Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2011

done Rajasthan PET Solved Paper-2011

  • question_answer1) The x and y coordinates of a particle at any time t are given\[x=7t+4{{t}^{2}}\]and\[y=5t,\]where\[x\]and y are in metre and t in second. The acceleration of particle at\[t=5s\]is

    A) zero

    B) \[\text{8 }m/{{s}^{2}}\]

    C) \[20\text{ }m/{{s}^{2}}\]

    D) \[\text{40 }m/{{s}^{2}}\]

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  • question_answer2) Find the velocity of the particle moving in a circular path having a centripetal force of 10 N whose mass is 100 g and radius of circular path is 50 cm

    A) \[\sqrt{500}\]m/s

    B) \[\sqrt{50}\]m/s

    C) \[\sqrt{30}\]m/s

    D) \[\sqrt{60}\]m/s

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  • question_answer3) A small object placed on a rotating horizontal turn-table just slips when it is placed at a distance of 4 cm from the axis of rotation. If the angular velocity of the turn-table is doubled the object slips when its distance from the axis of rotation is

    A) 1 cm

    B) 2 cm

    C) 4 cm

    D) 8 cm

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  • question_answer4) A bullet moving with speed 200 m/s is just able to pierce a wooden block of 6 cm thickness. What velocity is required to just pierce a block of 8 cm?

    A) 400\[\sqrt{3}\]m/s

    B) 400 m/s

    C) 400/\[\sqrt{3}\]m/s

    D) 400\[\sqrt{2}\]m/s

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  • question_answer5) A bullet of 5 g is fired with a velocity of 800 m/s. The velocity of bullet becomes 200 m/s when it pierces a wooden block 2 m thick. What is the average resistance offered by the wooden block?

    A) 8.5 kN

    B) 7.5 kN

    C) 6.5 kN

    D) 30 kN

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  • question_answer6) On a massless rod four masses are fixed as shown in figure. What is the moment of inertia about an axis passing through centre of rod

    A) \[\frac{{{l}^{2}}}{2}\left( M+\frac{m}{4} \right)\]

    B) \[\frac{{{l}^{2}}}{2}\left( \frac{M}{4}+m \right)\]

    C) \[\frac{{{l}^{2}}}{4}\left[ M+\frac{m}{4} \right]\]

    D) \[\frac{{{l}^{2}}}{4}\left[ \frac{M}{4}+m \right]\]

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  • question_answer7) The two waves, whose intensities are\[9:16\]are made to interfere. The ratio of maximum and minimum intensities in the interference pattern is

    A) 16 : 9

    B) 4 : 3

    C) 25 : 7

    D) 49 : 1

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  • question_answer8) At what temperature is rms speed of air molecules double of that at NTP?

    A) \[819{}^\circ C\]

    B) \[719{}^\circ C\]

    C) \[909{}^\circ C\]

    D) None of these

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  • question_answer9) A balloon contains\[500\text{ }{{m}^{3}}\]of helium at\[27{}^\circ C\]and 1 atmosphere pressure. The volume of the helium at\[-3{}^\circ C\]temperature and 0.5 atmosphere pressure will be

    A) \[500\,{{m}^{3}}\]

    B) \[700\,{{m}^{3}}\]

    C) \[900\,{{m}^{3}}\]

    D) \[1000\,{{m}^{3}}\]

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  • question_answer10) The rate of outflow of liquid through an orifice does not depend upon

    A) radius of the orifice

    B) height of the liquid column

    C) acceleration due to gravity

    D) density of the liquid

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  • question_answer11) Two lamps of powers\[{{P}_{1}}\]and\[{{P}_{2}}\]are placed on either side of a paper having an oil spot. The lamps are at distances of 1 m and 2 m respectively on either side of the paper and the oil spot is invisible. What is the value of\[{{P}_{1}}/{{P}_{2}}\]?

    A) 0.25

    B) 0.40

    C) 0.50

    D) 0.60

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  • question_answer12) A parallel plate capacitor of value 1.77 \[\mu \]F is to be designed using a dielectric material (dielectric constant = 200), breakdown strength of\[3\times {{10}^{6}}\] V/m. In order to make such a capacitor which can withstand a potential difference of 20 V across the plates, the separation between the plates d and area A of the plates respectively are

    A) \[6.6\times {{10}^{-6}}m,{{10}^{3}}{{m}^{2}}\]

    B) \[6.6\times {{10}^{-5}}m,{{10}^{4}}{{m}^{2}}\]

    C) \[6.6\times {{10}^{-4}}m,\text{ }{{10}^{5}}{{m}^{2}}\]

    D) \[6.6\times {{10}^{-6}}m,\text{ }{{10}^{2}}{{m}^{2}}\]

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  • question_answer13) Mid way between the two equal and similar charges, we place the third equal and similar charge. Which of the following statements is correct?

    A) The third charge experiences a net force inclined to the line joining the charges

    B) The third charge is in stable equilibrium

    C) The third charge is in unstable equilibrium

    D) The third charge experience a net force perpendicular to the line joining the charges

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  • question_answer14) A magnetic field of 20 T is normal to a coil of 100 turns and area\[{{10}^{-2}}{{m}^{2}}\]. If the coil is removed from the magnetic field is 2 ms, what is the induced emf set up in the coil?

    A) 2 kV

    B) 5 kV

    C) 7 kV

    D) 10 kV

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  • question_answer15) The first line of Balmer series has wavelength 6563 A. What will be the wavelength of the first member of Lyman seires?

    A) 1215.4\[\overset{o}{\mathop{\text{A}}}\,\]

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

    C) 7500\[\overset{o}{\mathop{\text{A}}}\,\]

    D) 600\[\overset{o}{\mathop{\text{A}}}\,\]

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  • question_answer16) What will be the angular momentum in fourth orbit if L is the angular momentum of the electron in the second orbit of H-atom?

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

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

    C) 2L

    D) \[\frac{3}{2}L\]

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  • question_answer17) If half-life of a radioactive atom is 2.3 days then its decay constant would be

    A) 0.1

    B) 0.2

    C) 0.3

    D) 2.3

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  • question_answer18) The half-life period of a radioactive substance is 5 min. The amount of substance decayed in 20 min will be

    A) 93.75%

    B) 75%

    C) 25%

    D) 6.25%

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  • question_answer19) The torque acting on a magnetic dipole of moment\[{{\mathbf{P}}_{m}}\]when placed in a magnetic field B is

    A) \[{{P}_{m}}B\]

    B) \[{{\mathbf{P}}_{m}}\times \mathbf{B}\]

    C) \[{{\mathbf{P}}_{m}}.\text{ }B\]

    D) None of these

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  • question_answer20) A charged particle with velocity\[2\times {{10}^{3}}\]m/s passes undeflected through electric and magnetic field is 1.5 T. The electric field intensity would be

    A) \[2\times {{10}^{3}}N/C\]

    B) \[1.5\times {{10}^{3}}N/C\]

    C) \[3\times {{10}^{3}}N/C\]

    D) \[\frac{4}{3}\times {{10}^{-3}}N/C\]

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  • question_answer21) An electron is accelerated through a potential difference of 45.5 V. The velocity acquired by it is (in m/s)

    A) \[{{10}^{6}}\]

    B) zero

    C) \[4\times {{10}^{6}}\]

    D) \[4\times {{10}^{4}}\]

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  • question_answer22) What is the magnitude of the emf generated between the ends of the axle of a railway carriage 1 m in length when it is moving with a velocity of 30 km/h along horizontal track? Earth's horizontal magnetic field of induction\[=0.4\times {{10}^{-4}}T\]and angle of dip \[=60{}^\circ \]

    A) \[6.77\times {{10}^{-4}}V\]

    B) \[5.77\times {{10}^{-4}}V\]

    C) \[5.23\times {{10}^{-4}}V\]

    D) \[5.47\times {{10}^{-4}}V\]

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  • question_answer23) Three identical charges placed at the vertices of an equilateral triangle. The force experienced by each charge \[\left( if\,k=\frac{1}{4}\pi {{\varepsilon }_{0}} \right)\] is

    A) \[2k\,\frac{{{q}^{2}}}{{{r}^{2}}}\]

    B) \[\frac{k{{q}^{2}}}{2{{r}^{2}}}\]

    C) \[\sqrt{3}k\frac{{{q}^{2}}}{{{r}^{2}}}\]

    D) \[\frac{k{{q}^{2}}}{\sqrt{2{{r}^{2}}}}\]

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  • question_answer24) A capacitor of capacitance 6\[\mu \]F is charged upto 100 V. The energy stored in the capacitor is

    A) 0.6 J

    B) 0.06 J

    C) 0.03 J

    D) 0.3 J

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  • question_answer25) The electric field due to an infinitely long thin wire at a distance R varies as

    A) 1/R

    B) \[1/{{R}^{2}}\]

    C) R

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

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  • question_answer26) A magnet of magnetic moment M is freely suspended in a uniform magnetic field of strength B. The work done in rotating the magnet through \[60{}^\circ \]to\[90{}^\circ \]is

    A) \[-MB\text{ }(1-cos\text{ }90{}^\circ )\]

    B) \[-MB(cos\text{ }60{}^\circ -cos\text{ }90{}^\circ )\]

    C) \[-MB(0cos\text{ }60{}^\circ )\]

    D) \[-MB(sin\text{ }60{}^\circ -cos\text{ }90{}^\circ )\]

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  • question_answer27) A 750 Hz, 20 V source is connected to a resistance of\[100\,\Omega ,\]an inductance of 0.1803 H and a capacitance of 10\[\mu \]F all in series. What is the time in which resistance (thermal capacity\[=2\text{ }J/{}^\circ C\]) will get heated by\[10{}^\circ C\]?

    A) 380 s

    B) 384 s

    C) 470 s

    D) 479 s

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  • question_answer28) A capacitor discharges through an inductor of 0.02 H. If the frequency of discharge is 100 Hz then what is the capacitance of the capacitor?

    A) 14.67 \[\mu \]F

    B) 12.67 \[\mu \]F

    C) 9.67 \[\mu \]F

    D) 4.67 \[\mu \]F

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  • question_answer29) Which of the following is the dimensional formula for capacitance X (potential) 2?

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

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

    C) \[[M{{L}^{-2}}{{T}^{-3}}]\]

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

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  • question_answer30) A bomb of 12 kg explods into two pieces of masses 4 kg and 8 kg. The velocity of 8 kg mass is 6 m/s. The kinetic energy of the other mass is

    A) 48 J

    B) 32 J

    C) 24 J

    D) 288 J

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  • question_answer31) The path difference between the two waves \[{{y}_{1}}={{a}_{1}}\sin \left( \omega t-\frac{2\pi x}{\lambda } \right)\] and \[{{y}_{2}}={{a}_{2}}\sin \left( \omega t-\frac{2\pi x}{\lambda }+\phi \right)is\]

    A) \[\frac{\lambda }{2\pi }\phi \]

    B) \[\frac{\lambda }{2\pi }\left( \phi \frac{\pi }{2} \right)\]

    C) \[\frac{2\pi }{\lambda }\left( \phi -\frac{\pi }{2} \right)\]

    D) \[\frac{2\pi }{\lambda }\phi \]

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  • question_answer32) What is the relation between particle velocity (v), the wave velocity and the slope (s) of the wave?

    A) \[v=-cs\]

    B) \[c=-vs\]

    C) \[{{v}^{2}}={{c}^{2}}s\]

    D) \[{{c}^{2}}={{v}^{2}}s\]

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  • question_answer33) The velocity of sound in oxygen at NTP is v. The velocity of sound in helium at NTP should be

    A) 4v

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

    C) 2v

    D) None of these

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  • question_answer34) Two spheres have identical masses and moment of inertia. One of them is solid and the other is hollow. The ratio of the radius of solid sphere to that of hollow sphere is

    A) \[\sqrt{2}\]

    B) \[\sqrt{2/5}\]

    C) \[\sqrt{5/3}\]

    D) \[\sqrt{2/3}\]

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  • question_answer35) A body cools in 7 min from\[60{}^\circ C\]to\[40{}^\circ C\]. What time does it take to cool from\[40{}^\circ C\]to\[28{}^\circ C\]if the surrounding temperature is\[10{}^\circ C\]?

    A) 3.5 min

    B) 14 min

    C) 7 min

    D) 10 min

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  • question_answer36) Two metal spheres of radii\[{{r}_{1}}\]and\[{{r}_{2}}\]are charged to the same potential. The ratio of the charge on the two spheres is

    A) 1

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

    C) \[{{r}_{1}}-{{r}_{2}}\]

    D) \[{{r}_{1}}/{{r}_{2}}\]

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  • question_answer37) What is the color of the interference fringe nearest to the white central maximum in case the source of light is white?

    A) Yellow

    B) Red

    C) Blue

    D) Violet

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  • question_answer38) What will be the kinetic energy of an electron having de-Broglie wavelength\[2\overset{o}{\mathop{\text{A}}}\,\]?

    A) 37.5 eV

    B) 75 eV

    C) 150 eV

    D) 30 eV

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  • question_answer39) Focal length of a convex lens will be maximum for

    A) blue light

    B) yellow light

    C) green light

    D) red light

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  • question_answer40) Pitch of a node depends upon

    A) frequency

    B) wavelength

    C) amplitude

    D) None of these

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  • question_answer41) Mass of one atom of an element is \[6.64\times {{10}^{-23}}g.\] This is equal to

    A) \[6.64\times {{10}^{-23}}u\]

    B) \[40.0u\]

    C) \[\frac{1}{40}u\]

    D) \[6.64u\]

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  • question_answer42) Point defects are present in

    A) ionic solids

    B) amorphous solid

    C) molecular solids

    D) liquids

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  • question_answer43) The average molecular speed is greatest in which of the following gas samples?

    A) 1.0 mol of\[{{O}_{2}}\]at 560 K

    B) 0.50 mol of Neat 500 K

    C) 0.20 mol of\[C{{O}_{2}}\]at 440 K

    D) 2.0 mol of He at 140 K

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  • question_answer44) Elevation in boiling point of an aqueous urea solution is\[0.52{}^\circ C[{{K}_{b}}=0.52{}^\circ mo{{l}^{-1}}kg].\]Hence, mole fraction of urea in this solution is

    A) 0.982

    B) 0.567

    C) 0.943

    D) 0.018

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  • question_answer45) Oxidation number of Cr in\[Cr{{O}_{5}}\]is

    A) +10

    B) +8

    C) +6

    D) +4

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  • question_answer46) For the reaction \[{{H}_{2}}(g)+C{{O}_{2}}(g)CO(g)+{{H}_{2}}O(g)\] If the initial concentration of \[[{{H}_{2}}]=[C{{O}_{2}}]\]and \[x\] mol/L of hydrogen is consumed at equilibrium, the correct expression of\[{{K}_{p}}\]is

    A) \[\frac{{{x}^{2}}}{{{(1-x)}^{2}}}\]

    B) \[\frac{{{x}^{2}}}{{{(2+x)}^{2}}}\]

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

    D) \[\frac{{{(1+x)}^{2}}}{{{(1-x)}^{2}}}\]

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  • question_answer47) The solubility of\[AgI\]in\[NaI\]solution is less than that in pure water because

    A) \[AgI\]forms complex with \[NaI\]

    B) of common ion effect

    C) solubility product of\[AgI\]is less

    D) the temperature of the solution decrease

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  • question_answer48) A buffer solution with pH 9 is to be prepared by mixing\[N{{H}_{4}}Cl\]and\[N{{H}_{4}}OH\]. Calculate the number of moles of\[N{{H}_{4}}Cl\]that should be added to 1 L of\[1.0\text{ }M\text{ }N{{H}_{4}}OH\].

    A) 3.4

    B) 2.6

    C) 1.5

    D) 1.99

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  • question_answer49) The emf of the cell involving following changes, \[Zn(s)+N{{i}^{2+}}(1M)\xrightarrow[{}]{{}}Z{{n}^{2+}}(1M)+Ni(s)\] is 0.5105 V. The standard emf of the cell is

    A) 0.540V

    B) 0.4810V

    C) 0.5696V

    D) 0.5105V

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  • question_answer50) Chlorination of toluene in presence of light and heat followed by treatment with aqueous \[NaOH\]gives

    A) o-cresol

    B) p-cresol

    C) mixture of o-cresol and p-cresol

    D) benzoic acid

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  • question_answer51) Identify the product in the following sequence 3, 4, 5-tnbromoanilme \[\xrightarrow[(ii){{H}_{3}}P{{O}_{2}}]{(i)Diazotisation}\]

    A) 3, 4, 5-tribromobenzene

    B) 1, 2, 3-tribromobenzene

    C) 3, 4, 5-tribromophenol

    D) 3, 4, 5-tribromonitrobenzene

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  • question_answer52) The order of first ionization energies of the elements \[Li,Be,B,Na\] is

    A) \[Li>Be>B>Na\]

    B) \[Be>B>Li>Na\]

    C) \[Na>Li>B>Be\]

    D) \[Be>Li>B>Na\]

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  • question_answer53) Effective magnetic moment\[S{{c}^{3+}}\]ion is

    A) 1.73

    B) zero

    C) 5.92

    D) 2.83

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  • question_answer54) Potassium permanganate acts as an oxidant in alkaline and acidic medium. The final products formed from\[KMn{{O}_{4}}\]in the two conditions are respectively

    A) \[Mn{{O}^{2-}}\]and \[M{{n}^{3+}}\]

    B) \[M{{n}^{3+}}\]and \[M{{n}^{2+}}\]

    C) \[M{{n}^{2+}}\]and \[M{{n}^{3+}}\]

    D) \[Mn{{O}_{2}}\]and \[M{{n}^{2+}}\]

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  • question_answer55) An alkene having the molecular formula \[{{C}_{9}}{{H}_{18}}\]on ozonolysis gives 2, 2-dimethyl propanal and butanone. The alkene is

    A) 2, 2, 2-trimethyl-3-hexene

    B) 2, 2, 6-trimethyl-3-hexane

    C) 2, 2, 4-trimethyl 3-hexene

    D) 2, 3, 4-trimethyl-2-hexene

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  • question_answer56) The number of optical isomers of\[C{{H}_{3}}CH(OH)CH(OH)CHO\]is

    A) 2

    B) 3

    C) 6

    D) 4

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  • question_answer57) The amine which will not liberate nitrogen on reaction with nitrous acid is

    A) trimethyl amine

    B) ethyl amine

    C) sec-butyl amine

    D) iso-propyi amine

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  • question_answer58) Find the two third life\[({{t}_{2/3}})\]a first order reaction in which\[k=5.48\times {{10}^{-14}}\]per second.

    A) \[2.01\times {{10}^{13}}s\]

    B) \[201\times {{10}^{13}}s\]

    C) \[201\times {{10}^{20}}s\]

    D) \[0.201\times {{10}^{10}}s\]

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  • question_answer59) Identify the compound Z in this reaction sequence \[C{{H}_{3}}C{{H}_{2}}COOH\xrightarrow[{}]{N{{H}_{3}}}X\xrightarrow[{}]{B{{r}_{2}}+KOH}Y\xrightarrow[{}]{HN{{O}_{2}}}Z\]

    A) \[C{{H}_{3}}OH\]

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

    C) \[C{{H}_{3}}C{{H}_{2}}OH\]

    D) \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH\]

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  • question_answer60) The orbital angular momentum of an electron revolving in p-orbital is

    A) zero

    B) \[\frac{h}{\sqrt{2\pi }}\]

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

    D) \[\frac{h}{2\sqrt{2\pi }}\]

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  • question_answer61) The pair whose both species are used in antiacid medicinal preparations is

    A) \[NaHC{{O}_{3}}\]and \[Mg{{(OH)}_{2}}\]

    B) \[N{{a}_{2}}C{{O}_{3}}\]and \[Ca{{(HC{{O}_{3}})}_{2}}\]

    C) \[Ca{{(HC{{O}_{3}})}_{2}}\]and \[Mg{{(OH)}_{2}}\]

    D) \[Ca{{(OH)}_{2}}\]and \[NaHC{{O}_{3}}\]

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  • question_answer62) \[{{F}_{2}}\]formed by reacting\[{{K}_{2}}Mn{{F}_{6}}\]with

    A) \[Sb{{F}_{5}}\]

    B) \[Mn{{F}_{3}}\]

    C) \[KSb{{F}_{6}}\]

    D) \[Mn{{F}_{4}}\]

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  • question_answer63) Four successive members of the first row of transition elements are listed below with their atomic numbers. Which one of them is expected to have the highest third ionization enthalpy?

    A) Vanadium \[(Z=23)\]

    B) Chromium \[(Z=24)\]

    C) Iron \[(Z=26)\]

    D) Manganese \[(Z=25)\]

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  • question_answer64) Which of the following reactions is an example of redox reactions?

    A) \[AgN{{O}_{3}}+NaCl\xrightarrow[{}]{{}}AgCl+NaN{{O}_{3}}\]

    B) \[N{{a}_{2}}C{{O}_{3}}+Si{{O}_{2}}\xrightarrow{{}}N{{a}_{2}}Si{{O}_{3}}+C{{O}_{2}}\]

    C) \[Ca{{(HC{{O}_{3}})}_{3}}+Ca{{(OH)}_{2}}\xrightarrow[{}]{{}}\] \[2CaC{{O}_{3}}+2{{H}_{2}}O\]

    D) \[10HN{{O}_{3}}+{{I}_{2}}\xrightarrow{{}}2HI{{O}_{3}}+10N{{O}_{2}}\] \[+4{{H}_{2}}O\]

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  • question_answer65) \[PC{{l}_{3}}\]and cold water reacts to produce which of the following?

    A) \[{{H}_{3}}P{{O}_{3}}\]

    B) \[{{H}_{3}}P{{O}_{2}}\]

    C) \[{{H}_{4}}{{P}_{2}}{{O}_{7}}\]

    D) \[{{H}_{3}}P{{O}_{4}}\]

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  • question_answer66) Which of the following is not an ore of magnesium?

    A) Magnesite

    B) Dolomite

    C) Gypsum

    D) Camallite

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  • question_answer67) Brown ring in the test of\[NO_{3}^{-}\]is formed due to the formation of

    A) \[[Fe{{[{{H}_{2}}O]}_{5}}.NO]S{{O}_{4}}\]

    B) \[[Fe{{[S{{O}_{4}}]}_{2}}.NO]{{H}_{2}}O\]

    C) \[F{{e}_{2}}{{(S{{O}_{4}})}_{3}}.NO\]

    D) None of the above

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  • question_answer68) Which one of the hollowing will most readily be dehydrated in acidic conditions?

    A)

    B)

    C)

    D)

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  • question_answer69) Sulphide ores of metals are usually concentrated by froth floatation process. Which one of the following sulphide ores offers an exception and is concentrated by chemical leaching?

    A) Argentite

    B) Galena

    C) Copper pyrite

    D) Sphalerite

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  • question_answer70) Soldiers of Napolean army which at Alps during freezing winter suffered a serious problem as regards to die tin buttons of their uniforms. White metallic tin buttons got covered to grey powder. This transformation is related to

    A) an interaction with nitrogen of the air at very low temperatures

    B) a change in the partial pressure of oxygen in the air

    C) a change in the crystalline structure of tin

    D) an interaction with water vapour contained in the humid air

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  • question_answer71) Which of the following is a mixed oxide?

    A) \[F{{e}_{2}}{{O}_{3}}\]

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

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

    D) \[P{{b}_{3}}{{O}_{4}}\]

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  • question_answer72) The structure of\[XeO{{F}_{4}}\]is

    A) planar

    B) tetrahedral

    C) square pyramidal

    D) pyramidal

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  • question_answer73) A metal M forms chlorides in its +2 and +4 oxidation states. Which of the following statements about these chlorides is correct?

    A) \[MC{{l}_{2}}\]is more volatile than \[MC{{l}_{4}}\]

    B) \[MC{{l}_{2}}\]is more soluble in anhydrous ethanol than\[MC{{l}_{4}}\]

    C) \[MC{{l}_{2}}\]is more ionic than\[MC{{l}_{4}}\]

    D) \[MC{{l}_{2}}\]is more easily hydrolysed than\[MC{{l}_{4}}\]

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  • question_answer74) Atomic emission spectra of an element cannot be used to

    A) identify the atom

    B) determine the mass number of the nucleus of atom

    C) measure the difference in energy between pairs of stationary state of atom

    D) All of the above

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  • question_answer75) For the reaction of one mole of zinc dust with one mole of sulphuric acid in a bomb calorimeter,\[\Delta U\]and W corresponds to

    A) \[\Delta U<0,W=0\]

    B) \[\Delta U<0,W<0\]

    C) \[\Delta U>0,W=0\]

    D) \[\Delta U>0,W>0\]

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  • question_answer76) The enthalpy changes for the following processes are listed below \[C{{l}_{2}}(g)2Cl(g),242.3kJmo{{l}^{-1}}\] \[{{I}_{2}}(g)2I(g),151.0\,kJmo{{l}^{-1}}\] \[ICl(g)I(g)+Cl(g),211.3\,kJmo{{l}^{-1}}\] \[{{I}_{2}}(s){{I}_{2}}(g),62.76\,kJmo{{l}^{-1}}\] Given that the standard states for iodine and chlorine are\[{{I}_{2}}(s)\]and\[C{{l}_{2}}(g)\]the standard enthalpy of formation of\[ICI(g)\]is

    A) \[-14.6kJmo{{l}^{-1}}\]

    B) \[-16.8\text{ }kJ\text{ }mo{{l}^{-1}}\]

    C) \[+\text{ }16.8\text{ }kJ\text{ }mo{{l}^{-1}}\]

    D) \[+\text{ }244.8\text{ }kJ\text{ }mo{{l}^{-1}}\]

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  • question_answer77) When glucose reacts with bromine water, the main product is

    A) acetic acid

    B) saccharic acid

    C) glyceraldehyde

    D) gluconicacid

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  • question_answer78) Amylopectin is a polymer of

    A) \[\alpha -D-\]glucose

    B) \[\alpha -D-\]fructose

    C) lactose

    D) amylose

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  • question_answer79) \[2C{{H}_{3}}-\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,=O\xrightarrow[Reduction]{Mg-Hg+{{H}_{2}}O}A\xrightarrow[{}]{{{H}^{+}}}B\] Identify the B in the above sequence

    A) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]

    B) \[C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ OH \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]

    C) \[C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ OH \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]

    D) None of the above

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  • question_answer80) Which one of the following compound gives aspirin on reacting with acetic anhydride in presence of\[{{H}_{2}}S{{O}_{4}}\]?

    A)

    B)

    C)

    D)

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  • question_answer81) If a plane meets the coordinate axes at A, B and C, in such a way that the centroid of \[\Delta ABC\]is at the point (1, 2, 3), the equation of the plane is

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

    B) \[\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1\]

    C) \[\frac{x}{1}+\frac{y}{2}+\frac{z}{3}=1/3\]

    D) None of these

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  • question_answer82) Equation of a line passing through\[(-1,2,-3)\] and perpendicular to the plane \[2x+3y+z+5=0\]is

    A) \[\frac{x-1}{-1}=\frac{y+2}{1}=\frac{z-3}{-1}\]

    B) \[\frac{x+1}{-1}=\frac{y-2}{1}=\frac{z+3}{1}\]

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

    D) None of the above

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  • question_answer83) The equation of the plane containing the line\[r=i+j+\lambda 2i+j+4k)\]is

    A) \[r.(i+2j-k)=3\]

    B) \[r.(i+2j-k)=6\]

    C) \[r.(-i-2j+k)=3\]

    D) None of the above

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  • question_answer84) If \[y=sin(sinx)\]and \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}\tan x+f(x)=0,\]then\[f(x)\]equals to

    A) \[si{{n}^{2}}x.sin(cos\text{ }x)\]

    B) sin2 x cos(sin x)

    C) \[co{{s}^{2}}x.sin(\cos \text{ }x)\]

    D) \[co{{s}^{2}}x\text{ }sin\text{ }(sin\text{ }x)\]

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  • question_answer85) The maximum value of the function \[f(x)=\sin (x+\pi /6)+\cos (x+\pi /6)\] in the interval\[(0,\text{ }\pi /2)\]occurs at

    A) \[\pi /12\]

    B) \[\pi /6\]

    C) \[\pi /4\]

    D) \[\pi /3\]

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  • question_answer86) \[\underset{x\to 0}{\mathop{\lim }}\,{{\left\{ \tan \left( \frac{\pi }{4}+x \right) \right\}}^{1/x}}\]

    A) e

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

    C) \[\sqrt{e}\]

    D) \[1/\sqrt{e}\]

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  • question_answer87) The value of b for which the function \[f(x)=\left\{ \begin{matrix} 5x-4, & 0<x\le 1 \\ 4{{x}^{2}}+3bx, & 1<x<2 \\ \end{matrix} \right.\]is continuous at every point of its domain is

    A) \[-1\]

    B) 0

    C) 1

    D) 13/3

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  • question_answer88) The area bounded by the x-axis, the curve\[y=f(x)\]and the lines\[x=1\]and\[x=b\]is equal to\[\sqrt{{{b}^{2}}+1}-\sqrt{2}\]for all\[b>1,\]then\[f(x)\]is

    A) \[\sqrt{x-1}\]

    B) \[\sqrt{x+1}\]

    C) \[\sqrt{{{x}^{2}}+1}\]

    D) \[\frac{x}{\sqrt{1+{{x}^{2}}}}\]

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  • question_answer89) If\[{{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}\theta d\theta },\]then\[{{I}_{8}}+{{I}_{6}}\]is equal to

    A) 1/4

    B) 1/5

    C) 1/6

    D) 1/7

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  • question_answer90) Equation of tangent to the curve\[x=a{{\cos }^{3}}t,\]\[y=a{{\sin }^{3}}t\]at\[t\]is

    A) \[x\sec t-y\cos ect=\alpha \]

    B) \[x\sec t+y\cos ect=\alpha \]

    C) \[x\cos ect+ysect=\alpha \]

    D) None of the above

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  • question_answer91) \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{n}}}{{{e}^{x}}}=0\]for

    A) \[n=0\]only

    B) n is any whole number

    C) \[n=2\]only

    D) no value of n

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  • question_answer92) Let\[p(x)={{a}^{2}}+bx,\]\[q(x)=l{{x}^{2}}+mx+n,\]if \[p(1)-q(1)=0,\]\[p(2)-q(2)=1\]and \[p(3)-q(3)=4,\]then\[p(2)-q(2)=1\]equals to

    A) 0

    B) 5

    C) 6

    D) 9

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  • question_answer93) If\[a<0<b,\]then\[\int_{a}^{b}{\frac{|x|}{x}}dx\]

    A) \[a-b\]

    B) \[b-a\]

    C) \[a+b\]

    D) \[-a-b\]

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  • question_answer94) \[\frac{d}{dx}\left\{ {{\sin }^{2}}{{\cot }^{-1}}\frac{1}{\sqrt{\frac{1+x}{1-x}}} \right\}\]

    A) 0

    B) \[-1/2\]

    C) 1/2

    D) \[-1\]

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  • question_answer95) The integral \[\int_{-1/2}^{1/2}{\left\{ [x]+\log \left( \frac{1+x}{1-x} \right) \right\}dx}=?\] Where\[[.]\]is the greatest integer function.

    A) \[-1/2\]

    B) 0

    C) 1

    D) \[2\log (1/2)\]

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  • question_answer96) \[\int{\frac{{{\sin }^{-1}}\sqrt{x}-{{\cos }^{-1}}\sqrt{x}}{{{\sin }^{-1}}\sqrt{x}+{{\cos }^{-1}}\sqrt{x}}}dx=?\]

    A) \[\frac{2}{\pi }[\sqrt{x-{{x}^{2}}}+(1-2x){{\sin }^{-1}}\sqrt{x}]x+C\]

    B) \[\frac{2}{\pi }[\sqrt{x-{{x}^{2}}}-(1-2x){{\sin }^{-1}}\sqrt{x}]-x+C\]

    C) \[\frac{2}{\pi }[\sqrt{x-{{x}^{2}}}+(1-2x){{\sin }^{-1}}\sqrt{x}]-x+C\]

    D) None of the above

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  • question_answer97) Let\[f:R\to R,\text{ }g:R\to R,\]be two functions such that\[f(x)=2x-3,\text{ }g(x)={{x}^{3}}+5\]the function\[{{(fog)}^{-1}}(x)\]is equal to

    A) \[{{\left( \frac{x+7}{2} \right)}^{1/3}}\]

    B) \[{{\left( x-\frac{7}{2} \right)}^{1/3}}\]

    C) \[{{\left( \frac{x-2}{7} \right)}^{1/3}}\]

    D) \[{{\left( \frac{x-7}{2} \right)}^{1/3}}\]

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  • question_answer98) If\[(a\text{ }sec\,\theta ,\text{ b }tan\,\theta )\]and\[(a\text{ }sec\phi ,\text{ b }tan\,\phi )\]are the ends of a focal chord of\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]then \[\tan \theta /2\tan \phi /2\]is equal to

    A) \[\frac{e-1}{e+1}\]

    B) \[\frac{1-e}{1+e}\]

    C) \[\frac{1+e}{1-e}\]

    D) \[\frac{e+1}{e-1}\]

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  • question_answer99) If the angle between tangents drawn to \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]from (0, 0) is\[\pi /2,\]then

    A) \[{{g}^{2}}+{{f}^{2}}=3c\]

    B) \[{{g}^{2}}+{{f}^{2}}=2c\]

    C) \[{{g}^{2}}+{{f}^{2}}=5c\]

    D) \[{{g}^{2}}+{{f}^{2}}=4c\]

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  • question_answer100) If\[a.b=b.c=c.a=0,\]then\[a.(b\times c)\]is equal to

    A) a lion-zero vector

    B) 1

    C) \[-1\]

    D) \[|a|\,|b|\,|c|\]

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  • question_answer101) A variable line drawn through the point (1, 3) meets the\[x-\]axis at A and y-axis at B. If the rectangle OAPB is completed, where 0 is the origin, then locus of y is

    A) \[1/y+3/x=1\]

    B) \[x+3y=1\]

    C) \[1/x+3/y=1\]

    D) \[3x+y=1\]

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  • question_answer102) If a, b, c are non-zero non-collinear vectors and\[a\times b=b\times c=c\times a,\]then\[a+b+c\]is equal to

    A) \[abc\]

    B) \[-1\]

    C) 2

    D) 0

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  • question_answer103) The two parabolas\[{{y}^{2}}=4ax\]and\[{{y}^{2}}=4c(x-b)\]cannot have a common normal, other than the axis, unless

    A) \[\frac{a-c}{b}>2\]

    B) \[\frac{b}{a-c}>2\]

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

    D) None of these

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  • question_answer104) If the number\[\frac{{{(1-i)}^{n}}}{{{(1+i)}^{n-2}}}\]is real and positive, then n is

    A) any integer

    B) \[2\lambda \]

    C) \[4\lambda +1\]

    D) None of these

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  • question_answer105) The number of five digit telephone numbers having at least one of their digits repeated is

    A) 90000

    B) 100000

    C) 30240

    D) 69760

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  • question_answer106) In the binomial expansion of\[{{(a-b)}^{n}},n\ge 5,\] the sum of the 5th and 6th terms is zero, then a/b equals

    A) \[\frac{n-5}{6}\]

    B) \[\frac{n-4}{5}\]

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

    D) \[\frac{6}{n-5}\]

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  • question_answer107) A value of\[\sqrt{i}+\sqrt{-i}\]is

    A) 0

    B) \[\sqrt{2}\]

    C) \[-i\]

    D) \[i\]

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  • question_answer108) Let\[{{z}_{1}}\]and\[{{z}_{2}}\]be complex numbers such that \[{{z}_{1}}\ne {{z}_{2}}\]and\[|{{z}_{1}}|=|{{z}_{2}}|.\]If\[{{z}_{1}}\]has positive real part and\[{{z}_{2}}\]has negative imaginary part, then\[\frac{{{z}_{1}}+{{z}_{2}}}{{{z}_{1}}-{{z}_{2}}}\]may be

    A) zero

    B) real and positive

    C) real and negative

    D) purely imaginary or zero

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  • question_answer109) Let\[{{S}_{n}}\]denote the sum of first n terms of an AP, if\[{{S}_{2n}}=3{{S}_{n}},\]then the ratio -3n is equal to

    A) 4

    B) 6

    C) \[\pm 3\]

    D) \[\pm 4\]

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  • question_answer110) In 324 throws of 4 dice, the expected number of times 3 sixes occur is

    A) 81

    B) 5

    C) 9

    D) 31

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  • question_answer111) If the roots of the equation\[{{x}^{2}}+px+q=0\]differ by 1, then

    A) \[{{p}^{2}}=4q\]

    B) \[{{p}^{2}}=4q+1\]

    C) \[{{p}^{2}}=4q-1\]

    D) \[{{p}^{2}}=q\]

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  • question_answer112) If\[\alpha ,\beta \]and\[\gamma \]are the roots of the equation \[{{x}^{3}}+px+q=0,\]then value of the determinant \[\left| \begin{matrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \\ \end{matrix} \right|\]is

    A) \[p\]

    B) \[q\]

    C) \[{{p}^{2}}-2q\]

    D) \[0\]

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  • question_answer113) If\[\frac{1}{a},\frac{1}{b},\frac{1}{c}\]are in AP, then\[\left( \frac{1}{a}+\frac{1}{b}-\frac{1}{c} \right)\left( \frac{1}{b}+\frac{1}{c}-\frac{1}{a} \right)\]is equal to

    A) \[\frac{4}{ac}-\frac{3}{{{b}^{2}}}\]

    B) \[\frac{{{b}^{2}}-ac}{{{a}^{2}}{{b}^{2}}{{c}^{2}}}\]

    C) \[\frac{4}{ac}-\frac{1}{{{b}^{2}}}\]

    D) None of these

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  • question_answer114) If A and B are square matrices of the same order and A is non-singular, then for a positive integer n,\[{{({{A}^{-1}}BA)}^{n}}\]is equal to

    A) \[{{A}^{-n}}{{B}^{n}}{{A}^{n}}\]

    B) \[{{A}^{n}}{{B}^{n}}{{A}^{-n}}\]

    C) \[{{A}^{-1}}{{B}^{n}}A\]

    D) \[n({{A}^{-1}}BA)\]

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  • question_answer115) Two numbers are a and b. What is the relation between their GP, AP and HP. If AP denotes A GP denotes G and HP denotes H?

    A) \[H=\frac{2AG}{A+G}\]

    B) \[A=H/{{G}^{2}}\]

    C) \[H={{G}^{2}}/A\]

    D) \[G={{H}^{2}}/A\]

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  • question_answer116) The chance of throwing a total of 3 or 5 or 11 with two dice is

    A) 5/36

    B) 1/9

    C) 2/9

    D) 19/36

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  • question_answer117) The number of roots of the equation \[x+2\text{ }\tan x=\pi /2\]in the interval\[[0,2\pi ]\]is

    A) 1

    B) 2

    C) 3

    D) infinite

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  • question_answer118) In a\[\Delta ABC,\]if\[\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\]and the side\[a=2,\]then area of the triangle is

    A) 1

    B) 2

    C) \[\sqrt{3}/2\]

    D) \[\sqrt{3}\]

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  • question_answer119) If\[{{\sin }^{-1}}\left( \frac{2a}{1+{{a}^{2}}} \right)+{{\sin }^{-1}}\left( \frac{2b}{1+{{b}^{2}}} \right)=2{{\tan }^{-1}}x,\] then\[x\]is equal to

    A) \[\frac{a-b}{1+ab}\]

    B) \[\frac{b}{1+ab}\]

    C) \[\frac{b}{1-ab}\]

    D) \[\frac{a+b}{1-ab}\]

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  • question_answer120) If\[tan\text{ }A-tan\text{ }B=x\]and\[cot\text{ }B-cot\text{ }A=y,\]then \[cot(A-B)\]is equal to

    A) \[x+y\]

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

    C) \[\frac{1}{x}+\frac{1}{y}\]

    D) \[x+2y\]

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