question_answer1) Which of the following pairs have identical dimensions?
A) Momentum and force done clear
B) Pressure and surface tension done clear
C) Moment of force and angular momentum done clear
D) Surface tension and surface energy done clear
View Answer play_arrowquestion_answer2) A train 100 m long travelling at 40 m/s starts overtaking another train 200 m long travelling at 30 m/s. The time taken by the first train to pass the second train completely is
A) 30 s done clear
B) 40 s done clear
C) 50 s done clear
D) 60 s done clear
View Answer play_arrowquestion_answer3) A constant power P is applied to a particle of mass m. The distance travelled by the particle when its velocity increases from \[{{v}_{1}}\] to \[{{v}_{2}}\] is (neglect friction)
A) \[\frac{\text{m}}{\text{3P}}\text{(v}\,_{\text{2}}^{\text{3}}\text{-v}\,_{\text{1}}^{\text{3}}\text{)}\] done clear
B) \[\frac{\text{m}}{\text{3P}}\text{(}{{\text{v}}_{2}}\text{-}{{\text{v}}_{1}}\text{)}\] done clear
C) \[\frac{3P}{m}\text{(v}\,_{2}^{2}\text{-v}\,_{1}^{2}\text{)}\] done clear
D) \[\frac{m}{3P}\text{(v}\,_{2}^{2}\text{-v}\,_{1}^{2}\text{)}\] done clear
View Answer play_arrowquestion_answer4) A spring of constant \[5\,\times {{10}^{3}}\,N/m\] is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is
A) 6.25 Nm done clear
B) 12.5 Nm done clear
C) 18.75 Nm done clear
D) 25.00 Nm done clear
View Answer play_arrowquestion_answer5) Four spheres each having mass m and radius r are placed with their centres on the four comers of a square of side a. Then the moment of inertia of the system about an axis along one of the sides of the square is
A) \[\frac{8}{5}m{{r}^{2}}\] done clear
B) \[\frac{8}{5}m{{r}^{2}}+m{{a}^{2}}\] done clear
C) \[\frac{8}{5}m{{r}^{2}}+2m{{a}^{2}}\] done clear
D) \[\frac{4}{5}m{{r}^{2}}+4m{{a}^{2}}\] done clear
View Answer play_arrowquestion_answer6) If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is
A) \[2R\] done clear
B) \[\frac{R}{2}\] done clear
C) \[R\] done clear
D) \[\frac{R}{4}\] done clear
View Answer play_arrowquestion_answer7) A 2 kg copper block is heated to \[500{}^\circ C\] and then it is placed on a large block of ice at \[0{}^\circ C\]. If the specific heat capacity of copper is 400 J/kg/C and latent heat of water is \[3.5\times {{10}^{5}}J/kg\]. The amount of ice that can melt is
A) 7/8 kg done clear
B) 7/5 kg done clear
C) 8/7 kg done clear
D) 5/7 kg done clear
View Answer play_arrowquestion_answer8) Number of waves in 8 cm of vacuum is same as number of waves in x cm of a medium. Refractive index of medium is 4/3, then the value x is
A) 32/3 cm done clear
B) 12 cm done clear
C) 6 cm done clear
D) 4 cm done clear
View Answer play_arrowquestion_answer9) Consider a gas with density \[\rho \] and \[\overline{\text{c}}\] as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is
A) \[\frac{1}{3}\rho {{\overline{\text{c}}}^{2}}\] done clear
B) \[\frac{1}{3}\rho {{(c+v)}^{2}}\] done clear
C) \[\frac{1}{3}\rho {{(\overline{c}-v)}^{2}}\] done clear
D) \[\frac{1}{3}\rho {{({{\overline{c}}^{2}}-v)}^{2}}\] done clear
View Answer play_arrowquestion_answer10) At 127?C radiated energy is \[2.7\,\times {{10}^{-3}}\,J/s\]. At what temperature radiated energy is \[4.32\,\times {{10}^{6}}J/s\]?
A) 400 K done clear
B) 4000 K done clear
C) 80000 K done clear
D) 40000 K done clear
View Answer play_arrowquestion_answer11) The minimum phase difference between two simple harmonic oscillations,
A) \[{{y}_{1}}=\frac{1}{2}\sin \,\omega t+\frac{\sqrt{3}}{2}\cos \,\omega t\] \[{{y}_{2}}=\sin \,\omega t+\,\omega t,\,\text{is}\] \[\frac{7\pi }{12}\] done clear
B) \[\frac{\pi }{12}\] done clear
C) \[\frac{-\pi }{6}\] done clear
D) \[\frac{\pi }{6}\] done clear
View Answer play_arrowquestion_answer12) A rubber cord catapult has cross-sectional area \[25\,m{{m}^{2}}\] and initial length of rubber cord is 10 cm. It is stretched to 5 cm and then released to project a missile of mass 5 g. Taking \[{{Y}_{rubber}}\,=5\times {{10}^{8}}N{{m}^{-2}},\] velocity of projected missile is
A) \[20\,m{{s}^{-1}}\] done clear
B) \[100\,m{{s}^{-1}}\] done clear
C) \[250\,m{{s}^{-1}}\] done clear
D) \[200\,m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer13) The material of a wire has a density of \[1.4\,g/c{{m}^{3}}\]. If it is not wetted by a liquid of surface tension 44 dyne/cm, then the maximum radius of the wire which can float on the surface of liquid is
A) \[\frac{10}{28}cm\] done clear
B) \[\frac{10}{14}cm\] done clear
C) \[\frac{10}{7}cm\] done clear
D) \[0.7cm\] done clear
View Answer play_arrowquestion_answer14) Binding energy of satellite is \[4\times {{10}^{8}}J\]. Its PE is
A) \[-4\times {{10}^{8}}J\] done clear
B) \[-8\times {{10}^{8}}J\] done clear
C) \[8\times {{10}^{8}}J\] done clear
D) \[4\times {{10}^{8}}J\] done clear
View Answer play_arrowquestion_answer15) A current of 0.01 mA passes through the potentiometer wire of a resistivity of \[{{10}^{9}}\Omega \] and area of cross-section \[{{10}^{-2}}c{{m}^{2}}\]. The potential gradient is
A) \[\text{1}{{\text{0}}^{\text{9}}}\text{V/m}\] done clear
B) \[\text{1}{{\text{0}}^{11}}\text{V/m}\] done clear
C) \[\text{1}{{\text{0}}^{10}}\text{V/m}\] done clear
D) \[\text{1}{{\text{0}}^{8}}\text{V/m}\] done clear
View Answer play_arrowquestion_answer16) A particle of mass m attached with a string of length l is just revolving on the vertical circle without slacking of the string. If \[{{v}_{A,}}{{v}_{B}}\] and\[{{v}_{D}}\] are speeds at positions A, B and D, then
A) \[{{v}_{B}}>{{v}_{D}}>{{v}_{V}}\] done clear
B) tension in string at D = 3 mg done clear
C) \[{{v}_{D}}=\sqrt{3gl}\] done clear
D) All of the above done clear
View Answer play_arrowquestion_answer17) A bucket of water is being revolved in vertical circle of radius 1 m. Minimum frequency required to prevent the water from getting down the path is \[(g=10m/{{s}^{2}})\]
A) \[\frac{2\pi }{\sqrt{10}}\] done clear
B) \[\frac{2\pi }{\sqrt{5}}\] done clear
C) \[\frac{\sqrt{10}}{2\pi }\] done clear
D) \[\frac{\sqrt{5}}{2\pi }\] done clear
View Answer play_arrowquestion_answer18) A round disc of moment of inertia \[{{I}_{2}}\] about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia \[{{l}_{1}}\] rotating with an angular velocity co about the same axis. The final angular velocity of the combination of discs is
A) \[\frac{{{I}_{2}}\omega }{{{I}_{1}}+{{I}_{2}}}\] done clear
B) \[\omega \] done clear
C) \[\frac{{{I}_{1}}\omega }{{{I}_{1}}+{{I}_{2}}}\] done clear
D) \[\frac{({{I}_{1}}+{{I}_{2}})\omega }{{{I}_{1}}}\] done clear
View Answer play_arrowquestion_answer19) Two discs have same mass and thickness. Their materials are of densities \[{{\rho }_{1}}\] and \[{{\rho }_{2.}}\] The ratio of their moment of inertia about central axis will be
A) \[{{\rho }_{1}}:{{\rho }_{2}}\] done clear
B) \[{{\rho }_{1}}:{{\rho }_{2}}:1\] done clear
C) \[1:{{\rho }_{1}}\,{{\rho }_{2}}\] done clear
D) \[{{\rho }_{2}}:\,{{\rho }_{1}}\] done clear
View Answer play_arrowquestion_answer20) A 4 m long wire of resistance \[8\,\Omega \] is connected in series with a battery of emf 2 V and a resistor of \[7\Omega .\] The internal resistance of the battery is \[1\Omega .\] What is the potential gradient along the wire?
A) \[1.00\,V{{m}^{-1}}\] done clear
B) \[0.75\,V{{m}^{-1}}\] done clear
C) \[0.50\,V{{m}^{-1}}\] done clear
D) \[0.25\,V{{m}^{-1}}\] done clear
View Answer play_arrowquestion_answer21) A uniform wire of \[16\,\Omega \] resistance is made into the form of a square. Two opposite corners of the square are connected by a wire of resistance \[16\,\Omega .\] The effective resistance between the other two opposite comers is
A) \[32\,\Omega \] done clear
B) \[16\,\Omega \] done clear
C) \[8\,\Omega \] done clear
D) \[4\,\Omega \] done clear
View Answer play_arrowquestion_answer22) A \[6\times {{10}^{-4}}\,F\] parallel plate air capacitor is connected to a 500 V batten. When air is replaced by another dielectric material, \[7.5\,\times {{10}^{-4}}C\] charge flows into the capacitor. The value of the dielectric constant of the material is
A) 1.5 done clear
B) 2.0 done clear
C) 1.0025 done clear
D) 3.5 done clear
View Answer play_arrowquestion_answer23) The 90 pF capacitor is connected to a 12 V battery. How many electrons are transferred from one plate to another?
A) \[1.1\,\times {{10}^{9}}\] done clear
B) \[6.7\,\times {{10}^{9}}\] done clear
C) \[4\times {{10}^{19}}\] done clear
D) \[5\times {{10}^{19}}\] done clear
View Answer play_arrowquestion_answer24) Given mass number of gold = 197, Density of gold \[=19.7\,g/c{{m}^{3}}\] Avogadros number \[=6\times {{10}^{23}}\]. The radius of the gold atom is approximately
A) \[1.5\times {{10}^{-8}}m\] done clear
B) \[1.7\times {{10}^{-9}}m\] done clear
C) \[1.5\times {{10}^{-10}}m\] done clear
D) \[1.5\times {{10}^{-12}}m\] done clear
View Answer play_arrowquestion_answer25) In Youngs double slit experiment, two slits are separated by 1 m. The slits are illuminated by a light of wavelength 650 nm. The source of light is placed symmetrically with respect to the two slits. Interference pattern is observed on a screen at a distance of 1 m from the slits. The distance between the third dark fringe and the fifth bright fringe from the centre of the pattern will be
A) 1.62 mm done clear
B) 2.62 mm done clear
C) 5.62 mm done clear
D) 3.62 mm done clear
View Answer play_arrowquestion_answer26) R is a radius of a planet and p is its density. The escape velocity on its surface will be
A) \[{{R}^{2}}\sqrt{4\pi G\rho /3}\] done clear
B) \[R\sqrt{4\pi G\rho /3}\] done clear
C) \[{{R}^{2}}\sqrt{8\pi G\rho /3}\] done clear
D) \[R\sqrt{8\pi G\rho /3}\] done clear
View Answer play_arrowquestion_answer27) A satellite is moving in a circular orbit at a certain height above the earths surface. It takes \[5.26\,\times {{10}^{3}}\,s\] to complete one revolution with a centripetal acceleration equal to \[9.32\,\,m/{{s}^{2}}\]. The height of satellite orbiting above the earth is (Earths radius \[=6.37\,\times {{10}^{6}}\,m\])
A) 220 km done clear
B) 160 km done clear
C) 70 km done clear
D) 120 km done clear
View Answer play_arrowquestion_answer28) The surface tension of soap solution is 0.03 N/m. The amount of work done in forming a bubble of radius 5 cm is
A) 3.77 J done clear
B) 1.885 J done clear
C) \[0.95\times {{10}^{-3}}J\] done clear
D) \[1.9\times {{10}^{-3}}J\] done clear
View Answer play_arrowquestion_answer29) The minimum velocity of capillary waves on the surface of water is (surface tension of water is \[=7.2\,\times {{10}^{-2}}N/m\])
A) 0.23 m/s done clear
B) 0.46 m/s done clear
C) 0.69 m/s done clear
D) 0.92 m/s done clear
View Answer play_arrowquestion_answer30) 30. A wire has a breaking stress of\[6\times {{10}^{5}}N/{{m}^{2}}\] and a density of \[3\times {{10}^{4}}kg/{{m}^{3}}\]. The length of the wire of the same material which will break under its town weight, (if \[g=10\,m/{{s}^{2}}\]) is
A) 2000 m done clear
B) 2500 m done clear
C) 20 m done clear
D) 2 m done clear
View Answer play_arrowquestion_answer31) A man measures the period of simple pendulum inside a stationary lift and finds it to be T second. If the lift accelerates downwards with acceleration of \[\frac{g}{4},\] the period of oscillation will be
A) \[T\times \frac{\sqrt{3}}{2}s\] done clear
B) \[T\times \frac{2}{\sqrt{3}}s\] done clear
C) \[\frac{T}{2}s\] done clear
D) \[\sqrt{T}s\] done clear
View Answer play_arrowquestion_answer32) A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. If the radius were halved and temperature be doubled, the power radiated in watt would be
A) 1800 done clear
B) 900 done clear
C) 3600 done clear
D) 850 done clear
View Answer play_arrowquestion_answer33) If the emissive power of black surface at same temperature is \[400\,W/{{m}^{2}},\] the emissive and absorptive powers of the surface assuming it was initially ordinary surface, are (Given, Mass of the body m = 4.2 kg, area of body \[=5\times {{10}^{-2}}{{m}^{2}},\] rate of cooling \[\frac{d\theta }{dt}=\frac{1}{12}\times {{10}^{-2}}{{\,}^{\text{o}}}\text{C/min,}\] specific heat\[s=420J/kg{{\,}^{\text{0}}}\text{C)}\]
A) e=\[a\]= 0.0735 done clear
B) e = \[a\] = 0.0435 done clear
C) e =\[a\]=0.0535 done clear
D) e=\[a\]= 0.0235 done clear
View Answer play_arrowquestion_answer34) The expression for total kinetic energy per unit volume of gas is
A) \[\frac{E}{V}=\frac{P}{2}\] done clear
B) \[\frac{E}{V}=\frac{1}{3}P\] done clear
C) \[\frac{E}{V}=\frac{2}{3}P\] done clear
D) \[\frac{E}{V}=\frac{3}{2}P\] done clear
View Answer play_arrowquestion_answer35) A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational KE per. oxygen molecule that per nitrogen molecule is
A) 1 : 1 done clear
B) 1 : 2 done clear
C) 2 : 1 done clear
D) depends on the moments of inertia of the two molecules done clear
View Answer play_arrowquestion_answer36) The wavelength and frequency of beam of light in water of refractive index 4/3 having wavelength 0.48 micron in air are
A) \[0.16\,\times {{10}^{-6}}\,m,\,\,6.25\,\times {{10}^{14}}\,Hz\] done clear
B) \[0.36\,\times {{10}^{-6}}\,m,\,\,6.25\,\times {{10}^{14}}\,Hz\] done clear
C) \[0.36\,\times {{10}^{-6}}\,m,\,\,3.25\,\times {{10}^{14}}\,Hz\] done clear
D) \[0.26\,\times {{10}^{-6}}\,m,\,\,3.25\,\times {{10}^{14}}\,Hz\] done clear
View Answer play_arrowquestion_answer37) A ray of light is incident on glass slab making an angle of incidence sin\[^{-1}\left( \frac{\sqrt{3}}{2} \right).\] What will be the angle of refraction in glass of refractive index 1.5?
A) \[40{}^\circ \text{ }18\] done clear
B) \[24{}^\circ \text{ }49\] done clear
C) \[25{}^\circ \text{ }17\] done clear
D) \[35{}^\circ \text{ }16\] done clear
View Answer play_arrowquestion_answer38) An electron at rest is accelerated through a potential difference of 200 V. If the electron acquires a velocity \[8.4\,\times {{10}^{6}}\,m/s,\] the value of e/m of electron is
A) \[1.76\,\times {{10}^{-4}}C/kg\] done clear
B) \[1.76\,\times {{10}^{14}}C/kg\] done clear
C) \[1.76\,\times {{10}^{11}}C/kg\] done clear
D) \[1.76\,\times {{10}^{-16}}C/kg\] done clear
View Answer play_arrowquestion_answer39) A radio transmitter operates at a frequency of 880 kHz and power of 10 kW. The number of photons emitted per second is
A) \[13.27\,\times {{10}^{4}}\] done clear
B) \[13.27\,\times {{10}^{34}}\] done clear
C) \[1327\,\times {{10}^{34}}\] done clear
D) \[1.71\times {{10}^{31}}\] done clear
View Answer play_arrowquestion_answer40) What is the voltage gain in a common emitter amplifier, when input resistance is \[3\,\Omega \] and load resistance is \[24\,\Omega \] with \[\beta =60\,?\]
A) 480 done clear
B) 2.4 done clear
C) 4.8 done clear
D) 8.4 done clear
View Answer play_arrowquestion_answer41) The input resistance or a common emitter transistor amplifier, if the output resistance is \[500\,k\Omega ,\], the current gain \[\alpha \] = 0.98 and the power gain is \[6.0625\,\times {{10}^{6}},\] is
A) 198 \[\Omega \] done clear
B) \[300\,\Omega \] done clear
C) \[100\,\Omega \] done clear
D) \[400\,\Omega \] done clear
View Answer play_arrowquestion_answer42) Which of the following transitions in hydrogen atom produces longest wavelength of radiation (or photon of minimum energy)?
A) \[n=2,p=4\] done clear
B) \[n=3,p=4\] done clear
C) \[n=6,p=8\] done clear
D) \[n=5,p=6\] done clear
View Answer play_arrowquestion_answer43) If\[\left( \frac{0.51\times {{10}^{-10}}}{4} \right)\]m, is the radius of smallest electron orbit in hydrogen like atom, then this atom is
A) H-atom done clear
B) \[H{{e}^{+}}\] done clear
C) \[L{{i}^{2+}}\] done clear
D) \[B{{e}^{3+}}\] done clear
View Answer play_arrowquestion_answer44) A series resonant circuit contains \[L=\frac{5}{\pi }mH,\] \[C=\frac{200}{\pi }\mu F\] and R = 100 \[\Omega \] If a source of emf It e = 200 sin 1000 \[1000\,\pi t\] is applied, then the rms current is
A) 2 A done clear
B) 200\[\sqrt{2}\] A done clear
C) 100\[\sqrt{2}\] A done clear
D) 1.41 A done clear
View Answer play_arrowquestion_answer45) A rod of length 1.0 m is rotated in a plane perpendicular to a uniform magnetic field of induction 0.25 T with a frequency of 12 rev/s. The induced emf across the ends of the rod is
A) 18.89 V done clear
B) 3 V done clear
C) 15 V done clear
D) 9.42 V done clear
View Answer play_arrowquestion_answer46) A ferromagnetic material is heated above its curie temperature. Which one is a correct statement?
A) Ferromagnetic domains are perfectly arranged done clear
B) Ferromagnetic domains become random done clear
C) Ferromagnetic domains are not influenced done clear
D) Ferromagnetic material changes into diamagnetic material done clear
View Answer play_arrowquestion_answer47) A material is placed in a magnetic field and. It is thrown out of it. Then the material is
A) paramagnetic done clear
B) diamagnetic done clear
C) ferromagnetic done clear
D) non-magnetic done clear
View Answer play_arrowquestion_answer48) A charged particle of mass m and charge q is accelerated through a potential difference of V volt. It enters a region of uniform magnetic field which is directed perpendicular to the direction of motion of the particle. The particle will move on a circular path of radius given by
A) \[\sqrt{\frac{Vm}{q{{B}^{2}}}}\] done clear
B) \[\frac{2Vm}{q{{B}^{2}}}\] done clear
C) \[\sqrt{\frac{2Vm}{q}}.\left( \frac{1}{B} \right)\] done clear
D) \[\sqrt{\frac{Vm}{q}}.\left( \frac{1}{B} \right)\] done clear
View Answer play_arrowquestion_answer49) An electron moves at right angle to a magnetic field of \[1.5\times {{10}^{-2}}T\] with a speed of \[6\times {{10}^{7}}\,m/s\]. If the specific charge on the electron is \[1.7\,\times {{10}^{11}}\,C/kg,\] the radius of the circular path will be
A) 2.9 cm done clear
B) 3.9 cm done clear
C) 2.35 cm done clear
D) 2 cm done clear
View Answer play_arrowquestion_answer50) In a circuit, 5 percent of total current passes through a galvanometer. If resistance of the galvanometer is G. Then the value of the shunt is
A) 19 G done clear
B) 20 G done clear
C) \[\frac{G}{20}\] done clear
D) \[\frac{G}{19}\] done clear
View Answer play_arrowquestion_answer51) Given, C (diamond)\[+\,{{O}_{2}}\xrightarrow{{}}C{{O}_{2}};\Delta H =-395\,kJ\] C (graphite) \[+\,{{O}_{2}}\xrightarrow{{}}C{{O}_{2}};\Delta H =-393\,kJ\] The heat of formation of diamond from graphite is
A) \[+\,2.0\,kJ\] done clear
B) \[-1.5\,kJ\] done clear
C) \[-788\,kJ\] done clear
D) \[788\,kJ\] done clear
View Answer play_arrowquestion_answer52) The type of isomerism observed in benzaldoxime is
A) optical done clear
B) functional done clear
C) geometrial done clear
D) tautomerism done clear
View Answer play_arrowquestion_answer53) Sodium metal is prepared commercially by electrolysis of fused NaCl by
A) Downs process done clear
B) Nelson cell done clear
C) Solvay process done clear
D) Castner and Kellners cell done clear
View Answer play_arrowquestion_answer54) The value of \[x\] is maximum for
A) \[MgS{{O}_{4}}.\,x\,{{H}_{2}}O\] done clear
B) \[CaS{{O}_{4}}.\,x\,{{H}_{2}}O\] done clear
C) \[BaS{{O}_{4}}.\,x\,{{H}_{2}}O\] done clear
D) All have the same value of \[x\] done clear
View Answer play_arrowquestion_answer55) Heating of ore in absence of air below its melting point is called
A) leaching done clear
B) roasting done clear
C) smelting done clear
D) calcination done clear
View Answer play_arrowquestion_answer56) In fluorine group of Periodic Table, on going down
A) ionic radius increases done clear
B) electronegativity increases done clear
C) ionization potential increases done clear
D) reactivity increases done clear
View Answer play_arrowquestion_answer57) The ether that undergoes electrophilic substitution reactions is
A) \[C{{H}_{3}}O{{C}_{2}}{{H}_{5}}\] done clear
B) \[{{C}_{6}}{{H}_{5}}OC{{H}_{3}}\] done clear
C) \[C{{H}_{3}}OC{{H}_{3}}\] done clear
D) \[{{C}_{2}}{{H}_{5}}O{{C}_{2}}{{H}_{5}}\] done clear
View Answer play_arrowquestion_answer58) The order of reactivity of alcohols towards sodium metal is
A) Primary > Secondary > Tertiary done clear
B) Primary < Secondary < Tertiary done clear
C) Primary < Secondary > Tertiary done clear
D) Primary > Secondary < Tertiary done clear
View Answer play_arrowquestion_answer59) If one mole of a substance is present in 1 kg of solvent then its concentration is called
A) molar cone. done clear
B) molal cone. done clear
C) normality done clear
D) strength wt/wt. done clear
View Answer play_arrowquestion_answer60) If the pressure and absolute temperature of 2 L of carbondioxide gas are doubled, the value of the gas would become
A) 2 L done clear
B) 4 L done clear
C) 5 L done clear
D) 7 L done clear
View Answer play_arrowquestion_answer61) \[C{{H}_{3}}CO{{O}^{-}}\] ion is a
A) weak conjugate base done clear
B) strong conjugate base done clear
C) weak conjugate acid done clear
D) strong conjugate add done clear
View Answer play_arrowquestion_answer62) The hybrid state of C in charcoal is
A) \[s{{p}^{3}}\] done clear
B) \[s{{p}^{2}}\] done clear
C) \[sp\] done clear
D) No specific state done clear
View Answer play_arrowquestion_answer63) The shape of \[\text{Cl}{{\text{F}}_{\text{3}}}\]molecule is
A) triangular planar done clear
B) pyramidal done clear
C) T-shape done clear
D) trigonal bipyramidal done clear
View Answer play_arrowquestion_answer64) Equivalent weight of crystalline oxalic acid is
A) 90 done clear
B) 63 done clear
C) 53 done clear
D) 45 done clear
View Answer play_arrowquestion_answer65) If \[x\,\text{mol}\,{{\text{L}}^{-1}}\]is the solubility of \[\text{KAl(S}{{\text{O}}_{\text{4}}}{{\text{)}}_{\text{2}}}\] then \[{{\text{K}}_{\text{sp}}}\]is equal to
A) \[{{x}^{3}}\] done clear
B) \[4{{x}^{4}}\] done clear
C) \[{{x}^{4}}\] done clear
D) \[4{{x}^{3}}\] done clear
View Answer play_arrowquestion_answer66) In the reaction, \[{{N}_{2}}(g)+{{O}_{2}}(g)2NO(g)-180.7\,kJ,\] on increasing the temperature, the production of NO
A) increases done clear
B) decreases done clear
C) remains same done clear
D) Cannot be predicted done clear
View Answer play_arrowquestion_answer67) In an experiment, 20 mL of decinormal \[HCl\] solution was added to 10 mL of a decinormal \[\text{AgN}{{\text{O}}_{\text{3}}}\]solution. \[\text{AgCl}\]was precipitated out and the excess acid was titrated against a decinormal \[\text{NaOH}\] solution. Volume of \[\text{NaOH}\].required for this back titration is
A) 10 mL done clear
B) 5 mL done clear
C) 20 mL done clear
D) 30 mL done clear
View Answer play_arrowquestion_answer68) Consider the following statements.
I. The colour of the hydrophobic sol depends on the wavelength of the light scattered by the dispersed particle. |
II. The smaller the gold number value of a hydrophilic colloid, the greater is its protective power. |
III. The movement of sol particle under an applied electric potential is called electro osmosis. |
A) I and II done clear
B) I and III done clear
C) II and III done clear
D) I, II and III done clear
View Answer play_arrowquestion_answer69) Natural gas is
A) \[CO+{{H}_{2}}\] done clear
B) \[CO+{{N}_{2}}\] done clear
C) \[C{{H}_{4}}+{{O}_{2}}+{{N}_{2}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer70) Colemanite is
A) \[N{{a}_{2}}{{B}_{4}}{{O}_{7}}.10{{H}_{2}}O\] done clear
B) \[C{{a}_{2}}{{B}_{6}}{{O}_{11}}.5{{H}_{2}}O\] done clear
C) \[NaB{{O}_{2}}\] done clear
D) \[{{H}_{3}}B{{O}_{3}}\] done clear
View Answer play_arrowquestion_answer71) Arsenic drugs are mainly used in the treatment of
A) jaundice done clear
B) typhoid done clear
C) syphilis done clear
D) cholera done clear
View Answer play_arrowquestion_answer72) Which of the following statements is not correct?
A) Methylamine is more basic than \[\text{N}{{\text{H}}_{\text{3}}}\] done clear
B) Amines form hydrogen bonds done clear
C) Ethylamine has higher boiling point than propane done clear
D) Dimethylamine is less basic than methylamine done clear
View Answer play_arrowquestion_answer73) Which one of the following will be most basic?
A) Aniline done clear
B) p-methoxyaniline done clear
C) p-nitroaniline done clear
D) Benzylamine done clear
View Answer play_arrowquestion_answer74) The final product of oxidation of 2-propanol with hot cone. \[\text{HN}{{\text{O}}_{\text{3}}}\]is
A) propanal done clear
B) ethanoic acid done clear
C) propanone done clear
D) ethanol done clear
View Answer play_arrowquestion_answer75) Bimolecular reduction of acetone gives
A) diacetoneamine done clear
B) pinacol done clear
C) chloretone done clear
D) propane done clear
View Answer play_arrowquestion_answer76) Aldehydes and ketones give addition reaction with
A) hydrazine done clear
B) phenyl hydrazine done clear
C) semicarbazide done clear
D) hydrogen cyanide done clear
View Answer play_arrowquestion_answer77) Amongst the following, the compound which is most difficult to sulphonate is
A) benzene done clear
B) nitrobenzene done clear
C) toluene done clear
D) chlorobenzene done clear
View Answer play_arrowquestion_answer78) Acetonitrile is prepared by treating an alcoholic solution of methyl iodide with
A) silver cyanide done clear
B) potassium cyanide done clear
C) hydrogen cyanide done clear
D) ammonia done clear
View Answer play_arrowquestion_answer79) During polymerization of acetylene to benzene, the state of hybridisation of carbon changes from
A) \[s{{p}^{2}}\]to \[sp\] done clear
B) \[s{{p}^{3}}\]to \[sp\] done clear
C) \[sp\]to \[s{{p}^{3}}\] done clear
D) \[sp\]to \[s{{p}^{2}}\] done clear
View Answer play_arrowquestion_answer80) Which one of the following series contains electrophiles only?
A) \[{{H}_{2}}O,S{{O}_{3}},{{H}_{3}}{{O}^{+}}\] done clear
B) \[N{{H}_{3}},{{H}_{2}}O,AlC{{l}_{3}}\] done clear
C) \[AlC{{l}_{3}},S{{O}_{3}},\overset{+}{\mathop{N}}\,{{O}_{2}}\] done clear
D) \[{{H}_{2}}O,\overset{+}{\mathop{C}}\,l,N{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer81) The equilibrium constants for the reactions \[{{N}_{2}}+3{{H}_{2}}2N{{H}_{3}}\] and \[\frac{1}{2}{{N}_{2}}+\frac{3}{2}{{H}_{2}}N{{H}_{3}}\] are\[{{K}_{1}}\]and \[{{K}_{2}}\]respectively. Which one of the following is the correct relationship?
A) \[{{K}_{1}}=2{{K}_{2}}\] done clear
B) \[{{K}_{1}}=\frac{1}{2}{{K}_{2}}\] done clear
C) \[{{K}_{2}}=\sqrt{{{K}_{1}}}\] done clear
D) \[{{K}_{1}}={{K}_{2}}\] done clear
View Answer play_arrowquestion_answer82) When we increase the temperature, the rate of reaction increases because of
A) more number of collisions done clear
B) decrease in mean free path done clear
C) more number of energetic electrons done clear
D) less number of energetic electrons done clear
View Answer play_arrowquestion_answer83) The pH of buffer of \[\text{N}{{\text{H}}_{\text{4}}}\text{Cl}\]type is given by
A) \[pH=p{{K}_{b}}\] done clear
B) \[pH=1/2p{{K}_{b}}-1/2\,\log [salt]/[base]\] done clear
C) \[pH=14-p{{K}_{b}}-\log [salt]/[base]\] done clear
D) \[pH=pOH-p{{K}_{b}}+\log [salt]/[base]\] done clear
View Answer play_arrowquestion_answer84) Azimuthal quantum number determines the
A) size done clear
B) spin done clear
C) orientation done clear
D) angular momentum of orbitals done clear
View Answer play_arrowquestion_answer85) The formation of colloid from suspension is called
A) peptisation done clear
B) condensation done clear
C) sedimentation done clear
D) fragmentation done clear
View Answer play_arrowquestion_answer86) Other things being equal, the EMF of a Daniell cell may be increased by
A) keeping low temperature done clear
B) using large copper electrodes done clear
C) using large zinc electrodes done clear
D) decreasing concentration of \[\text{C}{{\text{u}}^{\text{2+}}}\]ions done clear
View Answer play_arrowquestion_answer87) Which one of the following can be considered as a weak electrolyte?
A) \[\text{NaCl}\] done clear
B) \[\text{HCl}\] done clear
C) \[C{{H}_{3}}COOH\] done clear
D) \[{{K}_{2}}S{{O}_{4}}\] done clear
View Answer play_arrowquestion_answer88) lodoform can be prepared from all except
A) acetaldehyde done clear
B) 3-methyl-2-butanone done clear
C) iso-butyl alcohol done clear
D) acetophenone done clear
View Answer play_arrowquestion_answer89) The end product C in the following sequence of chemical reactions is \[C{{H}_{3}}COOH\xrightarrow{CaC{{O}_{3}}}A\xrightarrow{Heat}B\xrightarrow{N{{H}_{2}}OH}C\]
A) acetaldehyde oxime done clear
B) formaldehyde oxime done clear
C) methyl nitrate done clear
D) acetoxime done clear
View Answer play_arrowquestion_answer90) Synthetic human hair wigs are made from a copolymer of vinyl chloride and acrylonitrile and is called
A) PVC done clear
B) polyacrylonitrile done clear
C) cellulose done clear
D) dynel done clear
View Answer play_arrowquestion_answer91) Which one of the following is not an example of chain growth polymer?
A) Neoprene done clear
B) Buna-S done clear
C) PMMA done clear
D) Glyptal done clear
View Answer play_arrowquestion_answer92) Most abundant water pollutant is
A) detergents done clear
B) industrial wastes done clear
C) pesticides done clear
D) oil spills done clear
View Answer play_arrowquestion_answer93) Paulings electronegativity values for elements are useful in predicting
A) polarity of the molecules done clear
B) position in the EMF series done clear
C) coordination numbers done clear
D) dipole moments done clear
View Answer play_arrowquestion_answer94) A neutral ferilizer among the following is
A) CAN done clear
B) ammonium sulphate done clear
C) ammonium nitrate done clear
D) Urea done clear
View Answer play_arrowquestion_answer95) Transition metal with low oxidation number will act as
A) an oxidizing agent done clear
B) a base done clear
C) an acid done clear
D) None of these done clear
View Answer play_arrowquestion_answer96) In \[\text{LiAl}{{\text{H}}_{\text{4}}}\text{,}\]the ligand is
A) H done clear
B) \[{{\text{H}}^{\text{+}}}\] done clear
C) \[{{\text{H}}^{-}}\] done clear
D) \[2{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer97) Iodide of Millons base is
A) \[\text{Hg}{{\text{I}}_{\text{2}}}\] done clear
B) \[{{\text{K}}_{\text{2}}}\text{Hg}{{\text{I}}_{\text{4}}}\] done clear
C) \[\text{N}{{\text{H}}_{\text{4}}}\text{HgO}\text{.HgI}\] done clear
D) \[\text{N}{{\text{H}}_{\text{4}}}\text{I}\] done clear
View Answer play_arrowquestion_answer98) Ce-58 is a member of
A) \[s-\]block elements done clear
B) \[p-\]block elements done clear
C) \[d-\]block elements done clear
D) \[f-\]block elements done clear
View Answer play_arrowquestion_answer99) Complete hydrolysis of \[\text{Xe}{{\text{F}}_{\text{2}}}\]gives
A) Xe done clear
B) \[{{\text{O}}_{\text{2}}}\] done clear
C) HF done clear
D) All of these done clear
View Answer play_arrowquestion_answer100) The alloy best suited for making metre scales is
A) stainless steel done clear
B) invar done clear
C) alnicos done clear
D) tungsten steel done clear
View Answer play_arrowquestion_answer101) The value of \[\sum\limits_{n=1}^{13}{({{i}^{n}}+{{i}^{n+1}}),}\]where \[i=\sqrt{-1}\] equals
A) \[i\] done clear
B) \[i-1\] done clear
C) \[-i\] done clear
D) 0 done clear
View Answer play_arrowquestion_answer102) If \[4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,\] then the value of \[x\]is
A) 0 done clear
B) \[1/2\] done clear
C) 1 done clear
D) \[-\text{ }1\] done clear
View Answer play_arrowquestion_answer103) There are n different books and p copies of each. The number of ways in which a selection can be made from them, is
A) \[{{n}^{p}}\] done clear
B) \[{{p}^{n}}\] done clear
C) \[{{(p+1)}^{n}}-1\] done clear
D) \[{{(n+1)}^{p}}-1\] done clear
View Answer play_arrowquestion_answer104) The circle \[{{S}_{1}}\]with centre \[{{C}_{1}}({{a}_{1}},{{b}_{1}})\]and radius \[{{r}_{1}}\]touches externally the circle \[{{S}_{2}}\]with centre \[{{C}_{2}}({{a}_{2}},{{b}_{2}})\]and radius \[{{r}_{2}}.\] If the tangent at their common point passes through the origin, then
A) \[(a_{1}^{2}+a_{2}^{2})+(b_{1}^{2}+b_{2}^{2})=r_{1}^{2}+r_{2}^{2}\] done clear
B) \[(a_{1}^{2}-a_{2}^{2})+(b_{1}^{2}-b_{2}^{2})=r_{1}^{2}-r_{2}^{2}\] done clear
C) \[{{(a_{1}^{2}-{{b}_{2}})}^{2}}+(a_{2}^{2}+b_{2}^{2})=r_{1}^{2}+r_{2}^{2}\] done clear
D) \[(a_{1}^{2}-b_{1}^{2})+(a_{1}^{2}+b_{2}^{2})=r_{1}^{2}+r_{2}^{2}\] done clear
View Answer play_arrowquestion_answer105) If three vectors a, b, c are such that \[a\ne 0\]and \[a\times b=2(a\times c),|a|=|c|=1,|b|=4\]and the angle between b and c is \[{{\cos }^{-1}}\left( \frac{1}{4} \right).\]Also \[b-2c=\lambda a,\]then find the value of \[\lambda \]
A) \[~\pm \,4\] done clear
B) 14 done clear
C) \[\pm \text{ }2~\] done clear
D) 12 done clear
View Answer play_arrowquestion_answer106) A vector which makes equal angle with the vectors \[1/3(i-2j+2k),1/5(-4i-3k)\]and j is
A) \[5i+j+jk\] done clear
B) \[-6i+j+5k\] done clear
C) \[5i-j-5k\] done clear
D) \[5i+j-5k\] done clear
View Answer play_arrowquestion_answer107) If \[a.b=0\]and \[a+b\]makes an angle of \[{{30}^{o}}\] with a, then
A) \[|b|=2|a|\] done clear
B) \[|a|=2|b|\] done clear
C) \[|a|=\sqrt{3}|b|\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer108) In Simpsons one-third rule the curve \[y=f(x)\]is assumed to be a
A) circle done clear
B) parabola done clear
C) hyperbola done clear
D) None of these done clear
View Answer play_arrowquestion_answer109) Objective of LPP is
A) a constraint done clear
B) a function to be optimized done clear
C) a relation between the variables done clear
D) None of the above done clear
View Answer play_arrowquestion_answer110) The variance of first \[n\] natural number is
A) \[\frac{{{n}^{2}}+1}{12}\] done clear
B) \[\frac{{{n}^{2}}-1}{12}\] done clear
C) \[\frac{(n+1)(2n+1)}{6}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer111) In Boolean algebra, which of the following statement is correct
A) \[(a+b)=a+b\] done clear
B) \[(a+b)=a.b\] done clear
C) \[(a+b)=(a.b)\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer112) The function \[{{x}^{x}}\]decreases in the interval
A) (0, e) done clear
B) (0, 1) done clear
C) (0, 1/e) done clear
D) None of these done clear
View Answer play_arrowquestion_answer113) The period of the function \[f(x)=(\sin 3x)+|\cos 6x|\]is
A) \[\pi \] done clear
B) \[2\pi /3\] done clear
C) \[2\pi \] done clear
D) \[\pi /2\] done clear
View Answer play_arrowquestion_answer114) The differential equation representing the family of curves \[{{y}^{2}}=2x(x+\sqrt{c}),\]where c is a positive perimeter, is of
A) order 1, degree 3 done clear
B) order 2, degree 2 done clear
C) degree 3, order 3 done clear
D) degree 4, order 4 done clear
View Answer play_arrowquestion_answer115) If \[\int_{{}}^{{}}{\sqrt{1+\sin x}}.f(x)dx=\frac{2}{3}{{(1+\sin x)}^{3/2}}+C,\] then \[f(x)\] is equal to
A) \[\cos x\] done clear
B) \[\sin x\] done clear
C) \[\tan x\] done clear
D) 1 done clear
View Answer play_arrowquestion_answer116) \[\int_{{}}^{{}}{x\sqrt{\frac{1-x}{1+x}}}dx\]is equal to
A) \[\left( \frac{x}{2}-1 \right)\sqrt{1-{{x}^{2}}}+\frac{1}{2}{{\sin }^{-1}}x+C\] done clear
B) \[\left( \frac{x}{2}-1 \right)\sqrt{1-{{x}^{2}}}-\frac{1}{2}{{\sin }^{-1}}x+C\] done clear
C) \[\sqrt{1-{{x}^{2}}}+\frac{1}{2}{{\sin }^{-1}}x+C\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer117) If \[x=\sec \theta -\cos \theta \]and \[y={{\sec }^{n}}\theta -{{\cos }^{n}}\theta ,\]then \[{{\left( \frac{dy}{dx} \right)}^{2}}\]is
A) \[\frac{{{n}^{2}}({{y}^{2}}+4)}{{{x}^{2}}+4}\] done clear
B) \[\frac{{{n}^{2}}({{y}^{2}}-4)}{{{x}^{2}}}\] done clear
C) \[n\frac{({{y}^{2}}-4)}{{{x}^{2}}-4}\] done clear
D) \[{{\left( \frac{ny}{x} \right)}^{2}}-4\] done clear
View Answer play_arrowquestion_answer118) The area formed by triangular shaped region bounded by the curves \[y=\sin x,y=\cos x\]and \[x=0\]is
A) \[(\sqrt{2}-1)sq\,unit\] done clear
B) \[\text{1}\,\text{sq}\,\text{unit}\] done clear
C) \[\sqrt{\text{2}}\,\text{sq}\,\text{units}\] done clear
D) \[(\sqrt{2}+1)\,sq\,unit\] done clear
View Answer play_arrowquestion_answer119) Find the value of \[\int_{0}^{\pi /2}{\frac{dx}{1+{{\tan }^{3}}x}}\]
A) 0 done clear
B) 1 done clear
C) \[\pi /2\] done clear
D) \[\pi /4\] done clear
View Answer play_arrowquestion_answer120) The angle of intersection of the curve \[y={{x}^{2}}\] and \[6y=7-{{x}^{3}}\]at \[(1,1)\] is
A) \[\pi /4\] done clear
B) \[\pi /3\] done clear
C) \[\pi /2\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer121) If \[{{I}_{m,n}}=\int_{0}^{1}{{{x}^{m}}{{(\log x)}^{n}}}dx,\]then it is equal to
A) \[\frac{n}{n+1}{{I}_{m,n}}_{-1}\] done clear
B) \[\frac{-m}{n+1}{{I}_{m,n-1}}\] done clear
C) \[\frac{-n}{m+1}{{I}_{m,n-1}}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer122) \[\frac{d}{dx}\cos e{{c}^{-1}}\left( \frac{1+{{x}^{2}}}{2x} \right)\]is equal to
A) \[\frac{-2}{(1+{{x}^{2}})},x\ne 0\] done clear
B) \[\frac{2}{(1+{{x}^{2}})},x\ne 0\] done clear
C) \[\frac{2(1-{{x}^{2}})}{(1+{{x}^{2}})|1-{{x}^{2}}|},x\ne \pm 1,0\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer123) If \[\underset{x\to 0}{\mathop{\lim }}\,\phi (x)={{a}^{3}},a\ne 0,\] then \[\underset{x\to 0}{\mathop{\lim }}\,\phi (x/a)\] is equal to
A) \[{{a}^{2}}\] done clear
B) \[1/{{a}^{3}}\] done clear
C) \[1/{{a}^{2}}\] done clear
D) \[{{a}^{3}}\] done clear
View Answer play_arrowquestion_answer124) If \[(1+tan\theta )(1+tan\phi )=2,\]then \[(\theta +\phi )\]is equal to
A) \[{{30}^{o}}\] done clear
B) \[{{45}^{o}}\] done clear
C) \[{{60}^{o}}\] done clear
D) \[~{{75}^{o}}\] done clear
View Answer play_arrowquestion_answer125) If in a\[\Delta A B C,\cos A+\cos B+\cos C=3/2,\] then triangle is
A) right angled done clear
B) isosceles done clear
C) acute done clear
D) equilateral done clear
View Answer play_arrowquestion_answer126) If the line \[x-1=0\]is the directrix of parabola \[{{y}^{2}}-kx+8=0,\] then one of the value of \[k\]is
A) 1/8 done clear
B) 8 done clear
C) 4 done clear
D) 1/4 done clear
View Answer play_arrowquestion_answer127) The centre of the sphere through the points \[(0,3,4),(0,5,0),(4,0,3)\]and \[(-3,4,0)\]is
A) \[(1/4,3,7/4)\] done clear
B) (0, 0, 0) done clear
C) \[(-4,3,0)\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer128) Solve \[(y\,\log \,x-1)ydx=x\,dy\]
A) \[y(\log ex+cx)=1\] done clear
B) \[y(\log ex+cx)\] done clear
C) \[y(\log ex-(x))=-1\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer129) If \[f(x)=\int_{-1}^{x}{|t|dt,x\ge -1,}\]then
A) \[f\]and\[f\] are continuous for \[x+1>0\] done clear
B) \[f\]is continuous but \[f\] is not continuous for \[x+1>0\] done clear
C) \[f\] and\[f\] are not continuous at \[x=0\] done clear
D) \[f\]is continuous at \[x=0\]but\[f\] is not so done clear
View Answer play_arrowquestion_answer130) AB, AC are tangents to a parabola \[{{y}^{2}}=4ax,\]If \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] are the lengths of perpendiculars from A, B, C on any tangents to the parabola, then
A) \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]are in GGP done clear
B) \[{{l}_{2}},{{l}_{1}},{{l}_{3}}\]are in GP done clear
C) \[{{l}_{3}},{{l}_{1}},{{l}_{2}}\]are in GP done clear
D) \[{{l}_{3}},{{l}_{2}},{{l}_{1}}\]are in GP done clear
View Answer play_arrowquestion_answer131) A family of lines is given by \[(1+2\lambda )x+(1-\lambda )y+\lambda =0,\,\lambda \] being the parameter. The line belonging to this family at the maximum distance from the point\[(1,4)\]is
A) \[4x-y+1=0\] done clear
B) \[33x+12y+7=0\] done clear
C) \[12x+33y=7\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer132) If the eccentricity of the hyperbola \[{{x}^{2}}-{{y}^{2}}{{\sec }^{2}}\alpha =5\]is \[\sqrt{3}\]times the eccentricity of the ellipse \[{{x}^{2}}{{\sec }^{2}}\alpha +{{y}^{2}}=25,\]then the value of \[\alpha \] is
A) \[\pi /6\] done clear
B) \[\pi /4\] done clear
C) \[\pi /3\] done clear
D) \[\pi /2\] done clear
View Answer play_arrowquestion_answer133) Lines of regressions of \[y\] on \[x\] and \[x\] on \[y\] are respectively \[y=ax+b\]and\[x=\alpha y+\beta ,\] If mean of \[x\]and\[y\] series is same, then its value. is
A) \[\frac{b}{1-a}\] done clear
B) \[\frac{1-a}{b}\] done clear
C) \[\frac{\beta }{1-\beta }\] done clear
D) \[\frac{a}{1-\alpha }\] done clear
View Answer play_arrowquestion_answer134) A solution of the differential equation \[{{\left( \frac{dy}{dx} \right)}^{2}}-x\frac{dy}{dx}+y=0\]is
A) \[y=2\] done clear
B) \[y=2x\] done clear
C) \[y=2x-4\] done clear
D) \[y=2{{x}^{2}}-4\] done clear
View Answer play_arrowquestion_answer135) The relation between the time t and distance \[x\] is given by \[t=p{{x}^{2}}+qx,\]where p and q are constants. The relation between velocity v and acceleration \[f\] is
A) \[f\propto v\] done clear
B) \[f\propto {{v}^{4}}\] done clear
C) \[f\propto {{v}^{2}}\] done clear
D) \[f\propto {{v}^{3}}\] done clear
View Answer play_arrowquestion_answer136) The product of\[{{x}^{1/2}}.{{x}^{1/4}},{{x}^{1/8}}....\infty \]equals
A) 0 done clear
B) 1 done clear
C) \[x\] done clear
D) \[\infty \] done clear
View Answer play_arrowquestion_answer137) If the equation \[{{x}^{2}}+ix+a=0,\]\[{{x}^{2}}-2x+ia=0,a\ne 0\]have a common root, then
A) a is real done clear
B) \[a=1/2+i\] done clear
C) \[a=1/2-i\] done clear
D) the other root is also common done clear
View Answer play_arrowquestion_answer138) The distance between the lines \[y=2x+4\]and \[3y=6x-5\] is equal to
A) 1 done clear
B) \[3/\sqrt{5}\] done clear
C) \[\frac{17\sqrt{5}}{15}\] done clear
D) \[\frac{17}{\sqrt{3}}\] done clear
View Answer play_arrowquestion_answer139) The equation\[\frac{{{x}^{2}}}{12-k}+\frac{{{y}^{2}}}{8-k}=1\]represents
A) a hyperbola, if k < 8 done clear
B) an ellipse, if \[k>8\] done clear
C) a hyperbola, if \[8<k<12\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer140) The series \[\frac{1}{(n+1)}+\frac{1}{2{{(n+1)}^{2}}}+\frac{1}{3{{(n+1)}^{3}}}+...\] has the same sum as the series
A) \[\frac{1}{n}-\frac{1}{2{{n}^{2}}}+\frac{1}{3{{n}^{3}}}-\frac{1}{4{{n}^{4}}}+...\] done clear
B) \[\frac{1}{n}+\frac{1}{2{{n}^{2}}}+\frac{1}{3{{n}^{3}}}+\frac{1}{4{{n}^{4}}}+...\] done clear
C) \[\frac{1}{n}+\frac{1}{{{2}^{2}}}.\frac{1}{{{n}^{2}}}+\frac{1}{{{2}^{3}}}.\frac{1}{{{n}^{3}}}+...\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer141) The sum of the infinite series \[\frac{2}{3!}+\frac{4}{5!}+\frac{6}{7!}+\frac{8}{9!}+....\infty \]is
A) \[e\] done clear
B) \[{{e}^{-1}}\] done clear
C) \[2e\] done clear
D) \[{{e}^{2}}\] done clear
View Answer play_arrowquestion_answer142) If the roots of the equation \[a(b-c){{x}^{2}}+b(c-a)x+c(a-b)=0\]are equal, then a, b, c are in
A) AP done clear
B) GP done clear
C) HP done clear
D) None of these done clear
View Answer play_arrowquestion_answer143) The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, then the probability of his shooting the target is
A) 1 done clear
B) \[1-{{(0.7)}^{10}}\] done clear
C) \[{{(0.7)}^{10}}\] done clear
D) \[{{(0.3)}^{10}}\] done clear
View Answer play_arrowquestion_answer144) Let A and B be two events such that\[P(A)=0.3\] and \[P(A\cup B)=0.8\]If A and B. are independent events. Then, \[P(B)\] is equal to
A) 5/7 done clear
B) 2/3 done clear
C) 1 done clear
D) None of these done clear
View Answer play_arrowquestion_answer145) The number of distinct real roots of \[\left| \begin{matrix} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \\ \end{matrix} \right|=0\]in the interval\[x\in \left[ \frac{-\pi }{4},\frac{\pi }{4} \right]\]is
A) 0 done clear
B) 2 done clear
C) 1 done clear
D) 3 done clear
View Answer play_arrowquestion_answer146) If \[A=\left| \begin{matrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \\ \end{matrix} \right|,\] then the value of\[|A||adj(A)|\]is
A) \[{{a}^{3}}\] done clear
B) \[{{a}^{6}}\] done clear
C) \[{{a}^{9}}\] done clear
D) \[{{a}^{27}}\] done clear
View Answer play_arrowquestion_answer147) The term independent of \[x\]in \[{{\left[ \sqrt{\frac{x}{3}}+\sqrt{\frac{3}{2{{x}^{2}}}} \right]}^{10}}\] is
A) \[{{\,}^{10}}{{C}_{1}}\] done clear
B) \[5/12\] done clear
C) 1 done clear
D) None of these done clear
View Answer play_arrowquestion_answer148) \[\frac{\frac{1}{2}.\frac{2}{2}}{{{1}^{3}}}+\frac{\frac{2}{2}.\frac{3}{2}}{{{1}^{3}}+{{2}^{3}}}+\frac{\frac{3}{2}.\frac{4}{2}}{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}+...\]upto \[n\] terms
A) \[\frac{n-1}{2}\] done clear
B) \[\frac{n}{n+1}\] done clear
C) \[\frac{n+1}{n+2}\] done clear
D) \[\frac{(n+1)}{n}\] done clear
View Answer play_arrowquestion_answer149) The solution of the equation \[{{\cos }^{2}}\theta +\sin \theta +1=0,\] lies in the interval
A) \[\left( \frac{-\pi }{4},\frac{\pi }{4} \right)\] done clear
B) \[\left( \frac{\pi }{4},\frac{3\pi }{4} \right)\] done clear
C) \[\left( \frac{3\pi }{4},\frac{5\pi }{4} \right)\] done clear
D) \[\left( \frac{5\pi }{4},\frac{7\pi }{4} \right)\] done clear
View Answer play_arrowquestion_answer150) \[{{\log }_{3}}2,lo{{g}_{6}}2,{{\log }_{12}}2\]are in
A) AP done clear
B) GP done clear
C) HP done clear
D) None of these done clear
View Answer play_arrow
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