Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

done Jamia Millia Islamia Solved Paper-2005

  • question_answer1) The inductance between A and D is:

    A) 3.66 H

    B) 9 H

    C) 0.66 H

    D) 1 H

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  • question_answer2) A ball whose kinetic energy is E, is projected at an angle of\[45{}^\circ \]to the horizontal. The kinetic energy of the ball at the highest point of its flight will be:

    A) E

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

    C) E/2

    D) zero

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  • question_answer3) From a building two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically). If\[{{v}_{A}}\]and\[{{v}_{B}}\]are their respective velocities on reaching the ground, then

    A) \[{{v}_{B}}>{{v}_{A}}\]

    B) \[{{v}_{A}}={{v}_{B}}\]

    C) \[{{v}_{A}}>{{v}_{B}}\]

    D) their velocities depends on their masses

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  • question_answer4) If a body loses half of its velocity on penetrating 3cm in a wooden block, then how much will it penetrate more before coming to rest?

    A) 1 cm

    B) 2 cm

    C) 3 cm

    D) 4 cm

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  • question_answer5) If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero, then the satellite will:

    A) continue to move in its orbit with same velocity

    B) move tangentially to the original orbit with the same velocity

    C) become stationary in its orbit

    D) move towards the earth

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  • question_answer6) If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter a:

    A) low resistance in parallel

    B) high resistance in parallel

    C) high resistance in series

    D) low resistance in series

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  • question_answer7) If in a circular coil A of radius R, current\[i\]is flowing and in another coil B of radius 2R a current\[2i\]is flowing, then the ratio of the magnetic fields,\[{{B}_{A}}\]and\[{{B}_{B}}\]produced by them will be:

    A) 1

    B) 2

    C) 1/2

    D) 4

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  • question_answer8) If two mirrors are kept at\[60{}^\circ \]to each other, then the number of images formed by them is:

    A) 5

    B) 6

    C) 7

    D) 8

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  • question_answer9) A wire when connected to 220V mains supply has power dissipation\[{{P}_{1}}\]. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is\[{{P}_{2}}\]. Then\[{{P}_{2}}:{{P}_{1}}\]is

    A) 1

    B) 4

    C) 2

    D) 3

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  • question_answer10) If 13.6eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from\[n=2\]is:

    A) 10.2 eV

    B) 0 eV

    C) 3.4 eV

    D) 6.8 eV

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  • question_answer11) Tube A has both ends open while tube B has one end closed, otherwise they are identical. The ratio of fundamental frequency of tubes A and B is:

    A) \[1:2\]

    B) \[1:4\]

    C) \[2:1\]

    D) \[4:1\]

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  • question_answer12) A tuning fork arrangement (pair) produces 4 beats/sec with one fork of frequency 288 .cps. A little wax is placed on the unknown fork and it then produces 2 beats/sec. The frequency of the unknown folk is:

    A) 286 cps

    B) 292 cps

    C) 294 cps

    D) 288 cps

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  • question_answer13) A wave\[y=a\sin (\omega t-kx)\]on a string meets with another wave producing a node at\[x=0\]. Then the equation of the unknown wave is:

    A) \[y=a\sin (\omega t+kx)\]

    B) \[y=-a\sin (\omega t+kx)\]

    C) \[y=a\sin (\omega t-kx)\]

    D) \[y=-a\sin (\omega t-kx)\]

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  • question_answer14) On moving a charge of 20 coulombs by 2 cm, 2 J of work is done, then the potential difference between the points is:

    A) 0.1 V

    B) 8 V

    C) 2 V

    D) 0.5 V

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  • question_answer15) If an electron and a proton having same momenta enter perpendicularly to a magnetic field, then:

    A) curved path of electron and proton will be same (ignoring the sense of revolution)

    B) they will move under flecked

    C) curved path of electron is more curved than that of proton

    D) path of proton is more curved

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  • question_answer16) Energy required to move a body of mass m from an orbit of radius 2R to 3R is:

    A) \[GMm/12{{R}^{2}}\]

    B) \[GMm/3{{R}^{2}}\]

    C) \[GMm/8R\]

    D) \[GMm/6R\]

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  • question_answer17) If a spring has time period T, and is cut into n equal parts, then the time period of each part will be:

    A) \[T\sqrt{n}\]

    B) \[T/\sqrt{n}\]

    C) \[nT\]

    D) \[T\]

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  • question_answer18) A charged particle q is placed at the centre\[O\] of cube of length L (ABCDEFGH). Another same charge q is placed at a distance L from Then the electrons flux through ABCD is:

    A) \[q/4\pi {{\varepsilon }_{0}}L\]

    B) zero

    C) \[q/2\pi {{\varepsilon }_{0}}L\]

    D) \[q/3\pi {{\varepsilon }_{0}}L\]

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  • question_answer19) If in the circuit, power dissipation is 150 W, then R is:

    A) \[2\,\Omega \]

    B) \[6\,\Omega \]

    C) \[5\,\Omega \]

    D) \[4\,\Omega \]

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  • question_answer20) Wavelength of light used in an optical instrument are\[{{\lambda }_{1}}=4000\,\overset{o}{\mathop{\text{A}}}\,\]and\[{{\lambda }_{2}}=5000\,\overset{o}{\mathop{\text{A}}}\,,\]then ratio of their respective resolving powers (corresponding to\[{{\lambda }_{1}}\]and\[{{\lambda }_{2}}\]) is:

    A) \[16:25\]

    B) \[9:1\]

    C) \[4:5\]

    D) \[5:4\]

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  • question_answer21) Two identical particles move towards each other with velocity 2v and v respectively. The velocity of centre of mass is

    A) v

    B) v/3

    C) v/2

    D) zero

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  • question_answer22) If a current is passed through a spring then the spring will:

    A) expand

    B) compress

    C) remain same

    D) none of these

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  • question_answer23) Heat given to a body which raises its temperature by\[1{}^\circ C\]is:

    A) water equivalent

    B) thermal capacity

    C) specific heat

    D) temperature gradient

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  • question_answer24) At absolute zero, Si acts as:

    A) non-metal

    B) metal

    C) insulator

    D) none of these

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  • question_answer25) Electromagnetic waves are transverse in nature is evident by:

    A) polarization

    B) interference

    C) reflection

    D) diffraction

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  • question_answer26) Which of the following is used in optical fibres?

    A) Total internal reflection

    B) Scattering

    C) Diffraction

    D) Refraction

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  • question_answer27) The escape velocity of a body depends upon mass as:

    A) \[{{m}^{0}}\]

    B) \[{{m}^{1}}\]

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

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

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  • question_answer28) Which of the following are not electro- magnetic waves?

    A) Cosmic-rays

    B) y rays

    C) \[\beta -rays\]

    D) X-rays

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  • question_answer29) Identify the pair whose dimensions are equal:

    A) torque and work

    B) stress and energy

    C) force and stress

    D) force and work

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  • question_answer30) If\[{{\theta }_{i}}\] is the inversion temperature,\[{{\theta }_{n}}\]is the neutral temperature,\[{{\theta }_{c}}\]. is the temperature of the cold junction then:

    A) \[{{\theta }_{i}}+{{\theta }_{c}}={{\theta }_{n}}\]

    B) \[{{\theta }_{i}}-{{\theta }_{c}}=2{{\theta }_{n}}\]

    C) \[\frac{{{\theta }_{i}}-{{\theta }_{c}}}{2}={{\theta }_{n}}\]

    D) \[{{\theta }_{c}}-{{\theta }_{i}}=2{{\theta }_{n}}\]

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  • question_answer31) Infrared radiations are detected by:

    A) spectrometer

    B) pyrometer

    C) nanometer

    D) photometer

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  • question_answer32) If\[{{N}_{0}}\]is the original mass of the substance of half-life period\[{{t}_{1/2}}=5\]years, then the amount of substance left after 15 years is:

    A) \[{{N}_{0}}/8\]

    B) \[{{N}_{0}}/16\]

    C) \[{{N}_{0}}/2\]

    D) \[{{N}_{0}}/4\]

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  • question_answer33) By increasing the temperature, the specific resistance of a conductor and a semiconductor:

    A) increases for both

    B) decreases for both

    C) increases, decreases respectively

    D) decreases, increases respectively

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  • question_answer34) If there are n capacitors in parallel connected to V volt source, then the energy stored is equal to:

    A) \[CV\]

    B) \[\frac{1}{2}nC{{V}^{2}}\]

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

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

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  • question_answer35) Which of the following is more close to a black body?

    A) Black board paint

    B) Green leaves

    C) Black holes

    D) Red roses

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  • question_answer36) Which statement is incorrect?

    A) All reversible cycles have same efficiency

    B) Reversible cycle has more efficiency than an irreversible one

    C) Carnot cycle is a reversible one

    D) Carnot cycle has the maximum efficiency in all cycles

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  • question_answer37) Length of a string tied to two rigid supports is 40cm. Maximum length (wavelength in cm) of a stationary wave produced on it, is:

    A) 20

    B) 80

    C) 40

    D) 120

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  • question_answer38) The power factor of an A.C. circuit having resistance R and inductance L (connected in series) and an angular velocity\[\omega \]is:

    A) \[R/\omega L\]

    B) \[R{{({{R}^{2}}+{{\omega }^{2}}{{L}^{2}})}^{1/2}}\]

    C) \[\omega L/R\]

    D) \[R/{{({{R}^{2}}-{{\omega }^{2}}{{L}^{2}})}^{1/2}}\]

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  • question_answer39) An astronomical telescope has a large aperture to:

    A) reduce spherical aberration

    B) have high resolution

    C) increase span of observation

    D) have low dispersion

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  • question_answer40) The kinetic energy needed to project a body of mass m from the earths surface (radius R) to infinity is:

    A) \[mgR/2\]

    B) \[2mgR\]

    C) \[mgR\]

    D) \[mgR/4\]

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  • question_answer41) Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will:

    A) increase

    B) decrease

    C) remain same

    D) decrease for some, while increase for others

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  • question_answer42) When temperature increases, the frequency of a tuning fork:

    A) increases

    B) decreases

    C) remains same

    D) increases or decreases depending on the material

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  • question_answer43) If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should:

    A) increase

    B) remain unchanged

    C) decrease

    D) first increase then decrease

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  • question_answer44) The energy band gap is maximum in:

    A) metals

    B) superconductors

    C) insulators

    D) semiconductors

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  • question_answer45) The part of a transistor which is most heavily doped to produce large number of majority carriers is:

    A) emitter

    B) base

    C) collector

    D) can be any of the above three

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  • question_answer46) In a simple harmonic oscillator, at the mean position:

    A) kinetic energy is minimum, potential energy is maximum

    B) both kinetic and potential energies are maximum

    C) kinetic energy is maximum, potential energy is minimum

    D) both kinetic and potential energies are minimum

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  • question_answer47) Initial angular velocity of a circular disc of mass M is\[{{\omega }_{1}}\]. Then two small spheres of mass m are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

    A) \[\left( \frac{M+m}{M} \right){{\omega }_{1}}\]

    B) \[\left( \frac{M+m}{m} \right){{\omega }_{1}}\]

    C) \[\left( \frac{M}{M+4m} \right){{\omega }_{1}}\]

    D) \[\left( \frac{M}{M+2m} \right){{\omega }_{1}}\]

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  • question_answer48) The minimum velocity (in\[m{{s}^{-1}}\]) with which a car driver must traverse a flat curve of radius 150m and coefficient of friction 0.6 to avoid skidding is:

    A) 60

    B) 30

    C) 15

    D) 25

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  • question_answer49) A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in \[m{{s}^{-1}}\]) through a small hole on the side wall of the cylinder near its bottom, is:

    A) 10

    B) 20

    C) 25.5

    D) 5

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  • question_answer50) A spring of force constant 800 N/m has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm is:

    A) 16 J

    B) 8 J

    C) 32 J

    D) 24 J

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  • question_answer51) A child swinging on a swing in sitting position, stands up, then the time period of the swing will:

    A) increase

    B) decrease

    C) remain same

    D) increase if the child is long and decrease if the child is short

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  • question_answer52) A lift is moving down with acceleration a. Aman in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively:

    A) \[g,g\]

    B) \[g-a.\text{ }g-a\]

    C) \[g-a,g\]

    D) \[a,g\]

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  • question_answer53) The mass of a product liberated on anode in an electrochemical cell depends on:

    A) \[{{(It)}^{1/2}}\]

    B) \[It\]

    C) \[I/t\]

    D) \[{{I}^{2}}t\]

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  • question_answer54) At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at\[47{}^\circ C\]?

    A) 80 K

    B) \[-73\text{ }K\]

    C) 3 K

    D) 20 K

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  • question_answer55) The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its:

    A) speed

    B) mass

    C) charge

    D) magnetic induction

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  • question_answer56) Which of the following is a redox reaction?

    A) \[NaCl+KN{{O}_{3}}\xrightarrow[{}]{{}}NaN{{O}_{3}}+KCl\]

    B) \[Ca{{C}_{2}}{{O}_{4}}+2HCl\xrightarrow[{}]{{}}CaC{{l}_{2}}+{{H}_{2}}{{C}_{2}}{{O}_{4}}\]

    C) \[Ca{{(OH)}_{2}}+2N{{H}_{4}}Cl\xrightarrow[{}]{{}}\]\[CaC{{l}_{2}}+2N{{H}_{3}}+2{{H}_{2}}O\]

    D) \[2K[Ag{{(CN)}_{2}}]+Zn\xrightarrow[{}]{{}}\] \[2Ag+{{K}_{2}}[Zn{{(CN)}_{4}}]\]

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  • question_answer57) For an ideal gas, number of mol per litre in terms of its pressure P, temperature T and gas constant R is:

    A) PT/R

    B) PRT

    C) P/RT

    D) RT/P

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  • question_answer58) Number of\[P-O\]bonds in\[{{P}_{4}}{{O}_{10}}\]is:

    A) 17

    B) 16

    C) 15

    D) 6

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  • question_answer59) \[K{{O}_{2}}\]is used in space and submarines because it:

    A) absorbs\[C{{O}_{2}}\]and increases\[{{O}_{2}}\]concentration

    B) absorbs moisture

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

    D) produces ozone

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  • question_answer60) Which of the following ions has the maximum magnetic moment?

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

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

    C) \[T{{i}^{2+}}\]

    D) \[C{{r}^{2+}}\]

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  • question_answer61) Acetylene does not react with:

    A) Na

    B) ammonical\[AgN{{O}_{3}}\]

    C) \[HCl\]

    D) \[NaOH\]

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  • question_answer62) Compound A given below is:

    A) antiseptic

    B) antibiotic

    C) analgesic

    D) pesticide

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  • question_answer63) For the following cell with hydrogen electrodes at two different pressures\[{{p}_{1}}\]and\[{{p}_{2}}\]\[\underset{{{p}_{1}}}{\mathop{pt({{H}_{2}})}}\,|\underset{1\,M}{\mathop{{{H}^{+}}(aq).}}\,|\underset{{{p}_{2}}}{\mathop{Pt({{H}_{2}})}}\,\]emf is given by:

    A) \[\frac{RT}{F}{{\log }_{e}}\frac{{{p}_{1}}}{{{p}_{2}}}\]

    B) \[\frac{RT}{2F}{{\log }_{e}}\frac{{{p}_{1}}}{{{p}_{2}}}\]

    C) \[\frac{RT}{F}{{\log }_{e}}\frac{{{p}_{2}}}{{{p}_{1}}}\]

    D) \[\frac{RT}{2F}{{\log }_{e}}\frac{{{p}_{2}}}{{{p}_{1}}}\]

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  • question_answer64) Acetylene reacts with hypochlorous acid to form:

    A) \[C{{l}_{2}}CHCHO\]

    B) \[ClC{{H}_{2}}COOH\]

    C) \[C{{H}_{3}}COCl\]

    D) \[ClC{{H}_{2}}CHO\]

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  • question_answer65) On heating benzyl amine with chloroform and ethanolic KOH, product obtained is:

    A) benzyl alcohol

    B) benzaldehyde

    C) benzonitrile

    D) benzyl isocyanide

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  • question_answer66) Which of the following reaction is possible at anode?

    A) \[{{F}_{2}}+2{{e}^{-}}\xrightarrow[{}]{{}}2{{F}^{-}}\]

    B) \[2{{H}^{+}}+\frac{1}{2}{{O}_{2}}+2{{e}^{-}}\xrightarrow[{}]{{}}{{H}_{2}}O\]

    C) \[2Cr_{2}^{3+}+7{{H}_{2}}O\xrightarrow[{}]{{}}C{{r}_{2}}O_{7}^{2-}+14{{H}^{+}}+6{{e}^{-}}\]

    D) \[F{{e}^{2+}}\xrightarrow[{}]{{}}F{{e}^{3+}}+{{e}^{-}}\]

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  • question_answer67) Which of the following concentration factor is affected by change in temperature?

    A) Molarity

    B) Molality

    C) Mol fraction

    D) Weight fraction

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  • question_answer68) Cyanide process is used for the extraction of:

    A) barium

    B) silver

    C) boron

    D) zinc

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  • question_answer69) Following reaction\[{{(C{{H}_{3}})}_{3}}CBr+{{H}_{2}}O\xrightarrow[{}]{{}}{{(C{{H}_{3}})}_{3}}COH+HBr\]is an example of:

    A) elimination reaction

    B) free radical substitution

    C) nucleophilic substitution

    D) electrophilic substitution

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  • question_answer70) A metal M forms water soluble\[MS{{O}_{4}}\] and inert \[MO.\text{ }MO\]in aqueous solution forms insoluble \[M{{(OH)}_{2}}\]soluble in\[NaOH\]. Metal M is:

    A) Be

    B) Mg

    C) Ca

    D) Si

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  • question_answer71) Half life of a substance A following first order kinetics is 5 days. Starting with 100 g of A, amount left after 15 days is:

    A) 25 g

    B) 50 g

    C) 12.5 g

    D) 6.25 g

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  • question_answer72) The most stable ion is:

    A) \[{{[Fe{{(OH)}_{5}}]}^{3-}}\]

    B) \[{{[FeC{{l}_{6}}]}^{3-}}\]

    C) \[{{[Fe{{(CN)}_{6}}]}^{3-}}\]

    D) \[{{[Fe{{({{H}_{2}}O)}_{6}}]}^{3+}}\]

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  • question_answer73) A substance forms zwitter ion. It can have functional groups:

    A) \[-N{{H}_{2}},-COOH\]

    B) \[-N{{H}_{2}},-S{{O}_{3}}H\]

    C) both (a) and (b)

    D) none of these

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  • question_answer74) If\[F{{e}^{3+}}\]and\[C{{r}^{3+}}\]both are present in group III of qualitative analysis, then distinction can be made by:

    A) addition of\[N{{H}_{4}}OH\]in presence of\[N{{H}_{4}}Cl\]when only\[Fe{{(OH)}_{3}}\]is precipitated

    B) addition of\[N{{H}_{4}}OH\]in presence of\[N{{H}_{4}}Cl\]when\[Cr{{(OH)}_{3}}\]and\[Fe{{(OH)}_{3}}\]both are precipitated and on adding\[B{{r}_{2}}\]water and \[NaOH,Cr{{(OH)}_{3}}\]dissolves

    C) precipitate of\[Cr{{(OH)}_{3}}\]and\[Fe{{(OH)}_{3}}\]as obtained in are treated! with cone.\[HCl\] when only\[Fe{{(OH)}_{3}}\]dissolves

    D) and (b) the (c) correct.

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  • question_answer75) In an organic compound of molar mass 108 g \[mo{{l}^{-1}}C,H\] and N atoms are present in \[9:1:3.5\]by weight. Molecular formula can be:

    A) \[{{C}_{6}}{{H}_{8}}{{N}_{2}}\]

    B) \[{{C}_{7}}{{H}_{10}}N\]

    C) \[{{C}_{5}}{{H}_{6}}{{N}_{3}}\]

    D) \[{{C}_{4}}{{H}_{18}}{{N}_{3}}\]

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  • question_answer76) Solubility of\[Ca{{(OH)}_{2}}\]is\[S\text{ }mol\text{ }litr{{e}^{-1}}\]. The solubility product\[({{K}_{sp}})\]under the same condition is:

    A) \[4{{S}^{3}}\]

    B) \[3{{S}^{4}}\]

    C) \[4{{S}^{2}}\]

    D) \[{{S}^{3}}\]

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  • question_answer77) Heat required to raise the temperature of 1 mol of a substance by\[1{}^\circ \]is called:

    A) specific heat

    B) molar heat capacity

    C) water equivalent

    D) specific gravity

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  • question_answer78) \[\beta -\]particle is emitted in a radioactive reaction when:

    A) a proton changes to neutron

    B) a neutron changes to proton

    C) a neutron changes to electron

    D) an electron changes to neutron

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  • question_answer79) In a mixture of A and B, components show negative deviation when:

    A) \[A-B\] interaction is stronger than\[A-A\] and\[B-B\]interaction

    B) \[A-B\]interaction is weaker than\[A-A\]and \[B-B\]interaction

    C) \[\Delta {{V}_{mix}}>0,\Delta {{S}_{mix}}>0\]

    D) \[\Delta {{V}_{mix}}=0,\Delta {{S}_{mix}}>0\]

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  • question_answer80) Refining of impure copper with zinc impurity is to be done by electrolysis using electrons as: Cathode Anode

    A) pure copper pure zinc

    B) pure zinc pure copper

    C) pure copper impure copper

    D) pure zinc impure zinc

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  • question_answer81) Aluminium is extracted by the electrolysis of:

    A) alumina

    B) bauxite

    C) molten cryolite

    D) alumina mixed with molten cryolite

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  • question_answer82) For an aqueous solution, freezing point is\[-0.186{}^\circ C\]. Elevation of the boiling point of the same solution is (\[{{K}_{f}}=1.86{}^\circ mo{{l}^{-1}}kg\]and \[{{K}_{f}}=0.512{}^\circ mo{{l}^{-1}}kg\]):

    A) \[0.186{}^\circ \]

    B) \[0.0512{}^\circ \]

    C) \[1.86{}^\circ \]

    D) \[5.12{}^\circ \]

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  • question_answer83) Underlined carbon is\[s{{p}^{3}}\]hybridised in:

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

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

    C) \[C{{H}_{3}}\underline{C}ON{{H}_{2}}\]

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

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  • question_answer84) Bond angle of\[109{}^\circ 28\]is found in:

    A) \[N{{H}_{3}}\]

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

    C) \[C{{H}_{5}}\]

    D) \[N{{H}_{4}}\]

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  • question_answer85) For a reaction\[A+2B\xrightarrow[{}]{{}}C,\]rate is given by \[+\frac{d[C]}{dt}=k[A][B],\]hence the order of the reaction is:

    A) 3

    B) 2

    C) 1

    D) 0

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  • question_answer86) \[C{{H}_{3}}MgI\]is an organometallic compound due to:

    A) \[Mg-I\]bond

    B) \[C-I\]bond

    C) \[C-Mg\]bond

    D) \[C-H\]bond

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  • question_answer87) One of the following species acts as both Bronsted acid and base:

    A) \[{{H}_{2}}PO_{2}^{-}\]

    B) \[HPO_{3}^{2-}\]

    C) \[HPO_{4}^{2-}\]

    D) all of the above

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  • question_answer88) Hybridisation of the underline atom changes in:

    A) \[\underline{A}l{{H}_{3}}\]changes to\[AlH_{4}^{-}\]

    B) \[{{H}_{2}}\underline{O}\]changes to\[{{H}_{3}}{{O}^{+}}\]

    C) \[\underline{N}{{H}_{3}}\]changes to\[NH_{4}^{+}\]

    D) in all cases

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  • question_answer89) Racemic mixture is formed by mixing two:

    A) isomeric compounds

    B) chiral compounds

    C) meso compounds

    D) enantiomers with chiral carbon

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  • question_answer90) The number of lone pairs on\[Xe\]in\[Xe{{F}_{2}},\]\[Xe{{F}_{4}}\] and\[Xe{{F}_{6}}\]respectively are:

    A) 3, 2, 1

    B) 2, 4, 6

    C) 1, 2, 3

    D) 6, 4, 2

    View Answer play_arrow
  • question_answer91) An aqueous solution of\[1\,M\,NaCl\]and\[1M\text{ }HCl\]is:

    A) not a buffer but\[pH<7\]

    B) not a buffer but\[pH>7\]

    C) a buffer with\[pH<7\]

    D) a buffer with\[pH>7\]

    View Answer play_arrow
  • question_answer92) Consider following two reactions\[A\xrightarrow[{}]{{}}Product-\frac{d[A]}{dt}={{k}_{1}}{{[A]}^{0}}\]\[B\xrightarrow[{}]{{}}Product-\frac{d[B]}{dt}={{k}_{2}}[B]\]]\[{{k}_{1}}\]and\[{{k}_{2}}\] are expressed in terms of molarity\[(mol\text{ }{{L}^{-1}})\]and time\[(se{{c}^{-1}})\]as:

    A) \[se{{c}^{-1}},M\,{{\sec }^{-1}}{{L}^{-1}}\]

    B) \[M\,se{{c}^{-1}},M\,{{\sec }^{-1}}\]

    C) \[se{{c}^{-1}},{{M}^{-1}}\,{{\sec }^{-1}}\]

    D) \[M\,se{{c}^{-1}},{{L}^{-1}}\,{{\sec }^{-1}}\]

    View Answer play_arrow
  • question_answer93) RNA contains:

    A) ribose sugar and thymine

    B) ribose sugar and uracil

    C) deoxyribose sugar and uracil

    D) deoxyribose sugar and thymine

    View Answer play_arrow
  • question_answer94) For a cell given below: \[\underset{-}{\mathop{Ag|A{{g}^{+}}}}\,||\underset{+}{\mathop{C{{u}^{2+}}|Cu}}\,\]\[A{{g}^{+}}+{{e}^{-}}\xrightarrow[{}]{{}}Ag\] \[E{}^\circ =x\]\[C{{u}^{2+}}+2{{e}^{-}}\xrightarrow[{}]{{}}Cu,\] \[E{}^\circ =y\]E? cell is:

    A) \[x+2y\]

    B) \[2x+y\]

    C) \[y-x\]

    D) \[y-2x\]

    View Answer play_arrow
  • question_answer95) Based on kinetic theory of gases following laws can be proved:

    A) Boyles law

    B) Charles law

    C) Avogadros law

    D) all of these

    View Answer play_arrow
  • question_answer96) \[Mn{{O}_{4}}\]is a good oxidising agent in different medium changing to \[MnO_{4}^{-}\xrightarrow[{}]{{}}M{{n}^{2+}}\] \[\xrightarrow[{}]{{}}MnO_{4}^{2-}\] \[\xrightarrow[{}]{{}}Mn{{O}_{2}}\] \[\xrightarrow[{}]{{}}M{{n}_{2}}{{O}_{3}}\] Changes in oxidation number respectively are:

    A) 1,3,4,5

    B) 5,4,3,2

    C) 5,1,3,4

    D) 2,6,4,3

    View Answer play_arrow
  • question_answer97) For the reaction:\[{{H}_{2}}+{{I}_{2}}\xrightarrow[{}]{{}}2HI,\]the differential rate law is:

    A) \[-\frac{d[{{H}_{2}}]}{dt}=-\frac{d[{{I}_{2}}]}{dt}=2\frac{d[HI[}{dt}\]

    B) \[-2\frac{d[{{H}_{2}}]}{dt}=-2\frac{d[{{I}_{2}}]}{dt}=\frac{d[HI]}{dt}\]

    C) \[-\frac{d[{{H}_{2}}]}{dt}=-\frac{d[{{I}_{2}}]}{dt}=\frac{d[HI]}{dt}\]

    D) \[-\frac{d[{{H}_{2}}]}{2dt}=-\frac{d[{{I}_{2}}]}{2dt}=\frac{d[HI]}{dt}\]

    View Answer play_arrow
  • question_answer98) Number of atoms in 560 g of Fe (atomic mass\[56\text{ }g\text{ }mo{{l}^{-1}}\]) is:

    A) is twice that of 70 g N

    B) is half that of 20 g H

    C) both are correct

    D) none is correct

    View Answer play_arrow
  • question_answer99) Geometrical isomerism is not shown by:

    A) 1, 1-dichloro-l-pentene

    B) 1, 2-dichloro-l-pentene

    C) 1, 3-dichloro-2-pentene

    D) 1, 4-dichloro-2-pentene

    View Answer play_arrow
  • question_answer100) Number of atoms in the unit cell of Na (BCC type crystal) and Mg (FCC type crystal) are respectively:

    A) 4, 4

    B) 4, 2

    C) 2, 4

    D) 1, 1

    View Answer play_arrow
  • question_answer101) Which of the following compounds has incorrect IUPAC nomenclature?

    A) \[\underset{ethylbutanoate}{\mathop{C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}\overset{\begin{smallmatrix} O \\ |\,| \end{smallmatrix}}{\mathop{C}}\,O{{C}_{2}}{{H}_{5}}}}\,\]

    B) \[\underset{3-methyl\text{ }butanal}{\mathop{C{{H}_{3}}\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,C{{H}_{2}}CHO}}\,\]

    C) \[\underset{2-methyl-3-pentanone}{\mathop{C{{H}_{3}}\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CH\overset{\begin{smallmatrix} O \\ |\,| \end{smallmatrix}}{\mathop{C}}\,}}\,C{{H}_{2}}C{{H}_{3}}}}\,\]

    D) \[\underset{2-methyl-3-butanol}{\mathop{C{{H}_{3}}\underset{\begin{smallmatrix} | \\ {{H}_{3}}C \end{smallmatrix}}{\mathop{C}}\,H\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,C{{H}_{3}}}}\,\]

    View Answer play_arrow
  • question_answer102) End product of the following reaction is:\[C{{H}_{3}}C{{H}_{2}}COOH\xrightarrow[red\,p]{C{{l}_{2}}}\] \[\xrightarrow[{}]{alcoholic\text{ }KOH}\]

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

    B) \[\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,C{{H}_{2}}COOH\]

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

    D) \[\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,COOH\]

    View Answer play_arrow
  • question_answer103) For the following reaction in gaseous phase\[CO+\frac{1}{2}{{O}_{2}}\xrightarrow[{}]{{}}C{{O}_{2}}\]\[{{K}_{c}}/{{K}_{p}}\]is:

    A) \[{{(RT)}^{1/2}}\]

    B) \[{{(RT)}^{-1/2}}\]

    C) \[(RT)\]

    D) \[{{(RT)}^{-1}}\]

    View Answer play_arrow
  • question_answer104) Energy of H-atom in the ground state is\[-13.6\] eV, hence energy in the second excited state is:

    A) \[-6.8eV\]

    B) \[-3.4eV\]

    C) \[-1.51eV\]

    D) \[-4.53eV\]

    View Answer play_arrow
  • question_answer105) A square planar complex is formed by hybridisation of the following atomic orbitals:

    A) \[s,{{p}_{x}},{{p}_{y}},{{p}_{z}}\]

    B) \[s,\text{ }{{p}_{x}}\text{ }{{p}_{y}},\text{ }{{p}_{z}}\text{, }d\]

    C) \[d,\text{ s, }\,\text{ }{{p}_{x}},\text{ }{{p}_{y}}\]

    D) \[\text{s, }{{p}_{x}},\text{ }{{p}_{y}},{{p}_{z}}\,d,\,d\]

    View Answer play_arrow
  • question_answer106) Type of isomerism shown by\[[Cr{{(N{{H}_{3}})}_{5}}N{{O}_{2}}]C{{l}_{2}}\]is:

    A) optical

    B) ionization

    C) geometrical

    D) linkage

    View Answer play_arrow
  • question_answer107) One of the following equilibria is not affected by change in volume of the flask:

    A) \[PC{{l}_{5}}(g)PC{{l}_{3}}(g)+C{{l}_{2}}(g)\]

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

    C) \[{{N}_{2}}(g)+{{O}_{2}}(g)2NO(g)\]

    D) \[S{{O}_{2}}C{{l}_{2}}(g)S{{O}_{2}}(g)+C{{l}_{2}}(g)\]

    View Answer play_arrow
  • question_answer108) Uncertainty in position of a particle of 25 g in space is\[{{10}^{-5}}m\]. Hence uncertainty in velocity \[(m{{s}^{-1}})\]is (Plancks constant\[h=6.6\times {{10}^{-34}}Js\]):

    A) \[2.1\times {{10}^{-28}}\]

    B) \[2.1\times {{10}^{-34}}\]

    C) \[0.5\times {{10}^{-34}}\]

    D) \[5.0\times {{10}^{-24}}\]

    View Answer play_arrow
  • question_answer109) Consider the following reactions at\[1100{}^\circ C\] (I) \[2C+{{O}_{2}}\xrightarrow[{}]{{}}2CO,\]\[\Delta G{}^\circ =-460kJmo{{l}^{-1}}\] (II) \[2Zn+{{O}_{2}}\xrightarrow[{}]{{}}2ZnO,\]\[\Delta G{}^\circ =-360kJ\,mo{{l}^{-1}}\] Based on these, select correct alternate:

    A) zinc can be oxidised by\[CO\]

    B) zinc oxide can be reduced by carbon

    C) both are correct

    D) none is correct

    View Answer play_arrow
  • question_answer110) A reaction is non-spontaneous at the freezing point of water but is spontaneous at the boiling point of water then: \[\Delta H\] \[\Delta S\]

    A) \[+ve~~~~~~~~~~~+ve\]

    B) \[-ve~~~~~~~~~~~-ve\]

    C) \[-ve~~~~~~~~~~~+ve\]

    D) \[+ve~~~~~~~~~~~-ve\]

    View Answer play_arrow
  • question_answer111) If\[\alpha \ne \beta \]and\[{{\alpha }^{2}}=5\alpha -3,\text{ }{{\beta }^{2}}=5\beta -3,\]then the equation having\[\alpha /\beta \]and\[\beta /\alpha \]as its roots is:

    A) \[3{{x}^{2}}+19x+3=0\]

    B) \[3{{x}^{2}}-19x+3=0\]

    C) \[3{{x}^{2}}-19x-3=0\]

    D) \[{{x}^{2}}-16x+1=0\]

    View Answer play_arrow
  • question_answer112) If\[y={{(x+\sqrt{1+{{x}^{2}}})}^{n}},\]then \[(1+{{x}^{2}})\frac{{{d}^{2}}y}{d{{x}^{2}}}+x\frac{dy}{dx}\]is:

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

    B) \[-{{n}^{2}}y\]

    C) \[-y\]

    D) \[2{{x}^{2}}y\]

    View Answer play_arrow
  • question_answer113) If\[1,{{\log }_{3}}\sqrt{({{3}^{1-x}}+2)},{{\log }_{3}}({{4.3}^{x}}-1)\]are in A.P, then\[x\]equals:

    A) \[lo{{g}_{3}}4\]

    B) \[1-lo{{g}_{3}}4\]

    C) \[1-lo{{g}_{4}}3\]

    D) \[lo{{g}_{4}}3\]

    View Answer play_arrow
  • question_answer114) A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is\[\frac{1}{2},\frac{1}{3}\]and\[\frac{1}{4}\]. Probability that the problem is solved is:

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

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

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

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

    View Answer play_arrow
  • question_answer115) The period of\[{{\sin }^{2}}\theta \]is:

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

    B) \[\pi \]

    C) \[2\pi \]

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

    View Answer play_arrow
  • question_answer116) \[l,m,n\]are the\[{{p}^{th}},{{q}^{th}}\]and\[{{r}^{th}}\]term of an G.P. and all positive, then \[\left| \begin{matrix} \log l & p & 1 \\ \log m & q & 1 \\ \log n & r & 1 \\ \end{matrix} \right|\]equals:

    A) 3

    B) 2

    C) 1

    D) zero

    View Answer play_arrow
  • question_answer117) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1-\cos 2x}}{\sqrt{2}x}\]is:

    A) \[\lambda \]

    B) \[-1\]

    C) zero

    D) does not exist

    View Answer play_arrow
  • question_answer118) A triangle with vertices\[(4,0),(-1,-1),(3,5)\]is:

    A) isosceles and right angled

    B) isosceles but not right angled

    C) right angled but not isosceles

    D) neither right angled nor isosceles

    View Answer play_arrow
  • question_answer119) In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?:

    A) 73

    B) 65

    C) 68

    D) 74

    View Answer play_arrow
  • question_answer120) \[{{\cot }^{-1}}(\sqrt{\cos \alpha })={{\tan }^{-1}}(\sqrt{\cos \alpha })=x,\]then\[\sin x\]is equal to:

    A) \[{{\tan }^{2}}\left( \frac{\alpha }{2} \right)\]

    B) \[co{{t}^{2}}\left( \frac{\alpha }{2} \right)\]

    C) \[\tan \alpha \]

    D) \[\cot \left( \frac{\alpha }{2} \right)\]

    View Answer play_arrow
  • question_answer121) The order and degree of the differential equation\[{{\left( 1+3\frac{dy}{dx} \right)}^{2/3}}=4\frac{{{d}^{2}}y}{d{{x}^{3}}}\]are:

    A) \[\left( 1,\frac{2}{3} \right)\]

    B) \[(3,1)\]

    C) \[(3,3)\]

    D) \[(1,2)\]

    View Answer play_arrow
  • question_answer122) A plane which passes through the point (3,2,0) and the line\[\frac{x-4}{1}=\frac{y-7}{5}=\frac{z-4}{4}\]is:

    A) \[x-y+z=1\]

    B) \[x+y+z=5\]

    C) \[x+2y-z=1\]

    D) \[2x-y+z=5\]

    View Answer play_arrow
  • question_answer123) The solution of the equation\[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{-2x}}\]is:

    A) \[\frac{{{e}^{-2x}}}{4}\]

    B) \[\frac{{{e}^{-2x}}}{4}+cx+d\]

    C) \[\frac{1}{4}{{e}^{-2x}}+c{{x}^{2}}+d\]

    D) \[\frac{1}{4}{{e}^{-2x}}+c+d\]

    View Answer play_arrow
  • question_answer124) \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{{{x}^{2}}+5x+3}{{{x}^{2}}+x+2} \right)}^{x}}\]is equal to:

    A) \[{{e}^{4}}\]

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

    C) \[{{e}^{3}}\]

    D) \[e\]

    View Answer play_arrow
  • question_answer125) The domain of\[{{\sin }^{-1}}[{{\log }_{3}}(x/3)]\]is:

    A) \[[1,9]\]

    B) \[[-1,9]\]

    C) \[[-9,1]\]

    D) \[[-9,-1]\]

    View Answer play_arrow
  • question_answer126) The value of\[{{2}^{1/4}}{{.4}^{1/8}}{{.8}^{1/6}}....\infty \]is:

    A) 1

    B) 2

    C) 3/2

    D) 4

    View Answer play_arrow
  • question_answer127) Fifth term of an G.P. is 2, then the product of its 9 terms is

    A) 256

    B) 512

    C) 1024

    D) none of these

    View Answer play_arrow
  • question_answer128) \[\int_{0}^{10x}{|\sin x|dx}\]is:

    A) 20

    B) 8

    C) 10

    D) 18

    View Answer play_arrow
  • question_answer129) \[{{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}x}dx,\]then\[\underset{n\to \infty }{\mathop{\lim }}\,n[{{I}_{n}}+{{I}_{n+2}}]\]equals:

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

    B) 1

    C) \[\infty \]

    D) zero

    View Answer play_arrow
  • question_answer130) \[\int_{0}^{2}{[{{x}^{2}}]}\,dx\]is:

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

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

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

    D) \[-\sqrt{2}-\sqrt{3}+5\]

    View Answer play_arrow
  • question_answer131) .\[\int_{-\pi }^{\pi }{\frac{2x(1+\sin x)}{1+{{\cos }^{2}}x}}dx\]is:

    A) \[\frac{{{\pi }^{2}}}{4}\]

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

    C) zero

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

    View Answer play_arrow
  • question_answer132) The period of the function\[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x\]is:

    A) \[\pi \]

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

    C) \[2\pi \]

    D) none of these

    View Answer play_arrow
  • question_answer133) The domain of definition of the function\[f(x)=\sqrt{{{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right)}\]is:

    A) [1, 4]

    B) [1, 0]

    C) [0, 5]

    D) [5, 0]

    View Answer play_arrow
  • question_answer134) If\[\sin y=a\sin (x+y),\]then\[\frac{dy}{dx}\]is:

    A) \[\frac{\sin a}{{{\sin }^{2}}(a+y)}\]

    B) \[\frac{{{\sin }^{2}}(a+y)}{\sin a}\]

    C) \[\sin a{{\sin }^{2}}(a+y)\]

    D) \[\frac{{{\sin }^{2}}(a-y)}{\sin a}\]

    View Answer play_arrow
  • question_answer135) If\[{{x}^{y}}={{e}^{x-y}}\]then\[\frac{dy}{dx}\]is:

    A) \[\frac{1+x}{1+\log x}\]

    B) \[\frac{1-\log x}{1+\log x}\]

    C) not defined

    D) \[\frac{logx}{(1+\log x)}\]

    View Answer play_arrow
  • question_answer136) The two curves\[{{x}^{3}}-3x{{y}^{2}}+2=0\]and\[3{{x}^{2}}y-{{y}^{3}}-2=0\]:

    A) cut at right angles

    B) touch each other

    C) cut at an angle\[\frac{\pi }{3}\]

    D) cut at an angle\[\frac{\pi }{4}\]

    View Answer play_arrow
  • question_answer137) The function\[f(x)={{\cot }^{-1}}x+x\]increases in the interval:

    A) \[(1,\infty )\]

    B) \[(-1,\infty )\]

    C) \[(-\infty ,\infty )\]

    D) \[(0,\infty )\]

    View Answer play_arrow
  • question_answer138) The greatest value of\[f(x)={{(x+1)}^{1/3}}-{{(x-1)}^{1/3}}\]on [0, 1] is:

    A) 1

    B) 2

    C) 3

    D) 1/3

    View Answer play_arrow
  • question_answer139) Evaluate\[\int_{0}^{\pi /2}{\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}}dx\]:

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

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

    C) zero

    D) 1

    View Answer play_arrow
  • question_answer140) \[\int{\frac{dx}{x({{x}^{n}}+1)}}\]is equal to:

    A) \[\frac{1}{n}\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c\]

    B) \[\frac{1}{n}\log \left( \frac{{{x}^{n}}+1}{{{x}^{n}}} \right)+c\]

    C) \[\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c\]

    D) none of these

    View Answer play_arrow
  • question_answer141) The area bounded by the curve\[y=2x-x\] and the straight line\[y=-x\]is given by:

    A) \[\frac{9}{2}\]

    B) \[\frac{43}{6}\]

    C) \[\frac{35}{6}\]

    D) none of these

    View Answer play_arrow
  • question_answer142) The differential equation of all non-vertical lines in a plane is:

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

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

    C) \[\frac{dy}{dx}=0\]

    D) \[\frac{dx}{dy}=0\]

    View Answer play_arrow
  • question_answer143) Given two vectors\[\hat{i}-\hat{j}\]and\[\hat{i}+2\hat{j}\]the unit vector coplanar with the two vectors and perpendicular to first is:

    A) \[\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})\]

    B) \[\frac{1}{\sqrt{5}}(2\hat{i}+\hat{j})\]

    C) \[\pm \frac{1}{\sqrt{2}}(\hat{i}+\hat{k})\]

    D) none of these

    View Answer play_arrow
  • question_answer144) The vector\[\hat{i}+x\hat{j}+3\hat{k}\]is rotated through an angle\[\theta \]and doubled in magnitude, then it becomes\[4\hat{i}+(4x-2)\hat{i}+2\hat{k}\]. The value of\[x\] is:

    A) \[\left( -\frac{2}{3},2 \right)\]

    B) \[\left( \frac{1}{3},2 \right)\]

    C) \[\left( \frac{2}{3},0 \right)\]

    D) \[(2,7)\]

    View Answer play_arrow
  • question_answer145) A paralleiopiped is formed by planes drawn through the points (2,3,5) and (5,9,7), parallel to the coordinate planes. The length of a diagonal of the parallelepiped to piped is:

    A) \[7\]

    B) \[\sqrt{38}\]

    C) \[\sqrt{155}\]

    D) None of these

    View Answer play_arrow
  • question_answer146) The equation of the plane containing the line \[\frac{x-{{x}_{1}}}{l}=\frac{y-{{y}_{1}}}{m}=\frac{z-{{z}_{1}}}{n}\]is\[a(x-{{x}_{1}})+b(y-{{y}_{1}})+c(z-{{z}_{1}})=0,\]where:

    A) \[a{{x}_{1}}+b{{y}_{1}}+c{{z}_{1}}=0\]

    B) \[al+bm+cn=0\]

    C) \[\frac{a}{l}=\frac{b}{m}=\frac{c}{n}\]

    D) \[l{{x}_{1}}+m{{y}_{1}}+n{{z}_{1}}=0\]

    View Answer play_arrow
  • question_answer147) A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is:

    A) \[\frac{1}{25}\]

    B) \[\frac{24}{25}\]

    C) \[\frac{2}{25}\]

    D) None of these

    View Answer play_arrow
  • question_answer148) If A and B are two mutually exclusive events, then

    A) \[P(A)<P(\overline{B})\]

    B) \[P(A)>P(\overline{B})\]

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

    D) None of these

    View Answer play_arrow
  • question_answer149) The equation of the directrix of the parabola \[{{y}^{2}}+4v+4x+2=0\]is:

    A) \[x=-1\]

    B) \[x=1\]

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

    D) \[x=\frac{3}{2}\]

    View Answer play_arrow
  • question_answer150) Let\[{{T}_{n}}\]denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If\[{{T}_{n+1}}-{{T}_{n}}=21\]then\[n\] equals:

    A) 5

    B) 7

    C) 6

    D) 4

    View Answer play_arrow
  • question_answer151) In a triangle ABC, \[2ca\sin \frac{A-B+C}{2}\] is equal to:

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

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

    C) \[{{b}^{2}}-{{c}^{2}}-{{a}^{2}}\]

    D) \[{{c}^{2}}-{{a}^{2}}-{{b}^{2}}.\]

    View Answer play_arrow
  • question_answer152) For\[x\in R\,\,\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x-3}{x+2} \right)}^{x}}\]is equal to:

    A) \[e\]

    B) \[{{e}^{-1}}\]

    C) \[{{e}^{-5}}\]

    D) \[{{e}^{5}}\]

    View Answer play_arrow
  • question_answer153) The in centre of the triangle with vertices \[(1,\sqrt{3}),(0,0)\]and\[(2,0)\]is:

    A) \[\left( 1,\frac{\sqrt{3}}{2} \right)\]

    B) \[\left( \frac{2}{3},\frac{1}{\sqrt{3}} \right)\]

    C) \[\left( \frac{2}{3},\frac{\sqrt{3}}{2} \right)\]

    D) \[\left( 1,\frac{1}{\sqrt{3}} \right)\]

    View Answer play_arrow
  • question_answer154) If the vectors\[\overrightarrow{a},\overrightarrow{b}\]and\[\overrightarrow{c}\]from the sides BC, CA and AB respectively, of a triangle ABC then:

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

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

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

    D) \[\overrightarrow{a}\times \overrightarrow{a}+\overrightarrow{a}\times \overrightarrow{c}+\overrightarrow{c}\times \overrightarrow{a}=0\]

    View Answer play_arrow
  • question_answer155) If\[\omega \]is an imaginary cube root of unity then \[{{(1+\omega +{{\omega }^{2}})}^{7}}\]equals:

    A) \[128\omega \]

    B) \[-128\omega \]

    C) \[128\,{{\omega }^{2}}\]

    D) \[-128\,{{\omega }^{2}}\]

    View Answer play_arrow
  • question_answer156) If\[\left| \begin{matrix} 6i & -3i & 1 \\ 4 & 3i & -1 \\ 20 & 3 & i \\ \end{matrix} \right|=x+iy\]then:

    A) \[x=3,y=1\]

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

    C) \[x=0,\text{ y}=3\]

    D) \[x=0,\text{ }y=0\]

    View Answer play_arrow
  • question_answer157) \[{{\sin }^{2}}\theta =\frac{4xy}{{{(x+y)}^{2}}}\]is true if and only if:

    A) \[x+y\ne 0\]

    B) \[x=y,x\ne 0,y\ne 0\]

    C) \[x=y\]

    D) \[x\ne 0,y\ne 0\]

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  • question_answer158) The radius of the circle passing through the foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\]and having its centre at (0, 3) is:

    A) 4

    B) 3

    C) \[\sqrt{12}\]

    D) \[\frac{7}{2}\]

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  • question_answer159) The probability of India winning a test match against West-Indies is\[\frac{1}{2}\]assuming independence from match to match the probability that in a match series Indias second win occurs at the third test is:

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

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

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

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

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  • question_answer160) If\[(\omega \ne 1)\]is a cubic root of unity, then\[\left| \begin{matrix} 1 & 1+i+{{\omega }^{2}} & {{\omega }^{2}} \\ 1-i & -1 & {{\omega }^{2}}-1 \\ -i & -1+\omega -i & -1 \\ \end{matrix} \right|\]equals:

    A) zero

    B) 1

    C) \[i\]

    D) \[\omega \]

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  • question_answer161) A biased coin with probability\[p,0<p<1\]of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is\[\frac{2}{5},\]then p equals:

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

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

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

    D) \[\frac{3}{5}\]

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  • question_answer162) A fair die is tossed eight times. The probability that a third six is observed on the eight throw is:

    A) \[\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{7}}}\]

    B) \[\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{8}}}\]

    C) \[\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{6}}}\]

    D) none of these

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  • question_answer163) Let\[f(2)=4\]and\[f(2)=4\]Then\[\underset{x\to 2}{\mathop{\lim }}\,\frac{xf(2)-2f(x)}{x-2}\]is given by:

    A) 2

    B) \[-2\]

    C) \[-4\]

    D) 3

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  • question_answer164) Three straight lines\[2x+11y-5=0,\] \[24x+7y-20=0\]and\[4x-3y-2=0\]:

    A) form a triangle

    B) arc only concurrent

    C) are concurrent with on line bisecting the angle between the other two

    D) none of these

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  • question_answer165) A straight line through the point (2, 2) intersects the lines\[\sqrt{3}x+y=0\]and \[\sqrt{3}x-y=0\]at the points A and B. The equation to the line AB so that the triangle OAB is equilateral is:

    A) \[x-2=0\]

    B) \[y-2=0\]

    C) \[x+y-4=0\]

    D) none of these

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  • question_answer166) The greatest distance of the point\[P(10,7)\]from the circle\[{{x}^{2}}+{{y}^{2}}-4x-2y-20=0\]is:

    A) \[10\]

    B) 15

    C) 5

    D) none of these

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  • question_answer167) The equation of the tangent to the circle\[{{x}^{2}}+{{y}^{2}}+4x-4y+4=0\]which make equal intercepts on the positive coordinate axes is:

    A) \[x+y=2\]

    B) \[x+y=2\sqrt{2}\]

    C) \[x+y=4\]

    D) \[x+y=8\]

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  • question_answer168) The equation of the ellipse whose foci are \[(\pm ,2,0)\]and eccentricity\[\frac{1}{2}\]is:

    A) \[\frac{{{x}^{2}}}{12}+\frac{{{y}^{2}}}{16}=1\]

    B) \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{12}=1\]

    C) \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{8}=1\]

    D) none of these

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  • question_answer169) The equation of the chord joining two points \[({{x}_{1}},{{y}_{2}})\]and\[({{x}_{2}},{{y}_{2}})\]on the rectangular hyperbola\[xy={{c}^{2}}\]is:

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

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

    C) \[\frac{x}{{{y}_{1}}+{{y}_{2}}}+\frac{y}{{{x}_{1}}+{{x}_{2}}}=1\]

    D) \[\frac{x}{{{y}_{1}}-{{y}_{2}}}+\frac{y}{{{x}_{1}}-{{x}_{2}}}=1\]

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  • question_answer170) If the vectors\[\overrightarrow{c},\overrightarrow{a}=x\hat{i}+y\hat{j}+z\hat{j}\]and\[\hat{b}=\hat{j}\]are such that \[\overrightarrow{a},\overrightarrow{c}\] and\[\overrightarrow{b}\]form a right handed system then\[\overrightarrow{c}\]is:

    A) \[z\hat{j}-x\hat{k}\]

    B) \[\overrightarrow{0}\]

    C) \[y\hat{j}\]

    D) \[-z\hat{i}+x\hat{k}\]

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