# Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2005

### done J and K - CET Engineering Solved Paper-2005

• question_answer1) A boat carrying a number of large stones is floating in a water tank. What would happen to the water level, if a few stones are unloaded into water?

A) Rises

B) Falls

C) Remains unchanged

D) Rises till half the number of stones are unloaded and then begins to fall

• question_answer2) A container with square base of side a is filled up to a height H with a liquid. A hole is made at a depth h from the free surface of water. With what acceleration the container must be accelerated, so that the water does not come out?

A) $g$

B) $\frac{g}{2}$

C) $\frac{2gH}{2}$

D) $\frac{2gh}{2}$

• question_answer3) If two soap bubbles of equal radii r coalesce, then the radius of curvature of interface between two bubbles will be

A) r

B) zero

C) infinity

D) $\frac{1}{2r}$

• question_answer4) What is the mass of $2\text{ }L$of nitrogen at $~22.4\text{ }arm$pressure and $273\text{ }K$?

A) $28\text{ }g$

B) $14\times 22.4\text{ }g$

C) $56\text{ }g$

D) None of these

• question_answer5) $2\text{ }g$of water condenses when passed through $40\text{ }g$of water initially at${{25}^{o}}C$. The- condensation of steam raises the temperature of water to ${{54.3}^{o}}C$. What is the latent heat of steam?

A) $540\,\,cal/g$

B) $536\,\,cal/g$

C) $270\,\,cal/g$

D) $480\,\,cal/g$

• question_answer6) Petrol engine does the work during

A) suction stroke

B) exhaust stroke

D) combustion

• question_answer7) The spectral energy distribution of a star is maximum at twice temperature as that of sun. The total energy radiated by star is

A) twice as that of the sun

B) same as that of the sun

C) sixteen times as that of the sun

D) one-sixteenth of sun

• question_answer8) Two simple pendulums of lengths $1.44\text{ }m$and $1\text{ }m$ start swinging together. After how many vibrations will they again start swinging together?

A) 5 oscillations of smaller pendulum

B) 6 oscillations of smaller pendulum

C) 4 oscillations of bigger pendulum

D) 6 oscillations of bigger pendulum

• question_answer9) A wave has velocity u in medium P and velocity $2u$ in medium Q. If the wave is incident in medium P at an angle ${{30}^{o}},$then the angle of refraction will be

A) ${{30}^{o}}$

B) ${{45}^{o}}$

C) ${{60}^{o}}$

D) ${{90}^{o}}$

• question_answer10) In $1\text{ }m$long open pipe what is the harmonic of resonance obtained with a tuning fork of frequency $480\text{ }Hz$?

A) First

B) Second

C) Third

D) Fourth

• question_answer11) Three sources of equal intensities with frequencies 400,401 and 402 vib/s are sounded together. The number of beat/s is

A) zero

B) $1$

C) $2$

D) $4$

• question_answer12) Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is $7:8,$ then the ratio of lengths of the two pendulums will be

A) $7:8$

B) $8:7$

C) $49:64$

D) $64:49$

• question_answer13) In a resonance pipe the first and second resonances are obtained at depths $22.7\text{ }cm$and $70.2\text{ }cm$respectively. What will be the end correction?

A) $1.05\,\,cm$

B) $115.5\,\,cm$

C) $92.5\,\,cm$

D) $113.5\,\,cm$

• question_answer14) The intensity level of sound A is 30 dB greater than of B. How many times more intense is the sound A than B?

A) $10$

B) $100$

C) $1000$

D) $2$

• question_answer15) An open tube is in resonance with string. If tube is dipped in water, so that $75%$of length of tube is inside water, then the ratio of the frequency $({{v}_{o}})$ of tube to string is

A) ${{v}_{o}}$

B) $2{{v}_{o}}$

C) $\frac{2}{3}{{v}_{o}}$

D) $\frac{3}{2}{{v}_{o}}$

• question_answer16) Two masses ${{m}_{1}}$ and ${{m}_{2}}$ are suspended together by a massless spring of constant k. When the masses are in equilibrium ${{m}_{1}},$ is removed without disturbing the system. The amplitude of oscillations is

A) $\frac{{{m}_{1}}g}{k}$

B) $\frac{{{m}_{2}}g}{k}$

C) $\frac{({{m}_{1}}+{{m}_{2}})g}{k}$

D) $\frac{({{m}_{1}}-{{m}_{2}})g}{k}$

• question_answer17) If a conducting medium is placed between two charges, then the electric force between will become

A) zero

B) infinity

C) $1N$

D) 1 dyne

• question_answer18) If an electron moves from rest from a point at which potential is $50\text{ }V$to another point at which potential is $70\text{ }V,$ then its kinetic energy in the final state will be

A) $3.2\times {{10}^{-20}}J~$

B) $3.2\times {{10}^{-18}}J$

C) $3.2\times {{10}^{-19}}J$

D) zero

• question_answer19) In the following diagram the work done in moving a point charge from point P to point A, B and C is respectively as ${{W}_{A}},$ ${{W}_{B}}$ and ${{W}_{C}},$ then

A) ${{W}_{A}}={{W}_{B}}={{W}_{C}}$

B) ${{W}_{A}}={{W}_{B}}={{W}_{C}}=0$

C) ${{W}_{A}}>{{W}_{B}}>{{W}_{C}}$

D) ${{W}_{A}}<{{W}_{B}}<{{W}_{C}}$

• question_answer20) The electric field due to an electric dipole at a distance r from its centre in axial position is E. If the dipole is rotated through an angle of ${{90}^{o}}$about its perpendicular axis, the electric field at the same point will be

A) $E$

B) $\frac{E}{4}$

C) $\frac{E}{2}$

D) $2E$

• question_answer21) If eight similar charge drops combine to form a bigger drop, then the ratio of capacitance of bigger drop to that of smaller drop will be

A) $2:1$

B) $8:1$

C) $4:1$

D) $16:1$

• question_answer22) The value of current I in figure is

A) $4\,A$

B) $6\,A$

C) $3\,A$

D) $5\,A$

• question_answer23) The plates of a charged condenser are connected to a voltmeter. If the plates are moved apart, the reading of voltmeter will

A) increase

B) decrease

C) remain unchanged

D) information is insufficient

• question_answer24) The n rows each containing m cells in series are joined in parallel. Maximum current is taken from this combination across an external resistance of 30 resistance. If the total number of cells used are 24 and internal resistance of each cell is $0.5\text{ }Q$then

A) $m=8,\text{ }n=3$

B) $m=6,\text{ }n=4$

C) $m=12,\text{ }n=2$

D) $m=2,\text{ }n=12$

• question_answer25) A railway compartment is lit up by thirteen lamps each taking $2.1\text{ }A$at$15\text{ }V$. The heat generated per second in each lamp will be m

A) $4.35\text{ }cal$

B) $5.73\text{ }cal$

C) $7.5\text{ }cal$

D) $2.5\text{ }cal$

• question_answer26) The chemical equivalent of copper and zinc are 32 and 108 respectively. When copper and silver voltameter are connected in series and electric current is passed through for sometimes, $1.6\text{ }g$of copper is deposited. Then, the mass of silver deposited will be

A) $3.5\text{ }g$

B) $2.8g$

C) $5.4\text{ }g$

D) None of these

• question_answer27) If the emf of a thermocouple, one junction of which is kept $0{}^\circ C$is given by $e=at+\frac{1}{2}b{{t}^{2}}$ then the neutral temperature will be

A) $\frac{a}{b}$

B) $-\frac{a}{b}$

C) $\frac{a}{2b}$

D) $-\frac{1}{ab}$

• question_answer28) The direction of magnetic lines of force produced by passing a direct current in a conductor is given by

A) Lenz'slaw

B) Fleming's left hand rule

C) Right hand palm rule

D) Maxwell's law

• question_answer29) A proton, a deuteron and an alpha particle are accelerated through same potential difference and then they enter a normal uniform magnetic field. The ratio of their kinetic energies will be

A) $2:1:3$

B) $1:1:2$

C) $1:1:1$

D) $1:2:4$

• question_answer30) For the magnetic field to be maximum due to a small element of current carrying conductor at a point, the angle between the element and the line joining the element to the given point must be

A) ${{0}^{o}}$

B) ${{90}^{o}}$

C) ${{180}^{o}}$

D) ${{45}^{o}}$

• question_answer31) A circular coil of 20 turns and radius 10 cm is placed in uniform magnetic field of $0.10\text{ }T$normal to the plane of the coil. If the current in coil is 5 A, then the torque acting on the coil will be

A) $31.4\text{ }Nm$

B) $3.14\text{ }Nm$

C) $0.314\text{ }Nm$

D) zero

• question_answer32) The earth's magnetic field inside an iron box as compared to that outside the box is

A) less

B) more

C) zero

D) same

• question_answer33) The intensity of magnetic field due to an isolated pole of strength m at a point distant r from it will be

A) $\frac{m}{{{r}^{2}}}$

B) $m{{r}^{2}}$

C) $\frac{{{r}^{2}}}{m}$

D) $\frac{m}{r}$

• question_answer34) The dimensions of self-inductance L are

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

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

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

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

• question_answer35) Quantity that remains unchanged in a transformer is

A) voltage

B) current

C) frequency

D) None of these

• question_answer36) If the capacity of a condenser is 1 F, then its resistance in a DC circuit will be

A) zero

B) infinity

C) $1\Omega$

D) $\frac{1}{2}\,\,\Omega$

• question_answer37) The time taken by an alternating current of $50\text{ }Hz$ in reaching from zero to its maximum value will be

A) $0.5s$

B) $0.005s$

C) $0.05\text{ }s$

D) $5s$

• question_answer38) If the area to be covered for TV telecast is doubled, then height of transmitting antenna (TV tower) will have to be

A) doubled

B) halved

D) kept unchanged

• question_answer39) An electromagnetic radiation has an energy $14.4\text{ }eV$. To which region of electromagnetic spectrum does it belong?

A) Ultraviolet region

B) Visible region

C) X-ray region

D) y-ray region

• question_answer40) When a ray of light is incident normally on a surface, then

A) total internal reflection takes place

B) it passes undeviated

C) it undergoes dispersion

D) it gets absorbed by the surface

• question_answer41) A ray of light passes through a glass plate of thickness t and refractive index u. If the speed of light in vacuum is c, then the time taken by light in passing through the plate will be

A) $\mu t$

B) $\frac{\mu t}{c}$

C) $\frac{tc}{\mu }$

D) $\frac{t}{\mu c}$

• question_answer42) In Young's double slit experiment with monochromatic light, the central fringe will be

A) coloured

B) white

C) bright

D) black

• question_answer43) In the phenomenon of interference, energy is

A) destroyed at bright'fringes

B) created at dark fringes

C) conserved but it is redistributed

D) same at all points

• question_answer44) A very thin film that reflects white light appears

A) coloured

B) white

C) black

D) red

• question_answer45) The size of an obstacle in order to observe diffraction of light must be

A) of any order

B) of the order of wavelength

C) much larger than wavelength

D) much smaller than wavelength

• question_answer46) If the binding energies of a deuteron and an alpha-particle are $1.125\text{ }MeV$and $7.2\text{ }MeV,$ respectively, then the more stable of the two is

A) deuteron

B) alpha-particle

C) both [a] and [b]

D) sometimes deuteron and sometimes alpha particle

• question_answer47) The particle A is converted into C via following reaction, $A\xrightarrow{{}}B{{+}_{2}}H{{e}^{4}}$ $B\xrightarrow{{}}C+2{{e}^{-}}$ Then

A) A and C are isobars

B) A and C are isotopes

C) A and B are isobars

D) A and B are isotopes

• question_answer48) On bombardment of ${{U}^{235}}$ by slow neutrons, 200 MeV energy is released. If the power output of atomic reactor is $1.6\text{ }MW,$ then the rate of fission will be

A) $5\times {{10}^{16}}/s$

B) $10\times {{10}^{16}}/s$

C) $15\times {{10}^{16}}/s$

D) $20\times {{10}^{16}}/s$

• question_answer49) The fussion process is possible at high temperatures, because at higher temperatures

A) the nucleus disintegrates

B) the molecules disintegrates

C) atoms become ionized

D) the nucleus get sufficient energy to overcome the strong forces of repulsion

• question_answer50) For maintaining sustained chain reaction, the following is required

A) protons

B) electrons

C) neutrons

D) positrons

• question_answer51) Sun maintains its shining because of the

A) fission of helium

B) chemical reaction

C) fusion of hydrogen nuclei

D) burning of carbon

• question_answer52) Atomic reactor is based on

A) controlled chain reaction

B) uncontrolled chain reaction

C) nuclear fission

D) nuclear fussion

• question_answer53) If the frequency of light incident on metal surface is doubled, then kinetic energy of emitted electron will become

A) doubled

B) less than double

C) more than double

D) nothing can be said

• question_answer54) The energy gap of silicon is $1.14\text{ }eV$. At what wavelength the silicon will stop to absorb the photon?

A) $10877\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $\text{9888 }\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $1087.7\,\,\overset{\text{o}}{\mathop{\text{A}}}\,$

D) $1000\,\,\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer55) n-p-n transistor are preferred to p-n-p transistor because they have

A) low cost

B) low dissipation energy

C) capability of handling large power

D) electrons having high mobility than holes

• question_answer56) In a transistor in common-emitter configuration, the ratio of power gain to voltage gain is

A) $\alpha$

B) $\frac{\beta }{\alpha }$

C) $\beta \times \beta$

D) $\beta$

• question_answer57) The ionic bond is absent in

A) $NaCl$

B) $CsCl$

C) $LiF$

D) ${{H}_{2}}O$

• question_answer58) As the temperature rises the resistance offered by metal

A) increases

B) decreases

C) remains same

D) None of these

• question_answer59) Density of liquid in CGS system is $0.625\text{ }g/c{{m}^{3}}$ What is its magnitude in SI system?

A) $0.625$

B) $0.0625$

C) $0.00625$

D) $625$

• question_answer60) If the length of rod A is $3.25\pm 0.01\,cm$and that of B is $4.19\pm 0.01\text{ }cm,$ then the rod B is longer than rod A by

A) $0.94\pm 0.00\text{ }cm$

B) $0.94\pm 0.01\text{ }cm$

C) $0.94\pm 0.02\text{ }cm$

D) $0.94\pm 0.005\text{ }cm$

• question_answer61) A man is $45\text{ }m$behind the bus, when the bus start accelerating from rest with-acceleration $2.5m/{{s}^{2}}$. With what minimum velocity should the man start running to catch the bus?

A) $12\text{ }m/s$

B) $14\text{ }m/s$

C) $15\text{ }m/s$

D) $16\text{ }m/s$

• question_answer62) A particle moves along x-axis as $x=4\,(t-2)+a{{(t-2)}^{2}}$ Which of the flowing is true?

A) The initial velocity of particle is 4

B) The acceleration of particle is $2a$

C) The particle is at origin at $t=0$

D) None of the above

• question_answer63) The momentum of the particle at any instant is given by $3\,\cos 4t\,\hat{i}+3\,\sin \,4t\,\hat{j}$. What is the angle between momentum and force-acting on it?

A) ${{60}^{o}}$

B) ${{30}^{o}}$

C) ${{45}^{o}}$

D) ${{90}^{o}}$

• question_answer64) A boat moves with a speed of $5\text{ }km/h$relative to water in a river flowing with a speed of $3\text{ }km/h$and having a width of$1\text{ }km$. The time taken around a round trip is

A) $5\text{ }min$

B) $60\text{ }min$

C) $20\text{ }min$

D) $30\text{ }min$

• question_answer65) A man is standing at the centre of frictionless pond of ice. How can he get himself to the shore?

A) By throwing his shirt in vertically upward direction

B) By spitting horizontally

C) He will wait for the ice to melt in pond

D) Unable to get at the shore

• question_answer66) If the heart pushes $1\text{ }cc$of blood in 1 s under pressure $20000\text{ }N{{m}^{2}},$the power of heart is

A) $0.02\text{ }W$

B) $400\text{ }W$

C) $5\times {{10}^{-10}}W$

D) $0.2\text{ }W$

• question_answer67) A body of mass $4\text{ }kg$moving with velocity $12\text{ }m/s$collides with another body of mass $\text{6 }kg$ at rest. If two, bodies stick together after collision, then the loss of kinetic energy of system is

A) zero

B) $288\text{ }J$

C) $172.8\text{ }J$

D) $144\text{ }J$

• question_answer68) A man does a given amount of work in $10\text{ }s$. Another man does the' same amount of work in $20\text{ }s$. The ratio of the output power of first man to the second man is

A) $1$

B) $1/2$

C) $2/1$

D) None of these

• question_answer69) Turning effect is produced by

A) tangential component of force

C) transverse component of force

D) None of the above

• question_answer70) For spheres each of mass M and radius R are placed with their centres on the four comers A, B, C and D of a square of side b. The spheres A and B are hollow and C and D are solids. The moment of inertia of the system about side AD of square is

A) $\frac{8}{3}M{{R}^{2}}+2M{{b}^{2}}$

B) $\frac{8}{5}M{{R}^{2}}+2M{{b}^{2}}$

C) $\frac{32}{15}M{{R}^{2}}+2M{{b}^{2}}$

D) $32M{{R}^{2}}+4M{{b}^{2}}$

• question_answer71) A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of $0.5\text{ }m/s$. What is the height of the plane of circle from vertex of the funnel?

A) $0.25\text{ }cm$

B) $2\text{ }cm$

C) $4\text{ }cm$

D) $2.5\text{ }cm$

• question_answer72) Two masses ${{m}_{1}}$ and ${{m}_{2}}({{m}_{1}}>{{m}_{2}})$are connected by massless flexible and inextensible string passed over massless and frictionless pulley. The acceleration of centre of mass is

A) ${{\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)}^{2}}g$

B) $\frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}g$

C) $\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}-{{m}_{2}}}g$

D) zero

• question_answer73) A satellite moves in a circle around the earth. The radius of this circle is equal to one-half of the radius of the moon's orbit. The satellite completes one revolution is

A) $\frac{1}{2}$ lunar month

B) $\frac{2}{3}$ lunar month

C) ${{2}^{-3/2}}$ lunar month

D) ${{2}^{3/2}}$ lunar month

• question_answer74) Earth binds the atmosphere because of

A) gravity

B) oxygen between earth and atmosphere

C) both and

D) None of the above

• question_answer75) A geostationary satellite is revolving around the earth. To make it escape from gravitational field of earth, its velocity must be increased

A) $100%$

B) $41.4%$

C) $50%$

D) $59.6%$

• question_answer76) Who used the quantum theory for the first time to explain the structure of atom?

A) de-Broglie

B) Bohr

C) Heisenberg

D) Einstein

• question_answer77) The boiling point of water decreases at high altitudes because

A) the atmospheric pressure is low

B) the temperature is low

C) the atmospheric pressure is high

D) the temperature is high

• question_answer78) In a solid lattice, the cation has left a lattice site and is located at interstitial position, the lattice defect is

A) interstitial defect

B) vacancy defect

C) Frenkel defect

D) Schottky defect

• question_answer79) The entropy of crystalline substances at absolute zero going by the third law of thermodynamics should be taken as

A) 100

B) 50

C) zero

D) different for different substances

• question_answer80) $\Delta G$for a spontaneous reaction is

A) zero

B) negative

C) positive

D) could be positive or negative

• question_answer81) The IUPAC name for $C{{H}_{3}}CO-C{{H}_{3}}$is

A) dimethyl ketone

B) acetone

C) propanal

D) propanone

• question_answer82) Which of the following is not an endothermic reaction?

A) Dehydrogenation

B) Ethane to ethene

C) Combustion of propane

D) Change of chlorine molecule into chlorine atoms

• question_answer83) A process in which the system does not exchange heat with the surroundings is known as

A) isothermal

B) isobaric

C) isochoric

• question_answer84) Which of the following is not a non-eletrolyte?

A) Acetic acid

B) Glucose

C) Ethanol

D) Urea

• question_answer85) The unit $\text{oh}{{\text{m}}^{-1}}$is used for

A) molar conductivity

B) equivalent conductivity

C) specific conductivity

D) conductance

• question_answer86) The tendency of an electrode to lose electrons is known as

A) eletrode potential

B) reduction potential

C) oxidation potential

D) emf

• question_answer87) For the feasibility of a redox reaction in a cell, the emf should be

A) positive

B) fixed

C) zero

D) negative

• question_answer88) If the rate reaction$A\to B$doubles on increasing the concentration of A by 4 times, the order of the reaction is

A) 2

B) 1

C) $\frac{1}{2}$

D) 4

• question_answer89) Fog is a colloidal solution of

A) solid in gas

B) liquid in gas

C) gas in liquid

D) gas in solid

• question_answer90) Muddy water can be purified through coagulation by using

A) common salt

B) alums

C) sand

D) lime

• question_answer91) Formation of ammonia from ${{\text{H}}_{\text{2}}}$and ${{\text{N}}_{2}}$by Haber's process using Fe is an example of

A) heterogeneous catalysis

B) homogeneous catalysis

C) enzyme catalysis

D) non-catalytic process

• question_answer92) The reason for almost doubling the rate of reaction on increasing the temperature of the reaction system by $10{{\,}^{o}}C$is

A) the value of threshold energy increases

B) collision frequency increases

C) the fraction of the molecule having energy equal to threshold energy increases

D) activation energy decreases

• question_answer93) The pH of an aqueous solution having hydroxide ion concentration as $1\times {{10}^{-5}}$ is

A) 5

B) 9

C) 4.5

D) 11

• question_answer94) Which of the following is not a Lewis acid?

A) $B{{F}_{3}}$

B) $AlC{{l}_{3}}$

C) $S{{O}_{2}}$

D) ${{H}_{2}}O$

• question_answer95) The precipitation takes place only when the product of concentrations of ions

A) exceeds the solubility product

B) is less than the solubility product

C) is negligible

D) is equal to the solubility products

• question_answer96) Which of the following has lowest electron affinity?

A) $Cl$

B) $I$

C) $F$

D) $Br$

• question_answer97) In the calcium fluoride structure the coordination number of the cation and anions are respectively

A) 6, 6

B) 8, 4

C) 4, 4

D) 4, 8

• question_answer98) The total number of orbitals possible for principal quantum number $n$ is

A) $n$

B) ${{n}^{2}}$

C) $2n$

D) $2{{n}^{2}}$

• question_answer99) The pair having similar geometry is

A) $PC{{l}_{3}},N{{H}_{4}}$

B) $BeC{{l}_{2}},\,{{H}_{2}}O$

C) $C{{H}_{4}},CC{{l}_{4}}$

D) $I{{F}_{5}},P{{F}_{5}}$

• question_answer100) The $d-$orbital invovled in $s{{p}^{3}}d-$hybridisation is

A) ${{d}_{{{x}^{2}}-{{y}^{2}}}}$

B) ${{d}_{xy}}$

C) ${{d}_{{{z}^{2}}}}$

D) ${{d}_{zx}}$

• question_answer101) If 8.0 g of a radioactive substance has a half-life of 10 h, the half-life of 2.0 g of the same substance is

A) 2.6 h

B) 5h

C) 10 h

D) 40 h

• question_answer102) Loss of a beta paticle is equivalent to

A) increase of one neutron only

B) decrease of one neutron only

C) both [a] and [b]

D) none of the above

• question_answer103) Which of the following is incorrect?

A) Relative lowering of vapour pressure is independent of the nature of the solute and the solvent

B) The ralative lowering of vapour pressure its a colligative property

C) Vapour pressure of a solution is lower than the vapour pressure of the solvent

D) The relative lowering of vapour pressure is directly proportional to the original pressure

• question_answer104) The presence of the chlorine atom on benzene ring makes the second substituent enter at a position

A) ortho

B) meta

C) para

D) ortho/para

• question_answer105) Hydrogen is not obtained when zinc reacts with

A) cold water

B) hot $\text{NaOH}$solution

C) dil ${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$

D) dil $\text{HCl}$

• question_answer106) The oxidation number of xenon in $\text{XeO}{{\text{F}}_{2}}$is

A) zero

B) 2

C) 4

D) 3

• question_answer107) Which of the following is most volatile?

A) $\text{HF}$

B) $\text{HCl}$

C) $\text{HBr}$

D) $\text{ }\!\!~\!\!\text{ HI}$

• question_answer108) The form of iron having the highest carbon content is

A) cast iron

B) wrought ton

C) stainless steel

D) mild steel

• question_answer109) Which belongs to the actinides series?

A) $Ce$

B) $~Cf$

C) $Ca~$

D) $~Cs$

• question_answer110) Which of the following is planar?

A) $Xe{{F}_{2}}$

B) $Xe{{O}_{3}}F$

C) $Xe{{O}_{2}}{{F}_{2}}$

D) $Xe{{F}_{4}}$

• question_answer111) $\text{Cr}{{\text{O}}_{\text{3}}}$dissovles in aqueous $\text{NaOH}$to give

A) $CrO_{4}^{2-}$

B) $Cr(OH)_{3}^{-}$

C) $C{{r}_{2}}O_{7}^{2-}$

D) $Cr{{(OH)}_{2}}$

• question_answer112) Which of the following is a tribasic acid?

A) $~{{H}_{3}}P{{O}_{4}}$

B) $~HP{{O}_{3}}$

C) ${{H}_{4}}{{P}_{2}}{{O}_{7}}$

D) $~{{H}_{4}}{{P}_{2}}{{O}_{6}}$

• question_answer113) Ethylene diamine is an example of

A) monodentate ligand

B) bidentate ligand

C) tridentate ligand

D) polydentate ligand

• question_answer114) The molecule having a pyramidal shape out of the following is

A) $C{{O}_{2}}$

B) $~B{{F}_{3}}$

C) $S{{F}_{4}}$

D) $~N{{H}_{3}}$

• question_answer115) Which of the following doesn't give a ppt. with silver nitrate solution?

A) Ethyl bromide

B) Sodium bromide

C) Calcium chloride

D) Sodium chloride

• question_answer116) Which is the most stable carbocation?

A) $iso-$propyl cation

B) Triphenylmethyl cation

C) Ethyl cation

D) $n-$propyl cation

• question_answer117) Which is most acidic of the following?

A) Methane

B) Acetylene

C) 1-butene

D) Neo-pentane

• question_answer118) Which is the most reactive of the following?

A) Ethyl acetate

B) Acetic anhydride

C) Acetamide

D) Acetyl chloride

• question_answer119) Which of the following will be chiral?

A) $C{{H}_{3}}CHC{{l}_{2}}$

B) $C{{H}_{3}}CHBrCl$

C) $C{{D}_{2}}C{{l}_{2}}$

D) $C{{H}_{2}}ClBr$

• question_answer120) Electronic configuration of deuterium atom is

A) $1{{s}^{1}}$

B) $2{{s}^{2}}$

C) $2{{s}^{1}}$

D) $1{{s}^{2}}$

• question_answer121) Which of the following is a phenol?

A) Pentanoic acid

B) Phthalic acid

C) Picric acid

D) Phosphoric acid

• question_answer122) Which of the following is not an organometallic compound?

A) ${{C}_{2}}{{H}_{5}}ONa$

B) $C{{H}_{3}}MgI$

C) Tetraethyl

D) $K{{C}_{4}}{{H}_{9}}$

• question_answer123) The correct order of electron affinity is

A) $B<C<O>N$

B) $B>C>N>O$

C) $\text{O}>C>B>N$

D) $\text{O}<C<B<N$

• question_answer124) Ziegler Natta catalyst is an organometallic compound containing

A) iron

B) titanium

C) rhodium

D) zirconium

• question_answer125) Which of the following cannot undergo nucleophilic substitution under ordinary conditions?

A) Chlorobenzene

B) Tert-butylchloride

C) Isopropyl chloride

D) None of the above

• question_answer126) The compound which contains all the four${{1}^{o}},{{2}^{o}},{{3}^{o}}$and ${{4}^{o}}$ carbon atoms is

A) $2,3-$dimethyl pentane

B) $3-$chloro$-2,3-$dimethylpentane

C) $2,3,4-$trimethylpentane

D) $3,3-$dimethylpentane

• question_answer127) Brass, bronze and german silver have one common metal. This is

A) Zn

B) Fe

C) Al

D) Cu

• question_answer128) Which of the following is the green coloured powder produced when ammoniunium dichromate is used in fire works?

A) $Zn$

B) $Fe$

C) $Al$

D) $Cu$

• question_answer129) The $\pi -$bonded organometallic compound which has ethene as one of its component is

A) Zeise's salt

B) ferrocene

C) dibenzene chromium

D) tetraethyl tin

• question_answer130) Malachite is an ore of

A) $Fe$

B) $Ag$

C) $Cr$

D) $Cu$

• question_answer131) The most acidic of the following is

A) $ClC{{H}_{2}}COOH$

B) ${{C}_{6}}{{H}_{5}}COOH$

C) $C{{D}_{3}}COOH$

D) $C{{H}_{3}}C{{H}_{2}}COOH$

• question_answer132) Which of the following is an electrophile?

A) ${{H}_{2}}O$

B) $S{{O}_{3}}$

C) $~N{{H}_{3}}$

D) $~ROR$

• question_answer133) An aromatic compound among other things should have a$\pi -$electron cloud containing $(4n+2)\,\pi$electrons where $n$can't be

A) 1/2

B) 3

C) 2

D) 1

• question_answer134) Glycerol is an alcohol which can be classified as

A) trihydric

B) monohydric

C) dihydric

D) hexahydric

• question_answer135) The oxidation number of cobalt in $K[Co{{(CO)}_{4}}]$is

A) $+\,1$

B) $+\,3$

C) $~-1$

D) $-3$

• question_answer136) Bromination of alkanes involves

A) carbanions

B) carbocations

C) carbenes

• question_answer137) Methylphenyl ether can be obtained by reacting

A) phenolate ions and methyl iodide

B) methoxide ipns and bromobenzene

C) methanol and phenol

D) bromo benzene and methyl bromide

• question_answer138) Which is not correct?

A) Phenol is more acidic than acetic acid

B) Ethanol is less acidic than phenol

C) Ethanol has higher boiling point than ethane

D) Ethane is a non-linear molecule

• question_answer139) Ascorbic acid is also known as

A) vitamin A

B) vitamin B

C) vitamin C

D) vitamin D

• question_answer140) Reaction of phenol with chloroform/sodium hydroxide to give $o-$hydroxy benzaldehyde involves the formation of

A) dichloro carbine

B) trichloro carbene

C) chlorine atoms

D) chlorine molecules

• question_answer141) One of the following that cannot undergo dehydrohalogenation is

A) $iso-$propyl bromide

B) ethariol

C) ethyl bromide

D) none of the above

A) $S+{{O}_{2}}\to S{{O}_{2}}$

B) $2S{{O}_{2}}+\,{{O}_{2}}\to 2S{{O}_{3}}$

C) $C+{{O}_{2}}\to C{{O}_{2}}$

D) All of these

• question_answer143) Acetic acid will be obtained on oxidation of

A) ethanol

B) propanal

C) methanal

D) glyoxal

• question_answer144) A carboxylic acid is converted into its anhydride using

A) thionyl chloride

B) sulphur chloride

C) sulphuric acid

D) phosphorus pentoxide

A) Glucose is a disaccharide

B) Starch is a polysaccharide

C) Glucose and fructose are not anomers

D) Invert sugar consists of glucose and fructose

• question_answer146) What kind of isomerism is possible for 1-chloro-2-nitroethene?

A) Functional group isomerism

B) Position isomerism

C) E/Z isomerism

D) Optical isomerism

A) ethyl alcohol

B) ethyl bromide

C) bromobenzene

D) chlorobenzene

• question_answer148) Peptides are formed from

A) aliphatic amines

B) carbohydrates

C) a-amino acids

D) aromatic amines

• question_answer149) Calcium carbide on reaction with water yields

A) methane

B) ethane

C) ethene

D) ethyne

• question_answer150) The correct set of the four quantum numbers of a $4d$ electron is

A) $4,2,1-\frac{1}{2}$

B) $4,2,1,0$

C) $4,3,2,+\frac{1}{2}$

D) $4,3,-2,+\frac{1}{2}$

• question_answer151) In a class of 30 pupils. 12 take needls work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three, then the number of pupils taking 2 subjects is

A) $16$

B) $6$

C) $8$

D) $20$

• question_answer152) If $f(2x+3)=\sin x+{{2}^{x}},$ then $f(4m-2n+3)$ is equal to

A) $\sin \,(m-2n)+{{2}^{2m-n}}$

B) $\sin \,(2m-n)+{{2}^{(m-n)2}}$

C) $\sin \,(m-2n)+{{2}^{(m+n)2}}$

D) $\sin (2m-n)+{{2}^{2m-n}}$

• question_answer153) If ${{z}_{1}}=1+2i$ and ${{z}_{2}}=3+5i,$ then $\operatorname{Re}[{{\bar{z}}_{2}}{{z}_{1}}/{{z}_{2}}]$is equal to

A) $-31/17$

B) $17/22$

C) $-17/31$

D) $22/17$

• question_answer154) If $|z+8|+|z-8|=16,$ where z is a complex number, then the point z will lie on

A) circle

B) an ellipse

C) a straight line

D) None of these

• question_answer155) If twice the 11 th term of an AP is equal to 7times its 21st term, then its 25th term is equal to

A) $24$

B) $120$

C) $0$

D) None of these

• question_answer156) If one of the roots of equation ${{x}^{2}}+ax+3=0$ is 3 and one of the roots of the equation ${{x}^{2}}+ax+b=0$is three times the other root, then the value of b is equal to

A) $3$

B) $4$

C) $2$

D) $1$

• question_answer157) If S is the sum of an infinite GP, the first term a, then the common ratio r is given by

A) $\frac{a-S}{S}$

B) $\frac{S-a}{S}$

C) $\frac{a}{1-S}$

D) $\frac{S-a}{a}$

• question_answer158) The coefficient of ${{x}^{4}}$in the expansion of ${{\left( \frac{x}{2}-\frac{3}{{{x}^{2}}} \right)}^{10}}$is.

A) $405/226$

B) $504/289$

C) $450/263$

D) None of the above

• question_answer159) The figure formed by joining the points $(4,0)$ s$(3,5)$and $(-1,-1)$ in pairs is

A) a right angled triangle

B) an acute angled triangle

C) an obtuse angled triangle

D) None of the above

• question_answer160) The ortho centre of the triangle with vertices $(-2,-6),\,\,\,(-2,4)$ and $(1,3)$ is

A) $(3,\,1)$

B) $(1,\,1/3)$

C) $(1,3)$

D) None of these

• question_answer161) The in centre of a triangle with vertices $(7,1),$ $(-1,5)$ and $(3+2\sqrt{3},3+4\sqrt{3})$is

A) $\left( 3+\frac{2}{\sqrt{3}},\,3+\frac{4}{\sqrt{3}} \right)$

B) $\left( 1+\frac{2}{3\sqrt{3}},1+\frac{4}{3\sqrt{3}} \right)$

C) $(7,1)$

D) None of the above

• question_answer162) Let a be the distance between line $-x+y=2$ and $x-y=2$and $\beta$ be the distance between the lines $4x-3y=5$ and $6y-8x=1,$ then

A) $20\sqrt{2}\beta =11\alpha$

B) $20\sqrt{2}\alpha =11\beta$

C) $11\sqrt{2}\beta =20\alpha$

D) None of these

• question_answer163) The equations of the tangents to circle $5{{x}^{2}}+5{{y}^{2}}=1,$ parallel to line $3x+4y=1$ are

A) $3x+4y=\pm 2\sqrt{5}$

B) $6x+8y=\pm \sqrt{5}$

C) $3x+4y=\pm \sqrt{5}$

D) None of the above

• question_answer164) From the point $(-1,-6)$ two tangents are drawn to the parabola${{y}^{2}}=4x$. Then, the angle between the two tangents is

A) ${{30}^{o}}$

B) ${{45}^{o}}$

C) ${{60}^{o}}$

D) ${{90}^{o}}$

• question_answer165) If the foci of an ellipse are $(\pm \sqrt{5},0)$ and its eccentricity is $\sqrt{5}/3,$ then the equation of the ellipse is

A) $9{{x}^{2}}+4{{y}^{2}}=36$

B) $4{{x}^{2}}+9{{y}^{2}}=36$

C) $36{{x}^{2}}+9{{y}^{2}}=4$

D) $9{{x}^{2}}+36{{y}^{2}}=4$

• question_answer166) If $y=(1+\tan \,A)\,(1-\tan B),$where $A-B=\frac{\pi }{4},$then ${{(y+1)}^{y+1}}$ is equal to

A) $9$

B) $4$

C) $27$

D) $81$

• question_answer167) If $x\,\,\sin \theta -y\,\cos \,\theta =0$and $x\,{{\sin }^{3}}\theta +y\,{{\cos }^{3}}\theta =\sin \theta \,\,\cos \theta ,$ then ${{x}^{2}}+{{y}^{2}}$ is equal to

A) $0$

B) $2$

C) $4$

D) $1$

• question_answer168) If $\tan x=\frac{b}{a},$ then the value of $a\,\cos \,2x+b\,\sin \,2x$is

A) $a$

B) $b$

C) $a+b$

D) ${{a}^{2}}+{{b}^{2}}$

• question_answer169) If the expansion in powers of x of the function $\frac{1}{(1-ax)\,(1-bx)}$is ${{a}_{0}}-{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+{{a}_{3}}{{x}^{3}}+.....,$ then ${{a}_{n}}$ is

A) $\frac{{{b}^{n+1}}-{{a}^{n+1}}}{b-a}$

B) $\frac{{{a}^{n}}-{{b}^{n}}}{b-a}$

C) $\frac{{{a}^{n+1}}-{{b}^{n+1}}}{b-a}$

D) $\frac{{{b}^{n}}-{{a}^{n}}}{b-a}$

• question_answer170) If n is any integer, then the general solution of the equation $\cos \theta -\sin \theta =\frac{1}{\sqrt{2}}$ is

A) $\theta =2n\pi -\frac{\pi }{12}$ or$\theta =2n\pi +\frac{7\pi }{12}$

B) $\theta =n\pi +\frac{\pi }{12}$

C) $\theta =2n\pi +\frac{\pi }{12}$ or $\theta =2n\pi -\frac{7\pi }{12}$

D) $\theta =2n\pi +\frac{\pi }{12}$ or $\theta =2n\pi -\frac{7\pi }{12}$

• question_answer171) . The value of ${{\cos }^{-1}}\,(\cos \,12)-{{\sin }^{-1}}\,(\sin 14)$ is

A) $-2$

B) $8\pi -26$

C) $4\pi +2$

D) None of these

• question_answer172) If a, b and c are the sides of a triangle such that ${{a}^{4}}+{{b}^{4}}+{{c}^{4}}=2{{c}^{2}}({{a}^{2}}+{{b}^{2}}),$ then the angles opposite to the side C is

A) ${{45}^{o}}$ or ${{90}^{o}}$

B) ${{30}^{o}}$ or ${{135}^{o}}$

C) ${{45}^{o}}$ or ${{135}^{o}}$

D) ${{60}^{o}}$ or ${{120}^{o}}$

• question_answer173) The value of the determinant $\left| \begin{matrix} 0 & {{b}^{3}}-{{a}^{3}} & {{c}^{3}}-{{a}^{3}} \\ {{a}^{3}}-{{b}^{3}} & 0 & {{c}^{3}}-{{b}^{3}} \\ {{a}^{3}}-{{c}^{3}} & {{b}^{3}}-{{c}^{3}} & 0 \\ \end{matrix} \right|$is equal to

A) ${{a}^{3}}-{{b}^{3}}-{{c}^{3}}$

B) ${{a}^{3}}-{{b}^{3}}-{{c}^{3}}$

C) $0$

D) $-{{a}^{3}}+{{b}^{3}}+{{c}^{3}}$

• question_answer174) The integer represented by the determinant $\left| \begin{matrix} 215 & 342 & 511 \\ 6 & 7 & 8 \\ 36 & 49 & 54 \\ \end{matrix} \right|$ is exactly divisible by

A) $146$

B) $21$

C) $20$

D) $335$

• question_answer175) A root of the equation $\left| \begin{matrix} 3-x & -6 & 3 \\ -6 & 3-x & 3 \\ 3 & 3 & -6-x \\ \end{matrix} \right|=0$ is given by

A) $x=0$

B) $x=6$

C) $x=3$

D) None of these

• question_answer176) The determinant $\left| \begin{matrix} 4+{{x}^{2}} & -6 & -2 \\ -6 & 9+{{x}^{2}} & 3 \\ -2 & 3 & 1+{{x}^{2}} \\ \end{matrix} \right|$ is not divisible by

A) $x$

B) ${{x}^{3}}$

C) $14+{{x}^{2}}$

D) ${{x}^{5}}$

• question_answer177) If X is a square matrix of order $3\times 3,\lambda$ is a scalar, then adj $(\lambda x)$is equal to

A) $\lambda \,\,adj\,\,(X)$

B) ${{\lambda }^{3}}\,\,adj\,\,(X)$

C) ${{\lambda }^{2}}\,\,adj\,\,(X)$

D) ${{\lambda }^{4}}\,\,adj\,\,(X)$

• question_answer178) If $f(\theta )=\left[ \begin{matrix} \cos \,\theta & -\sin \theta & 0 \\ \sin \,\theta & \cos \,\theta & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right],$then ${{\{f(\theta )\}}^{-1}}$is equal to

A) $f(-\theta )$

B) $f(-\theta )$

C) $f(2\theta )$

D) None of these

• question_answer179) The minors of $-4$ and $9$ and the cofactors of $-4$and 9 in matrix $\left[ \begin{matrix} -1 & -2 & 3 \\ -4 & -5 & -6 \\ -7 & 8 & 9 \\ \end{matrix} \right]$ are respectively

A) $42,3,-42,3$

B) $-42,-3,42$

C) $42,3,42,3,-3$

D) $42,3,-42,3$

• question_answer180) If $X=\left[ \begin{matrix} -x & -y \\ z & t \\ \end{matrix} \right],$ then transpose of adj (X) is

A) $\left[ \begin{matrix} t & z \\ -y & -x \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} t & y \\ -z & -x \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} t & -z \\ y & -x \\ \end{matrix} \right]$

D) None of these

• question_answer181) Let PQRS be a parallelogram whose diagonals PR and QS intersect at O?. If O is origin, then $\overrightarrow{OP}+\overrightarrow{OQ}+\overrightarrow{OR}+\overrightarrow{OS}$is equal to

A) $\overrightarrow{OO'}$

B) $2\overrightarrow{O}O'$

C) $3\overrightarrow{O}Q'$

D) $4\overrightarrow{O}O'$

• question_answer182) If the vectors $2\hat{i}+\hat{j}-\hat{k},-\hat{i}+2\hat{j}+\lambda \hat{k}$ and $-5\,\hat{i}+2\hat{j}-\hat{k}$are coplanar, then the value of $\lambda$ is equal to

A) $-13$

B) $13/9$

C) $-13/9$

D) $-9/13$

• question_answer183) If the scalar projection of the vectors $x\,\hat{i}+\hat{j}+\hat{k}$ on the vector $2\hat{i}-\hat{j}+5\hat{k}$ is $\frac{1}{\sqrt{30}},$ then the value of x is

A) $-3/2$

B) $6$

C) $-6$

D) $3$

• question_answer184) If $\vec{x}+\vec{y}+\vec{z}=\vec{0},\,|\vec{x}|=|\vec{y}|=|\vec{z}|=2$ and $\theta$ is angle between $\vec{y}$ and $\vec{z},$ then the value of $\text{cose}{{\text{c}}^{2}}\theta +{{\cot }^{2}}\theta$ is equal to

A) $4/3$

B) $5/3$

C) $1/3$

D) $1$

• question_answer185) If the position vectors of two points P and Q are respectively $9\,\hat{i}-\hat{j}+5\hat{k}$and $\hat{i}+3\hat{j}+5\hat{k}$ and the line segment PQ intersects the YOZ plane at a point R, then $PR:RQ$is equal to

A) $9:1$

B) $1:9$

C) $-1:9$

D) $-9:1$

• question_answer186) If $\vec{u},\vec{v}$ and $\vec{w}$ are three mutually perpendicular unit vectors, then $|\vec{u}+\vec{v}+\vec{w}|$is equal to

A) $\sqrt{3}$

B) $1$

C) $3$

D) None of the above

• question_answer187) The angle between the vectors $\vec{a}+\vec{b}$ and $\vec{a}-\vec{b}$when $\vec{a}=(1,1,4)$ and $\vec{b}=(1,-1,4)$ is

A) ${{90}^{o}}$

B) ${{45}^{o}}$

C) ${{30}^{o}}$

D) ${{15}^{o}}$

• question_answer188) The line of intersection of the planes $\vec{r}.(\hat{i}-3\hat{j}+\hat{k})=1$ and $\vec{r}.(2\hat{i}+5\hat{j}-3\hat{k})=2$ is parallel to the vector

A) $-4\hat{i}+5\hat{j}+11\hat{k}$

B) $4\hat{i}+5\hat{j}+11\hat{k}$

C) $-4\hat{i}-5\hat{j}+11\hat{k}$

D) $-4\hat{i}+5\hat{j}-11\hat{k}$

• question_answer189) A plane meet the coordinate axes at P, Q and R such that the position vector of the centroid of $\Delta PQR$ is $2\hat{i}-5\hat{j}+8\hat{k}$. Then, the equation of the plane is

A) $\vec{r}.(20\,\hat{i}-8\hat{j}+5\hat{k})=120$

B) $\vec{r}.(20\,\hat{i}-8\hat{j}+5\hat{k})=1$

C) $\vec{r}.(20\,\hat{i}-8\hat{j}+5\hat{k})=2$

D) $\vec{r}.(20\,\hat{i}-8\hat{j}+5\hat{k})=20$

• question_answer190) The distance of the point $(2,3,4)$ from the line $1-x=\frac{y}{2}=\frac{1}{3}(1+z)$ is

A) $\frac{1}{7}\sqrt{35}$

B) $\frac{4}{7}\sqrt{35}$

C) $\frac{2}{7}\sqrt{35}$

D) $\frac{3}{7}\sqrt{35}$

• question_answer191) The equation of the plane passing through the points $(0,1,2)$ and $(-1,\,0,3)$ and perpendicular to the plane $2x+3y+z=5$ is

A) $3x-4y+18z+32=0$

B) $3x+4y-18x+32=0$

C) $4x+3y-17z+31=0$

D) $4x-3y+z+1=0$

• question_answer192) A line joining the points $(1,2,0)$ and $(4,13,5)$ is perpendicular to a plane. Then, the coefficients of x, y and z in the equation of the plane are; respectively

A) $5,15,5$

B) $3,11,5$

C) $3,-11,5$

D) $-5,-15,5$

• question_answer193) The image of the point $P(1,3,4)$ in the plane $2x-y+z+3=0$ is

A) $(3,\,5,-2)$

B) $(-3,\,5,2)$

C) $(3,-5,2)$

D) $(-1,\,4,2)$

• question_answer194) The distance between the line $\vec{r}=2\hat{i}-2\hat{j}+3\hat{k}+\lambda (\hat{i}-\hat{j}+4\hat{k})$ and the plane $\vec{r}.(\hat{i}+5\hat{j}+\hat{k})=5$ is

A) $\frac{10}{3}$

B) $\frac{3}{10}$

C) $\frac{10}{3\sqrt{3}}$

D) $\frac{10}{9}$

• question_answer195) The distance between the planes $2x+y+2z=8$and $4x+2y+4z+5=0$

A) $3/2$

B) $7/2$

C) $2/5$

D) $0$

• question_answer196) If $\alpha ,\beta$ and $\gamma$ are the roots of equation ${{x}^{3}}-3{{x}^{2}}+x+5=0,$ then $y=\Sigma {{\alpha }^{2}}+\alpha \beta \gamma$satisfies the equation.

A) ${{y}^{3}}+y+2=0$

B) ${{y}^{3}}-{{y}^{2}}-y-2=0$

C) ${{y}^{3}}+3{{y}^{2}}-y-3=0$

D) ${{y}^{2}}+4{{y}^{2}}+5y+20=0$

• question_answer197) If l(x) is the least integer not less than x and g(,x) is the greatest integer not greater than x, then $\underset{x\to e+\pi }{\mathop{\lim }}\,\{l(x)+g(x)\}$ is equal to

A) $9$

B) $13$

C) $1$

D) None of these

• question_answer198) The value of $\underset{x\to 0}{\mathop{\lim }}\,\frac{{{27}^{x}}-{{9}^{x}}-{{3}^{x}}+1}{\sqrt{5}-\sqrt{4}+\cos x}$ is

A) $\sqrt{5}\,{{(\log 3)}^{2}}$

B) $8\sqrt{5}\,{{(\log 3)}^{2}}$

C) $16\sqrt{5}\,(\log 3)$

D) $10\sqrt{5}\,{{(\log 3)}^{2}}$

• question_answer199) The value of $\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{x}^{n}}}{{{x}^{n}}+1},$where $x<-1$ is

A) $1/2$

B) $-1/2$

C) $1$

D) None of these

• question_answer200) The value of $\underset{x\to \pi /2}{\mathop{\lim }}\,\,\frac{{{2}^{\cot \,x}}-{{2}^{\cos \,x}}}{\cot \,x-\,\cos \,x}$is

A) $\log \,2$

B) $1$

C) $2$

D) None of these

• question_answer201) The point of discontinuity of tan x is

A) $x=n\pi$

B) $x=n\pi /6$

C) $x=(2n+1)\pi /2$

D) $x=n\pi /3$

• question_answer202) Let $f(x)=\left\{ \begin{matrix} (1/2)\,\{g(x)+(x)\}\,\,sin\,(x),\,x\ge 1 \\ \sin \,x/x,\,x<1 \\ \end{matrix} \right.$ where $g(x)=\left\{ \begin{matrix} 1, & if & x>0 \\ -1, & if & x<0 \\ 0, & if & x=0 \\ \end{matrix} \right.$ Then, $\underset{x\to 1}{\mathop{\lim }}\,\,\,f(x)$ is equal to

A) $0$

B) $2$

C) $sin\text{ }1$

D) None of these

• question_answer203) The function $f(x)=\frac{2{{x}^{2}}+7}{{{x}^{3}}+3{{x}^{2}}-x-3}$is discontinuous for

A) $x=1$only

B) $x=1$ and $x=-1$only

C) $x=1,\,x=-1,\,x=-3$only

D) $x=1,\,x=-1,\,x=-3$ and other values of x

• question_answer204) If $f(x)=\left\{ \begin{matrix} x, & for & <x<1 \\ 2-x, & for & 1\le x<2 \\ x-(1/2){{x}^{2}}, & for & x=2 \\ \end{matrix} \right.$ Then, $f'(1)$is equal to

A) $-1$

B) $1$

C) $0$

D) None of these

• question_answer205) If $y={{\cos }^{-1}}\cos (|x|-f(x)),$ where $f(x)=\left\{ \begin{matrix} 1, & if & x>0 \\ -1, & if & x<0 \\ 0, & if & x=0 \\ \end{matrix} \right.$ Then, ${{(dy/dx)}_{x=\frac{5\pi }{4}}}$is equal to

A) $-1$

B) $1$

C) $0$

D) can't be determined

• question_answer206) If ${{x}^{m}}{{y}^{n}}={{(x+y)}^{m+n}},$ then ${{(dy/dx)}_{x=1,\,y=2}}$ is equal to

A) $1/2$

B) $2$

C) $2m/n$

D) $~m/2n$

• question_answer207) The function $f(x)=2{{x}^{3}}-3{{x}^{2}}+90x+174$ is increasing in the interval

A) $1/2<x<1$

B) $1/2<x<2$

C) $3<x<59/4$

D) $-\infty <x<\infty$

• question_answer208) The equation of the tangent to the curve $x=2\,{{\cos }^{3}}\theta$ and $y=3\,{{\sin }^{3}}\theta$ at the point $\theta =\pi /4$ is

A) $2x+3y=3\sqrt{2}$

B) $2x-3y=3\sqrt{2}$

C) $3x+2y=3\sqrt{2}$

D) $3x-2y=3\sqrt{2}$

• question_answer209) The minimum value of $4{{e}^{2x}}+9{{e}^{-2x}}$ is

A) $11$

B) $12$

C) $10$

D) $14$

• question_answer210) The point of parabola $2y={{x}^{2}},$ which is nearest to the point $(0,\,\,3)$ is

A) $(\pm 4,\,8)$

B) $(\pm 1,1/2)$

C) $(\pm 2,2)$

D) None of these

• question_answer211) In the mean value theorem $f(b)-f(a)=(b-a)\,f'(c),$ if $a=4,\text{ }b=9$and $f(x)=\sqrt{x},$ then the value of c is

A) $8.00$

B) $5.25$

C) $4.00$

D) $6.25$

• question_answer212) If x is any arbitrary constant, then $\int{{{2}^{{{2}^{{{2}^{x}}}}}}}.\,{{2}^{{{2}^{x}}}}.\,{{2}^{x}}\,\,dx$is equal to

A) $\frac{\int{{{2}^{{{2}^{x}}}}}\,dx}{{{(In\,\,2)}^{3}}}+c$

B) $\frac{\int{{{2}^{{{2}^{{{2}^{x}}}}}}}\,dx}{{{(In\,\,2)}^{3}}}+c$

C) $\int{{{2}^{{{2}^{{{2}^{x}}}}}}}\,\,{{(In\,\,2)}^{3}}+c$

D) None of the above

• question_answer213) The derivative of function $f(x)$ is ${{\tan }^{4}}x$. If $f(x)=0,$ then $\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{x}$is equal to

A) $1$

B) $0$

C) $-1$

D) none of these

• question_answer214) The value of $\int_{1}^{{{e}^{2}}}{\frac{dx}{x{{(1+\log \,x)}^{2}}}}$ is

A) $2/3$

B) $1/3$

C) $3/2$

D) In 2

• question_answer215) If $2f(x)-3f(1/x)=x,$ then $\int_{1}^{2}{f(x)\,\,dx}$ is equal to

A) $(3/5)$ In 2

B) $(-3/5)$ ($1+$In 2)

C) $(-3/5)$ In 2

D) None of these

• question_answer216) If A is the area of the region bounded by the curve $y=\sqrt{3x+4},$ x-axis and the lines $x=-1$and $x=4$and B is that area bounded by curve ${{y}^{2}}=3x+4,$x axis and the lines $x=-1$and $x=4,$ then $A:B$is equal to

A) $1:1$

B) $2:1$

C) $1:2$

D) None of these

• question_answer217) If c is an arbitrary constant, then the general solution of the differential equation $ydx-xdy=xy\,\,dx$is given by

A) $y=cx{{e}^{-x}}$

B) $y=cy{{e}^{-x}}$

C) $y+{{e}^{-x}}=cx$

D) $y{{e}^{x}}=cx$

• question_answer218) The solution of $dy=\cos \,x(2-y\,\text{cosec x)}\,\text{dx}$where $y=\sqrt{2},$ when $x=\pi /4$ is

A) $y\sin \,x+\frac{1}{2}\,\text{cosec x}$

B) $y=\tan \,(x/2)+\cot (x/2)$

C) $y=(1/\sqrt{2})\,\sec \,(x/2)+\sqrt{2}\,\cos \,\,(x/2)$

D) None of the above

• question_answer219) The probability that at least one of the event A and B occurs is $0.6$. If A and B occur simultaneously with probability $0.2,$ then $P(\bar{A})+P(\bar{B})$is equal to

A) $0.4$

B) $0.8$

C) $1.2$

D) $1.4$

• question_answer220) A die is thrown. If it shows a six, we draw a ball from a bag consisting, if 2 black balls and 6 white balls. If it does not show a six, then we toss a coin. Then, the sample spate of this experiment consists of

A) 13 points

B) 18 points

C) 10 points

D) None of the above

• question_answer221) The probability of getting a total of at least 6 in the simultaneously throw of three dice is

A) $6/108$

B) $5/27$

C) $1/24$

D) $103/108$

• question_answer222) A sample of a 4 items is drawn at a random without replacement from a lot of 10 items containing 3 defectives. If X denotes the number of defective items in the sample, then $P(0<X<3)$ is equal to

A) $3/10$

B) $4/5$

C) $1/2$

D) $1/6$

• question_answer223) Two cards are drawn successfully with replacement from a well shuffled deck of 52 cards, then the mean of the number of aces is

A) $1/13$

B) $3/13$

C) $2/13$

D) None of the above

• question_answer224) An um contains 4 white and 3 red balls. Three balls are drawn with replacement from this um. Then, the standard deviation of the number of red balls drawn is

A) $6/7$

B) $36/49$

C) $5/7$

D) $25/49$

• question_answer225) A and B are two independent events such that $P(A)=1/2$ and $P(A)=1/2$ then P (neither A nor B) is equal to

A) $2/3$

B) $1/6$

C) $5/6$

D) $1/3$