaldehyde done clear
C) anisole done clear
D) phenyl benzoate done clear
View Answer play_arrowquestion_answer64) 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 done clear
B) benzoic acid has higher molar mass than benzene done clear
C) benzoic acid gets associated in benzene done clear
D) benzoic acid gets dissociated in benzene done clear
View Answer play_arrowquestion_answer65) The formula mass of Moms salt is 392. The iron present in it is oxidized by\[KMn{{O}_{4}}\]in acid medium. The equivalent mass of Mohrs salt is
A) 392 done clear
B) 31.6 done clear
C) 278 done clear
D) 156 done clear
View Answer play_arrowquestion_answer66) 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\[{{10}^{-7}}M\] done clear
B) between\[{{10}^{-7}}M\]to\[{{10}^{-8}}M\] done clear
C) \[>{{10}^{-5}}M\] done clear
D) \[<{{10}^{-8}}M\] done clear
View Answer play_arrowquestion_answer67) The decomposition of a certain mass of\[CaC{{O}_{3}}\]gave\[11.2\,\,d{{m}^{3}}\]of\[C{{O}_{2}}\]gas at STP. The mass of\[KOH\]required to completely I neutralize the gas is
A) 56 g done clear
B) 28 g done clear
C) 42 g done clear
D) 20 g done clear
View Answer play_arrowquestion_answer68) The basicity of aniline is less than that of cyclohexylamine. This is due to
A) \[+R-\]effect of\[-N{{H}_{2}}\]group done clear
B) \[-I-\]effect of\[-N{{H}_{2}}\]group done clear
C) \[-R-\]effect of\[-N{{H}_{2}}\]group done clear
D) hyperconjugation effect done clear
View Answer play_arrowquestion_answer69) A distinctive and characteristic functional group of fats is
A) a peptide group done clear
B) an ester group done clear
C) an alcoholic group done clear
D) a ketonic group done clear
View Answer play_arrowquestion_answer70) Which of the following compound is expected to be optically active?
A) \[{{(C{{H}_{3}})}_{2}}CHCHO\] done clear
B) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}CHO\] done clear
C) \[C{{H}_{3}}C{{H}_{2}}CHBrCHO\] done clear
D) \[C{{H}_{3}}C{{H}_{2}}CB{{r}_{2}}CHO\] done clear
View Answer play_arrowquestion_answer71) Which cycloalkane has the lowest heat of combustion per\[C{{H}_{2}}\]group?
A) Cyclopropane done clear
B) Cyclobutane done clear
C) Cyclopentane done clear
D) Cyclohexane done clear
View Answer play_arrowquestion_answer72) The physical states of dispersing phase and dispersion medium in colloid like pesticide spray respectively, are
A) gas, liquid done clear
B) solid, gas done clear
C) liquid, solid done clear
D) liquid, gas done clear
View Answer play_arrowquestion_answer73) Potassium dichromate is used
A) in electroplating done clear
B) as a reducing agent done clear
C) it oxidizes ferrous ions into ferric ions in acidic media as an oxidizing agent done clear
D) as an insecticide done clear
View Answer play_arrowquestion_answer74) Which one of the following statements is incorrect for the sucrose?
A) It is obtained from cane sugar done clear
B) It is not reducing sugar done clear
C) On hydrolysis, it gives equal quantities of D-glucose and D-fructose done clear
D) It gives aspartame when it is heated at\[{{210}^{o}}C\] done clear
View Answer play_arrowquestion_answer75) Inductive effect involves
A) displacement of \[\sigma \]-electrons done clear
B) delocalisation of \[\pi \]-electrons done clear
C) delocalisation of \[\sigma \]-electrons done clear
D) displacement of \[\pi \]-electrons done clear
View Answer play_arrowquestion_answer76) The atomic number of\[Ni\]and\[Cu\]are 28 and 29 respectively. The electronic configuration \[1{{s}^{2}},\,\,2{{s}^{2}},\,\,2{{p}^{6}},\,\,3{{s}^{2}}\,\,3{{p}^{6}}\,\,3{{d}^{10}}\]represents
A) \[C{{u}^{+}}\] done clear
B) \[C{{u}^{2+}}\] done clear
C) \[N{{i}^{2+}}\] done clear
D) \[Ni\] done clear
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) \[{{[CoF]}^{3-}}\] done clear
B) \[{{[CO{{(N{{H}_{3}})}_{6}}]}^{3+}}\] done clear
C) \[{{[Fe{{(CN)}_{6}}]}^{3-}}\] done clear
D) \[{{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}\] done clear
View Answer play_arrowquestion_answer78) 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 done clear
B) Both\[{{O}_{2}}\]and\[Xe\]are gases done clear
C) \[{{O}_{2}}\]and\[Xe\]have comparable ionization energies done clear
D) Both (a) and (c) done clear
View Answer play_arrowquestion_answer79) The density of a gas is\[1.964\,\,g\,\,d{{m}^{-3}}\]at\[273\,\,K\]and\[76\,\,cm\,\,Hg\]. The gas is
A) \[C{{H}_{4}}\] done clear
B) \[{{C}_{2}}{{H}_{6}}\] done clear
C) \[C{{O}_{2}}\] done clear
D) \[Xe\] done clear
View Answer play_arrowquestion_answer80) \[\Delta {{G}^{o}}vs\,\,T\]plot in the Ellinghams diagram slopes downwards for the reactions
A) \[Mg+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}MgO\] done clear
B) \[2Ag+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}A{{g}_{2}}O\] done clear
C) \[CO+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}\] done clear
D) All of the above done clear
View Answer play_arrowquestion_answer81) When a mixture of calcium benzoate and calcium acetate is dry distilled, the resulting compound is
A) acetophenone done clear
B) benzaldehyde done clear
C) benzophenone done clear
D) acetaldehyde done clear
View Answer play_arrowquestion_answer82) In a metallic crystal
A) the valence electrons constitute a sea of mobile electrons done clear
B) the valence electrons are localized in between the kernels done clear
C) the valence electrons remain within the field of influence of their own kernels done clear
D) None of the above done clear
View Answer play_arrowquestion_answer83) Which of the following is correct, based on molecular orbital theory for peroxide ion?
A) Its bond order is one and it is paramagnetic done clear
B) Its bond order is two and it is diamagnetic done clear
C) Its bond order is one and it is diamagnetic done clear
D) Its bond order is two and it is paramagnetic done clear
View Answer play_arrowquestion_answer84) Insulin regulates the metabolism of
A) minerals done clear
B) ammo acids done clear
C) glucose done clear
D) vitamins done clear
View Answer play_arrowquestion_answer85) Which of the following electrolyte will have maximum flocculation value for\[Fe{{(OH)}_{3}}\]sol?
A) \[NaCl\] done clear
B) \[N{{a}_{2}}S\] done clear
C) \[{{(N{{H}_{4}})}_{3}}P{{O}_{4}}\] done clear
D) \[{{K}_{2}}S{{O}_{4}}\] done clear
View Answer play_arrowquestion_answer86) The concentration of a reactant X decreases from\[0.1M\]to\[0.005M\]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) \[1.73\times {{10}^{-4}}M\,\,{{\min }^{-1}}\] done clear
B) \[3.47\times {{10}^{-4}}M\,\,{{\min }^{-1}}\] done clear
C) \[3.47\times {{10}^{-5}}M\,\,{{\min }^{-1}}\] done clear
D) \[7.5\times {{10}^{-4}}M\,\,{{\min }^{-1}}\] done clear
View Answer play_arrowquestion_answer87) At\[pH=4\], glycine exists as
A) \[{{H}_{3}}N-C{{H}_{2}}-CO{{O}^{-}}\] done clear
B) \[{{H}_{3}}N-C{{H}_{2}}-COOH\] done clear
C) \[{{H}_{2}}N-C{{H}_{2}}-COOH\] done clear
D) \[{{H}_{2}}N-C{{H}_{2}}-CO{{O}^{-}}\] done clear
View Answer play_arrowquestion_answer88) Which of the following taking place in the blast furnace is endothermic?
A) \[CaC{{O}_{3}}\xrightarrow{{}}CaO+C{{O}_{2}}\] done clear
B) \[2C+{{O}_{2}}\xrightarrow{{}}2CO\] done clear
C) \[C+{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}\] done clear
D) \[F{{e}_{2}}{{O}_{3}}+3CO\xrightarrow{{}}2Fe+3C{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer89) The\[emf\,\,{{E}^{o}}\]of the following cells are: \[AG|A{{g}^{+}}(1M)||C{{u}^{2+}}(1M)|Cu;\,\,{{E}^{o}}=-0.46\,\,V\] \[Zn|Z{{n}^{2+}}(1M)||C{{u}^{2+}}(1M)|Cu;\,\,{{E}^{o}}=1.10\,\,V\] emf of the following cell is \[Zn|Z{{n}^{2+}}(1M)||A{{g}^{+}}(1M)|Ag\]
A) \[0.64\,\,V\] done clear
B) \[1.10\,\,V\] done clear
C) \[1.56\,\,V\] done clear
D) \[-0.64\,\,V\] done clear
View Answer play_arrowquestion_answer90) The formation of cyanohydrin from acetone is which type of reaction?
A) Electrophilic substitution reaction done clear
B) Electrophilic addition reaction done clear
C) Nucleophilic addition reaction done clear
D) Nucleophilic substitution reaction done clear
View Answer play_arrowquestion_answer91) Name the end product in the following series of reactions \[C{{H}_{3}}COOH\xrightarrow{N{{H}_{3}}}A\xrightarrow{Heat}B\xrightarrow[\Delta ]{{{P}_{4}}{{O}_{14}}}C\]
A) \[C{{H}_{3}}OH\] done clear
B) \[C{{H}_{4}}\] done clear
C) \[C{{H}_{3}}COON{{H}_{4}}\] done clear
D) \[C{{H}_{3}}CN\] done clear
View Answer play_arrowquestion_answer92) The presence of unpaired electron in phosphorous atom is explained by which principle?
A) Aufbau principle done clear
B) Faults exclusion principle done clear
C) Hunds rule done clear
D) Heisenbergs principle done clear
View Answer play_arrowquestion_answer93) If a cricket ball having mass of\[200\,\,g\]is thrown with a speed of\[3\times {{10}^{3}}\,\,cm/s\], then calculate the wavelength related to it.
A) \[2.2\times {{10}^{-27}}cm\] done clear
B) \[1.104\times {{10}^{-32}}cm\] done clear
C) \[1.104\times {{10}^{-32}}cm\] done clear
D) \[1.104\times {{10}^{-33}}cm\] done clear
View Answer play_arrowquestion_answer94) Which type of stacking pattern is found in sodium chloride crystal lattice?
A) \[a-b-a-b\] done clear
B) \[a-a-a\] done clear
C) \[a-b-c-a-b-c\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer95) Equivalent weight of a bivalent metal is 37.2. The molecular weight of its chloride is
A) 412.2 done clear
B) 216 done clear
C) 145.4 done clear
D) 108.2 done clear
View Answer play_arrowquestion_answer96) Phenolphthalein is obtained by heating phthalic anhydride with \[conc.{{H}_{2}}S{{O}_{4}}\]and
A) benzyl alcohol done clear
B) benzene done clear
C) phenol done clear
D) benzoic acid done clear
View Answer play_arrowquestion_answer97) Freezing point of urea solution is\[-{{0.6}^{o}}C\]. How much urea\[(m.wt.=60g/mol)\]will be required to dissolve in 3 kg water? \[({{k}_{f}}={{1.5}^{o}}C\,\,kg\,\,mo{{l}^{-1}})\]
A) 24 g done clear
B) 36 g done clear
C) 60 g done clear
D) 72 g done clear
View Answer play_arrowquestion_answer98) If\[K<1.0\], what will be the value of\[\Delta {{G}^{o}}\]of the following?
A) Zero done clear
B) 1.0 done clear
C) Positive done clear
D) Negative done clear
View Answer play_arrowquestion_answer99) The normality of a solution containing 32.5 g of\[{{(COOH)}_{2}}\cdot 2{{H}_{2}}O\]per\[0.5\,\,L\]is
A) \[10\,\,N\] done clear
B) \[1\,\,N\] done clear
C) \[2\,\,N\] done clear
D) \[0.1\,\,N\] done clear
View Answer play_arrowquestion_answer100) For the titration of\[KOH\]vs\[{{(COOH)}_{2}}\cdot 2{{H}_{2}}O\], the suitable indicator is
A) methyl orange done clear
B) phenolphthalein done clear
C) methyl red done clear
D) All can be used done clear
View Answer play_arrowquestion_answer101) The radius of\[N{{a}^{+}}\]is\[95\,\,\text{pm}\]and that of\[C{{l}^{-}}\]ion is\[181\,\,\text{pm}\]. The coordination number of\[N{{a}^{+}}\]is
A) 8 done clear
B) 6 done clear
C) 4 done clear
D) unpredictable done clear
View Answer play_arrowquestion_answer102) In van der Waals equation of state of the gas law, the constant V is a measure of
A) intermolecular repulsion done clear
B) intermolecular attraction done clear
C) volume occupied by the molecules done clear
D) intermolecular collisions per unit volume done clear
View Answer play_arrowquestion_answer103) Which reaction intermediate is formed during the condensation reaction between acetaldehyde and formaldehyde?
A) \[:C{{H}_{2}}CHO\] done clear
B) \[\overset{+}{\mathop{C}}\,{{H}_{2}}CHO\] done clear
C) \[\overset{+}{\mathop{C}}\,{{H}_{2}}OH\] done clear
D) \[:\bar{C}HCHO\] done clear
View Answer play_arrowquestion_answer104) \[2,\,\,2\mathbf{-}\]dichloro propane on hydrolysis yields
A) acetone done clear
B) \[2,\,\,2\mathbf{-}\]propane diol done clear
C) iso-propyl alcohol done clear
D) acetaldehyde done clear
View Answer play_arrowquestion_answer105) Phenols are more acidic than alcohols because
A) phenoxide ion is stabilized by resonance done clear
B) phenols are more soluble in polar solvents done clear
C) phenoxide ions do not exhibit resonance done clear
D) alcohols do not lose H atoms at all done clear
View Answer play_arrowquestion_answer106) Lemon gives sour taste because of
A) citric acid done clear
B) tartaric acid done clear
C) oxalic acid done clear
D) acetic acid done clear
View Answer play_arrowquestion_answer107) When ammonium chloride is added to ammonia solution, the pH of the resulting solution will be
A) increased done clear
B) seven done clear
C) decreased done clear
D) unchanged done clear
View Answer play_arrowquestion_answer108) Which of the following has highest second ionization energy?
A) Calcium done clear
B) Chromium done clear
C) Iron done clear
D) Cobalt done clear
View Answer play_arrowquestion_answer109) The standard reduction potentials at\[298K\]for the following half-cell reactions are given below \[Z{{n}^{2+}}(aq)+2{{e}^{-}}Zn(s)-0.762\] \[C{{r}^{3+}}(aq)+3{{e}^{-}}Cr(s)-0.74\] \[2{{H}^{+}}(aq)+2{{e}^{-}}{{H}_{2}}(g)-0.00\] \[F{{e}^{3+}}(aq)+{{e}^{-}}F{{e}^{2+}}(aq)-0.77\] Which one of the following is the strongest reducing agent?
A) \[Zn(s)\] done clear
B) \[Cr(s)\] done clear
C) \[{{H}_{2}}(g)\] done clear
D) \[F{{e}^{2+}}(aq)\] done clear
View Answer play_arrowquestion_answer110) Following reaction, \[{{(C{{H}_{3}})}_{3}}CBr+{{H}_{2}}O\xrightarrow{{}}{{(C{{H}_{3}})}_{3}}COH+HBr\]is an example of
A) elimination reaction done clear
B) free radical substitution done clear
C) nucleophilic substitution done clear
D) electrophilic substitution done clear
View Answer play_arrowquestion_answer111) The unit of rate for a first order reaction is
A) \[L\,\,{{s}^{-1}}\] done clear
B) \[mo{{l}^{-1}}\,\,L\,\,{{s}^{-1}}\] done clear
C) \[mol\,\,{{L}^{-1}}\,\,{{s}^{-1}}\] done clear
D) \[mol\,\,{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer112) \[Iso-\]propyl amine with excess of acetyl chloride will give
A) \[{{(C{{H}_{3}}CO)}_{2}}N-C-{{(C{{H}_{3}})}_{3}}\] done clear
B) \[{{(C{{H}_{3}})}_{2}}CH-\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\mathop{N}}\,-COC{{H}_{3}}\] done clear
C) \[{{(C{{H}_{3}})}_{2}}CHN{{(CO{{H}_{3}})}_{2}}\] done clear
D) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\mathop{N}}\,-COC{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer113) \[{{C}_{2}}{{H}_{5}}CHO\]and\[{{(C{{H}_{3}})}_{2}}CO\]can be distinguished by testing with
A) phenyl hydrazine done clear
B) hydroxyl amine done clear
C) Fehling solution done clear
D) sodium bisulphite done clear
View Answer play_arrowquestion_answer114) Glucose molecule reacts with\[X\]number of molecules of phenylhydrazine to yield osazone. The value of T is
A) four done clear
B) one done clear
C) two done clear
D) three done clear
View Answer play_arrowquestion_answer115) The oxidation number of chromium in\[Cr{{O}_{5}}\]is
A) +3 done clear
B) + 5 done clear
C) + 10 done clear
D) + 6 done clear
View Answer play_arrowquestion_answer116) Liquor ammonia bottles are opened only after cooling. This is because
A) it is a mild explosive done clear
B) it generates high vapour pressure done clear
C) Both (a) and (b) done clear
D) it is lachrymatory done clear
View Answer play_arrowquestion_answer117) What will be the proportion of moles of metal \[(Cu:Ni:Ag)\]at cathode according to the second law of Faraday?
A) \[1:2:1\] done clear
B) \[2:2:1\] done clear
C) \[1:2:2\] done clear
D) \[1:1:2\] done clear
View Answer play_arrowquestion_answer118) Which equation is true to calculate the energy of activation, if the rate of reaction is doubled by increasing temperature from\[{{T}_{1}}K\]to\[{{T}_{2}}K\]?
A) \[{{\log }_{10}}\frac{{{k}_{1}}}{{{k}_{2}}}=\frac{{{E}_{a}}}{2.303R}\left[ \frac{1}{{{T}_{1}}}-\frac{1}{{{T}_{2}}} \right]\] done clear
B) \[{{\log }_{10}}\frac{{{k}_{2}}}{{{k}_{1}}}=\frac{{{E}_{a}}}{2.303R}\left[ \frac{1}{{{T}_{2}}}-\frac{1}{{{T}_{1}}} \right]\] done clear
C) \[{{\log }_{10}}\frac{1}{2}=\frac{{{E}_{a}}}{2.303}\left[ \frac{1}{{{T}_{2}}}-\frac{1}{{{T}_{1}}} \right]\] done clear
D) \[{{\log }_{10}}2=\frac{{{E}_{a}}}{2.303R}\left[ \frac{1}{{{T}_{1}}}-\frac{1}{{{T}_{2}}} \right]\] done clear
View Answer play_arrowquestion_answer119) For a reversible reaction : \[X(g)+3Y(g)2Z(g);\,\,\Delta H=-40kJ\] 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) \[400\,\,K\] done clear
B) \[500\,\,K\] done clear
C) \[273\,\,K\] done clear
D) \[373\,\,K\] done clear
View Answer play_arrowquestion_answer120) Which of the following gives aldol condensation reaction?
A) \[{{C}_{6}}{{H}_{5}}OH\] done clear
B) \[{{C}_{6}}{{H}_{5}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-{{C}_{6}}{{H}_{5}}\] done clear
C) \[C{{H}_{3}}C{{H}_{2}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\] done clear
D) \[{{(C{{H}_{3}})}_{3}}C-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-{{C}_{6}}{{H}_{5}}\] done clear
View Answer play_arrowquestion_answer121) The range of the function\[f\left( x \right)={{x}^{2}}+\frac{1}{{{x}^{2}}+1}\]is
A) \[[1,\,\,\infty )\] done clear
B) \[[2,\,\,\infty )\] done clear
C) \[\left[ \frac{3}{2},\,\,\infty \right)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer122) If\[f\left( x \right)=\left\{ \begin{matrix} a{{x}^{2}}+b, & b\ne 0,\,\,x\le 1 \\ b{{x}^{2}}+ax+c, & x>1 \\ \end{matrix} \right.\],then \[f\left( x \right)\]is continuous and differentiable at\[x=1\], if
A) \[c=0,\,\,a=2b\] done clear
B) \[a=b,\,\,c\in R\] done clear
C) \[a=b,\,\,c=0\] done clear
D) \[a=b,\,\,c\ne 0\] done clear
View Answer play_arrowquestion_answer123) If a circle passes through the point\[(1,\,\,2)\]and cuts the circle\[{{x}^{2}}+{{y}^{2}}=4\]orthogonally, then the equation of the locus of its centre is
A) \[{{x}^{2}}+{{y}^{2}}-3x-8y+1=0\] done clear
B) \[{{x}^{2}}+{{y}^{2}}-2x-6y-7=0\] done clear
C) \[2x+4y-9=0\] done clear
D) \[2x+4y-1=0\] done clear
View Answer play_arrowquestion_answer124) If\[\int{f\left( x \right)}\sin x\cos x\,\,dx\] \[=\frac{1}{2({{b}^{2}}-{{a}^{2}})}\log [f(x)]+c,\] then\[f\left( x \right)\]is equal to
A) \[\frac{1}{{{a}^{2}}{{\sin }^{2}}x+{{b}^{2}}{{\cos }^{2}}x}\] done clear
B) \[\frac{1}{{{a}^{2}}{{\sin }^{2}}x-{{b}^{2}}{{\cos }^{2}}x}\] done clear
C) \[\frac{1}{{{a}^{2}}{{\cos }^{2}}x-{{b}^{2}}{{\sin }^{2}}x}\] done clear
D) \[\frac{1}{{{a}^{2}}{{\cos }^{2}}x+{{b}^{2}}{{\sin }^{2}}x}\] done clear
View Answer play_arrowquestion_answer125) The points representing complex number 2 for which\[\left| z-3 \right|=\left| z-5 \right|\]lie on the locus given by
A) an ellipse done clear
B) a circle done clear
C) a straight line done clear
D) None of the above done clear
View Answer play_arrowquestion_answer126) The value of\[\alpha \], for which the equation\[{{x}^{2}}-(\sin \alpha -2)x-(1+\sin \alpha )=0\]has roots whose sum of square is least, is
A) \[\frac{\pi }{3}\] done clear
B) \[\frac{\pi }{4}\] done clear
C) \[\frac{\pi }{2}\] done clear
D) \[\frac{\pi }{6}\] done clear
View Answer play_arrowquestion_answer127) For\[n\in N,\,\,{{10}^{n-2}}\ge 81n\], is
A) \[n>5\] done clear
B) \[n\ge 5\] done clear
C) \[n<5\] done clear
D) \[n>8\] done clear
View Answer play_arrowquestion_answer128) The two consecutive terms in the expansion of\[{{(3+2x)}^{74}}\]whose coefficients are equal are
A) 11, 12 done clear
B) 7, 8 done clear
C) 30, 31 done clear
D) None of these done clear
View Answer play_arrowquestion_answer129) The value of\[2.\overline{357}\]is
A) \[\frac{2355}{999}\] done clear
B) \[\frac{2355}{1000}\] done clear
C) \[\frac{2355}{1111}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer130) Let\[{{S}_{n}}=\frac{1}{{{1}^{3}}}+\frac{1}{{{1}^{3}}}+\frac{2}{{{2}^{3}}}+...+\frac{1+2+...+n}{{{1}^{3}}+{{2}^{3}}+...+n}\] \[n=1,2,3,...\]. Then,\[{{S}_{n}}\]is not greater than
A) \[\frac{1}{2}\] done clear
B) 1 done clear
C) 2 done clear
D) 4 done clear
View Answer play_arrowquestion_answer131) If\[E(\theta )=\left[ \begin{matrix} {{\cos }^{2}}\theta & \cos \theta \sin \theta \\ \cos \theta \sin \theta & {{\sin }^{2}}\theta \\ \end{matrix} \right]\]and\[\theta \]and\[\phi \] differ by an odd multiple of\[\frac{\pi }{2}\], then\[E(\theta )E(\phi )\]is a
A) unit matrix done clear
B) null matrix done clear
C) diagonal matrix done clear
D) None of the above done clear
View Answer play_arrowquestion_answer132) A parabola is drawn with its focus at\[(3,\,\,4)\]and vertex at the focus of the parabola\[{{y}^{2}}-12x-4y+4=0\]. The equation of the parabola is
A) \[{{y}^{2}}-8x-6y+25=0\] done clear
B) \[{{y}^{2}}-6x+8y-25=0\] done clear
C) \[{{x}^{2}}-6x-8y+25=0\] done clear
D) \[{{x}^{2}}+6x-8y-25=0\] done clear
View Answer play_arrowquestion_answer133) If\[p,\,\,p\]denote the lengths of the perpendiculars from the focus and the centre of an ellipse with semi major axis of length a respectively on a tangent to the ellipse and\[r\]denotes the focal distance of the point, then
A) \[ap=rp+1\] done clear
B) \[rp=ap\] done clear
C) \[ap=rp+1\] done clear
D) \[ap=rp\] done clear
View Answer play_arrowquestion_answer134) The equation of perpendicular bisectors of sides\[AB\]and\[AC\]of a\[\Delta ABC\]are\[x-y+5=0\] and\[x+2y=0\]respectively. If the coordinates of vertex\[A\]are\[(1,\,\,-2)\], the equation of\[BC\]is
A) \[14x+23y-40=0\] done clear
B) \[14x-23y+40=0\] done clear
C) \[23x+14y-40=0\] done clear
D) \[23x-14y+40=0\] done clear
View Answer play_arrowquestion_answer135) If\[\cos \theta =-\frac{\sqrt{3}}{2}\]and\[\sin \alpha =-\frac{3}{5}\], where\[\theta \]does not lie in the third quadrant, then \[\frac{2\tan \alpha +\sqrt{3}\tan \theta }{{{\cot }^{2}}\theta +\cos \alpha }\]is equal to
A) \[\frac{7}{22}\] done clear
B) \[\frac{5}{22}\] done clear
C) \[\frac{9}{22}\] done clear
D) \[\frac{22}{5}\] done clear
View Answer play_arrowquestion_answer136) A parallelogram is constructed on the vectors \[\overset{\to }{\mathop{\mathbf{a}}}\,=3\overset{\to }{\mathop{\alpha }}\,-\overset{\to }{\mathop{\beta }}\,,\,\,\overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\alpha }}\,+3\overset{\to }{\mathop{\beta }}\,\], if\[\left| \overset{\to }{\mathop{\alpha }}\, \right|=\left| \overset{\to }{\mathop{\beta }}\, \right|=2\]and angle between\[\overset{\to }{\mathop{\alpha }}\,\]and\[\overset{\to }{\mathop{\beta }}\,\]is\[\frac{\pi }{3}\], then length of a diagonal of the parallelogram is
A) \[4\sqrt{5}\] done clear
B) \[4\sqrt{3}\] done clear
C) \[4\sqrt{17}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer137) The value of\[c\], so that for all real\[x\], the vectors\[cx\widehat{\mathbf{i}}-6\widehat{\mathbf{j}}+3\widehat{\mathbf{k}}\],\[x\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}+2cx\widehat{\mathbf{k}}\]make an obtuse angle, are
A) \[c<0\] done clear
B) \[0<c<\frac{4}{3}\] done clear
C) \[-\frac{4}{3}<c<0\] done clear
D) \[c>0\] done clear
View Answer play_arrowquestion_answer138) The solution of the equation \[y-x\frac{dy}{dx}=a\left( {{y}^{2}}+\frac{dy}{dx} \right)\]
A) \[y=c(x+a)(1-ay)\] done clear
B) \[y=c(x+a)(1+ay)\] done clear
C) \[y=c(x-a)(1+ay)\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer139) The order of the differential equation whose general solution is given by\[y=({{c}_{1}}+{{c}_{2}})\cos (x+{{c}_{3}})-{{c}_{4}}{{e}^{x\_{{c}_{5}}}}\], where\[{{c}_{1}},\,\,{{c}_{2}},\,\,{{c}_{3}},\,\,{{c}_{4}},\,\,{{c}_{5}}\]are arbitrary constants, is
A) 4 done clear
B) 3 done clear
C) 2 done clear
D) 5 done clear
View Answer play_arrowquestion_answer140) If\[f(x)={{x}^{3}}+b{{x}^{2}}+cx+d\]and\[0<{{b}^{2}}<c\], then in\[(-\infty ,\,\,\infty )\]
A) \[f(x)\]is strictly increasing function done clear
B) \[f(x)\]has a local maxima done clear
C) \[f(x)\]strictly decreasing function done clear
D) \[f(x)\]is bounded done clear
View Answer play_arrowquestion_answer141) \[\frac{d}{dx}{{\sin }^{-1}}(x\sqrt{1-x}+\sqrt{x}\sqrt{1-{{x}^{2}}})\]
A) \[-\frac{1}{2x\sqrt{1-x}}-\frac{1}{\sqrt{1-{{x}^{2}}}}\] done clear
B) \[\frac{1}{2\sqrt{x}\sqrt{1-x}}-\frac{1}{\sqrt{1-{{x}^{2}}}}\] done clear
C) \[\frac{1}{2\sqrt{x}\sqrt{1-x}}+\frac{1}{\sqrt{1-{{x}^{2}}}}\] done clear
D) \[-\frac{1}{2\sqrt{x}\sqrt{1-x}}+\frac{1}{\sqrt{1-{{x}^{2}}}}\] done clear
View Answer play_arrowquestion_answer142) \[\int{\frac{x{{\tan }^{-1}}x}{{{(1+{{x}^{2}})}^{3}}}}dx\]is equal to
A) \[\frac{x-{{\tan }^{-1}}x}{1-{{x}^{2}}}+c\] done clear
B) \[\frac{x+{{\tan }^{-1}}x}{\sqrt{1-{{x}^{2}}}}+c\] done clear
C) \[\frac{x-{{\tan }^{-1}}x}{\sqrt{1+{{x}^{2}}}}+c\] done clear
D) \[\frac{x+\sqrt{1-{{x}^{2}}}}{\sqrt{1+{{x}^{2}}}}+c\] done clear
View Answer play_arrowquestion_answer143) Let\[A=\left[ \begin{matrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \\ \end{matrix} \right]\], where\[0\le \theta \le 2\pi \]. Then, the range of\[\left| A \right|\]is
A) 0 done clear
B) {2, 4} done clear
C) [2, 4] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer144) If\[y=\left| \cos x \right|+\left| \sin x \right|\], then\[\frac{dy}{dx}\]at\[x=\frac{2\pi }{3}\]is
A) 0 done clear
B) 1 done clear
C) \[\frac{1-\sqrt{3}}{2}\] done clear
D) \[\frac{\sqrt{3}-1}{2}\] done clear
View Answer play_arrowquestion_answer145) \[\underset{n\to \infty }{\mathop{\lim }}\,\left( \frac{1}{1-{{n}^{2}}}+\frac{2}{1-{{n}^{2}}}+...+\frac{n}{1-{{n}^{2}}} \right)\]is equal to
A) 0 done clear
B) \[-\frac{1}{2}\] done clear
C) \[\frac{1}{2}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer146) Let\[f(x)=\left\{ \begin{matrix} \sin x, & x\ne n\pi \\ 2 & x=n\pi \\ \end{matrix} \right.\], where\[n\in I\]and\[g(x)=\left\{ \begin{matrix} {{x}^{2}}+1, & x\ne 2 \\ 3, & x=2 \\ \end{matrix} \right.\], then\[\underset{x\to 0}{\mathop{\lim }}\,g[f(x)]\]is
A) 1 done clear
B) 0 done clear
C) 3 done clear
D) does not exist done clear
View Answer play_arrowquestion_answer147) The intercept made by the tangent to the curve\[y=\int_{0}^{x}{|t|}\,\,dt\],which is parallel to the line \[y=2x\], on x-axis is equal to
A) 1 done clear
B) -2 done clear
C) 2 done clear
D) None of these done clear
View Answer play_arrowquestion_answer148) If\[P={{x}^{3}}-\frac{1}{{{x}^{3}}}\]and\[Q=x-\frac{1}{x},\,\,x\in (0,\,\,x)\], then minimum value of\[\frac{P}{{{Q}^{2}}}\]is
A) \[2\sqrt{3}\] done clear
B) \[-2\sqrt{3}\] done clear
C) does not exist done clear
D) None of these done clear
View Answer play_arrowquestion_answer149) Locus of the point which divides double ordinate of the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]in the ratio 1:2 internally, is
A) \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{9{{y}^{2}}}{{{b}^{2}}}=\frac{1}{9}\] done clear
B) \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{9{{y}^{2}}}{{{b}^{2}}}=1\] done clear
C) \[\frac{9{{y}^{2}}}{{{a}^{2}}}+\frac{9{{y}^{2}}}{{{b}^{2}}}=1\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer150) From any point on the hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]tangents are drawn to the hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=2\]. The area cut-off by the chord of contact on the asymptotes is equal to
A) \[\frac{ab}{2}\] done clear
B) \[ab\] done clear
C) \[2ab\] done clear
D) \[4ab\] done clear
View Answer play_arrowquestion_answer151) The value of the sum of the series\[3{{\cdot }^{n}}{{C}_{0}}-8{{\cdot }^{n}}{{C}_{1}}+{{13}^{n}}{{C}_{2}}-18{{\cdot }^{n}}{{C}_{3}}+...\]upto\[(n+1)\]terms is
A) 0 done clear
B) \[{{3}^{n}}\] done clear
C) \[{{5}^{n}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer152) If\[A\]is a skew-symmetric matrix, then trace of\[A\]is
A) 1 done clear
B) -1 done clear
C) 0 done clear
D) None of these done clear
View Answer play_arrowquestion_answer153) The arbitrary constant on which the value of the determinant \[\left| \begin{matrix} 1 & \alpha & {{\alpha }^{2}} \\ \cos (p-d)a & \cos pa & \cos (p-d)a \\ \sin (p-d)a & \sin pa & \sin (p-d)a \\ \end{matrix} \right|\]does not depend, is
A) \[\alpha \] done clear
B) p done clear
C) d done clear
D) a done clear
View Answer play_arrowquestion_answer154) The sum of the first n terms of the series\[\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+...\]is equal to
A) \[{{2}^{n}}-n+1\] done clear
B) \[1-{{2}^{n}}\] done clear
C) \[n+{{2}^{-n}}-1\] done clear
D) \[{{2}^{n}}-1\] done clear
View Answer play_arrowquestion_answer155) The base of a cliff is circular. From the extremities of a diameter of the base angles of elevation of the top of the cliff are \[{{30}^{o}}\]and\[{{60}^{o}}\]. If the height of the cliff be 500 m, then the diameter of the base of the cliff is
A) \[\frac{2000}{\sqrt{3}}m\] done clear
B) \[\frac{1000}{\sqrt{3}}m\] done clear
C) \[\frac{2000}{\sqrt{3}}m\] done clear
D) \[1000\sqrt{3}\,m\] done clear
View Answer play_arrowquestion_answer156) The most general solutions of the equation\[\sec x-1=(\sqrt{2}-1)\tan x\]are given by
A) \[n\pi +\frac{\pi }{8}\] done clear
B) \[2n\pi ,\,\,2n\pi +\frac{\pi }{4}\] done clear
C) \[2n\pi \] done clear
D) None of these done clear
View Answer play_arrowquestion_answer157) The maximum value of\[\sin \left( x+\frac{\pi }{6} \right)+\cos \left( x+\frac{\pi }{6} \right)\]in the interval \[\left( 0,\,\frac{\pi }{2} \right)\] is attained at
A) \[x=\frac{\pi }{12}\] done clear
B) \[x=\frac{\pi }{6}\] done clear
C) \[x=\frac{\pi }{3}\] done clear
D) \[x=\frac{\pi }{2}\] done clear
View Answer play_arrowquestion_answer158) If\[{{z}_{r}}=\cos \frac{r\alpha }{{{n}^{2}}}+i\sin \frac{r\alpha }{2}\], where\[r=1,\,\,2,\,\,3,....,\,\,n,\]then\[\underset{n\to \infty }{\mathop{\lim }}\,\,\,{{z}_{1}},\,\,{{z}_{2}}...{{z}_{n}}\]is equal to
A) \[\cos \alpha +i\sin \alpha \] done clear
B) \[\cos \left( \frac{\alpha }{2} \right)-i\sin \left( \frac{\alpha }{2} \right)\] done clear
C) \[{{e}^{i\alpha /2}}\] done clear
D) \[\sqrt[3]{{{e}^{i\alpha }}}\] done clear
View Answer play_arrowquestion_answer159) Negation of Paris is in France and London is in England is
A) Paris is in England and London is in France done clear
B) Paris is not in France or London is not in England done clear
C) Paris is in England or London is in France done clear
D) None of the above done clear
View Answer play_arrowquestion_answer160) The area enclosed between the curves\[y={{x}^{3}}\]and\[y=\sqrt{x}\]is
A) \[\frac{5}{3}sq\,\,unit\] done clear
B) \[\frac{5}{4}sq\,\,unit\] done clear
C) \[\frac{5}{12}sq\,\,unit\] done clear
D) \[\frac{12}{5}sq\,\,unit\] done clear
View Answer play_arrowquestion_answer161) Find the equation of the bisector of the obtuse angle between the lines\[3x-4y+7=0\]and\[-12x-5y+2=0\],
A) \[21x+77y-101=0\] done clear
B) \[99x-27y+81=0\] done clear
C) \[21x-77y+101=0\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer162) The equation of curve passing through the point\[\left( 1,\frac{\pi }{4} \right)\]and having slope of tangent at any point\[(x,\,\,y)\]as\[\frac{y}{x}-{{\cos }^{2}}\left( \frac{y}{x} \right)\]is
A) \[x={{e}^{1+\tan \left( \frac{y}{x} \right)}}\] done clear
B) \[x={{e}^{1-\tan \left( \frac{y}{x} \right)}}\] done clear
C) \[x={{e}^{1+\tan \left( \frac{x}{y} \right)}}\] done clear
D) \[x={{e}^{1-\tan \left( \frac{x}{y} \right)}}\] done clear
View Answer play_arrowquestion_answer163) If\[P(n):2+4+6+...+(2n),\,\,n\in N\], then\[P(k)=k(k+1)+2\]implies \[P(k+1)=(k+1)(k+2)+2\]is true for all\[k\in N.\] So, statement\[P(n)=n(n+1)+2\]is true for
A) \[n\ge 1\] done clear
B) \[n\ge 2\] done clear
C) \[n\ge 3\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer164) The differential equation of all non-vertical lines in a plane is
A) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=0\] done clear
B) \[\frac{{{d}^{2}}x}{d{{y}^{2}}}=0\] done clear
C) \[\frac{dy}{dx}=0\] done clear
D) \[\frac{dx}{dy}=0\] done clear
View Answer play_arrowquestion_answer165) The unit vector in ZOX plane and making angle \[{{45}^{o}}\]and \[{{60}^{o}}\]respectively with\[\overset{\to }{\mathop{\mathbf{a}}}\,=2\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}-\widehat{\mathbf{k}}\]and\[\overset{\to }{\mathop{\mathbf{b}}}\,=0\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\widehat{\mathbf{k}}\], is
A) \[-\frac{1}{\sqrt{2}}\widehat{\mathbf{i}}+\frac{1}{\sqrt{2}}\widehat{\mathbf{k}}\] done clear
B) \[\frac{1}{\sqrt{2}}\mathbf{\hat{i}}-\frac{1}{\sqrt{2}}\mathbf{\hat{k}}\] done clear
C) \[\frac{1}{3\sqrt{2}}\widehat{\mathbf{i}}+\frac{4}{3\sqrt{2}}\widehat{\mathbf{j}}+\frac{1}{3\sqrt{2}}\widehat{\mathbf{k}}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer166) If\[\int_{2}^{e}{\left( \frac{1}{\log x}-\frac{1}{{{(\log x)}^{2}}} \right)dx=a+\frac{b}{\log 2}}\],then
A) \[a=e,\,\,b=-2\] done clear
B) \[a=e,\,\,b=2\] done clear
C) \[a=-e,\,\,b=2\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer167) The circle\[{{x}^{2}}+{{y}^{2}}-4x-4y+4=0\]is inscribed in a triangle which has two of its sides along the coordinate axes. If the locus of the circumcentre of the triangle is\[x+y-xy+k\sqrt{{{x}^{2}}+{{y}^{2}}}=0\], then the value of \[k\]is equal to
A) 2 done clear
B) 1 done clear
C) -2 done clear
D) 3 done clear
View Answer play_arrowquestion_answer168) The points of discontinuity of tan x are
A) \[n\pi ,\,\,n\in I\] done clear
B) \[2n\pi ,\,\,n\in I\] done clear
C) \[(2n+1)\frac{\pi }{2},\,\,n\in I\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer169) The two curves\[{{x}^{3}}-3x{{y}^{2}}+2=0\]and\[3{{x}^{2}}y-{{y}^{3}}-2=0\]
A) cut at right angles done clear
B) touch each other done clear
C) cut at an angle\[\frac{\pi }{3}\] done clear
D) cut at an angle\[\frac{\pi }{4}\] done clear
View Answer play_arrowquestion_answer170) The period of the function \[f(x)=\frac{\sin 8x\cos x-\sin 6x\cos 3x}{\cos 2x\cos x-\sin 3x\sin 4x}\]
A) \[\pi \] done clear
B) \[2\pi \] done clear
C) \[\frac{\pi }{2}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer171) The derivative of\[f(\tan x)\]w.r.t.\[g(\sec x)\]at\[x=\frac{\pi }{4}\], where\[f(1)=2\]and\[g(\sqrt{2})=4\], is
A) \[\frac{1}{\sqrt{2}}\] done clear
B) \[\sqrt{2}\] done clear
C) 1 done clear
D) None of these done clear
View Answer play_arrowquestion_answer172) If\[a>0,\,\,b>0\]the maximum area of the triangle formed by the points\[O(0,\,\,0)\]\[A(a\cos \theta ,\,\,b\sin \theta )\]and\[B(a\cos \theta ,\,\,-b\sin \theta )\]is (in sq unit)
A) \[\frac{ab}{2}\]when\[\theta =\frac{\pi }{4}\] done clear
B) \[\frac{3ab}{4}\]when\[\theta =\frac{\pi }{4}\] done clear
C) \[\frac{ab}{2}\]when\[\theta =-\frac{\pi }{2}\] done clear
D) \[{{a}^{2}}{{b}^{2}}\] done clear
View Answer play_arrowquestion_answer173) If the two curves \[y={{a}^{x}}\]and\[y={{b}^{x}}\]intersect at an angle\[\alpha \], then tan a equals
A) \[\frac{\log a-\log b}{1+\log a\log b}\] done clear
B) \[\frac{\log a+\log b}{1-\log a\log b}\] done clear
C) \[\frac{\log a-\log b}{1-\log a\log b}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer174) The number of roots of the equation \[x-\frac{2}{x-1}=1-\frac{2}{x-1}\]
A) 1 done clear
B) 2 done clear
C) 0 done clear
D) infinitely many done clear
View Answer play_arrowquestion_answer175) The vector \[z=-4+5i\]is turned counter clockwise through an angle of\[{{180}^{o}}\]and stretched\[1\frac{1}{2}\]times. The complex number corresponding to newly obtained vector is
A) \[-6+\frac{15}{2}i\] done clear
B) \[6+\frac{15}{2}i\] done clear
C) \[6-\frac{15}{2}i\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer176) If\[A=[{{a}_{ij}}]\]is a4\[4\times 4\]matrix\[{{C}_{ij}}\]is the cofactor of the element\[{{a}_{ij}}\]in\[\left| A \right|\], then the expression\[{{a}_{11}}{{C}_{11}}+{{a}_{12}}{{C}_{12}}+{{a}_{13}}{{C}_{13}}+{{a}_{14}}{{C}_{14}}\]equal to
A) 0 done clear
B) -1 done clear
C) 1 done clear
D) \[\left| A \right|\] done clear
View Answer play_arrowquestion_answer177) If\[A=\left\{ x:\frac{\pi }{6}\le x\le \frac{\pi }{3} \right\}\]and \[f(x)=\cos x-x(1+x)\], then\[f(A)\]is equal to
A) \[\left[ -\frac{\pi }{3},\,\,-\frac{\pi }{6} \right]\] done clear
B) \[\left[ \frac{\pi }{6},\,\,\frac{\pi }{3} \right]\] done clear
C) \[\left[ \frac{1}{2}-\frac{\pi }{3}\left( 1+\frac{\pi }{3} \right),\,\,\frac{\sqrt{3}}{2}-\frac{\pi }{6}\left( 1+\frac{\pi }{6} \right) \right]\] done clear
D) \[\left[ \frac{1}{2}+\frac{\pi }{3}\left( 1-\frac{\pi }{3} \right),\,\,\frac{\sqrt{3}}{2}+\frac{\pi }{6}\left( 1-\frac{\pi }{6} \right) \right]\] done clear
View Answer play_arrowquestion_answer178) The contrapositive of\[(p\vee q)\Rightarrow r\]is
A) \[\tilde{\ }r\Rightarrow (p\vee q)\] done clear
B) \[r\Rightarrow (p\vee q)\] done clear
C) \[\tilde{\ }r\Rightarrow (\tilde{\ }p\wedge \tilde{\ }q)\] done clear
D) \[p\Rightarrow (q\vee r)\] done clear
View Answer play_arrowquestion_answer179) If the function\[f(x)=a{{x}^{3}}+b{{x}^{2}}+11x-6\]satisfies the condition of Rollers theorem in\[[1,\,\,3]\]and\[f\left( 2+\frac{1}{\sqrt{3}} \right)=0\], then the values of \[a,\text{ }b\]are respectively
A) - 1, 6 done clear
B) - 2, 1 done clear
C) 1, -6 done clear
D) \[-1,\,\,\frac{1}{2}\] done clear
View Answer play_arrowquestion_answer180) If\[f(x)=\cos (\log x)\], then \[f\left( \frac{1}{x} \right)f\left( \frac{1}{y} \right)-\frac{1}{2}\left[ f\left( \frac{x}{y} \right)+f(xy) \right]\] is equal to
A) \[\cos (x-y)\] done clear
B) \[\log (x-y)\] done clear
C) \[\cos (x+y)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer181) If\[\alpha ={{\sin }^{-1}}\frac{\sqrt{3}}{2}+{{\sin }^{-1}}\frac{1}{3}\]and\[\beta ={{\cos }^{-1}}\frac{\sqrt{3}}{2}+{{\cos }^{-1}}\frac{1}{3}\], then
A) \[\alpha >\beta \] done clear
B) \[\alpha =\beta \] done clear
C) \[\alpha <\beta \] done clear
D) \[\alpha +\beta =2\pi \] done clear
View Answer play_arrowquestion_answer182) If\[1+\sin \theta +{{\sin }^{2}}\theta +...\infty =4+2\sqrt{3},\,\,0<\theta <\pi \], \[\theta \ne \frac{\pi }{2}\], then
A) \[\theta =\frac{\pi }{3}\] done clear
B) \[\theta =\frac{\pi }{6}\] done clear
C) \[\theta =\frac{\pi }{3}\]or\[\frac{\pi }{6}\] done clear
D) \[\theta =\frac{\pi }{3}\]or\[\frac{2\pi }{3}\] done clear
View Answer play_arrowquestion_answer183) A round balloon of radius\[r\]subtends an angle \[\alpha \]at the eye of the observer, while the angle of elevation of its centre is\[\beta \]. The height of the centre of balloon is
A) \[r\cos ec\alpha \sin \frac{\beta }{2}\] done clear
B) \[r\sin \alpha \cos ec\frac{\beta }{2}\] done clear
C) \[r\sin \frac{\alpha }{2}\cos ec\beta \] done clear
D) \[r\cos ec\frac{\alpha }{2}\sin \beta \] done clear
View Answer play_arrowquestion_answer184) In\[\Delta ABC,\,\,{{(a-b)}^{2}}{{\cos }^{2}}\frac{C}{2}+{{(a+b)}^{2}}{{\sin }^{2}}\frac{C}{2}\]is equal to
A) \[{{a}^{2}}\] done clear
B) \[{{b}^{2}}\] done clear
C) \[{{c}^{2}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer185) In a triangle\[\left( 1-\frac{{{r}_{1}}}{{{r}_{2}}} \right)\left( 1-\frac{{{r}_{1}}}{{{r}_{2}}} \right)=2\], then the triangle is
A) right angled done clear
B) isosceles done clear
C) equilateral done clear
D) None of these done clear
View Answer play_arrowquestion_answer186) If\[a+b+c=0\], then the roots of the equation \[4a{{x}^{2}}+3bx+2c=0\]are
A) equal done clear
B) imaginary done clear
C) real done clear
D) None of these done clear
View Answer play_arrowquestion_answer187) The adjoining graph
A) Connected done clear
B) Disconnected done clear
C) Neither connected nor disconnected done clear
D) None of the above done clear
View Answer play_arrowquestion_answer188) The solution of\[{{\tan }^{-1}}x+2{{\cot }^{-1}}x=\frac{2\pi }{3}\]is
A) \[-\frac{1}{\sqrt{3}}\] done clear
B) \[\frac{1}{\sqrt{3}}\] done clear
C) \[-\sqrt{3}\] done clear
D) \[\sqrt{3}\] done clear
View Answer play_arrowquestion_answer189) The conjugate of the complex number\[\frac{{{(1+i)}^{2}}}{1-i}\]is
A) \[1-i\] done clear
B) \[1+i\] done clear
C) \[-1+i\] done clear
D) \[-1-i\] done clear
View Answer play_arrowquestion_answer190) A graph\[G\]has\[m\]vertices of odd degree and \[n\]vertices of even degree. Then which of the following statements is necessarily true?
A) \[m+n\]is an odd number done clear
B) \[m+n\]is an even number done clear
C) \[n+1\]is an even number done clear
D) \[m+1\]is an odd number done clear
View Answer play_arrowquestion_answer191) The value of\[\sin \left[ 2{{\cos }^{-1}}\frac{\sqrt{5}}{3} \right]\]is
A) \[\frac{\sqrt{5}}{3}\] done clear
B) \[\frac{2\sqrt{5}}{3}\] done clear
C) \[\frac{4\sqrt{5}}{9}\] done clear
D) \[\frac{2\sqrt{5}}{9}\] done clear
View Answer play_arrowquestion_answer192) In the group\[(G,{{\otimes }_{15}})\], where\[G=\{3,\,\,6,\,\,9,\,\,12\}\], \[{{\otimes }_{15}}\]is multiplication modulo 15, the identity element is
A) 3 done clear
B) 6 done clear
C) 12 done clear
D) 9 done clear
View Answer play_arrowquestion_answer193) A group\[(G,\,\,*)\]has 10 elements. The minimum number of elements of\[G\], which are their own inverses is
A) 2 done clear
B) 1 done clear
C) 9 done clear
D) 0 done clear
View Answer play_arrowquestion_answer194) \[\frac{3{{x}^{2}}+1}{{{x}^{2}}-6x+8}\]is equal to
A) \[3+\frac{49}{2(x-4)}-\frac{13}{2(x-2)}\] done clear
B) \[\frac{49}{2(x-4)}-\frac{13}{2(x-2)}\] done clear
C) \[\frac{-49}{2(x-4)}+\frac{13}{2(x-2)}\] done clear
D) \[\frac{49}{2(x-4)}+\frac{13}{2(x-2)}\] done clear
View Answer play_arrowquestion_answer195) The orthocentre of the triangle with vertices\[O(0,\,\,0),\,\,A\left( 0,\,\,\frac{3}{2} \right),\,\,B(-5,\,\,0)\]is
A) \[\left( \frac{5}{2},\,\,\frac{3}{4} \right)\] done clear
B) \[\left( \frac{-5}{2},\,\,\frac{3}{4} \right)\] done clear
C) \[\left( -5,\,\,\frac{3}{2} \right)\] done clear
D) \[(0,\,\,0)\] done clear
View Answer play_arrowquestion_answer196) The range in which\[y=-{{x}^{2}}+6x-3\]increasing, is
A) \[x<3\] done clear
B) \[x>3\] done clear
C) \[7<x<8\] done clear
D) \[5<x<6\] done clear
View Answer play_arrowquestion_answer197) The area bounded by the curve\[x=4-{{y}^{2}}\]and the y-axis is
A) 16 sq unit done clear
B) 32 sq unit done clear
C) \[\frac{32}{3}\]sq unit done clear
D) \[\frac{16}{3}\]sq unit done clear
View Answer play_arrowquestion_answer198) The number of positive divisors of 252 is
A) 9 done clear
B) 5 done clear
C) 18 done clear
D) 10 done clear
View Answer play_arrowquestion_answer199) The remainder obtained when 5124 is divided by 124 is
A) 5 done clear
B) 0 done clear
C) 2 done clear
D) 1 done clear
View Answer play_arrowquestion_answer200) Which of the following is not a group with respect to the given operation?
A) The set of even integers including zero under addition done clear
B) The set of odd integers under addition done clear
C) {0} under addition done clear
D) {1,-1} under multiplication done clear
View Answer play_arrowquestion_answer201) He is so ...... of his own idea that he will not entertain any suggestion from others.
A) hopeful done clear
B) enamoured done clear
C) jealous done clear
D) possessed done clear
View Answer play_arrowquestion_answer202) Undoubtedly, English is the most...... spoken language in the world today.
A) broadly done clear
B) widely done clear
C) greatly done clear
D) beautifully done clear
View Answer play_arrowquestion_answer203) I will be leaving for Delhi tonight and ...... to return by this weekend.
A) waiting done clear
B) plan done clear
C) going done clear
D) making done clear
View Answer play_arrowquestion_answer204) The vacancy ......... by the dismissal of the superintendent is expected to be filled up by the promotion of a U.D.C.
A) made done clear
B) created done clear
C) caused done clear
D) generated done clear
View Answer play_arrowquestion_answer205) HAGGLE
A) Postpone done clear
B) Accept done clear
C) Bargain done clear
D) Reject done clear
View Answer play_arrowquestion_answer206) ABSTRUSE
A) Awful done clear
B) Irrelevant done clear
C) Shallow done clear
D) Profound done clear
View Answer play_arrowquestion_answer207) PENCHANT
A) Like done clear
B) Eagerness done clear
C) Disability done clear
D) Dislike done clear
View Answer play_arrowquestion_answer208) BARTER
A) Deal done clear
B) Return done clear
C) Lend done clear
D) Exchange done clear
View Answer play_arrowquestion_answer209) Bringing about gentle and painless death from incurable disease
A) Gallows done clear
B) Suicide done clear
C) Euphoria done clear
D) Euthanasia done clear
View Answer play_arrowquestion_answer210) The act of killing ones wife
A) Avicide done clear
B) Canicide done clear
C) Uxoricide done clear
D) Genocide done clear
View Answer play_arrowquestion_answer211) Stage between boyhood and youth
A) Infancy done clear
B) Adolescence done clear
C) Puberty done clear
D) Maturity done clear
View Answer play_arrowquestion_answer212) Lack of enough blood
A) Amnesia done clear
B) Insomnia done clear
C) Anaemia done clear
D) Allergy done clear
View Answer play_arrowquestion_answer213) To set the people by ears
A) To box the people done clear
B) To insult and disgrace the people done clear
C) To punish heavily done clear
D) To excite people to a quarrel done clear
View Answer play_arrowquestion_answer214) To give chapter and verse for a thing
A) To produce the proof of something done clear
B) To eulogise the qualities of a thing done clear
C) To make publicity of a thing done clear
D) To attach artificial value to a thing done clear
View Answer play_arrowquestion_answer215) Dog in the manger
A) An undersized bull almost the shape of a dog done clear
B) A dog that has no kennel of its own done clear
C) A person who puts himself in difficulties an account of other people done clear
D) A person who prevents others from enjoying something useless to himself done clear
View Answer play_arrowquestion_answer216) To blow hot and cold
A) Changing weather done clear
B) To be untrustworthy done clear
C) To change opinion often done clear
D) To be rich and poor frequently done clear
View Answer play_arrowquestion_answer217) SAGACIOUS
A) Casual done clear
B) Cunning done clear
C) Foolish done clear
D) False done clear
View Answer play_arrowquestion_answer218) EPILOGUE
A) Conversation done clear
B) Dialogue done clear
C) Dramatic done clear
D) Prologue done clear
View Answer play_arrowquestion_answer219) AUSPICIOUS
A) Spicy done clear
B) Unfavorable done clear
C) Conspicuous done clear
D) Condemnatory done clear
View Answer play_arrowquestion_answer220) ENGULFED
A) Encircled done clear
B) Groped done clear
C) Disfigured done clear
D) Detached done clear
View Answer play_arrowquestion_answer221) Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group?
A) Hill done clear
B) Valley done clear
C) Dam done clear
D) River done clear
View Answer play_arrowquestion_answer222) In a certain code CREAM is written as NBDBQ. How in BREAD written in that code?
A) EBFAQ done clear
B) EBDAQ done clear
C) BEDQA done clear
D) BEFQA done clear
View Answer play_arrowquestion_answer223) If black means white, white means red, red means yellow, yellow means blue, blue means green, green means purple and purple means orange, then what is the colour of lemon?
A) Green done clear
B) Purple done clear
C) Orange done clear
D) Blue done clear
View Answer play_arrowquestion_answer224) Directions: In the following questions, find the word which holds the same relation with the third word as there in between the first two word. Hot: Oven : : Cold :?
A) Ice cream done clear
B) Air conditioner done clear
C) Snow done clear
D) Refrigerator done clear
View Answer play_arrowquestion_answer225) Directions: In the following questions, find the word which holds the same relation with the third word as there in between the first two word. Push : Pull : : Throw :?
A) Jump done clear
B) Collect done clear
C) Pick done clear
D) Game done clear
View Answer play_arrowquestion_answer226) Directions: In each of the following questions, one letter or a set of letter is missing, you have to understand the pattern of the series and insert the appropriate letter? R, M, ?, F, D, ?
A) C, B done clear
B) J, H done clear
C) H, C done clear
D) I, C done clear
View Answer play_arrowquestion_answer227) Directions: In each of the following questions, one letter or a set of letter is missing, you have to understand the pattern of the series and insert the appropriate letter? - bcc - ac - aabb - ab -cc
A) aab ca done clear
B) aba ca done clear
C) ba cab done clear
D) bca ca. done clear
View Answer play_arrowquestion_answer228) How many 9s are there in the following number series which are immediately preceded by 3 and followed by 6? 3 9 6 9 3 9 3 9 3 9 6 3 9 3 6 3 9 5 6 9 5 6 9 3 9 6 3 9
A) 0 done clear
B) 3 done clear
C) 2 done clear
D) 4 done clear
View Answer play_arrowquestion_answer229) Some boys are sitting in a row, P in sitting fourteenth from the left and Q is seventh from the right. If these are four boys between P and Q, how many boys are there in the row?
A) 25 done clear
B) 23 done clear
C) 21 done clear
D) 19 done clear
View Answer play_arrowquestion_answer230) Pointing to a photograph, a woman says, this mans sons sister in my mother-in-law. How is the womans husband related to the man in the photograph?
A) Grandson done clear
B) Son done clear
C) Son-in-law done clear
D) Nephew done clear
View Answer play_arrowquestion_answer231) The longest canal in the world is
A) Volga Baltic done clear
B) Beloye-more Baltic done clear
C) Suez Canal done clear
D) Grand China Canal done clear
View Answer play_arrowquestion_answer232) The oldest Hindu epic is
A) Mahabhashya done clear
B) Ramayan done clear
C) Mahabharata done clear
D) Ashtadhyayi done clear
View Answer play_arrowquestion_answer233) Who among the following is not associated with the Swaraj Party?
A) C.R. Das done clear
B) M.L. Kelkar done clear
C) Motilal Nehru done clear
D) Mahatma Gandhi done clear
View Answer play_arrowquestion_answer234) Where is the City of palaces?
A) London done clear
B) Kolkata done clear
C) Patiala done clear
D) Lucknow done clear
View Answer play_arrowquestion_answer235) Our National Song is
A) Sare Jahan Se Achcha done clear
B) Jana Gana Mana done clear
C) Vande Mataram done clear
D) All of the above done clear
View Answer play_arrowquestion_answer236) The Constitution of India was adopted by the Constituent Assembly on
A) Dec 11, 1946 done clear
B) Aug 15, 1957 done clear
C) Nov 26, 1949 done clear
D) Jan 26, 1949 done clear
View Answer play_arrowquestion_answer237) Gandhijis Dandi March started from
A) Bardoli done clear
B) Ahmedabad done clear
C) Surat done clear
D) Bombay done clear
View Answer play_arrowquestion_answer238) Who was the viceroy of India at the time of formation of the Indian National Congress?
A) Lord Canning done clear
B) Lord Dufferin done clear
C) Lord Mayo done clear
D) Lord Elgin done clear
View Answer play_arrowquestion_answer239) Which country was a major donor in financing the SAARC?
A) Pakistan done clear
B) Sri Lanka done clear
C) India done clear
D) Bangladesh done clear
View Answer play_arrowquestion_answer240) Where in the H. Q. of the European Economic Community?
A) Bonn done clear
B) Rome done clear
C) Brussels done clear
D) Hague done clear
View Answer play_arrow
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