Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2008

done Rajasthan PET Solved Paper-2008

  • question_answer1) According to Huygen's principle, the locus of all the particles of the medium, which at any instant are vibrating in the same phase, is called

    A) half period zone

    B) oscillator

    C) wave front

    D) ray of light

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  • question_answer2) In air the value of the total electric flux emitted from unit positive charge is

    A) \[{{\varepsilon }_{0}}\]

    B) \[{{({{\varepsilon }_{0}})}^{-1}}\]

    C) \[{{(4\pi {{\varepsilon }_{0}})}^{-1}}\]

    D) \[4\pi {{\varepsilon }_{0}}\]

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  • question_answer3) A rod AB is 1 m long. The temperature of its one end A is maintained at \[100{}^\circ C\] and other end B at WC. the temperature at a distance of 60 cm from point B is

    A) \[64{}^\circ C\]

    B) \[36{}^\circ C\]

    C) \[46{}^\circ C\]

    D) \[72{}^\circ C\]

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  • question_answer4) An oil on the water surface spreads like a thin layer because

    A) oil drop tries to become spherical due to the surface tension

    B) surface tension of water is greater than the surface tension of oil

    C) surface tension of water is equal to the surface of oil

    D) weight of oil is less than weight of water

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  • question_answer5) A ray of light is incident on the interface between water and glass at an angle i and retracted parallel to the water surface, then value of \[{{\mu }_{g}}\]will be

    A) \[(4/3)\sin i\]

    B) \[\frac{1}{\sin i}\]

    C) \[4/3\]

    D) \[1\]

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  • question_answer6) Find the ratio of electric field to potential EIV at the midpoint of electric dipole, if the distance between the charges is \[l\].

    A) \[1/l\]

    B) \[l\]

    C) \[2/l\]

    D) None of these

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  • question_answer7) Which diode is forward bias?

    A)

    B)

    C)

    D)

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  • question_answer8) In the given circuit when key S is closed then charge on the capacitors A and B are respectively

    A) 3q, 6q

    B) 6q, 3q

    C) 4.5q, 4.5q

    D) 5q, 4q

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  • question_answer9) The intensity distribution of X-rays from two coolidge tubes operated on different voltages \[{{V}_{1}}\]and\[{{V}_{2}}\]and using different target materials of atomic numbers\[{{Z}_{1}}\]and\[{{Z}_{2}}\]is shown in the figure. Which of the following inequalities is true?

    A) \[{{V}_{1}}>{{V}_{2}}\]and \[{{Z}_{1}}<{{Z}_{2}}\]

    B) \[{{V}_{1}}>{{V}_{2}}\]and \[{{Z}_{1}}>{{Z}_{2}}\]

    C) \[{{V}_{1}}<{{V}_{2}}\]and\[{{Z}_{1}}>{{Z}_{2}}\]

    D) \[{{V}_{1}}={{V}_{2}}\]and\[{{Z}_{1}}<{{Z}_{2}}\]

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  • question_answer10) The binding energy of deuteron\[_{1}^{2}H\]is 1.112 MeV per nucleon and an \[\alpha \]-particle\[_{2}^{4}He\]has a binding energy of 7.047 MeV per nucleon. Then is the fusion reaction\[_{1}^{2}H+_{1}^{2}H\xrightarrow[{}]{{}}_{2}^{4}H+Q,\]the energy Q released is

    A) 1 MeV

    B) 11.9 MeV

    C) 23.8 MeV

    D) 931 MeV

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  • question_answer11) How many second will light take to cover a distance of one fermi?

    A) \[{{10}^{-15}}s\]

    B) \[3\times {{10}^{8}}s\]

    C) \[3.33\times {{10}^{-24}}s\]

    D) \[3.3\times {{10}^{7}}s\]

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  • question_answer12) A body is moved in straight line by constant power of machine. What will be the relation the travelling distance and time?

    A) \[{{s}^{2}}\alpha \,{{t}^{3}}\]

    B) \[{{s}^{2}}\alpha \,{{t}^{3}}\]

    C) \[{{s}^{3}}\alpha \,{{t}^{2}}\]

    D) \[s\,\alpha \,{{t}^{3}}\]

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  • question_answer13) The square of resultant of two equal forces is three times of their product. The angle between them \[\overrightarrow{P}\] and \[\overrightarrow{Q}\] will be

    A) \[\pi /3\]

    B) \[\pi /4\]

    C) \[\pi /5\]

    D) \[\pi /6\]

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  • question_answer14) A body placed on the earth at static position. If it is pushed then the final state of centre of gravity will be

    A) near the earth

    B) at some height from the earth

    C) remain same

    D) remain at the same plane

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  • question_answer15) The particle of mass 50 kg is at rest. The work done to accelerates it by 20 in/s in 10 s is

    A) \[{{10}^{3}}J\]

    B) \[{{10}^{4}}J\]

    C) \[2\times {{10}^{3}}J\]

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

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  • question_answer16) The moment of inertia of a circular loop of radius R, at a distance of R/2 around a rotating axis parallel to horizontal diameter of loop is

    A) \[M{{R}^{2}}\]

    B) \[\frac{1}{2}M{{R}^{2}}\]

    C) \[2M{{R}^{2}}\]

    D) \[\frac{3}{4}M{{R}^{2}}\]

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  • question_answer17) If the earth stops moving around its polar axis then what will be effect on body placed at south axis?

    A) Remain same

    B) Increase

    C) Decrease but not zero

    D) Decrease zero

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  • question_answer18) In designing a beam for its use to support a load. The depression at centre is proportional to (where Y is Young's modulus)

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

    B) Y

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

    D) \[\frac{1}{{{Y}^{2}}}\]

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  • question_answer19) The temperature of sun is

    A) 1000 K

    B) 7000 K

    C) 10 K

    D) \[10\times {{10}^{6}}K\]

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  • question_answer20) A balloon is filled at\[27{}^\circ C\]and 1 atm pressure by 500 m3 He. At\[~-3{}^\circ C\]and 0.5 atm pressure, the volume of He will be

    A) \[700\text{ }{{m}^{3}}\]

    B) \[900\text{ }{{m}^{3}}\]

    C) \[1000\text{ }{{m}^{3}}\]

    D) \[500\text{ }{{m}^{3}}\]

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  • question_answer21) Which among the following is different from other's?

    A) Wavelength

    B) Velocity

    C) Frequency

    D) Amplitude

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  • question_answer22) The time period of two pendulums are T and 5T/4. They starts motion in SHM from equilibrium position. What will be the phase difference between them, after one complete oscillation by the big pendulum?

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

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

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

    D) \[30{}^\circ \]

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  • question_answer23) Hydrogen gas is filled in the bubble. For the sound wave, the bubble will be

    A) like a converging lens

    B) like a convex mirror

    C) like a concave lens

    D) None of the above

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  • question_answer24) Two charges are at a distance r exert a force F on each other. If the charges are doubled and distance between them is halved, then the new force acting on each charge is

    A) \[\frac{F}{8}\]

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

    C) \[4F\]

    D) \[16\,F\]

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  • question_answer25) The ratio of radius of two bubbles is 2 : 1. What is the ratio excess pressure inside them

    A) 1 : 2

    B) 1 : 4

    C) 2 : 1

    D) 4 : 1

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  • question_answer26) Brownian motion is evidence of

    A) kinetic energy of substance

    B) principle of electromagnetic

    C) Newton's law

    D) photoelectric phenomenon

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  • question_answer27) Beats are result of

    A) interference

    B) refraction

    C) reflection

    D) diffraction

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  • question_answer28) An ice block contains a glass ball when the see melts within the water containing vessel, the level of water

    A) will increase

    B) will decrease

    C) will remain same

    D) first increase and after that decrease

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  • question_answer29) Two bodies of masses 2 kg and 4 kg having velocities 2 m/s and 10 m/s respectively are coming close to each other under a gravitational force, then the velocity of centre of mass will be

    A) 5 m/s

    B) 6 m/s

    C) 8 m/s

    D) zero

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  • question_answer30) The displacement of oscillating body is given by\[y=A\text{ }sin(B+Ct+D)\]. The dimensions of ABCD are

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

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

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

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

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  • question_answer31) The ratio of intensities of two beams of light in interference is 9 : 1. The ratio of maximum and minimum intensities

    A) 10 : 8

    B) 9 : 1

    C) 4 : 1

    D) 2 : 1

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  • question_answer32) Four wires having same length, diameter and material are connected in the form of a square. If the resistance of each wire is R, then resistance of combination across any two opposite ends is

    A) R

    B) R/2

    C) R/4

    D) None of these

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  • question_answer33) The electric motor operating on a 200 volt DC supply draw a current of 10 A. If the power is 40%, then resistance of motor

    A) 20

    B) 8 n

    C) 12 n

    D) 16 n

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  • question_answer34) A capacitor of capacitance 2.0 \[\mu \]F is charged upto 200 V and then the plates of capacitor are connected to a resistance wire. The heat released in joule will be

    A) \[2\times {{10}^{-2}}\]

    B) \[4\times {{10}^{-2}}\]

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

    D) \[2\times {{10}^{10}}\]

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  • question_answer35) A voltmeter having a resistance of\[998\,\Omega \]is connected to a cell of emf 2 V and internal resistance\[2\,\Omega \]. The error in the measurement of emf will be

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

    B) \[2\times {{10}^{-3}}V\]

    C) \[4\times {{10}^{-3}}V\]

    D) \[2\times {{10}^{-1}}V\]

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  • question_answer36) The graph between the instantaneous concentration (N) of a radioactive element and time (t) is

    A)

    B)

    C)

    D)

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  • question_answer37) What is increased in step down transformer?

    A) current

    B) voltage

    C) power

    D) frequency

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  • question_answer38) According to modern physics the nature of light is

    A) only wave

    B) only particle

    C) Both wave and particle

    D) None of the above

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  • question_answer39) Which has more luminous efficiency?

    A) a 40 W bulb

    B) a 40 W tube light

    C) Both of same

    D) Cannot say

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  • question_answer40) When a light ray is travelling from one medium to another velocity of light ray doubles. If no total internal reflection occurs then the maximum value of incident angle will be

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

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

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

    D) \[30{}^\circ \]

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  • question_answer41) Photon and electron are given same energy\[({{10}^{-20}}J)\]. Wavelength associated with photon and electron are\[{{\lambda }_{p}}\]and\[{{\lambda }_{e}}\]the correct statement will be

    A) \[{{\lambda }_{p}}>{{\lambda }_{e}}\]

    B) \[{{\lambda }_{p}}<{{\lambda }_{e}}\]

    C) \[{{\lambda }_{p}}={{\lambda }_{e}}\]

    D) \[\frac{{{\lambda }_{e}}}{{{\lambda }_{p}}}=c\]

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  • question_answer42) The half-life of radioactive element is 600 yr. The fraction of sample that would remain after 3000 yr is

    A) 1 / 2

    B) 1 / 16

    C) 1 / 8

    D) 1 / 32

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  • question_answer43) The light of wavelength 5000\[\overset{o}{\mathop{\text{A}}}\,\]falls on a photosensitive plate of work function 1.9 eV. The kinetic energy of the emitted photoelectron is

    A) 0.58 eV

    B) 2.48 eV

    C) 1.24 eV

    D) 1.18 eV

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  • question_answer44) The number of electrons and holes in semiconductor at normal temperature will be

    A) equal

    B) zero

    C) unequal

    D) infinite

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  • question_answer45) The unit of thermal conductivity is

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

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

    C) \[WmK\]

    D) \[JK\]

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  • question_answer46) If vector \[2\widehat{i}-\widehat{j}+\widehat{k},\widehat{i}+2\widehat{j}-3\widehat{k}\]and \[3\widehat{i}+p\widehat{j}+5\widehat{k}\] are coplanar, find the value of p

    A) 16

    B) \[-4\]

    C) 4

    D) \[-8\]

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  • question_answer47) In the capacitor of capacitance C, charge Q and energy W is stored. If charge is increased upto 2Q, the energy stored will be

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

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

    C) 2 W

    D) 4 W

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  • question_answer48) At 300 K, the concentration of electron (He) and hole\[({{n}_{h}})\]in pure silicon is\[1.5\times {{10}^{16}}{{m}^{3}}\]. When indium is added,\[{{n}_{h}}\]become\[4.5\times {{10}^{22}}\]. Then\[{{n}_{e}}\]in doped silicon is

    A) \[9\times {{0}^{5}}\]

    B) \[5\times {{10}^{9}}\]

    C) \[2.25\times {{10}^{11}}\]

    D) \[3\times {{10}^{19}}\]

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  • question_answer49) A cylindrical conductors is placed near an another positive conductor. The total charge induced by the conductor is

    A) only positive

    B) only negative

    C) zero

    D) None of these

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  • question_answer50) If units of force, length and time are 1 kilo-newton, 1 km and 100 second respectively, then unit of mass will be

    A) 1000 kg

    B) 1kg

    C) 10000 kg

    D) 100 kg

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  • question_answer51) Which of the following compound does not contain carboxylic group\[(-COOH)\]?

    A) Acetic acid

    B) Lactic acid

    C) Benzoic acid

    D) Picric acid

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  • question_answer52) Which of the following compound will not obtain, on the distillation of calcium acetate with calcium formate?

    A) Acetone

    B) Formaldehyde

    C) Acetaldehyde

    D) Propionaldehyde

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  • question_answer53) Glucose gives silver mirror test because it contains

    A) \[-COOH\]group

    B) a basic group

    C) a ketonic group

    D) an aldehyde group

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  • question_answer54) Which compound is used to obtain Teflon polymer?

    A) Difluoro ethane

    B) Monofluoro ethane

    C) Tetrafluoro ethane

    D) Tetrafluoro ethane

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  • question_answer55) Which of the following equation shows the de-Broglie relationship?

    A) \[\frac{h}{mv}=p\]

    B) \[\lambda m=\frac{v}{p}\]

    C) \[\lambda =\frac{h}{mp}\]

    D) \[\lambda =\frac{h}{mv}\]

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  • question_answer56) Which of the following will the order of energy of subshells related to principal quantum number\[(n=4)\]?

    A) \[s<p<d<f\]

    B) \[s<d<p<f\]

    C) \[s<f<p<d\]

    D) \[p<s<d<f\]

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  • question_answer57) The electron shell is not spherical in, which of the following element?

    A) He

    B) Be

    C) B

    D) Li

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  • question_answer58) The correct electronic configuration of iron is

    A) \[1{{s}^{2}},2{{s}^{2}},2{{p}^{6}},3{{s}^{2}},3{{p}^{6}},4{{s}^{2}},3{{d}^{6}}\]

    B) \[1{{s}^{2}},2{{s}^{2}},2{{p}^{6}},3{{s}^{2}},3{{p}^{6}},4{{s}^{2}},3{{d}^{5}}\]

    C) \[1{{s}^{2}},2{{s}^{2}},2{{p}^{6}},3{{s}^{2}},3{{p}^{6}},4{{s}^{2}},3{{d}^{7}}\]

    D) \[1{{s}^{2}},2{{s}^{2}},2{{p}^{6}},3{{s}^{2}},3{{p}^{6}},4{{s}^{1}},3{{d}^{5}}\]

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  • question_answer59) According to VSEPR theory the geometry of water molecule is

    A) octahedral

    B) distorted tetrahedral

    C) trigonal planar

    D) trigonal bipyramidal

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  • question_answer60) On adding a non-volatile solution in a solvent, the vapour pressure of solvent reduces 10 mm of Hg. The mole fraction of solute is 0.2 in the solution. The vapour pressure of solution reduces to 20 mm of Hg on adding more solute in the solution. Now, what will the mole fraction of solvent in solution?

    A) 0.2

    B) 0.4

    C) 0.6

    D) 0.8

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  • question_answer61) Which of the following statement is false for ionic crystals?

    A) The boiling point and melting point of ionic crystals are high.

    B) These dissolves in water and other solvents.

    C) At low temperature, these are conductor of electricity in solid state.

    D) Their cohesive energy is high.

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  • question_answer62) 8 g amount of a radioactive substance remains 0.5 g after 1 h. What is its half-life?

    A) 10 min

    B) 15 min

    C) 30 min

    D) None of these

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  • question_answer63) In a radioactive change \[R\xrightarrow[{}]{-a}X\xrightarrow[{}]{-\beta }Y\xrightarrow[{}]{-\beta }Z\] R and Z are

    A) isotope

    B) isobar

    C) isomer

    D) isoneutronic

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  • question_answer64) The dissociation of\[X{{Y}_{2}}\]is as \[X{{Y}_{2}}(g)XY(g)+Y(g)\] The initial pressure of\[X{{Y}_{2}}\]is 600 mm of\[Hg\]. On establishing the equilibrium the total pressure becomes 800 mm of Hg. What is the value of K for the reaction, when the volume of system remains unchanged?

    A) 50

    B) 100

    C) 166.6

    D) 150

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  • question_answer65) The quantity of ionisation of decinormal solution of\[C{{H}_{3}}COOH\]is 1.3%. What is the pH value of this solution? (log 1.3=0.11)

    A) 2.89

    B) 3.89

    C) 4.89

    D) 0.89

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  • question_answer66) A buffer solution is obtained on adding 10 mL \[1.0\text{ }M\,C{{H}_{3}}COOH\]and 20 mL 0.5\[0.5\text{ }M\,C{{H}_{3}}COONa\]. It is diluted to 100 mL by distilled water. If\[p{{K}_{a}}=4.76\]for\[C{{H}_{3}}COOH,\]then the pH value of buffer solution

    A) 2.76

    B) 3.76

    C) 4.76

    D) 0.76

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  • question_answer67) Hess's law is used in the determination of

    A) heat of reaction

    B) heat of formation

    C) heat of bond formation

    D) All of the above

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  • question_answer68) 1.0 L of 1.0 M sodium hydroxide is neutralized by 1.0 L of 1.0 M methanoic acid. If the heat of formation of water is X then the heat of neutralization of this reaction is

    A) less than X

    B) more than X

    C) equal to X

    D) none of these

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  • question_answer69) 1.0 L of 2.0 M acetic acid is added with 1.0 L of 3.0 M ethyl alcohol. The following reaction takes place during this process \[C{{H}_{3}}COOH+{{C}_{2}}{{H}_{5}}OH\] \[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}+{{H}_{2}}O\] If each solution is diluted by adding 1.0 L water, then initial rate of the reaction will reduce

    A) 0.5 times

    B) 2.0 times

    C) 4.0 times

    D) 0.25 times

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  • question_answer70) For a reaction, the rate constant is \[0.693\times {{10}^{-1}}mi{{n}^{-1}}\]and initial concentration is 0.2 mol/L. Half-life period will be

    A) 400 s

    B) 600 s

    C) 800 s

    D) 100 s

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  • question_answer71) For chemical reaction \[{{N}_{2}}+3{{H}_{2}}\xrightarrow[{}]{{}}2N{{H}_{3}}\] \[\frac{d[N{{H}_{3}}]}{dt}=2\times {{10}^{-4}}mol\,{{L}^{-1}}{{s}^{-1}}\] The value of\[-\frac{d[{{H}_{2}}]}{dt}\]will

    A) \[1\times {{10}^{-4}}mol\,{{L}^{-1}}{{s}^{-1}}\]

    B) \[3\times {{10}^{-4}}mol\,{{L}^{-1}}{{s}^{-1}}\]

    C) \[4\times {{10}^{-4}}mol\,{{L}^{-1}}{{s}^{-1}}\]

    D) \[6\times {{10}^{-4}}mol\,{{L}^{-1}}{{s}^{-1}}\]

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  • question_answer72) Which of the following unit of energy show the maximum value of energy?

    A) Calorie

    B) Joule

    C) Erg

    D) Electron-volt

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  • question_answer73) The value of standard reduction potentials of three metallic cations X, Y and Z are + 0.52, \[-3.03\]and\[-1.18\]volt respectively. The order of reducing power of these metal will

    A) \[Y>Z>X\]

    B) \[X>Y>Z\]

    C) \[X>Z>Y\]

    D) \[Z>X>Y\]

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  • question_answer74) If \[F{{e}^{2+}}+2{{e}^{-1}}\xrightarrow[{}]{{}}Fe;\] \[E{}^\circ =-0.44V\] and \[Z{{n}^{2+}}+2{{e}^{-}}\xrightarrow[{}]{{}}Zn;\] \[E{}^\circ =-0.76\,V\] which of the following is the correct statement?

    A) Fe is more electropositive

    B) Zn is more electropositive

    C) Zn is more electronegative

    D) None of the above

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  • question_answer75) On the electrolysis of aqueous\[CuS{{O}_{4}}\]solution, by unreactive Pt electrodes, the reaction is occurred at anode

    A) \[2SO_{4}^{2-}\xrightarrow[{}]{{}}{{S}_{2}}O_{3}^{2-}+2\frac{1}{2}{{O}_{2}}+2{{e}^{-}}\]

    B) \[C{{u}^{2+}}+2{{e}^{-}}\xrightarrow[{}]{{}}Cu\]

    C) \[2{{H}_{2}}O\xrightarrow[{}]{{}}{{O}_{2}}+4{{H}^{+}}+4{{e}^{-}}\]

    D) \[2{{H}^{+}}+2{{e}^{-}}\xrightarrow[{}]{{}}{{H}_{2}}\]

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  • question_answer76) Which of the following chemical reaction represents homogeneous catalysis?

    A) \[{{N}_{2}}(g)+3{{H}_{2}}(g)\xrightarrow[{}]{Fe}2N{{H}_{3}}(g)\]

    B) \[2S{{O}_{2}}(g)+{{O}_{2}}(g)\xrightarrow[{}]{NO}2S{{O}_{3}}(g)\]

    C) \[CO(g)+3{{H}_{2}}(g)\xrightarrow[{}]{Ni}C{{H}_{4}}(g)+{{H}_{2}}O(g)\]

    D) \[2S{{O}_{2}}(g)+{{O}_{2}}(g)\xrightarrow[{}]{{{V}_{2}}{{O}_{5}}}2S{{O}_{3}}(g)\]

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  • question_answer77) Which of the following is correct for the reaction? \[MnO_{4}^{-}+CO_{4}^{2-}+{{H}^{+}}\xrightarrow[{}]{{}}M{{n}^{2+}}+C{{O}_{2}}+{{H}_{2}}O\]

    A) \[M{{n}^{2+}}\] - 5 \[C{{r}_{2}}O_{4}^{2-}\]-2 \[C{{O}_{2}}\]- 4 \[{{H}^{+}}\]-10

    B) \[M{{n}^{2+}}\] -2 \[C{{r}_{2}}O_{4}^{2-}\]- 5 \[C{{O}_{2}}\]-10 \[{{H}^{+}}\]-16

    C) \[M{{n}^{2+}}\] -6 \[C{{r}_{2}}O_{4}^{2-}\]-8 \[C{{O}_{2}}\]- 16 \[{{H}^{+}}\]-18

    D) \[M{{n}^{2+}}\] - 10 \[C{{r}_{2}}O_{4}^{2-}\]- 12 \[C{{O}_{2}}\]-24 \[{{H}^{+}}\]-12

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  • question_answer78) The oxidation number of Cr is changed on reaction of acidic\[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]with\[{{H}_{2}}S\]

    A) + 3 to + 6

    B) + 6 to + 3

    C) + 6 to + 2

    D) remains unchanged

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  • question_answer79) The oxidation number of oxygen is + 2 in, which of the following compound?

    A) \[{{H}_{2}}{{O}_{2}}\]

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

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

    D) \[O{{F}_{2}}\]

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  • question_answer80) Which of the following is the most electronegative?

    A) Lead

    B) Silicon

    C) Carbon

    D) Tin

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  • question_answer81) Which of the following is the s-block element?

    A) Aluminium

    B) Chromium

    C) Carbon

    D) Potassium

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  • question_answer82) Which of the following is the correct order of decreasing ionic radii of ions?

    A) \[{{N}^{3-}}>{{O}^{2-}}>{{F}^{-}}>N{{a}^{+}}\]

    B) \[{{N}^{3-}}>N{{a}^{+}}>{{O}^{2-}}>{{F}^{-}}\]

    C) \[N{{a}^{+}}>{{O}^{2-}}>{{N}^{3-}}>{{F}^{-}}\]

    D) \[N{{a}^{+}}>{{F}^{-}}>{{O}^{2-}}>{{N}^{3-}}\]

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  • question_answer83) The electronic configuration of a element is as \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}},3{{p}^{6}},3{{d}^{10}},4{{s}^{2}},4{{p}^{3}}\]The property of this element is similar to

    A) boron

    B) oxygen

    C) nitrogen

    D) chlorine

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  • question_answer84) Malachite is the ore of

    A) Fe

    B) Cu

    C) Zn

    D) Hg

    View Answer play_arrow
  • question_answer85) For the purification of blister copper, the copper is melted in the furnance and stirring with green logs of woot. The purpose of this

    A) to remove dissolved gases in blister copper

    B) by taking the impurities on the surface to oxidise them

    C) to increase the quantity of carbon in copper

    D) the impurities of metal oxide are reduced by hydrocarbon gases evolved from wood

    View Answer play_arrow
  • question_answer86) In the smelting of a metal ore, a substance is added, which forms a fusible product on mixing with impurities. The name of this substance is

    A) slag

    B) mud

    C) gangue

    D) flux

    View Answer play_arrow
  • question_answer87) Which of the following pair cannot remain together?

    A) \[NaHC{{O}_{3}}\]and\[NaCl\]

    B) \[NaHC{{O}_{3}}\]and\[NaOH\]

    C) \[NaHC{{O}_{3}}\]and\[N{{a}_{2}}C{{O}_{3}}\]

    D) \[N{{a}_{2}}C{{O}_{3}}\]and\[NaOH\]

    View Answer play_arrow
  • question_answer88) Which of the following has the highest melting point?

    A) Barium

    B) Strontium

    C) Calcium

    D) Radium

    View Answer play_arrow
  • question_answer89) The transition elements are generally

    A) diamagnetic

    B) paramagnetic

    C) neither diamagnetic nor paramagnetic

    D) both diamagnetic and paramagnetic

    View Answer play_arrow
  • question_answer90) The oxidation number of metal is zero in, which of the following co-ordination compound?

    A) \[[Pt{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]\]

    B) \[[Cr{{(CO)}_{6}}]\]

    C) \[[Cr{{(N{{H}_{3}})}_{3}}C{{l}_{3}}]\]

    D) \[[Cr{{(en)}_{2}}C{{l}_{2}}]\]

    View Answer play_arrow
  • question_answer91) \[[{{({{C}_{6}}{{H}_{5}})}_{2}}Pd{{(NCS)}_{2}}]\]and\[[{{({{C}_{6}}{{H}_{5}})}_{2}}Pd{{(SCN)}_{2}}]\]are

    A) linkage isomers

    B) coordination isomers

    C) ionisation isomers

    D) geometrical isomers

    View Answer play_arrow
  • question_answer92) The product forms mainly on the fusion of Na with aniline

    A) \[NaCN\]

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

    C) \[NaSCN\]

    D) \[NaN{{O}_{2}}\]

    View Answer play_arrow
  • question_answer93) The combustion of liquid benzene in oxygen is as \[2{{C}_{6}}{{H}_{6}}+15{{O}_{2}}\xrightarrow[{}]{{}}12C{{O}_{2}}+6{{H}_{2}}O\] How many litre of oxygen will require on complete combustion of 3.9 g liquid benzene at STP

    A) 11.2 L

    B) 22.4 L

    C) 8.4 L

    D) 7.4 L

    View Answer play_arrow
  • question_answer94) The IUPAC name of the following compounds is

    A) 3-methyl cyclo-l-butene-2-ol

    B) 4-methyl cyclo-but-2-ene-l-ol

    C) 4-methyl cyclo-but-l-ene-3-ol

    D) 2-methyl cyclo-3-butene-l-ol

    View Answer play_arrow
  • question_answer95) Which of the following compound does not show optical isomerism?

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

    B) \[C{{H}_{3}}CH(OH)C{{H}_{3}}\]

    C)

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

    View Answer play_arrow
  • question_answer96) In the following dehydration reaction the hybridised state of carbon changes \[C{{H}_{3}}CON{{H}_{2}}\xrightarrow[{}]{{{P}_{2}}{{O}_{5}}}C{{H}_{3}}CN+{{H}_{2}}O\]

    A) \[s{{p}^{3}}\]to\[s{{p}^{2}}\]

    B) \[sp\]to \[s{{p}^{2}}\]

    C) \[s{{p}^{2}}\]to\[sp\]

    D) \[sp\]to\[s{{p}^{3}}\]

    View Answer play_arrow
  • question_answer97) Acetylene reacts with\[HCN\]in the presence of \[Ba{{(CN)}_{2}}\]to give

    A) vinyl cyanide

    B) 1,1-dicyano ethane

    C) 1,2-dicyano ethane

    D) None of the above

    View Answer play_arrow
  • question_answer98) The substitution of chlorine becomes the most easiest in which of the following compound?

    A) Chloro benzene

    B) Vinyl chloride

    C) Allyl chloride

    D) p-chloro toluene

    View Answer play_arrow
  • question_answer99) Commercially, methanol is manufactured by which of the following method?

    A) Catalytic reduction of CO in the presence of \[ZnO,C{{r}_{2}}{{O}_{3}}\]

    B) The reaction of\[C{{H}_{4}}\]with water vapour in the presence of Ni catalyst at\[900{}^\circ C\]

    C) By the reaction of formaldehyde with\[LiAl{{H}_{4}}\]

    D) By the reaction of\[HCHO\]with aqueous\[KOH\]

    View Answer play_arrow
  • question_answer100) The order of acidic strength of phenol, p-cresol, m-nitrophenol and p-nitrophenol is

    A) phenol, p-cresol, p-nitrophenol, m-nitrophenol

    B) p-cresol, phenol, 2n-nitrophenol, p-nitrophenol

    C) p-cresol, m-nitrophenol, phenol, p-nitrophenol

    D) m-nitrophenol, phenol, p-cresol, p-nitrophenol

    View Answer play_arrow
  • question_answer101) \[\int_{0}^{\pi /2}{\frac{x\sin x.\cos x}{{{\cos }^{4x}}+{{\sin }^{4}}x}dx}\]is equal to

    A) \[\frac{{{\pi }^{2}}}{8}\]

    B) \[\frac{{{\pi }^{2}}}{16}\]

    C) 1

    D) 0

    View Answer play_arrow
  • question_answer102) The equation of tangent to the hyperbola \[2{{x}^{2}}-3{{y}^{2}}=6\]which is parallel to the line \[y-3x-4=0,\]is

    A) \[y=3x+8\]

    B) \[y=3x-8\]

    C) \[y=3x+2\]

    D) None of these

    View Answer play_arrow
  • question_answer103) If coefficient of correlation between two variables\[x\]and y is 0.32 and co variance is 8, variance of\[x\]is 25, then variance of y is

    A) 36

    B) 25

    C) 64

    D) None of these

    View Answer play_arrow
  • question_answer104) Ten coins are tossed together, then the probability of getting at least 7 heads is

    A) \[\frac{63}{256}\]

    B) \[\frac{121}{172}\]

    C) \[\frac{113}{512}\]

    D) \[\frac{11}{64}\]

    View Answer play_arrow
  • question_answer105) If\[{{b}_{yx}}=0.03\]and\[{{b}_{xy}}=0.3,\]then the approximate value of r is

    A) 0.003

    B) 0.095

    C) 0.3

    D) \[-0.3\]

    View Answer play_arrow
  • question_answer106) Using Simpson's\[\frac{1}{3}\]rd rule, the value of\[\int_{1}^{5}{f(x)}dx\]for the following data is

    \[x\] 1 2 3 4 5
    \[y\] 10 50 70 80 100

    A) 140.88

    B) 256.66

    C) 160.26

    D) None of these

    View Answer play_arrow
  • question_answer107) The feasible region represented by\[{{x}_{1}}+{{x}_{2}}\le 1,\] \[-3{{x}_{1}}+{{x}_{2}}\ge ({{x}_{1}},{{x}_{2}}\ge 0)\]is

    A) a polygon

    B) a singleton set

    C) an empty set

    D) None of these

    View Answer play_arrow
  • question_answer108) The point on the curve\[{{x}^{2}}=2y\]which is at a minimum distance from the point (0,5), is

    A) (2,2), (-2,2)

    B) \[(2\sqrt{2},4),(-2\sqrt{2},4)\]

    C) \[(\sqrt{6},3),(-\sqrt{6},3)\]

    D) \[(2\sqrt{3},6),(-2\sqrt{3},6)\]

    View Answer play_arrow
  • question_answer109) The solution of the differential equation\[\left( \frac{dy}{dx} \right)\tan y=\sin (x+y)+\sin (x-y)\]is

    A) \[sec\text{ }x-1/2\text{ }tan\text{ }y=c\]

    B) \[log\text{ }sin\text{ (}x+y)=c\]

    C) \[sec\text{ }x+tan\text{ }y=c\]

    D) \[sec\text{ }y+2\text{ }cos\text{ }x=c\]

    View Answer play_arrow
  • question_answer110) \[\overrightarrow{A}.\{(\overrightarrow{B}+\overrightarrow{C})\times (\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C})\}\] is equal to

    A) \[[\overrightarrow{A}\,\overrightarrow{B}\,\overrightarrow{C}]\]

    B) \[[\overrightarrow{B}\,\overrightarrow{A}\,\overrightarrow{C}]\]

    C) 0

    D) 1

    View Answer play_arrow
  • question_answer111) If \[y+\frac{{{y}^{3}}}{3}+\frac{{{y}^{5}}}{5}+....\infty =2\left[ x+\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5}+....\infty \right],\] then the value of y is

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

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

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

    D) None of these

    View Answer play_arrow
  • question_answer112) If\[x=\frac{1}{2}(\sqrt{3}+i),\]then\[{{x}^{3}}\]is equal to

    A) 1

    B) \[-1\]

    C) 2

    D) \[-i\]

    View Answer play_arrow
  • question_answer113) If the complex numbers\[sin\text{ }x+i\text{ }cos\text{ }2x\]and \[cos\,x-i\,sin2x\]are conjugate to each other, then the value of\[x\]is

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

    B) \[\frac{\pi }{8}\]

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

    D) None of these

    View Answer play_arrow
  • question_answer114) \[\underset{x\to 2}{\mathop{\lim }}\,\frac{|x-2|}{x-2}\]is equal to

    A) \[-1\]

    B) 1

    C) 2

    D) \[1-2\]

    View Answer play_arrow
  • question_answer115) If \[\left| \begin{matrix} x & {{x}^{2}} & 1+{{x}^{3}} \\ y & {{y}^{2}} & 1+{{y}^{3}} \\ z & {{z}^{2}} & 1+{{z}^{3}} \\ \end{matrix} \right|=0,\]then

    A) \[z=xy\]

    B) \[z=\frac{1}{xy}\]

    C) \[z=-\frac{1}{xy}\]

    D) None of these

    View Answer play_arrow
  • question_answer116) \[{{\cos }^{4}}\frac{\pi }{8}+{{\cos }^{4}}\frac{3\pi }{8}+{{\cos }^{4}}\frac{5\pi }{8}+{{\cos }^{4}}\frac{7\pi }{8}\]is equal to

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

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

    C) \[-1\]

    D) \[1\]

    View Answer play_arrow
  • question_answer117) In\[\Delta ABC,\]if\[\tan \frac{A}{2}=\frac{5}{6}\]and\[\tan \frac{B}{2}=\frac{20}{37},\]then\[a+c\]is equal to

    A)  b                 

    B)  2b

    C)  3b                 

    D)  4b

    View Answer play_arrow
  • question_answer118) In the interval\[[0,2\pi ],\]the number of solutions of the equation\[tan\text{ }x+sec\text{ }x=2\text{ }cos\text{ }x\]is

    A) 0

    B) 1

    C) 2

    D) 3

    View Answer play_arrow
  • question_answer119) The joint equation of the bisectors of the angles between the lines represented by the equation\[a{{x}^{2}}+hxy+b{{y}^{2}}=0\]is

    A) \[\frac{{{x}^{2}}-{{y}^{2}}}{a-b}=\frac{2xy}{h}\]

    B) \[\frac{{{x}^{2}}+{{y}^{2}}}{a+b}=\frac{xy}{2h}\]

    C) \[\frac{{{x}^{2}}-{{y}^{2}}}{a-b}=\frac{xy}{h}\]

    D) None of these

    View Answer play_arrow
  • question_answer120) The circle\[{{x}^{2}}+{{y}^{2}}-2cx-2cy+{{c}^{2}}=0\]touches both the axes and the line\[\frac{x}{3}+\frac{y}{4}=1\]. Its centre lies in the first quadrant, then the value of c is

    A) 1

    B) 2

    C) 3

    D) 6

    View Answer play_arrow
  • question_answer121) The angle between two diagonals of a cube is

    A) \[\frac{\pi }{3}\]

    B) \[{{\cos }^{-1}}\left( \frac{1}{3} \right)\]

    C) \[{{\cos }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]

    D) None of these

    View Answer play_arrow
  • question_answer122) If \[{{a}_{1}},{{a}_{2}},{{a}_{3}},....{{a}_{n}}\]are in AP when\[{{a}_{i}}>0\]for all\[i\], then the sum of the series \[\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{1}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+\frac{1}{\sqrt{{{a}_{3}}}+\sqrt{{{a}_{4}}}}\] \[+....+\frac{1}{\sqrt{{{a}_{n-1}}}+\sqrt{{{a}_{n}}}}\]is

    A) \[\frac{n+1}{\sqrt{{{a}_{1}}+{{a}_{n}}}}\]

    B) \[\frac{n+1}{\sqrt{{{a}_{1}}}-\sqrt{{{a}_{n}}}}\]

    C) \[\frac{n+1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\]

    D) \[\frac{n-1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\]

    View Answer play_arrow
  • question_answer123) Plane\[xy\]divides the line joining the points s (- 3, 4, - 8) and (5, - 6, 4) in the ratio

    A) \[2:3\]

    B) \[2:1\]

    C) \[4:5\]

    D) None of these

    View Answer play_arrow
  • question_answer124) The unit vectors which is perpendicular to both vectors\[3\hat{i}+\hat{j}+2\hat{k}\]and\[2\hat{i}-2\hat{j}+4\hat{k},\]is

    A) \[\frac{\hat{i}-\hat{j}-\hat{k}}{\sqrt{3}}\]

    B) \[\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\]

    C) \[\frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{3}}\]

    D) None of these

    View Answer play_arrow
  • question_answer125) If\[y={{\tan }^{-1}}\frac{\sqrt{(1+{{x}^{2}})}+\sqrt{(1-{{x}^{2}})}}{\sqrt{(1+{{x}^{2}})}-\sqrt{(1-{{x}^{2}})}},\]then\[\frac{dy}{dx}\]is equal to

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

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

    C) \[\frac{-x}{\sqrt{(x-{{x}^{4}})}}\]

    D) \[\frac{x\sqrt{1+{{x}^{2}}}}{1-{{x}^{4}}}\]

    View Answer play_arrow
  • question_answer126) Vectors\[\overrightarrow{a},\text{ }\overrightarrow{b}\]and\[\overrightarrow{c}\]are in the same plane, which of the following is false?

    A) \[\overrightarrow{a}.(\overrightarrow{b}\times \overrightarrow{c})=0\]

    B) \[\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})=0\]

    C) \[[\overrightarrow{a}+\overrightarrow{b}\text{ }\overrightarrow{b}+\overrightarrow{c}\text{ }\overrightarrow{c}+\overrightarrow{a}]=0\]

    D) \[\overrightarrow{a}=p\overrightarrow{b}+q\overrightarrow{c}\]

    View Answer play_arrow
  • question_answer127) If\[[A]\ne 0\]and order of A is 21, then adj (adj A) is equal to

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

    B) \[|A{{|}^{2}}\]

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

    D) \[|A{{|}^{n-2}}A\]

    View Answer play_arrow
  • question_answer128) \[\int{\frac{x+\sin x}{1+\cos x}}dx\]is equal to

    A) \[x\log (1+\cos x)+c\]

    B) \[\frac{1}{x}\log (1+\cos x)+c\]

    C) \[x\tan \frac{x}{2}+c\]

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

    View Answer play_arrow
  • question_answer129) The differential equation of the curve \[y=A{{e}^{x}}+B{{e}^{-x}}\]for different values of A and B, is

    A) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-2y=0\]

    B) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=y\]

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

    D) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\]

    View Answer play_arrow
  • question_answer130) The solution of\[\frac{dy}{dx}=\frac{{{y}^{2}}}{xy-{{x}^{2}}}\]is

    A) \[y=c{{e}^{x/y}}\]

    B) \[y=c{{e}^{y/x}}+x\]

    C) \[y=c{{e}^{y/x}}\]

    D) \[xy=c{{e}^{y/x}}\]

    View Answer play_arrow
  • question_answer131) If\[\underset{x\to a}{\mathop{\lim }}\,=\frac{{{a}^{x}}-{{x}^{a}}}{{{x}^{x}}-{{a}^{a}}}=-1,\]then

    A) \[a=1\]

    B) \[a=0\]

    C) \[a=e\]

    D) \[a=\frac{1}{e}\]

    View Answer play_arrow
  • question_answer132) Select four numbers from the numbers 1, 2, 3, 4, 5, 6, 7. The probability that the sum of these four numbers is less than 12, is

    A) \[\frac{3}{35}\]

    B) \[\frac{4}{35}\]

    C) \[\frac{2}{35}\]

    D) \[\frac{1}{35}\]

    View Answer play_arrow
  • question_answer133) Let A and B are two events, then the probability that exactly one event is occur, is

    A) \[P(A)+P(B)-2P(A\cap B)\]

    B) \[P(A)+P(B)-P(A\cap B)\]

    C) \[P(A)-P(B)\]

    D) None of the above

    View Answer play_arrow
  • question_answer134) The solution of the equation \[x\cos x\left( \frac{dy}{dx} \right)+y(x\sin x+\cos x)=1\]is

    A) \[y=x\text{ }tan\text{ }x+sin\text{ }x+c\]

    B) \[y=y\text{ }tan\text{ }x+c\]

    C) \[yx\text{ }sec\text{ }x=tan\text{ }x+c\]

    D) \[xy\text{ }cos\text{ }x=x+c\]

    View Answer play_arrow
  • question_answer135) If equation\[({{a}^{2}}+4a+3){{x}^{2}}+({{a}^{2}}-a-2)x\] \[+a(a+1)=0\]have more than two roots, then the value of a is

    A) 0

    B) 1

    C) \[-1\]

    D) None of these

    View Answer play_arrow
  • question_answer136) In an AP, the sum of the n, 2n and 3n terms are\[{{S}_{1}},{{S}_{2}}\]and\[{{S}_{3}}\]respectively, then

    A) \[{{S}_{2}}=3{{S}_{3}}-2{{S}_{1}}\]

    B) \[{{S}_{3}}=4({{S}_{1}}+{{S}_{2}})\]

    C) \[{{S}_{3}}=3({{S}_{2}}-{{S}_{1}})\]

    D) \[{{S}_{3}}=2({{S}_{2}}+{{S}_{1}})\]

    View Answer play_arrow
  • question_answer137) If\[^{n}{{C}_{r-1}}=36{{,}^{n}}{{C}_{r}}=84\]and\[^{n}{{C}_{r+1}}=126,\]then\[n\]is

    A) 8

    B) 9

    C) 10

    D) 11

    View Answer play_arrow
  • question_answer138) In a\[\Delta ABC,\]there are 3, 4 and 5 points on the sides AB, BC and CA respectively. The number of triangles formed by these points as vertices is

    A) 201

    B) 120

    C) 205

    D) 435

    View Answer play_arrow
  • question_answer139) In the expansion of \[1+\frac{a}{bx}1!+\frac{{{(a+bx)}^{2}}}{2!}\]\[+\frac{{{(a+bx)}^{3}}}{3!}+....\]the coefficient of\[{{x}^{n}}\]is

    A) \[\frac{{{e}^{a}}{{b}^{n}}}{n!}\]

    B) \[\frac{{{(b.a)}^{n}}}{n!}\]

    C) \[\frac{{{e}^{b}}.{{b}^{n}}}{(n-1)!}\]

    D) \[\frac{{{a}^{n}}{{b}^{n-1}}}{n!}\]

    View Answer play_arrow
  • question_answer140) \[\frac{{{C}_{0}}}{1}+\frac{{{C}_{2}}}{3}+\frac{{{C}_{4}}}{5}+\frac{{{C}_{6}}}{7}+....\]is equal to

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

    B) \[\frac{{{2}^{n+1}}}{n+3}\]

    C) \[\frac{{{2}^{n}}}{n+1}\]

    D) \[\frac{{{2}^{n-2}}}{n}\]

    View Answer play_arrow
  • question_answer141) The equation of the parabola whose vertex is \[(2,-1)\]and focus\[(3,-1),\]is

    A) \[{{y}^{2}}-4x-2y+9=0\]

    B) \[{{y}^{2}}+4x+2y-9=0\]

    C) \[{{y}^{2}}-4x+2y+9=0\]

    D) \[{{y}^{2}}+4x-2y+9=0\]

    View Answer play_arrow
  • question_answer142) The equations of lines joining the origin to the point of intersection of the curves\[y=x+3\]and\[4{{x}^{2}}+4{{y}^{2}}=1,\]are

    A) \[36({{x}^{2}}+{{y}^{2}})={{(x-y)}^{2}}\]

    B) \[12({{x}^{2}}+{{y}^{2}})={{(x+y)}^{2}}\]

    C) \[9({{x}^{2}}+{{y}^{2}})=4{{(x-y)}^{2}}\]

    D) None of the above

    View Answer play_arrow
  • question_answer143) The angle of elevation of a fighter jet plane from a point on the ground is\[60{}^\circ \]. After 10s the angle of elevation becomes\[30{}^\circ \]. If the speed of jet plane is 432 km/h, then the height of the jet plane from the ground is

    A) \[200\sqrt{3}m\]

    B) \[400\sqrt{3}m\]

    C) \[600\sqrt{3}m\]

    D) \[800\sqrt{3}m\]

    View Answer play_arrow
  • question_answer144) Which of the following is false?

    A) \[(AB)'=B'A'\]

    B) \[{{(AB)}^{\theta }}={{B}^{\theta }}{{A}^{\theta }}\]

    C) \[\overline{AB}=\overline{B}\,\,\overline{A}\]

    D) \[{{(AB)}^{-1}}={{B}^{-1}}{{A}^{-1}}\]

    View Answer play_arrow
  • question_answer145) The equation of plane which is parallel to\[x-\]axis and passes through the line \[\frac{x-2}{2}=\frac{y-3}{3}=\frac{z-4}{5}\]is

    A) \[2x+3y+5z=1\]

    B) \[2x-5y=4\]

    C) \[5y-3z-3=0\]

    D) \[3y+4z=0\]

    View Answer play_arrow
  • question_answer146) A force\[\overrightarrow{F}=5\hat{i}+10\hat{j}+16\hat{k}\] acts at a point, whose position vector is\[2\hat{i}-7\hat{j}+10\hat{k}\]. The moment of F about the point\[-5\hat{i}+6\hat{j}-10\hat{k}\]is

    A) \[41\hat{i}-8\hat{j}+55\hat{k}\]

    B) \[-408\hat{i}-12\hat{j}+135\hat{k}\]

    C) \[-36\hat{i}+14\hat{j}-35\hat{k}\]

    D) None of the above

    View Answer play_arrow
  • question_answer147) The equations of tangent to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]which cut equal intercepts from the axes, are

    A) \[y=\sqrt{3}x\pm \sqrt{3{{a}^{2}}+{{b}^{2}}}\]

    B) \[y=\pm x+\sqrt{{{a}^{2}}+{{b}^{2}}}\]

    C) \[y=\sqrt{3x}\pm +\sqrt{{{a}^{2}}+3{{b}^{2}}}\]

    D) None of the above

    View Answer play_arrow
  • question_answer148) Square matrix A will be an orthogonal matrix, if

    A) \[A\overline{A}=I\]

    B) \[AA'=I\]

    C) \[A{{A}^{\theta }}=I\]

    D) \[{{A}^{2}}=I\]

    View Answer play_arrow
  • question_answer149) In the interval \[[0,\pi ],\] the function\[f(x)={{e}^{x}}\sin x\]satisfies the Rolle's theorem, the value of 'c' is

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

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

    C) \[\frac{5\pi }{6}\]

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

    View Answer play_arrow
  • question_answer150) \[\int_{-a}^{a}{x\sqrt{({{a}^{2}}-{{x}^{2}})}}dx\]is equal to

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

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

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

    D) \[0\]

    View Answer play_arrow

   



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