Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2012

done Jamia Millia Islamia Solved Paper-2012

  • question_answer1) Two sound waves of slightly different frequencies propagating in the same direction produce beats due to

    A) interference

    B) diffraction

    C) reflection

    D) refraction

    View Answer play_arrow
  • question_answer2) An ice block floats in a liquid whose density is less than water. A part of block is outside the liquid. When whole of ice has melted, the liquid level will

    A) rise

    B) go down

    C) remain same

    D) first rise then go down

    View Answer play_arrow
  • question_answer3) Two bodies of different masses of 2 kg and 4 kg moving with velocities 2 m/s and 10 m/s towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass?

    A) 5 m/s

    B) 6 m/s

    C) 8 m/s

    D) Zero

    View Answer play_arrow
  • question_answer4) Given that the displacement of an oscillating particle is given by\[y=A\text{ }sin(Bx+Ct+D)\]. The dimensional formula for (ABCD) is

    A) \[[{{M}^{0}}{{L}^{-1}}{{T}^{0}}]\]

    B) \[[{{M}^{0}}{{L}^{0}}{{T}^{-1}}]\]

    C) \[[{{M}^{0}}{{L}^{-1}}{{T}^{-1}}]\]

    D) \[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]

    View Answer play_arrow
  • question_answer5) Two waves having intensities in the ratio of \[9:1\]produce interference. The ratio of maximum to minimum intensity is equal to

    A) \[10:8\]

    B) \[9:1\]

    C) \[4:1\]

    D) \[2:1\]

    View Answer play_arrow
  • question_answer6) If a magnet is suspended at angle\[30{}^\circ \]to the magnetic meridian, the dip needle makes an angle of\[45{}^\circ \]with the horizontal. The real dip is

    A) \[{{\tan }^{-1}}(\sqrt{3/2})\]

    B) \[{{\tan }^{-1}}(\sqrt{3})\]

    C) \[{{\tan }^{-1}}(\sqrt{2/3})\]

    D) \[{{\tan }^{-1}}(2/\sqrt{3})\]

    View Answer play_arrow
  • question_answer7) A radioactive element has half-life period of 600 years. After 3000 years, what amount will remain?

    A) \[\frac{1}{2}\]

    B) \[\frac{1}{16}\]

    C) \[\frac{1}{8}\]

    D) \[\frac{1}{32}\]

    View Answer play_arrow
  • question_answer8) Beyond which frequency, the ionosphere bends any incident electromagnetic radiation but do not reflect it back towards the earth?

    A) 50MHz

    B) 40MHz

    C) 30 MHz

    D) 20 MHz

    View Answer play_arrow
  • question_answer9) In intrinsic semiconductor at room temperature number of electrons and holes are

    A) equal

    B) zero

    C) unequal

    D) infinite

    View Answer play_arrow
  • question_answer10) The unit of thermal conductance is

    A) \[W{{K}^{-1}}\]

    B) \[J{{K}^{-1}}\]

    C) \[WK\]

    D) \[JK\]

    View Answer play_arrow
  • question_answer11) The value of P so that the vectors\[2i-j+k,\] \[i+2j-3k\]and\[3i+pj+5k\]are coplanar should be

    A) 16

    B) \[-4\]

    C) 4

    D) \[-8\]

    View Answer play_arrow
  • question_answer12) If the unit of force is 1 kN the length is 1 km and time 100 s, what will be the unit of mass?

    A) 1000kg

    B) 1kg

    C) 10000kg

    D) 100kg

    View Answer play_arrow
  • question_answer13) The maximum tension which an inextensible ring of mass 0.1 kg/m can bear is 10 N. The maximum velocity in m/s with which it can be rotated is

    A) 10

    B) \[\sqrt{10}\]

    C) 20

    D) 15

    View Answer play_arrow
  • question_answer14) If there were a reduction in gravitational effect, which of the following forces do you think would change in some respect?

    A) Magnetic force

    B) Electrostatic force

    C) Viscous force

    D) Archimedes uplift

    View Answer play_arrow
  • question_answer15) The breaking force for a wire of diameter\[D\]of a material is F. The breaking force for a wire of the same material of radius D is

    A) F

    B) 2F

    C) \[\frac{F}{4}\]

    D) 4F

    View Answer play_arrow
  • question_answer16) The maximum range of a gun on horizontal terrain is 16 km if\[g=10\text{ }m/{{s}^{2}}\]. What must be the muzzle velocity of the shell?

    A) 200 m/s

    B) 100 m/s

    C) 400 m/s

    D) 300 m/s

    View Answer play_arrow
  • question_answer17) The length, breadth and thickness of a block are given by\[l=12\text{ }cm,\text{ }b=6\text{ }cm\]and\[t=2.45\]cm. The volume of the block according to the idea of significant figures should be

    A) \[1\times {{10}^{2}}c{{m}^{3}}\]

    B) \[2\times {{10}^{2}}c{{m}^{3}}\]

    C) \[1.763\times {{10}^{2}}c{{m}^{3}}\]

    D) None of these

    View Answer play_arrow
  • question_answer18) Five particles of mass 2 kg are attached to the rim of a circular disc of radius 0.1 m and negligible mass. Moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane is

    A) \[1\,kg\,{{m}^{2}}\]

    B) \[0.1\,kg\,{{m}^{2}}\]

    C) \[2\,kg\,{{m}^{2}}\]

    D) \[0.2\,kg\,{{m}^{2}}\]

    View Answer play_arrow
  • question_answer19) The radius of the convex surface of plan convex lens is 20 cm and the refractive index of the material of the lens is 1.5. The focal length is

    A) 30 cm

    B) 50 cm

    C) 20 cm

    D) 40 cm

    View Answer play_arrow
  • question_answer20) An ice-cube of density\[900\text{ }kg/{{m}^{3}}\]is floating in water of density\[1000\text{ }kg/{{m}^{3}}\]. The percentage of volume of ice-cube outside the water is

    A) 20%

    B) 35%

    C) 10%

    D) 25%

    View Answer play_arrow
  • question_answer21) A sphere of diameter 0.2 m and mass 2 kg is rolling on an inclined plane with velocity\[v=0.5\text{ }m/s\]. The kinetic energy of the sphere is

    A) 0.1 J

    B) 0.3 J

    C) 0.5 J

    D) 0.42 J

    View Answer play_arrow
  • question_answer22) An electron moves at right angle to a magnetic field of\[1.5\times {{10}^{-2}}\]tesia with a speed of\[6\times {{10}^{7}}\] m/s. If the specific charge of the electron is \[1.7\times {{10}^{11}}\] C/kg. The radius of the circular path will be

    A) 2.9cm

    B) 3.9cm

    C) 2.35cm

    D) 2cm

    View Answer play_arrow
  • question_answer23) If work function of a metal is 4.2 eV, the cut off wavelength is

    A) \[8000\text{ }\overset{o}{\mathop{\text{A}}}\,\]

    B) \[7000\text{ }\overset{o}{\mathop{\text{A}}}\,\]

    C) \[\text{1472 }\overset{o}{\mathop{\text{A}}}\,\]

    D) \[\text{2950 }\overset{o}{\mathop{\text{A}}}\,\]

    View Answer play_arrow
  • question_answer24) A particle is executing the motion\[x=a\cos (\omega t-\theta )\]. The velocity of the particle is

    A) \[a\omega \,\cos \theta \]

    B) \[a\omega \]

    C) \[a\omega \,\sin \theta \]

    D) None of these

    View Answer play_arrow
  • question_answer25) A particle is executing two different simple harmonic motions, mutually perpendicular, of different amplitudes and having phase difference of\[\frac{\pi }{2}\]. The path of the particle will be

    A) circular

    B) straight line

    C) parabolic

    D) elliptical

    View Answer play_arrow
  • question_answer26) Equations of motion in the same direction are given by \[{{y}_{1}}=2a\,\sin (\omega t-kx)\] \[{{y}_{2}}=2a\,\sin (\omega t-kx-\theta )\] The amplitude of the medium particle will be

    A) \[2a\,\cos \theta \]

    B) \[\sqrt{2}a\,\cos \theta \]

    C) \[4a\,\cos \frac{\theta }{2}\]

    D) \[\sqrt{2}a\,\cos \frac{\theta }{2}\]

    View Answer play_arrow
  • question_answer27) The work function of sodium is 2.3 eV. The threshold wavelength of sodium will be

    A) \[2900\text{ }\overset{o}{\mathop{\text{A}}}\,\]

    B) \[\text{2500 }\overset{o}{\mathop{\text{A}}}\,\]

    C) \[\text{5380 }\overset{o}{\mathop{\text{A}}}\,\]

    D) \[\text{1200 }\overset{o}{\mathop{\text{A}}}\,\]

    View Answer play_arrow
  • question_answer28) The potential difference between points A and B is

    A) \[\frac{20}{7}V\]

    B) \[\frac{40}{7}V\]

    C) \[\frac{10}{7}V\]

    D) Zero

    View Answer play_arrow
  • question_answer29) A short linear object of length b lies along the axis of a concave mirror of focal length\[f\]at a distance u from the pole of the mirror, what is the size of image?

    A) \[\left( \frac{f}{u-f} \right)b\]

    B) \[{{\left( \frac{f}{u-f} \right)}^{2}}b\]

    C) \[\left( \frac{f}{u-f} \right){{b}^{2}}\]

    D) \[\left( \frac{f}{u-f} \right)\]

    View Answer play_arrow
  • question_answer30) A closed argon pipe and an open argan pipe are tuned to the same fundamental frequency. What is the ratio of their lengths?

    A) \[1:2\]

    B) \[2:1\]

    C) \[2:3\]

    D) \[4:3\]

    View Answer play_arrow
  • question_answer31) When a certain current is passed in the circuit as shown in figure, 10 kcal of heat is produced in\[5\,\Omega \]. resistance. How much heat is produced in\[4\,\Omega \]resistance?

    A) 4 kcal

    B) 2 kcal

    C) 5 kcal

    D) 3 kcal

    View Answer play_arrow
  • question_answer32) A steel scale measures the length of a copper wire as 80.0 cm, when both are at\[20{}^\circ C,\]the calibration temperature for the scale. What would the scale read for the length of the rod when both are at\[40{}^\circ C\]. Given: \[\alpha \]for steel\[=11\times {{10}^{-6}}per{}^\circ C\] and a for\[Cu=17\times {{10}^{-6}}per{}^\circ C\].

    A) 80.0096cm

    B) 80.0272 cm

    C) 1cm

    D) 25.2cm

    View Answer play_arrow
  • question_answer33) A tank is filled with water upto height H. When a hole is made at a distance h below the level of water. What will be the horizontal range of water jet?

    A) \[2\sqrt{h(H-h)}\]

    B) \[4\sqrt{h(H+h)}\]

    C) \[4\sqrt{h(H-h)}\]

    D) \[2\sqrt{h(H+h)}\]

    View Answer play_arrow
  • question_answer34) A raft of wood of mass 120 kg floats in water. The weight that can be put on the raft to make it just sink, should be \[{{d}_{raft}}=600\,kg/{{m}^{3}}\]

    A) 80kg

    B) 50kg

    C) 60kg

    D) 30kg

    View Answer play_arrow
  • question_answer35) A particle is kept at rest at the top of a sphere of diameter 42 m. When disturbed slightly, it slides down. At what height h from the bottom, the particle will leave the sphere

    A) 14m

    B) 28m

    C) 35m

    D) 7m

    View Answer play_arrow
  • question_answer36) If an insulated non-conducting sphere of radius R has charge density\[\rho \]. The electric field at a distance r from the centre of sphere\[(r>R)\]will be

    A) \[\frac{\rho R}{3{{\varepsilon }_{0}}}\]

    B) \[\frac{\rho r}{{{\varepsilon }_{0}}}\]

    C) \[\frac{\rho r}{3{{\varepsilon }_{0}}}\]

    D) \[\frac{3\rho R}{{{\varepsilon }_{0}}}\]

    View Answer play_arrow
  • question_answer37) The minimum wavelength of X-rays emitted by X-rays tube is\[0.4125\text{ }\overset{o}{\mathop{\text{A}}}\,\]. The accelerating voltage is

    A) 30 kV

    B) 50 kV

    C) 80 kV

    D) 60 kV

    View Answer play_arrow
  • question_answer38) A monoatomic gas supplied the heat Q very slowly keeping the pressure constant. The work done by the gas will be

    A) \[\frac{2}{3}Q\]

    B) \[\frac{3}{5}Q\]

    C) \[\frac{2}{5}Q\]

    D) \[\frac{1}{5}Q\]

    View Answer play_arrow
  • question_answer39) The refractive index of the material of the prism and liquid are 1.56 and 1.32 respectively. What will be the value of 9 for the following refraction?

    A) \[\sin \theta \ge \frac{13}{11}\]

    B) \[\sin \theta \ge \frac{11}{13}\]

    C) \[\sin \theta \ge \frac{3}{12}\]

    D) \[\sin \theta \ge \frac{1}{\sqrt{2}}\]

    View Answer play_arrow
  • question_answer40) The temperature of the black body increases from T to 2T. The factor by which the rate of emission will increase, is?

    A) 4

    B) 2

    C) 16

    D) 8

    View Answer play_arrow
  • question_answer41) A police jeep is chasing with velocity of 45 km/h a thief in another jeep moving with velocity 153 km/h. Police fires a bullet with muzzle velocity of 180 m/s. The velocity it will strike the car of the thief is

    A) 150 m/s

    B) 27 m/s

    C) 450 m/s

    D) 250 m/s

    View Answer play_arrow
  • question_answer42) What should be the minimum value of refractive index of the material of the prism for the reflections to take place as shown in the figure

    A) 1.7

    B) 1.4

    C) 1.2

    D) 2.7

    View Answer play_arrow
  • question_answer43) An L-C circuit is in the state of resonance. If \[C=0.1\text{ }\mu F\]and\[L=0.25\text{ }H\]. Neglecting ohmic resistance of circuit. What is the frequency of oscillations?

    A) 1007 Hz

    B) 100 Hz

    C) 109 Hz

    D) 500 Hz

    View Answer play_arrow
  • question_answer44) A person who can see things most clearly at a distance of 10 cm, requires spectacles to enable to see clearly things at a distance of 30 cm. What should be the focal length of the spectacles?

    A) 15 cm (concave)

    B) 15 cm (convex)

    C) 10 cm

    D) 0

    View Answer play_arrow
  • question_answer45) The dimensional formula for Youngs modulus is

    A) \[[M{{L}^{-1}}{{T}^{-2}}]\]

    B) \[[{{M}^{0}}L{{T}^{-2}}]\]

    C) \[[ML{{T}^{-2}}]\]

    D) \[[M{{L}^{2}}{{T}^{-2}}]\]

    View Answer play_arrow
  • question_answer46) When temperature of an ideal gas is increased from\[27{}^\circ C\]to\[227{}^\circ C,\]its rms speed is changed from 400 m/s to\[{{v}_{s}}\]. The\[{{v}_{s}}\] is

    A) 516 m/s

    B) 45 m/s

    C) 310 m/s

    D) 746 m/s

    View Answer play_arrow
  • question_answer47) A simple pendulum of length I has a maximum angular displacement 6. The maximum kinetic energy of the bob is

    A) \[mgl\text{ }(1-cos\text{ }\theta \text{)}\]

    B) \[0.5\text{ }mgl\]

    C) \[mgl\]

    D) \[0.5\text{ }mgl\]

    View Answer play_arrow
  • question_answer48) Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to

    A) \[\frac{1}{R}\]

    B) \[\frac{1}{\sqrt{R}}\]

    C) \[R\]

    D) \[\frac{1}{{{R}^{3/2}}}\]

    View Answer play_arrow
  • question_answer49) The radius R of the soap bubble is doubled under isothermal condition. If T be the surface tension of soap bubble. The work done in doing so is given by

    A) \[32\pi {{R}^{2}}T\]

    B) \[24\pi {{R}^{2}}T\]

    C) \[8\pi {{R}^{2}}T\]

    D) \[4\pi {{R}^{2}}T\]

    View Answer play_arrow
  • question_answer50) A body of specific heat\[0.2\text{ }kcal/kg{}^\circ C\]is heated through\[100{}^\circ C\].The percentage increase in its mass is

    A) 9%

    B) \[9.3\times {{10}^{-11}}%\]

    C) 10%

    D) None of these

    View Answer play_arrow
  • question_answer51) Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, find the ratio of the magnetic field due to one coil and the resultant magnetic field through both coils, if the same current is flown

    A) \[1:\sqrt{2}\]

    B) \[1:2\]

    C) \[1:2\]

    D) \[\sqrt{3}:1\]

    View Answer play_arrow
  • question_answer52) A prism of refractive index\[\sqrt{2}\]has a refracting angle of\[60{}^\circ \]. At what angle a ray must be. incident on it so that it suffers a minimum deviation

    A) \[45{}^\circ \]

    B) \[60{}^\circ \]

    C) \[90{}^\circ \]

    D) \[180{}^\circ \]

    View Answer play_arrow
  • question_answer53) A cone filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. What must be the maximum period of revolution?

    A) 2s

    B) 4s

    C) 1s

    D) 6s

    View Answer play_arrow
  • question_answer54) A conducting sphere of radius R = 20 cm is given a charge\[Q=16\mu C\]. What is E at centre?

    A) \[3.6\times {{10}^{6}}N/C\]

    B) \[1.8\times {{10}^{6}}N/C\]

    C) Zero

    D) \[0.9\times {{10}^{6}}N/C\]

    View Answer play_arrow
  • question_answer55) A coil having N turns carry a current as shown in the figure. The magnetic field intensity at point P is

    A) \[\frac{{{\mu }_{0}}Ni{{R}^{2}}}{2{{({{R}^{2}}+{{x}^{2}})}^{3/2}}}\]

    B) \[\frac{{{\mu }_{0}}Ni}{2\pi R}\]

    C) \[\frac{{{\mu }_{0}}Ni{{R}^{2}}}{{{(R+x)}^{2}}}\]

    D) Zero

    View Answer play_arrow
  • question_answer56) When glycerol is heated with\[KHS{{O}_{4}},\]it gives

    A) \[C{{H}_{2}}=CH-C{{H}_{3}}\]

    B) \[C{{H}_{2}}=CH-C{{H}_{2}}OH\]

    C) \[C{{H}_{2}}=CH-CHO\]

    D) \[C{{H}_{2}}=C=C{{H}_{2}}\]

    View Answer play_arrow
  • question_answer57) Nitrous oxide is

    A) acidic

    B) basic

    C) amphoteric

    D) neutral

    View Answer play_arrow
  • question_answer58) For the redox reaction\[MnO_{4}^{-}+{{C}_{2}}O_{4}^{2-}+{{H}^{+}}\xrightarrow[{}]{{}}M{{n}^{2+}}+C{{O}_{2}}\]\[+{{H}_{2}}O\]the correct coefficients for the balanced reaction are

    A)

    \[MnO_{4}^{-}\] \[{{C}_{2}}O_{4}^{2-}\] \[{{H}^{+}}\]
    2 5 16

    B)

    \[MnO_{4}^{-}\] \[{{C}_{2}}O_{4}^{2-}\] \[{{H}^{+}}\]
    16 5 2

    C)

    \[MnO_{4}^{-}\] \[{{C}_{2}}O_{4}^{2-}\] \[{{H}^{+}}\]
    5 16 2

    D)

    \[MnO_{4}^{-}\] \[{{C}_{2}}O_{4}^{2-}\] \[{{H}^{+}}\]
    2 16 5

    View Answer play_arrow
  • question_answer59) To dissolve 0.9 g metal, 100 mL of\[1\text{ }N\text{ }HCl\]is used. What is the equivalent weight of metal?

    A) 7

    B) 9

    C) 10

    D) 6

    View Answer play_arrow
  • question_answer60) The thermal decomposition of a molecule shows first order kinetics. The molecule decomposes 50% in 120 min. How much time it will take to decompose 90%?

    A) 300 min

    B) 360 min

    C) 398.8mm

    D) 400 min

    View Answer play_arrow
  • question_answer61) Which equation is correct for adiabatic process?

    A) \[Q=+W\]

    B) \[\Delta Q=0\]

    C) \[\Delta E=Q\]

    D) \[p+\Delta V=0\]

    View Answer play_arrow
  • question_answer62) What is the product of the reaction\[{{C}_{6}}{{H}_{5}}COOC{{H}_{3}}\xrightarrow[{}]{LiAl{{H}_{4}}}...+...?\]

    A) \[{{C}_{6}}{{H}_{5}}COOH+C{{H}_{3}}OH\]

    B) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}OH+C{{H}_{3}}OH\]

    C) \[{{C}_{6}}{{H}_{5}}CHO+C{{H}_{3}}COOH\]

    D) All of the above products

    View Answer play_arrow
  • question_answer63) The example of Friedel-Crafts reaction is

    A) \[{{C}_{6}}{{H}_{6}}+{{C}_{2}}{{H}_{5}}Cl\xrightarrow[{}]{AlC{{l}_{3}}}{{C}_{6}}{{H}_{5}}{{C}_{2}}{{H}_{5}}\]\[+HCl\]

    B) \[{{C}_{2}}{{H}_{5}}OH+HCl\xrightarrow[{}]{ZnC{{l}_{2}}}{{C}_{2}}{{H}_{5}}Cl+{{H}_{2}}O\]

    C) \[{{C}_{6}}{{H}_{5}}Cl+C{{H}_{3}}COCl\xrightarrow[{}]{AlC{{l}_{3}}}{{C}_{6}}{{H}_{5}}COC{{H}_{3}}\]\[+C{{l}_{2}}\]

    D) \[{{C}_{6}}{{H}_{5}}Br+Mg\xrightarrow[{}]{Ether}{{C}_{2}}{{H}_{5}}MgBr\]

    View Answer play_arrow
  • question_answer64) The night-blindness is developed due to shortage of which vitamin?

    A) Vitamin \[{{B}_{6}}\]

    B) Vitamin C

    C) Vitamin \[{{B}_{12}}\]

    D) Vitamin A

    View Answer play_arrow
  • question_answer65) Which one of the following forms propane nitrile as the major product?

    A) Ethyl bromide\[+\]alcoholic\[KCN\]

    B) Propyl bromide\[+\]alcoholic\[KCN\]

    C) Propyl bromide\[+\]alcoholic\[AgCN\]

    D) Ethyl bromide\[+\]alcoholic\[AgCN\]

    View Answer play_arrow
  • question_answer66) \[1\text{ }d{{m}^{3}}\]solution containing\[{{10}^{-5}}\]moles each of \[C{{l}^{-}}\]ions and\[CrO_{4}^{2-}\]ions is treated with\[{{10}^{-4}}\] moles of silver nitrate. Which one of the following observations is made? \[[{{K}_{sp}}A{{g}_{2}}Cr{{O}_{4}}=4\times {{10}^{-12}}]\] \[[{{K}_{sp}}AgCl=1\times {{10}^{-10}}]\]

    A) Precipitation does not occur

    B) Silver chromate gets precipitated first

    C) Silver chloride gets precipitated first

    D) Both silver chromate and silver chloride start precipitating simultaneously

    View Answer play_arrow
  • question_answer67) A white crystalline salt A reacts with dilute\[HCl\]to liberate a suffocating gas B and also forms a yellow precipitate. The gas B turns potassium dichromate acidified with dilute \[{{H}_{2}}S{{O}_{4}}\]to a green coloured solution C. A, B and C are respectively

    A) \[N{{a}_{2}}S{{O}_{3}},S{{O}_{2}},C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]

    B) \[N{{a}_{2}}{{S}_{2}}{{O}_{3}},S{{O}_{2}},C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]

    C) \[N{{a}_{2}}{{S}_{2}}{{O}_{3}},C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]

    D) \[N{{a}_{2}}S{{O}_{4}},S{{O}_{2}},C{{r}_{2}}{{(S{{O}_{4}})}_{3}}\]

    View Answer play_arrow
  • question_answer68) Which one of the following statements is true?

    A) Saponification of oil yields a dial

    B) Drying of oil involves hydrolysis

    C) Addition of antioxidant to oil minimizes rancidity

    D) Refining of oil involves hydrogenation

    View Answer play_arrow
  • question_answer69) 9.65 C of electric current is passed through fused anhydrous magnesium chloride. The magnesium metal thus, obtained is completely converted into a Grignard reagent. The number of moles of the Grignard reagent obtained is

    A) \[5\times {{10}^{-4}}\]

    B) \[1\times {{10}^{-4}}\]

    C) \[5\times {{10}^{-5}}\]

    D) \[1\times {{10}^{-5}}\]

    View Answer play_arrow
  • question_answer70) The letter\[D\]in D-glucose signifies

    A) configuration at all chiral carbons

    B) dextrorotatory

    C) that it is a monosaccharide

    D) configuration at a particular chiral carbon

    View Answer play_arrow
  • question_answer71) Chloroacetic acid is a stronger acid than acetic acid. This can be explained using

    A) \[-M\] effect

    B) \[-I\]effect

    C) \[+M\]effect

    D) \[+I\]effect

    View Answer play_arrow
  • question_answer72) Time required for 100 per cent completion of a zero order reaction is

    A) \[\frac{2k}{a}\]

    B) \[\frac{a}{2k}\]

    C) \[\frac{a}{k}\]

    D) \[ak\]

    View Answer play_arrow
  • question_answer73) One mole of an organic compound A with the formula\[{{C}_{3}}{{H}_{8}}O\]reacts completely with two moles of\[HI\]to form \[X\] and Y. When Y is boiled with aqueous alkali, it forms Z. Z answers the iodo form test. The compound A is

    A) propan-2-ol

    B) propan-1-ol

    C) ethoxyethane

    D) methoxyethane

    View Answer play_arrow
  • question_answer74) 1 g of silver gets distributed between\[10\text{ }c{{m}^{3}}\]of molten zinc and\[100\text{ }c{{m}^{3}}\]of molten lead at\[800{}^\circ C\]. The distribution constant is 300. The percentage of silver in the zinc layer is approximately

    A) 89

    B) 91

    C) 97

    D) 94

    View Answer play_arrow
  • question_answer75) In which one of the following, does the given amount of chlorine exert the least pressure in a vessel of capacity\[1\text{ }d{{m}^{3}}\]at 273 K?

    A) 0.0355 g

    B) 0.071 g

    C) \[6.023\times {{10}^{21}}\]molecules

    D) 0.02 mol

    View Answer play_arrow
  • question_answer76) For one mole of an ideal gas, increasing the temperature from\[10{}^\circ C\]to\[20{}^\circ C\]

    A) increases the average kinetic energy by two times

    B) increases the rms velocity by\[\sqrt{2}\]times

    C) increases the rms velocity by two times

    D) increases both the average kinetic energy and rms velocity, but not significantly

    View Answer play_arrow
  • question_answer77) Enthalpy of vaporization of benzene is\[+35.3kJ\] \[mo{{l}^{-1}}\]at its boiling point,\[80{}^\circ C\]. The entropy change in the transition of the vapour to liquid at its boiling point [in\[J{{K}^{-1}}mo{{l}^{-1}}\]]is

    A) \[-\,441\]

    B) \[-100\]

    C) \[+441\]

    D) \[+100\]

    View Answer play_arrow
  • question_answer78) The correct order of boiling points of the hydrides of nitrogen family is

    A) \[N{{H}_{3}}>P{{H}_{3}}>As{{H}_{3}}>Sb{{H}_{3}}\]

    B) \[P{{H}_{3}}<As{{H}_{3}}<N{{H}_{3}}<Sb{{H}_{3}}\]

    C) \[N{{H}_{3}}<P{{H}_{3}}<Sb{{H}_{3}}<As{{H}_{3}}\]

    D) \[N{{H}_{3}}<P{{H}_{3}}<As{{H}_{3}}<Sb{{H}_{3}}\]

    View Answer play_arrow
  • question_answer79) is

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer80) \[Ca{{C}_{2}}+{{N}_{2}}\xrightarrow[{}]{{}}X\]What is the X?

    A) \[CaCN\]

    B) \[Ca{{(CN)}_{2}}\]

    C) \[CaC{{N}_{2}}\]

    D) \[Ca{{C}_{2}}{{N}_{2}}\]

    View Answer play_arrow
  • question_answer81) Which of the following acts as an oxidizing agent?

    A) \[HN{{O}_{3}}\]

    B) \[C{{l}_{2}}\]

    C) \[FeC{{l}_{3}}\]

    D) All of these

    View Answer play_arrow
  • question_answer82) The shape of\[CI{{F}_{3}}\]is

    A) distorted T-shape

    B) pyramidal

    C) tetrahedral

    D) trigonal planar

    View Answer play_arrow
  • question_answer83) The\[{{t}_{1/2}}\]of first order reaction is

    A) dependent of initial concentration

    B) directly proportional to initial concentration

    C) indirectly proportional to initial concentration

    D) independent of initial concentration

    View Answer play_arrow
  • question_answer84) The\[{{K}_{sp}}\]of\[C{{a}_{3}}{{(P{{O}_{4}})}_{2}}\]is

    A) \[[C{{a}^{2+}}]{{[PO_{4}^{3-}]}^{2}}\]

    B) \[{{[C{{a}^{2+}}]}^{3}}[PO_{4}^{3-}]\]

    C) \[[C{{a}^{2+}}][PO_{4}^{3-}]\]

    D) \[{{[C{{a}^{2+}}]}^{3}}{{[PO_{4}^{3-}]}^{2}}\]

    View Answer play_arrow
  • question_answer85) The oxidation number of platinum in\[[Pt{{(N{{H}_{3}})}_{5}}Cl]C{{l}_{3}}\]is

    A) 2

    B) 3

    C) 4

    D) 6

    View Answer play_arrow
  • question_answer86) If\[\Delta G=46.06\text{ }kcal/mol,\]\[{{K}_{p}}\]at 300 K is

    A) \[{{10}^{-33.33}}\]

    B) \[{{10}^{-23.03}}\]

    C) \[{{10}^{-50.12}}\]

    D) \[{{10}^{+33.33}}\]

    View Answer play_arrow
  • question_answer87) \[{{N}_{2}}O\]is isoelectronic to\[C{{O}_{2}}\]and\[N_{3}^{-}\]. Which of the following is the structure of\[{{N}_{2}}O\]?

    A)

    B) \[N-O-N\]

    C) \[N-N-O\]

    D)

    View Answer play_arrow
  • question_answer88) The IUPAC name ofis

    A) 1-cyclohexa-2, 4-dienylethanone

    B) 3-cyclohexa-2, 4-dienylethanone

    C) 1-cyclohexa-3, 5-dienylethanone

    D) 3-cyclohexa-3, 5-dienylethanone

    View Answer play_arrow
  • question_answer89) The IUPAC name of compound\[{{K}_{3}}[Fe{{(CN)}_{5}}NO]\]is

    A) pentacyano nitrosyi potassium ferrate (II)

    B) potassium cyano pentanitrosyi ferrate (II)

    C) potassium pentacyanonitrosyi ferrate (III)

    D) potassium pentacyanonitrosyi ferrate (II)

    View Answer play_arrow
  • question_answer90) 3-pentanol on reaction with aluminium tertiary butoxide in the presence of acetone gives

    A) 3-pentanal

    B) 2-pehtanal

    C) 3-pentanohe

    D) 2-pentanone

    View Answer play_arrow
  • question_answer91) Identify X and Y

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer92) The product formed in the reaction n-hexanamide\[+B{{r}_{2}}+KOH,\]is

    A) hexanamine

    B) propanamme

    C) butanamine

    D) pentanamme

    View Answer play_arrow
  • question_answer93) \[X\xrightarrow[{}]{cone.\text{ }NaOH}Furoic\text{ }acid+Furyl\text{ }alcohol\]Compound X is

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer94) In a chemical reaction catalyst

    A) decreases the energy of activation

    B) increases the energy of activation

    C) does not change energy of activation

    D) None of the above

    View Answer play_arrow
  • question_answer95) \[N{{a}_{2}}S+N{{a}_{2}}[Fe{{(CN)}_{5}}NO]\xrightarrow[{}]{{}}\]purple colour. It is due to

    A) \[N{{a}_{4}}[Fe{{(CN)}_{3}}NOS]\]

    B) \[N{{a}_{3}}[Fe{{(CN)}_{5}}NOS]\]

    C) \[N{{a}_{4}}[Fe{{(CN)}_{5}}NO]\]

    D) \[N{{a}_{4}}[Fe{{(CN)}_{5}}NOS]\]

    View Answer play_arrow
  • question_answer96) Silver chloride dissolves in aqueous ammonia due to the formation of

    A) \[{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}\]

    B) \[[Ag{{(N{{H}_{3}})}_{2}}]\]

    C) \[{{[Ag{{(N{{H}_{4}})}_{2}}]}^{+}}\]

    D) \[[Ag{{(N{{H}_{4}})}_{2}}]\]

    View Answer play_arrow
  • question_answer97) Which of the following is most basic oxide?

    A) \[FeO\]

    B) \[{{K}_{2}}O\]

    C) \[Sn{{O}_{2}}\]

    D) \[CuO\]

    View Answer play_arrow
  • question_answer98) Degree of hydrolysis (to of a salt of weak acid and a strong base is given by

    A) \[h=\sqrt{{{K}_{h}}}\]

    B) \[h=\sqrt{\frac{C}{{{K}_{h}}}}\]

    C) \[h=\sqrt{\frac{{{K}_{h}}}{C}}\]

    D) None of these

    View Answer play_arrow
  • question_answer99) Hexachloroethane is also called

    A) artificial sweeter

    B) artificial camphor

    C) artificial polymer

    D) None of these

    View Answer play_arrow
  • question_answer100) The magnetic moment of\[[Co{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}\]is

    A) 1.73

    B) 2.83

    C) 6.6

    D) zero

    View Answer play_arrow
  • question_answer101) Hybridisation, shape and magnetic moment of \[{{[Ni{{(CN)}_{4}}]}^{2-}}\]ion

    A) \[ds{{p}^{2}},\]square planar, zero

    B) \[ds{{p}^{2}},\]square planar, 1.73

    C) \[s{{p}^{3}}{{d}^{2}},\]octahedral, zero

    D) \[{{d}^{2}}s{{p}^{3}},\]octahedral, 1.73

    View Answer play_arrow
  • question_answer102) If\[\Delta H=-\text{ }25kcal,\text{ }T=300\text{ }K\]and\[\Delta S=9\text{ }cal,\] then the reaction is

    A) spontaneous

    B) non-spontaneous

    C) equilibrium state

    D) None of these

    View Answer play_arrow
  • question_answer103) \[NaN{{H}_{2}}+{{N}_{2}}O\xrightarrow[{}]{{}}X+NaOH+N{{H}_{3}}\].What is the X?

    A) \[Na{{N}_{2}}\]

    B) \[N{{a}_{3}}N\]

    C) \[Na{{N}_{3}}\]

    D) None of these

    View Answer play_arrow
  • question_answer104) The amount of heat measured for a reaction in bomb calorimeter is

    A) \[\Delta G\]

    B) \[\Delta H\]

    C) \[\Delta E\]

    D) \[p.\Delta V\]

    View Answer play_arrow
  • question_answer105) Which one is a colligative property?

    A) Boiling point

    B) Vapour pressure

    C) Osmotic pressure

    D) Freezing point

    View Answer play_arrow
  • question_answer106) Which one of the following statements is incorrect about the molecularity of a reaction?

    A) Molecularity of a reaction is the number of molecules of the reactants present in the balanced equation

    B) Molecularity of a reaction is the number of molecules in the slowest step

    C) Molecularity is always a whole number

    D) There is no difference between order and molecularity of a reaction

    View Answer play_arrow
  • question_answer107) The kinetic theory of gases predicts that total kinetic energy of a gaseous assembly depends on

    A) pressure of the gas

    B) temperature of the gas

    C) volume of the gas

    D) pressure, volume and temperature of the gas

    View Answer play_arrow
  • question_answer108) Phenol dimerises in benzene having vant Hoff factor 0.54. What is the degree of association?

    A) 1.92

    B) 0.98

    C) 1.08

    D) 0.92

    View Answer play_arrow
  • question_answer109) 3 g of an oxide of a metal is converted to chloride completely and it yielded 5 g of chloride. The equivalent weight of the metal is

    A) 33.25

    B) 3.325

    C) 12

    D) 20

    View Answer play_arrow
  • question_answer110) The reaction\[2{{N}_{2}}{{O}_{5}}2{{N}_{2}}{{O}_{4}}+{{O}_{2}}\] is

    A) bimolecular and second order

    B) unimolecular and first order

    C) bimolecular and first order

    D) bimolecular and zero order

    View Answer play_arrow
  • question_answer111) If X and V are independent variables, then correlation coefficient is

    A) 1

    B) \[-1\]

    C) 1/2

    D) 0

    View Answer play_arrow
  • question_answer112) Let n persons sit on a round table. The odd against two specified persons sitting together is

    A) \[2:(n-3)\]

    B) \[(n-1):2\]

    C) \[(n-2):2\]

    D) \[(n-3):2\]

    View Answer play_arrow
  • question_answer113) If the roots of the equation\[\frac{{{x}^{2}}-bx}{ax-c}=\frac{m-1}{m+1}\]are equal and of opposite sign, then the value of m will be

    A) \[\frac{a-b}{a+b}\]

    B) \[\frac{b-a}{a+b}\]

    C) \[\frac{a+b}{a-b}\]

    D) \[\frac{b+a}{b-a}\]

    View Answer play_arrow
  • question_answer114) If \[\tan x=\frac{b}{a},\]then\[\sqrt{\frac{a+b}{a-b}}+\sqrt{\frac{a-b}{a+b}}\]is equal to

    A) \[\frac{2\sin x}{\sqrt{\sin 2x}}\]

    B) \[\frac{2\cos x}{\sqrt{\cos 2x}}\]

    C) \[\frac{2\cos x}{\sqrt{\sin 2x}}\]

    D) \[\frac{2\sin x}{\sqrt{\cos 2x}}\]

    View Answer play_arrow
  • question_answer115) If the lines of regression of Y on X and X on Y make angles\[30{}^\circ \]and\[60{}^\circ ,\]respectively with the positive direction of x-axis, then the correlation coefficient between X and Y is

    A) \[\frac{1}{\sqrt{2}}\]

    B) \[\frac{1}{2}\]

    C) \[1\]

    D) \[\frac{1}{3}\]

    View Answer play_arrow
  • question_answer116) The distance of the point\[(-1,-5,-10)\]from the point of intersection of line \[\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}\]and plane\[x-y+z=5\]is

    A) 10

    B) 8

    C) 21

    D) 13

    View Answer play_arrow
  • question_answer117) Iz\[\sqrt{3}\cos \theta +\sin \theta =\sqrt{2},\]then general value of\[\theta \]is

    A) \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}\]

    B) \[{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{3}\]

    C) \[n\pi +\frac{\pi }{4}-\frac{\pi }{3}\]

    D) \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{3}\]

    View Answer play_arrow
  • question_answer118) If for all values of x and y,\[f(x+y)=f(x)f(y)\]and\[f(5)=2,f(0)=3,\]then\[f(5)\]is

    A) 3

    B) 4

    C) 5

    D) 6

    View Answer play_arrow
  • question_answer119) If\[y=x-{{x}^{2}}+{{x}^{3}}-{{x}^{4}}+.....\infty ,\]then the value of \[x\]will be\[(-1<x<1)\]

    A) \[y+\frac{1}{y}\]

    B) \[\frac{y}{1+y}\]

    C) \[y-\frac{1}{y}\]

    D) \[\frac{y}{1-y}\]

    View Answer play_arrow
  • question_answer120) The number of vector of unit length perpendicular to plane of vector\[a=(1,1,0)\]and \[b=(0,1,1)\]is/are

    A) one

    B) two

    C) three

    D) infinite

    View Answer play_arrow
  • question_answer121) If \[\tan \frac{B-C}{2}=x\cos \frac{A}{2},\]then\[x\]is equal to

    A) \[\frac{c-a}{c+a}\]

    B) \[\frac{a-b}{a+b}\]

    C) \[\frac{b-c}{b+c}\]

    D) None of these

    View Answer play_arrow
  • question_answer122) One root of the equation\[\left| \begin{matrix} x+a & b & c \\ b & x+c & a \\ c & a & x+b \\ \end{matrix} \right|=0\]is

    A) \[-(a+b)\]

    B) \[-(b+c)\]

    C) \[-a\]

    D) \[-(a+b+c)\]

    View Answer play_arrow
  • question_answer123) Let\[x\]and y be two variables and\[x>1,\text{ }xy=1,\] then minimum value of\[x+y\]is

    A) 1

    B) 2

    C) 3

    D) \[3\frac{1}{3}\]

    View Answer play_arrow
  • question_answer124) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin (\pi {{\cos }^{2}}x)}{{{x}^{2}}}\]equals to

    A) \[-\pi \]

    B) \[\pi \]

    C) \[\frac{\pi }{2}\]

    D) \[-\frac{\pi }{2}\]

    View Answer play_arrow
  • question_answer125) If the function,\[f(x)={{x}^{3}}-6{{x}^{2}}+ax+b\] satisfies Rolles theorem in the interval [1, 3] and\[f\left( \frac{2\sqrt{3}+1}{\sqrt{3}} \right)=0,\]then

    A) \[a=-11\]

    B) \[a=-6\]

    C) \[a=6\]

    D) \[a=11\]

    View Answer play_arrow
  • question_answer126) The solution of differential equation\[y-x\frac{dy}{dx}=a\left( {{y}^{2}}+\frac{dy}{dx} \right)\]is

    A) \[(x+a)(x+ay)=cy\]

    B) \[(x+a)(1-ay)=cy\]

    C) \[(x+a)(1-ay)=c\]

    D) None of the above

    View Answer play_arrow
  • question_answer127) The maximum value of\[3\text{ }cos\text{ }\theta +4\text{ }sin\text{ }\theta \] is

    A) 3

    B) 4

    C) 5

    D) Nona of these

    View Answer play_arrow
  • question_answer128) The domain of the function\[\sqrt{{{\log }_{e}}({{x}^{2}}-6x+6)}\]is

    A) \[(-\infty ,3-\sqrt{3}]\cup [3+\sqrt{3},\infty ]\]

    B) \[(-\infty ,3-\sqrt{3}]\cup (3+\sqrt{3},\infty ]\]

    C) \[(-\infty ,1]\cup [5,\infty )\]

    D) \[(-\infty ,1)\cup (5,\infty )\]

    View Answer play_arrow
  • question_answer129) \[\int{{{e}^{x}}(1-\cot x+{{\cot }^{2}}x)}\,dx\]equals to

    A) \[{{e}^{x}}\cot x+C\]

    B) \[{{e}^{x}}\cos ecx+C\]

    C) \[-{{e}^{x}}\cot x+C\]

    D) \[-{{e}^{x}}\cos ecx+C\]

    View Answer play_arrow
  • question_answer130) The speed v of a particle moving along a straight line is given by\[a+b{{v}^{2}}={{x}^{2}}\](where X, is its distance from the origin). The acceleration of the particle is

    A) \[bx\]

    B) \[\frac{x}{a}\]

    C) \[\frac{x}{b}\]

    D) \[\frac{x}{ab}\]

    View Answer play_arrow
  • question_answer131) If a and b are two different positive real numbers, then which of the following statements is true?

    A) \[2\sqrt{ab}>a+b\]

    B) \[2\sqrt{ab}<a+b\]

    C) \[2\sqrt{ab}=a+b\]

    D) None of these

    View Answer play_arrow
  • question_answer132) The area of the circle passes through the point (4, 6) and whose centre is (1, 2) is

    A) \[5\pi \] sq units

    B) \[10\pi \]sq units

    C) \[25\pi \] sq units

    D) \[35\pi \]sq units

    View Answer play_arrow
  • question_answer133) If\[\omega \]is a cube root of unity, then\[\left| \begin{matrix} 1 & \omega & {{\omega }^{2}} \\ \omega & {{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & \omega \\ \end{matrix} \right|\]is equal to

    A) 1

    B) 0

    C) \[\omega \]

    D) \[{{\omega }^{2}}\]

    View Answer play_arrow
  • question_answer134) Equation of circle passes through the points of intersection of circles\[{{x}^{2}}+{{y}^{2}}=6\]and \[{{x}^{2}}+{{y}^{2}}-6x+8=0\]and point (1, 1) is

    A) \[{{x}^{2}}+{{y}^{2}}-6x+4=0\]

    B) \[{{x}^{2}}+{{y}^{2}}-3x+1=0\]

    C) \[{{x}^{2}}+{{y}^{2}}-4y+2=0\]

    D) \[{{x}^{2}}+{{y}^{2}}-6x-6y+10=0\]

    View Answer play_arrow
  • question_answer135) Function\[f(x)=\cos x-2ax\]is monotonically decreasing when

    A) \[a<\frac{1}{2}\]

    B) \[a>\frac{1}{2}\]

    C) \[a<0\]

    D) \[a>0\]

    View Answer play_arrow
  • question_answer136) Equation of the ellipse with eccentricity - and foci at\[(\pm 1,\text{ }0)\]is

    A) \[\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=1\]

    B) \[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{3}=1\]

    C) \[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{3}=\frac{4}{3}\]

    D) None of these

    View Answer play_arrow
  • question_answer137) How many words can be formed the letters of the word COMMITTEE?

    A) \[\frac{9!}{{{(2!)}^{2}}}\]

    B) \[\frac{9!}{{{(2!)}^{3}}}\]

    C) \[\frac{9!}{2!}\]

    D) \[9!\]

    View Answer play_arrow
  • question_answer138) The integrating factor of linear differential equation \[\frac{dy}{dx}+y\tan x-\sec x=0\]

    A) \[cos\text{ }x\]

    B) \[\sec \text{ }x\]

    C) \[{{e}^{\cos x}}\]

    D) \[{{e}^{\sin x}}\]

    View Answer play_arrow
  • question_answer139) The value of \[\frac{2}{3!}+\frac{4}{5!}+\frac{6}{7!}+....\]is

    A) \[e\]

    B) \[2e\]

    C) \[{{e}^{2}}\]

    D) \[2e\]

    View Answer play_arrow
  • question_answer140) Let\[f(x)=\left\{ \begin{matrix} 0, & x<0 \\ {{x}^{2}}, & x\ge 0 \\ \end{matrix} \right.\]is

    A) \[f\]is continuous but not differentiable

    B) \[f\]is differentiable but not continuous

    C) \[f\]is continuous and differentiable

    D) None of the above

    View Answer play_arrow
  • question_answer141) The lines\[3x-4y+4=0\]and\[6x-8y-7=0\]are tangents of the circle, then radius of the circle is

    A) \[\frac{1}{4}\]

    B) \[\frac{3}{4}\]

    C) \[\frac{5}{4}\]

    D) \[2\]

    View Answer play_arrow
  • question_answer142) Three vertices out of six vertices of a regular hexagon are chosen randomly. The probability of getting an equilateral triangle after joining three vertices is

    A) \[\frac{1}{5}\]

    B) \[\frac{1}{20}\]

    C) \[\frac{1}{10}\]

    D) \[\frac{3}{20}\]

    View Answer play_arrow
  • question_answer143) The equation of parabola whose focus is (5, 3) and directrix is\[3x-4y+1=0,\]is

    A) \[{{(4x+3y)}^{2}}-256x-142y+849=0\]

    B) \[{{(4x-3y)}^{2}}-256x-142y+849=0\]

    C) \[{{(3x+4y)}^{2}}-142x-256y+849=0\]

    D) \[{{(3x-4y)}^{2}}-256x-142y+849=0\]

    View Answer play_arrow
  • question_answer144) If\[f(x)=\frac{2-\sqrt{x+4}}{\sin 2x}(x\ne 0)\]is continuous function at\[x=0,\]then\[f(0)\]equals to

    A) \[\frac{1}{4}\]

    B) \[-\frac{1}{4}\]

    C) \[\frac{1}{8}\]

    D) \[-\frac{1}{8}\]

    View Answer play_arrow
  • question_answer145) Equation of the diameter of the circle \[{{x}^{2}}+{{y}^{2}}-6x+2y=0\]which passes through the origin is

    A) \[x+3y=0\]

    B) \[x-3y=0\]

    C) \[3x+y=0\]

    D) \[3x-y=0\]

    View Answer play_arrow
  • question_answer146) The equation of latusrectum of a parabola is \[x+y=8\]and the equation of the tangent at the vertex is\[x+y=12,\]then length of the latusrectum is

    A) \[4\sqrt{2}\]

    B) \[2\sqrt{2}\]

    C) 8

    D) \[8\sqrt{2}\]

    View Answer play_arrow
  • question_answer147) The point z moves on the Argand diagram such that \[|z-3i|=2,\]then its locus is

    A) y-axis

    B) a straight line

    C) a circle

    D) None of these

    View Answer play_arrow
  • question_answer148) In a\[\Delta ABC,\]if\[a=2x,b=2y\]and\[\angle C=120{}^\circ ,\]then the area of the triangle is

    A) \[xy\]

    B) \[xy\sqrt{3}\]

    C) \[3xy\]

    D) \[2xy\]

    View Answer play_arrow
  • question_answer149) \[\int{\frac{dx}{\sin x-\cos x+\sqrt{2}}}\]is equal to

    A) \[\frac{1}{\sqrt{2}}\tan \left( \frac{x}{2}+\frac{\pi }{8} \right)+C\]

    B) \[-\frac{1}{\sqrt{2}}\tan \left( \frac{x}{2}+\frac{\pi }{8} \right)+C\]

    C) \[\frac{1}{\sqrt{2}}\cot \left( \frac{x}{2}+\frac{\pi }{8} \right)+C\]

    D) \[-\frac{1}{\sqrt{2}}\cot \left( \frac{x}{2}+\frac{\pi }{8} \right)+C\]

    View Answer play_arrow
  • question_answer150) The roots of the equation\[\left| \begin{matrix} 1 & 4 & 20 \\ 1 & -2 & 5 \\ 1 & 2x & 5{{x}^{2}} \\ \end{matrix} \right|=0\]are

    A) \[-1,-2\]

    B) \[-1,2\]

    C) \[1,-2\]

    D) \[1,2\]

    View Answer play_arrow
  • question_answer151) If the roots of the equation\[a{{x}^{2}}+bx+c=0\]are and\[2l,\]then

    A) \[{{b}^{2}}=9ac\]

    B) \[2{{b}^{2}}=9ac\]

    C) \[{{b}^{2}}=-4ac\]

    D) \[{{a}^{2}}={{c}^{2}}\]

    View Answer play_arrow
  • question_answer152) \[\frac{d}{dx}\left[ {{\sin }^{2}}{{\cot }^{-1}}\left\{ \sqrt{\frac{1-x}{1+x}} \right\} \right]\]equals to

    A) \[-1\]

    B) \[\frac{1}{2}\]

    C) \[-\frac{1}{2}\]

    D) \[1\]

    View Answer play_arrow
  • question_answer153) \[{{\sin }^{6}}\theta +{{\cos }^{6}}\theta +3{{\sin }^{2}}\theta {{\cos }^{2}}\theta \]is equal to

    A) 0

    B) \[-1\]

    C) 1

    D) None of these

    View Answer play_arrow
  • question_answer154) Let\[P(a\sec \theta ,b\tan \theta )\]and\[Q(a\sec \phi ,b\tan \phi ),\]where\[\theta +\phi =\frac{\pi }{2}\]be two points on the hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]. If\[(h,k)\]is the point on intersection of the normals at P and Q, then k is equal to

    A) \[\frac{{{a}^{2}}+{{b}^{2}}}{a}\]

    B) \[-\left( \frac{{{a}^{2}}+{{b}^{2}}}{a} \right)\]

    C) \[\frac{{{a}^{2}}+{{b}^{2}}}{b}\]

    D) \[-\left( \frac{{{a}^{2}}+{{b}^{2}}}{b} \right)\]

    View Answer play_arrow
  • question_answer155) If\[\tan (A+B)=p,\tan (A-B)=q,\]then the value of tan 2A is

    A) \[\frac{p+q}{p-q}\]

    B) \[\frac{p-q}{1+pq}\]

    C) \[\frac{1+pq}{1-p}\]

    D) \[\frac{p+q}{1-pq}\]

    View Answer play_arrow
  • question_answer156) \[\int{\frac{dx}{\sqrt{{{e}^{2x}}-1}}}\]equals to

    A) \[{{\sin }^{-1}}({{e}^{x}})+C\]

    B) \[{{\cos }^{-1}}({{e}^{x}})+C\]

    C) \[{{\sec }^{-1}}({{e}^{x}})+C\]

    D) \[{{\tan }^{-1}}({{e}^{x}})+C\]

    View Answer play_arrow
  • question_answer157) If a curve\[y=a\sqrt{x}+bx\]passes through the point (1, 2) and the area bounded by the curve, line\[x=4\]and\[x-\]axis is 8 sq units, then

    A) \[a=3,b=-1\]

    B) \[a=3,b=1\]

    C) \[a=-3,b=1\]

    D) \[a=-3,b=-1\]

    View Answer play_arrow
  • question_answer158) The area of the region (in square unit) bounded by the curve\[{{x}^{2}}=4y,\]line\[x=2\]and\[x-\]axis is

    A) 1

    B) \[\frac{2}{3}\]

    C) \[\frac{4}{3}\]

    D) \[\frac{8}{3}\]

    View Answer play_arrow
  • question_answer159) The order and degree of the differential equation representing the family of curves \[{{y}^{2}}=2k(x+\sqrt{k})\](where, k is positive parameter) are respectively,

    A) 1 and 2

    B) 2 and 4

    C) 1 and 4

    D) 1 and 3

    View Answer play_arrow
  • question_answer160) In a\[\Delta ABC,\text{ }a=2cm,\text{ }b=3cm\text{ }and\text{ }c=4cm,\]then\[\angle A\]is

    A) \[{{\cos }^{-1}}\left( \frac{1}{24} \right)\]

    B) \[{{\cos }^{-1}}\left( \frac{11}{16} \right)\]

    C) \[{{\cos }^{-1}}\left( \frac{7}{8} \right)\]

    D) \[{{\cos }^{-1}}\left( -\frac{1}{4} \right)\]

    View Answer play_arrow
  • question_answer161) The slope of the tangent at\[(x,y)\]to a curve passing through a point (2, 1) is\[\frac{{{x}^{2}}+{{y}^{2}}}{2xy}\],then the equation of the curve is

    A) \[2({{x}^{2}}-{{y}^{2}})=3x\]

    B) \[2({{x}^{2}}-{{y}^{2}})=6y\]

    C) \[x({{x}^{2}}-{{y}^{2}})=6\]

    D) \[x({{x}^{2}}+{{y}^{2}})=10\]

    View Answer play_arrow
  • question_answer162) If in the expansion of\[{{(1+x)}^{20}},\]the coefficients of rth and\[(r+4)\]th terms are equal, then value of r is

    A) 7

    B) 8

    C) 9

    D) 10

    View Answer play_arrow
  • question_answer163) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\log }_{e}}(1+x)}{{{3}^{x}}-1}\]equals to

    A) \[{{\log }_{e}}3\]

    B) 0

    C) 1

    D) \[{{\log }_{3}}e\]

    View Answer play_arrow
  • question_answer164) If\[x=\exp \left\{ {{\tan }^{-1}}\left( \frac{y-{{x}^{2}}}{{{x}^{2}}} \right) \right\},\]then\[\frac{dy}{dx}\]equals to

    A) \[2x[1+\tan (\log x)]+2{{\sec }^{2}}(\log x)\]

    B) \[x[1+\tan (\log x)]+{{\sec }^{2}}(\log x)\]

    C) \[2x[1+\tan (\log x)]+{{x}^{2}}{{\sec }^{2}}(\log x)\]

    D) \[2x[1+\tan (\log x)]+{{\sec }^{2}}(\log x)\]

    View Answer play_arrow
  • question_answer165) If the roots of the equation\[5{{x}^{2}}-7x+k=0\]are reciprocal of each other, then value of k is

    A) 5

    B) 2

    C) 2

    D) 1

    View Answer play_arrow
  • question_answer166) The locus of a point whose difference of distance from points (3, 0) and\[(-3,0)\]is 4, is

    A) \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{5}=1\]

    B) \[\frac{{{x}^{2}}}{5}-\frac{{{y}^{2}}}{4}=1\]

    C) \[\frac{{{x}^{2}}}{2}-\frac{{{y}^{2}}}{3}=1\]

    D) \[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1\]

    View Answer play_arrow
  • question_answer167) If the first term of an AP is 2 and common difference is 4, then sum of 40 terms is

    A) 3200

    B) 1600

    C) 200

    D) 2800

    View Answer play_arrow
  • question_answer168) The distance between the directories of a rectangular hyperbola is 10 units, then distance between its foci is

    A) \[10\sqrt{2}\]

    B) \[5\]

    C) \[5\sqrt{2}\]

    D) \[20\]

    View Answer play_arrow
  • question_answer169) \[{{C}_{1}}+2{{C}_{2}}+3{{C}_{3}}+...+n{{C}_{n}}\]is equal to

    A) \[{{2}^{n}}\]

    B) \[n{{.2}^{n}}\]

    C) \[n{{.2}^{n-1}}\]

    D) \[n{{.2}^{n+1}}\]

    View Answer play_arrow
  • question_answer170) If a particle is thrown vertically upwards with a velocity of u cm/s under gravity, then the time for the particle to come to earth again is

    A) \[\frac{u}{g}s\]

    B) \[\frac{2u}{g}s\]

    C) \[\frac{u}{2g}s\]

    D) None of these

    View Answer play_arrow

   

You need to login to perform this action.
You will be redirected in 3 sec spinner

Free
Videos