# Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2001

### done CET - Karnataka Engineering Solved Paper-2001

• question_answer1) Two spherical black bodies of radii${{r}_{1}}$and ${{r}_{2}}$and with surface temperature${{T}_{1}}$and${{T}_{2}}$ respectively. Radiate the same power. Then the ratio of ${{r}_{1}}$and ${{r}_{2}}$will be:

A) ${{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{2}}$

B) ${{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}$

C) ${{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{2}}$

D) ${{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}$

• question_answer2) A source having frequency of 240 Hz is moving towards on observer with a speed of 20 m/s. when the observer is moving towards the source with a velocity of 20 m/s. Then apparent frequency heard by the observer, if velocity of sound is 330 m/s, will be:

A) 268 Hz

B) 271 Hz

C) 368 Hz

D) 250 Hz

• question_answer3) In the circuit shown in figure neglecting source resistance the voltmeter and ammeter reading will respectively, will be:

A) $~0\text{ }V,3\text{ }A$

B) $150\,V,3A$

C) $150\,V,6A$

D) $0\,V,8A$

• question_answer4) Three rods of same dimensions are arranged as shown in figure they have thermal conductivities ${{K}_{1}},{{K}_{2}}$and ${{K}_{3}}.$ The points P and Q are maintained at different temperatures for the heat to flow at the same rate along PRQ and PQ:

A) ${{K}_{3}}=\frac{1}{2}({{K}_{1}}+{{K}_{2}})$

B) ${{K}_{3}}={{K}_{1}}+{{K}_{2}}$

C) ${{K}_{3}}=\frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}$

D) ${{K}_{3}}=2({{K}_{1}}+{{K}_{2}})$

• question_answer5) PQRS is a square loop made of uniform conducting wire the current enters the loop at P and leaves at S. Then the magnetic field will be:

A) maximum at the centre of the loop

B) zero at the centre of loop

C) zero at all points inside the loop

D) zero at all points outside of the loop

• question_answer6) If the velocity of sound in air is 336 m/s. The maximum length of a closed pipe that would produce a just audible sound will be:

A) $3.2\,cm$

B) $4.2\,m$

C) $4.2\,cm$

D) $3.2\,m$

• question_answer7) How will the image formed by a convex lens be affected, if the central portion of the lens is wrapped in black papar as shown in the figure:

A) full image will be formed but without central portion

B) two image will be formed one due to each exposed half

C) full image will be formed but it is less bright

D) no image will be formed

• question_answer8) A ray of light is incident normally on one of the falls of a prism of angle ${{30}^{o}}$ and refractive index $\sqrt{2}.$ The angle of deviation will be:

A) ${{26}^{o}}$

B) ${{0}^{o}}$

C) ${{23}^{o}}$

D) ${{13}^{o}}$

• question_answer9) Translational kinetic energy of a gas molecule, for one mole of the gas, is equal to:

A) $2KT$

B) $\frac{1}{2}RT$

C) $\frac{3}{2}RT$

D) $\frac{2}{3}KT$

• question_answer10) If the radius of earth is reduced by 2% keeping its mass constant. Then the weight of the body on its surface will:

A) increases

B) decreases

C) remain same

D) either or

• question_answer11) An ideal gas is taken around PQRP as shown in the figure of PV diagram. The work done during a cycle is:

A) zero

B) $\frac{1}{2}PV$

C) PV

D) $2PV$

• question_answer12) In an as tronomial telescope, the focal length of objective lens and eye piece are 150 cm and 6 cm respectively. In normal adjustment the magnifying power is:

A) 20

B) 30

C) 60

D) 15

• question_answer13) In an experiment with Kund's tube, the distance between consecutive nodes is 5 cm, when air is inside and it is 13-4 cm, when hydrogen is inside then the velocity of sound in hydrogen will be (velocity of sound in air =330 m/s):

A) $~884.4\text{ }m/s$

B) $984.4\text{ }m/s$

C) $1084.4\text{ }m/s$

D) none of these

• question_answer14) A second harmonic has to be generated in a string of length I stretched between two rigid supports. The point where the string has to be plucked and touched are:

A) plucked at$\frac{l}{4}$and touch at$\frac{l}{2}$

B) plucked at$\frac{l}{4}$and touch at $\frac{3l}{4}$

C) plucked at$\frac{l}{2}$ and touched at $\frac{l}{4}$

D) plucked at$\frac{l}{2}$and touched at$\frac{3l}{4}$

• question_answer15) Five resistance are connected as shown in figure. The equivalent resistance between P and Q will be:

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

B) $\frac{20}{3}\Omega$

C) $\frac{16}{2}\Omega$

D) none of these

• question_answer16) In a parallel, plate capacitor of capacitance C, a metal sheet is inserted between the plates, parallel to them. If the thickness of the sheet is reduced to half of the separation between the plates. The capacitance will be:

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

B) $\frac{3C}{4}$

C) $4C$

D) $2C$

• question_answer17) The forward voltage in a diode increased the width of the depletion region:

A) does not change

B) decreases

C) increases

D) none of these

• question_answer18) An electric bulb is designed to draw power ${{P}_{0}}$at voltage ${{V}_{0}}.$If the voltage is V it draws a power${{P}_{2}}.$Then:

A) $P={{\left( \frac{{{V}_{0}}}{V} \right)}^{2}}{{P}_{0}}$

B) $P={{\left( \frac{V}{{{V}_{0}}} \right)}^{2}}{{P}_{0}}$

C) $P=\left( \frac{V}{{{V}_{0}}} \right){{P}_{0}}$

D) $P=\left( \frac{{{V}_{0}}}{V} \right){{P}_{0}}$

• question_answer19) A magnet dropped into a coil of conducting wire along its axis will fall with an acceleration:

A) more than g

B) equal to g

C) less than g

D) none of these

• question_answer20) The resistors of resistances $2\Omega ,4\Omega$and $8\Omega$ are connected in parallel, then the equivalent resistance of the combination will be:

A) $\frac{8}{7}\Omega$

B) $\frac{7}{8}\Omega$

C) $\frac{7}{4}\Omega$

D) $\frac{4}{9}\Omega$

• question_answer21) A ball of mass$1g$and charge ${{10}^{-8}}C$moves from a point A. Where potential is 600 volt to the point B where potential is zero. Velocity of the ball at the point B is 20 cm/s. The velocity of the ball at the point A will be:

A) $~22.8\text{ }cm/s$

B) $~228\text{ }cm/s$

C) $16.8\text{ }m/s$

D) $~168\text{ }m/s$

• question_answer22) A small object is placed 10 cm in front of a plane mirror. If you stand behind the object 30 cm from the mirror and look at its image, the distance recused for your eye will be:

A) 60 cm

B) 20 cm

C) 40 cm

D) 80 cm

• question_answer23) A milliammeter of range 10 mA has a coil of resistance $1\Omega .$ To use it as voltmeter of range 10 volt, the resistance that must be connected in series with it, will be:

A) $999\,\Omega$

B) $99\,\Omega$

C) $~1000\text{ }\Omega$

D) none of these

• question_answer24) While a capacitor remains connected to a battery and dielectric slab is applied between the plates, then:

A) potential difference between the plates is changed

B) charge flows from the battery to the capacitor

C) electric field between the plates increases

D) energy store in the capacitor Decreases

• question_answer25) There are two electric bulbs of 40 volt and 60 watt. The ratio of their resistance will be:

A) 5:4

B) 4 : 3

C) 3 : 2

D) 2 : 3

• question_answer26) A charge $q$is placed at the centre of the line joining two equal charges Q. The system of there charges will be in equilibrium if q is equal to:

A) $-\frac{Q}{4}$

B) $-\frac{Q}{2}$

C) $+\frac{Q}{2}$

D) $+\frac{Q}{4}$

• question_answer27) If a ball is thrown vertically upwards; assuming the air resistance to be constant and considerable, then:

A) time of ascent $\ge$ time of descent

B) time of ascent $=$ time of descent

C) time of ascent < time of descent

D) time of ascent > time of descent

• question_answer28) The work function for aluminium is 4.125 eV. The cutoff wavelength for photoelectric effect for aluminium will be:

A) 420 nm

B) 350 nm

C) 300 nm

D) 200 nm

• question_answer29) A bus is moving with a velocity of 5 m/s towards a huge well. The driver sounds a horn of frequency 165 Hz. If the speed of sound in air is 355 m/s, the number of beats heard per second by a passenger on the bus will be:

A) 6

B) 5

C) 3

D) 4

• question_answer30) If the critical angle for total internal reflection from a medium to vacuum is${{30}^{o}},$then velocity of light in the medium is:

A) $1.5\times {{10}^{8}}m/s$

B) $3\times {{10}^{8}}m/s$

C) $0.75\,m/s$

D) $6\times {{10}^{8}}\,m/s$

• question_answer31) In a stationary wave, all particles of the medium cross the mean position with:

A) different velocities at different instants

B) different velocities at same instants

C) same speed at all instants

D) different speed at all instants

• question_answer32) A cylinder of 5 litre capacity, filled with air at N.T.P. is connected with another evacuated cylinder of 30 litres of capacity the resultant air pressure in both the cylinders will be:

A) $38.85\text{ }cm$of Hg

B) $21.85\text{ }cm$of Hg

C) $10.85\text{ }cm$ of Hg

D) $~14.85\text{ }cm$ of Hg

• question_answer33) As the intensity of incident light increases then:

A) K.E. of photoelectron decreases

B) K.E. of photoelectron increases

C) photoelectric current increases

D) photoelectric current decreases

• question_answer34) Which of the following statement is not the true?

A) while taking reading of tangent galvanometer, the plane of the coil must be set at right angles to the earth's magnetic meridian

B) a short magnet is used in a tangent galvanometer since a long magnet would be heavy and may not easily move

C) measurements with the tangent galvanometer will be more accurate, when the deflection is around ${{45}^{o}}$

D) a tangent galvanometer can not be used in the polar region

• question_answer35) Pick out the statement which is not true:

A) shortest wavelength UV radiation are beneficial to living tissue while longer wavelength are harmful:

B) UV radiation have wavelength extending from 200 nm to 400 nm.

C) UV radiation are used for sterlisation of water

D) sun is natural source of UV radiation

• question_answer36) The relative permeability is represented by ${{\mu }_{r}}$and the susceptibility is denoted by $\chi$for a magnetic substance. Then for a paramagnetic substance:

A) ${{\mu }_{r}}<1,\chi <0$

B) ${{\mu }_{r}}<1,\chi >0$

C) ${{\mu }_{r}}>1,\chi <0$

D) ${{\mu }_{r}}>1,\chi >0$

• question_answer37) An electron moving in a circular orbit of radius $r$makes $n$rotation per second. The magnetic field produced at the centre has a magnitude of:

A) $\frac{{{\mu }_{0}}ne}{2r}$

B) $\frac{{{\mu }_{0}}{{n}^{2}}e}{2r}$

C) $\frac{{{\mu }_{0}}ne}{2\pi r}$

D) zero

• question_answer38) A train is moving towards north with a speed of 180 km/hr. If the vertical component of the earth's magnetic field is $0.2\times {{10}^{-4}}T,$the e .m. f. induced, in the axle 1-5m long, is:

A) 1.5 mV

B) 15 mV

C) 5.4 mV

D) 54 mV

• question_answer39) When a ceiling fan is switched off its angular velocity radius 50% while its makes 36 rotations. How many more rotation will it make before coming to rest (Assume uniform angular retardation):

A) 18

B) 12

C) 36

D) 48

• question_answer40) During an adiabatic process the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of ${{C}_{p}}/{{C}_{\upsilon }}$for the gas is:

A) $\frac{3}{2}$

B) $\frac{4}{3}$

C) 2

D) $\frac{5}{3}$

• question_answer41) Three fourth of the active nuclei present in a radioactive sample decay in 3/4 sec. The half life of the sample is:

A) $\frac{1}{2}\sec$

B) $1\,\sec$

C) $\frac{3}{8}\sec$

D) $\frac{3}{4}\sec$

• question_answer42) A gas at the temperature 250 K contained in a closed vessel. If the gas is heated through 1 K, percentage increase in its pressure will be:

A) $0.4%$

B) $0.2%$

C) $0.1%$

D) $0.8%$

• question_answer43) Transverse waves of same frequency are generated in two steel wires A and B. The diameter of A is twice of B and the tension in A is half that in B. The ratio of velocities of wave in A and B is:

A) $1:3\sqrt{2}$

B) $1:2\sqrt{2}$

C) $1:2$

D) $\sqrt{2}:1$

• question_answer44) A block of mass 1kg slide down a rough inclined plane of inclination ${{60}^{o}}$starting from its top. If coefficient of kinetic friction is 0.5 and length of the plane$d=1\text{ }m$then work done against friction is:

A) 2.45 J

B) 4.9J

C) 9.8 J

D) 19.6J

• question_answer45) A bar magnet of magnetic M is cut into two parts of equal length. The magnetic moment of each part will be

A) 12M

B) M

C) 0.5M

D) zero

• question_answer46) A body, thrown upwards with some velocity, reaches the maximum height of 20 m. Another body with double the mass thrown up, with double initial velocity will reach a maximum of:

A) 200 m

B) 16 am

C) 80 m

D) 40 m

• question_answer47) A particle having charge 100 times that of an electron is revolving in a circular path of radius 0-8 m with one rotation per second. Magnetic field produced at the centre of particle will be:

A) ${{10}^{-17}}{{\mu }_{0}}$

B) ${{10}^{-11}}{{\mu }_{0}}$

C) ${{10}^{-7}}{{\mu }_{0}}$

D) ${{10}^{-3}}{{\mu }_{0}}$

• question_answer48) The resultant of two forces 3P and IP is R If the first force is doubled then the resultant is also doubled. The angle between the two forces is:

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

B) ${{120}^{o}}$

C) ${{70}^{o}}$

D) ${{180}^{o}}$

• question_answer49) In an$~n-p-n$ transistor circuit, the collector current is 10 mA. If 90% of the electrons emitted reach the collector, the emitter current je and base current $IE$are given by:

A) ${{I}_{E}}=9\,mA,\,{{I}_{B}}=-1\,mA$

B) ${{I}_{E}}=-1\,mA,\,{{I}_{B}}=9\,mA$

C) ${{I}_{E}}=1\,mA,\,{{I}_{B}}=11\,mA$

D) ${{I}_{E}}=11\,mA,{{I}_{B}}=1\,mA$

• question_answer50) The energy of hydrogen atom in its ground state is $-13.6\text{ }eV.$ The energy of the level corresponding to the quantum number$n$is equal 5 is:

A) $-5.40\,eV$

B) $~-2.72\,eV$

C) $~-\text{ }0.85\text{ }eV$

D) $~-\text{ }0.54\text{ }eV$

• question_answer51) Which of the following relation is correct in magnetism?

A) ${{V}^{2}}=I+H$

B) $V={{I}^{2}}+{{H}^{2}}$

C) $I=V+H$

D) ${{I}^{2}}={{V}^{2}}+{{H}^{2}}$

• question_answer52) Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the1 centre are in the ratio 8:1. The radius of the coil is:

A) $1.0\,m$

B) $0.1\,m$

C) $0.15\,m$

D) $0.2\,m$

• question_answer53) A balloon starts rising from the ground with an acceleration of $1.25\,m/{{s}^{2}}$after 8s, a stone is released from the balloon. The stone will $(g=10\,m/{{s}^{2}})$:

A) reach the ground in 4 second

B) begin to move down after being released

C) have a displacement of 50 m

D) cover a distance of 40 m in reaching the ground

• question_answer54) If a white light is used in Young's double slit experiments then a very large number of coloured fringes can be seen:

A) with first order violet fringes being closer to the central white fringes

B) first order red fringes being closer to the central white fringes

C) with a central white fringe

D) with a central black fringe

• question_answer55) In the experiment of diffraction at a single slit, if the slit width is decreased, the width of the central maximum:

A) decreases in Fresnel?s diffraction but increases in Fraun hofer diffraction

B) increases in Fresnel?s diffraction but decreases in Fraun hofer diffraction

C) decreases in both Fresnel and Fraun hofer diffraction

D) increases in both Fresnel and Fraun hoofer diffraction

• question_answer56) A satellite with kinetic energy${{E}_{k}}$is revolving round the earth in a circular orbit. How much more kinetic energy should be given to it so that it may just escape into outer space.

A) ${{E}_{k}}$

B) $2{{E}_{k}}$

C) $\frac{1}{2}{{E}_{k}}$

D) $3{{E}_{k}}$

• question_answer57) The ionisation potential of hydrogen is $13.6\text{ }eV.$ Then the energy released when an electron jumps from $n=3$to $n=2$orbit, is:

A) $2.89\,eV$

B) $1.89\,eV$

C) $3.89\,eV$

D) $4.89\,eV$

• question_answer58) In an X-ray tube electrons bombarding the target produce X-rays of minimum wavelength $1\overset{\text{o}}{\mathop{\text{A}}}\,.$What must be the energy of bombarding electrons:

A) 13375 eV

B) 12375 eV

C) 14375 eV

D) 15375 eV

• question_answer59) Two progressive wave are represented by the following equations: ${{y}_{1}}=5\sin 2\pi (10t-0.1x)$ ${{y}_{2}}=10\sin 2\pi (20\,t-0.2x)$ The ratio of intensities will be:

A) 1 : 16

B) 1 : 4

C) 1 : 2

D) 1 : 1

• question_answer60) The frequency of a tuning fork is 384 per second and velocity of sound in air is 352 m/s. How far the sound has traversed while fork completes 36 vibration?

A) 3 m

B) 13 m

C) 23 m

D) 33m

• question_answer61) At what temperature will the RMS velocity of $\text{S}{{\text{O}}_{\text{2}}}$be the same as that of ${{\text{O}}_{\text{2}}}$ at$303\text{ }K$?

A) 403K

B) 303K

C) 606 K

D) 273 K

• question_answer62) Phenol is treated with bromine water and shaken well. The white precipitate formed during the process is:

A) $m-$bromophenol

B) 2, 4, 6 tribromophenol

C) $2-4$dibromophenol

D) a mixture of o-and $p-$bromophenols

• question_answer63) In thermite process the metal used as reducing agent is:

A) nickel

B) zinc

C) sodium

D) aluminium

• question_answer64) Which of the following compounds on boiling with alkaline $\text{KMn}{{\text{O}}_{\text{4}}}$and subsequent acidification will not give benzoic acid?

A) benzyl alcohol

B) acetophenone

C) anisole

D) toluene

• question_answer65) The base present in DNA, but not in RNA is:

A) guanine

C) uracil

D) thymine

• question_answer66) The total number of lattice arrangements in different crystal system is:

A) 7

B) 3

C) 8

D) 14

• question_answer67) The conversion of A to B follows second order kinetics. Doubling the concentration of A will increase the rate of formation of B by a factor of:

A) 4

B) 2

C) 1/4

D) 1/2

• question_answer68) $R-COO{{R}^{1}}+{{H}_{2}}O\xrightarrow{HCl}$$R-COOH+{{R}^{1}}OH.$ What type of reaction is this?

A) second order

B) unimolecular

C) pseudo-unimolecular

D) third order

• question_answer69) The unit of quantity of electricity is:

A) ohm

B) ampere

C) coulomb

D) volt

• question_answer70) $p{{K}_{a}}$values of two acids A and B are 4 and 5. The strengths of these two acids are related as:

A) acid A is 10 times stronger than acid B

B) strength of acid A : strengths of acid $B=4:5$

C) the strengths of the two acids can not be compared

D) acid B is 10 times stronger than acid A

• question_answer71) $\text{10}\,\text{d}{{\text{m}}^{\text{2}}}$of ${{\text{N}}_{2}}$gas and $\text{10}\,\text{d}{{\text{m}}^{3}}$of gas X at the same temperature and pressure contain the same number of molecules The gas X is:

A) $NO$

B) ${{H}_{2}}$

C) $C{{O}_{2}}$or $Co$

D) all of these

• question_answer72) When the electrons of hydrogen atoms return to L shell from shells of higher energy, we get a series of lines in the spectrum. This series is called:

A) Balmer series

B) Lyman series

C) Bracket! Series

D) Paschen series

• question_answer73) The alcohol obtained by the hydrolysis of oils and fats is:

A) glycol

B) glycerol

C) propanol

D) pentanol

• question_answer74) Which of the following alloys is used for making magnets for hearing aids?

A) ainico

B) german silver

C) invar

D) monel metal

• question_answer75) One $\text{d}{{\text{m}}^{\text{3}}}$of 2M ethanoic acid is mixed with one $\text{d}{{\text{m}}^{\text{3}}}$of 3M ethanol to form an ester $C{{H}_{3}}COOH+{{C}_{2}}{{H}_{5}}OH\xrightarrow{{}}$$C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}+{{H}_{2}}O$ The decrease in the initial rate if each solution is diluted with an equal volume of water would be:

A) 2 times

B) 4 times

C) 0.25 times

D) 0.5 times

• question_answer76) Which one of the following can be classified as a Bronstead base?

A) $NO_{3}^{-}$

B) ${{H}_{3}}{{O}^{+}}$

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

D) $NH_{4}^{+}$

• question_answer77) pH of a solution produced when an aqueous solution of pH 6 is mixed with an equal volume of an aqueous solution of pH 3 is about:

A) 3.3

B) 4.3

C) 4.0

D) 4.5

• question_answer78) Aluminium displaces hydrogen from acids, but copper does not. A Galvanic cell prepared by combining $\text{Cu/C}{{\text{u}}^{\text{2}}}\text{+}$and $\text{Al/A}{{\text{l}}^{\text{3+}}}$has an emf of$\text{2}\text{.0 V}$ at$\text{298 K}\text{.}$If the potential of copper electrode is$\text{+ 0}\text{.34 V,}$ that of aluminium electrode is:

A) $-\,2.3V$

B) $+\,2.34V$

C) $-1.66\,V$

D) $+\,1.66\,V$

• question_answer79) 1.5 moles of ${{\text{O}}_{\text{2}}}$ combine with Mg to form the oxide $\text{MgO}\text{.}$The mass of Mg that has combined is $\text{(Mg}\,\text{=}\,\text{24)}\,\text{:}$

A) 72 g

B) 36 g

C) 48 g

D) 24 g

• question_answer80) How much of$\text{NaOH}$is required to neutralise $\text{1500}\,\text{c}{{\text{m}}^{\text{3}}}$ of $\text{0}\text{.1}\,\text{N}\,\text{HCl?}$$\text{(Na}\,\text{=}\,\text{23):}$

A) 60 g

B) 6 g

C) 4 g

D) 40 g

• question_answer81) The boiling point of water is exceptionally high because:

A) water molecule is not linear

B) water molecule is linear

C) there is covalent bond between H and O

D) water molecules associate due to hydrogen bonding

• question_answer82) ${{\text{P}}_{\text{4}}}{{\text{O}}_{\text{10}}}$is not used with to dry $\text{N}{{\text{H}}_{\text{3}}}$gas because:

A) ${{\text{P}}_{\text{4}}}{{\text{O}}_{\text{10}}}$is basic and $\text{N}{{\text{H}}_{3}}$is acidic

B) ${{\text{P}}_{\text{4}}}{{\text{O}}_{\text{10}}}$is acidic and$\text{N}{{\text{H}}_{3}}$ is basic

C) ${{\text{P}}_{\text{4}}}{{\text{O}}_{\text{10}}}$is not a drying agent

D) ${{\text{P}}_{\text{4}}}{{\text{O}}_{\text{10}}}$ reacts with moisture in$\text{N}{{\text{H}}_{\text{3}}}$

• question_answer83) A radioactive isotope has a half life of 10 years. What percentage of the original amount of it remain after 20 years:

A) 0

B) 12.5

C) 8

D) 25

• question_answer84) 75% of a first order reaction is completed in 30 minutes. What is the time required for 93.75% of the reaction (in minutes)?

A) 45

B) 120

C) 90

D) 60

• question_answer85) Excess of $\text{N}{{\text{a}}^{\text{+}}}$ ions in our system causes:

A) high B.P.

B) low B.P.

C) diabetes

D) anaemia

• question_answer86) Alcoholic potash is used to bring about:

A) dehydrogenation

B) dehydration

C) dehydro halogenation

D) dehalogenation

• question_answer87) Which of the following organic compounds answers both iodoform test and Fehling's test?

A) methanol

B) ethanol

C) propane

D) ethanol

• question_answer88) Gold sol is an electronegative sol. The amount of electrolyte required to coagulate a certain amount of gold sol is minimum in the case of:

A) $CaC{{l}_{2}}$

B) $NaCl$

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

D) $N{{a}_{2}}S{{O}_{4}}$

• question_answer89) The oxidation number and the electronic configuration of sulphur in ${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$is:

A) $+\,4;\,1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}$

B) $+\,2;\,1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{2}}$

C) $+\,3;\,1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{1}}$

D) $+\,6;\,1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}$

• question_answer90) The mass of $\text{112}\,\text{c}{{\text{m}}^{\text{3}}}$of $\text{C}{{\text{H}}_{\text{4}}}$ gas at STP is:

A) 0.16 g

B) 0.8 g

C) 0.08 g

D) $1.6\,g$

• question_answer91) The volume of water to be added to $\text{100 c}{{\text{m}}^{\text{3}}}$of $\text{0}\text{.5}\,\text{N}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$to get decinormal concentration is:

A) $400\text{ }c{{m}^{3}}$

B) $~500\text{ }c{{m}^{3}}$

C) $~450\text{ }c{{m}^{3}}$

D) $~100\text{ }c{{m}^{3}}$

• question_answer92) In which of the following equilibrium systems is the rate of the backward reaction favoured by increase of pressure?

A) $PC{{l}_{5}}\rightleftharpoons PC{{l}_{3}}+C{{l}_{2}}$

B) $2S{{O}_{2}}+{{O}_{2}}\rightleftharpoons 2N{{H}_{3}}$

C) ${{N}_{2}}+3{{H}_{2}}\rightleftharpoons 2N{{H}_{3}}$

D) ${{N}_{2}}+{{O}_{2}}\rightleftharpoons 2NO$

• question_answer93) In order to decompose 9g water $\text{142}\text{.5 kJ}$heat is required. Hence the enthalpy of formation of water is:

A) $-142.5\,\,kJ$

B) $+\,142.5\,kJ$

C) $-285\,kJ$

D) $+\,285\,kJ$

• question_answer94) A quantity of $\text{PC}{{\text{l}}_{\text{5}}}$was heated in a $\text{10 d}{{\text{m}}^{\text{3}}}$vessel at $\text{250}{{\,}^{\text{o}}}\text{C}$$\text{PC}{{\text{l}}_{5}}(g)\rightleftharpoons PC{{l}_{3}}(g)C{{l}_{2}}(g)$ At equilibrium the vessel contains$0.1$mole of $\text{PC}{{\text{l}}_{\text{5}}}$and$0.2$mole of $\text{C}{{\text{l}}_{\text{2}}}\text{.}$ The equilibrium constant of the reaction is:

A) $0.05$

B) $0.02$

C) $0.025$

D) $0.04$

• question_answer95) Which among the following species has the highest ionisation potential?

A) B

B) Li

C) Ne

D) F

• question_answer96) Which one of the following metallic hydroxides does not dissolve in sodium hydroxide solution?

A) $Zn{{(OH)}_{2}}$

B) $Al{{(OH)}_{3}}$

C) $Fe{{(OH)}_{3}}$

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

• question_answer97) IUPAC name of ${{\text{K}}_{\text{3}}}\text{Fe(CN}{{\text{)}}_{\text{6}}}$is:

A) potassium ferricyanide

B) hexacyano ferrate (III)

C) potassium hexacyano ferrate (III)

D) potassium hexacyano ferrate (II)

• question_answer98) Unpleasant smell of carbylamine is obtained when chloroform and alcoholic KOH are heated with:

A) any aliphatic amine

B) any amine

C) any primary amine

D) any aromatic amine

• question_answer99) Which of the following is an aldohexose?

A) cellulose

B) sucrose

C) glucose

D) raffinose

• question_answer100) When a mixture of calcium acetate and calcium formate is dry distilled, the product formed as:

A) ethanal

B) butanone

C) methanal

D) acetophenone

• question_answer101) The test used for identifying peptide linkage in proteins is:

A) Borsche's test

B) Molisch's test

C) Ninhydrin test

D) Biuret test

• question_answer102) Which of the following is not used to distinguish ethene from ethane?

A) iodine in $\text{CC}{{\text{l}}_{4}}$

B) bromine in$\text{CC}{{\text{l}}_{4}}$

C) alkaline $\text{KMn}{{\text{O}}_{\text{4}}}$

D) ammonical $\text{C}{{\text{u}}_{\text{2}}}\text{C}{{\text{l}}_{\text{2}}}$

• question_answer103) To get a n-type doped semiconductor, impurity to be added to silicon should have the following number of valence electrons:

A) 1

B) 3

C) 5

D) 2

• question_answer104) For the equilibrium${{N}_{2}}(g)+3{{H}_{2}}(g)\rightleftharpoons 2N{{H}_{3}}(g),$ The equilibrium constant,${{K}_{p}}$is equal to:

A) ${{K}_{c}}={{(RT)}^{2}}$

B) ${{K}_{c}}(RT)$

C) $\frac{{{K}_{c}}}{{{(RT)}^{2}}}$

D) ${{K}_{c}}$

• question_answer105) 5 moles of $\text{S}{{\text{O}}_{\text{2}}}$and 5 moles of ${{\text{O}}_{2}}$ are allowed to react to form$\text{S}{{\text{O}}_{\text{3}}}$in a closed vessel. At the equilibrium stage 60% of $\text{S}{{\text{O}}_{2}}$is used up. The total number of moles of$\text{S}{{\text{O}}_{\text{2}}}\text{,}{{\text{O}}_{\text{2}}}$and$\text{S}{{\text{O}}_{\text{3}}}$in the vessel now is:

A) $10.0$

B) $8.5$

C) $10.5$

D) $3.9$

• question_answer106) For a given reaction${{t}_{1/2}}=\frac{1}{Ka}.$The Ka order of the reaction is:

A) 1

B) 0

C) 3

D) 2

• question_answer107) In the case of small cuts, bleeding is stopped by applying potash alum. Here alum acts as:

A) fungicide

B) disinfectant

C) germicide

D) coagulating agent

• question_answer108) For the reaction${{H}_{2}}O(s)\rightleftharpoons {{H}_{2}}O(l)$at $0{{\,}^{o}}C$and normal pressure :

A)  $\Delta H >T \Delta \,S$

B) $\Delta H =T \Delta \,S$

C)  $\Delta H =\Delta \,G$

D) $\Delta H <T\Delta \,S$

• question_answer109) When salicylic acid is distilled with zinc dust, the product obtained is:

A) zinc salicylate

B) salicylaldehyde

C) phenol

D) benzoic acid

• question_answer110) The percentage of${{\text{N}}_{\text{2}}}$ in urea is about

A) 28

B) 18

C) 85

D) 46

• question_answer111) On heating ethanol with excess of cone. ${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$at $\text{170}{{\,}^{\text{o}}}\text{C,}$ the product obtained is:

A) ethene

B) ethoxy ethane

C) ethyne

D) ethane

• question_answer112) To calculate the amount of work done in joules during reversible isothermal expansion of an ideal gas, the volume must be expressed in:

A) $d{{m}^{3}}$only

B) ${{m}^{3}}$only

C) any unit

D) $c{{m}^{3}}$unit

• question_answer113) The quantity of electricity required to liberate $\text{112 c}{{\text{m}}^{\text{3}}}$of hydrogen at STP from acidified water is:

A) 965 Coulombs

D) 96500 Coulombs

• question_answer114) Hydrogen ion concentration of an aqueous solution is $1\times {{10}^{-4}}M.$The solution is diluted with equal volume of water. Hydroxyl ion concentration of the resultant solution in terms of mol $d{{m}^{-3}}$is:

A) $1\times {{10}^{-8}}$

B) $1\times {{10}^{-6}}$

C) $2\times {{10}^{-10}}$

D) $0.5\times {{10}^{-10}}$

• question_answer115) The shape of cuprammonium ion is:

A) trigonal

B) tetrahedral

C) octahedral

D) square planar

• question_answer116) The enthalpy of combustion of ${{C}_{6}}{{H}_{6}}(l)$is $-3250\,kJ.$When $\text{0}\text{.39 g}$of benzene is burnt in excess of oxygen in an open vessel, the amount of heat liberated is:

A) $\text{16}\text{.25}\,\text{J}$

B) $\text{16}\text{.25}\,k\text{J}$

C) $32.5\,J$

D) $32.5\,kJ$

• question_answer117) In an adiabatic expansion of an ideal gas:

A)  $W=-\Delta E$

B) $W=\Delta E$

C)  $\Delta E=0$

D) $W=0$

• question_answer118) The solubility product of a binary weak electrolyte is $4\times {{10}^{-10}}\,$at 298 K. Its solubility in $\text{mol}\,\text{d}{{\text{m}}^{-3}}$at the same temperature is:

A) $4\times {{10}^{-5}}$

B) $2\times {{10}^{-5}}$

C) $8\times {{10}^{-10}}$

D) $16\times {{10}^{-20}}$

• question_answer119) Propane is the product obtained by dehydrogenation of:

A) 2-propanol

B) 1-propanol

C) propanal

D) $n-$propyl alcohol

• question_answer120) To get DDT chlorobenzene has to react with the following compound in the pressure of concentrated sulphuric acid:

A) trichloro ethane

B) dichloro acetone

C) dichloro acetaldehyde

D) trichloro acetaldehyde

• question_answer121) If ${{\,}^{n}}{{P}_{4}}=24{{\,}^{n}}{{C}_{5}},$then the value of $n:$

A) 10

B) 15

C) 9

D) 5

• question_answer122) The angle between the lines${{x}^{2}}+4xy+{{y}^{2}}=0$

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

B) ${{15}^{o}}$

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

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

• question_answer123) Separate equations of lines, whose equation is ${{x}^{2}}+xy-12{{y}^{2}}=0$are:

A) $x+4y=0$and$x+3y=0$

B) $2x-3y=0$and $x-4y=0$

C) $x-6y=0$and $x-3y=0$

D) $x+4y=0$and $x-3y=0$

• question_answer124) The value of$\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{{{e}^{x}}-1}{x} \right)$is:

A) $1/2$

B) $\infty$

C) 1

D) zero

• question_answer125) The value of$\underset{x\to 0}{\mathop{\lim }}\,\left[ \frac{\sqrt{a+x}-\sqrt{a-x}}{x} \right]$is:

A) 1

B) zero

C) $\sqrt{a}$

D) $\frac{1}{\sqrt{a}}$

• question_answer126) If $A=\left[ \begin{matrix} 2 & 3 \\ 4 & 6 \\ \end{matrix} \right],$then ${{A}^{-1}}$is equal to:

A) $\left[ \begin{matrix} 1 & 2 \\ -3/2 & 3 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 2 & -3 \\ 4 & 6 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} -2 & 4 \\ -3 & 6 \\ \end{matrix} \right]$

D) does not exists

• question_answer127) The distance between the foci of an ellipse is 16 and eccentricity is 1/2. Length of the major axis of the ellipse is:

A) 8

B) 64

C) 16

D) 32

• question_answer128) The value of $\left[ {{\tan }^{-1}}\left( \frac{1}{2} \right)+{{\tan }^{-1}}\left( \frac{1}{3} \right) \right]$is:

A) $\frac{\pi }{2}$

B) $\pi$

C) $\pi /4$

D) none of these

• question_answer129) If $\cos x+\cos y+\cos \alpha =0$and $\sin x+\sin y+\sin \alpha =0,$ then$\cot \left( \frac{x+y}{2} \right)=2$

A) $\sin \alpha$

B) $\cos \alpha$

C) $\cot \alpha$

D) $\sin \left( \frac{x+y}{2} \right)$

• question_answer130) If we express$\frac{{{(cos2\theta -i\sin 2\theta )}^{4}}{{(cos4\theta +i\sin 4\theta )}^{-5}}}{{{(cos3\theta +i\sin 3\theta )}^{-2}}{{(cos3\theta -i\sin 3\theta )}^{-9}}}$in the form of$x+iy,$we get:

A) $\cos 49\theta -i\sin 49\theta$

B) $\cos 23\theta +i\sin 23\theta$

C) $\cos 49\theta +i\sin 49\theta$

D) $\cos 21\theta +i\sin 21\theta$

• question_answer131) The conjugate of$\frac{{{(2+i)}^{2}}}{3+i},$in the form of $a+ib,$is:

A) $\frac{13}{2}+i\left( \frac{15}{2} \right)$

B) $\frac{13}{10}+\left( \frac{-15}{2} \right)i$

C) $\frac{13}{10}+i\left( \frac{9}{10} \right)$

D) none of these

• question_answer132) If $y=(1+{{x}^{2}}){{\tan }^{-1}}x-x,$then $\frac{dy}{dx}=$

A) ${{\tan }^{-1}}x$

B) $2x{{\tan }^{-1}}x$

C) $2x{{\tan }^{-1}}x$

D) $\frac{2x}{{{\tan }^{-1}}x}$

• question_answer133) The function$f(x)=2{{x}^{3}}-15{{x}^{2}}+36x+4$ maximum at:

A) $x=2$

B) $x=4$

C) $~x=0$

D) $x=3$

• question_answer134) $\frac{d}{dx}\left[ {{\tan }^{-1}}\left( \frac{a-x}{1+ax} \right) \right]$is equal to:

A) $-\frac{1}{1+{{x}^{2}}}$

B) $\frac{1}{1+{{a}^{2}}}-\frac{1}{1+{{x}^{2}}}$

C) $\frac{1}{1+{{\left( \frac{a-x}{1+ax} \right)}^{2}}}$

D) none of these

• question_answer135) If $1,\omega ,{{\omega }^{2}}$are the cube roots of unity, then their product is:

A) zero

B) $\omega$

C) $-1$

D) $1$

• question_answer136) The real part of $\frac{1}{1-\cos \theta +i\sin \theta }$is equal to:

A) $\frac{1}{4}$

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

C) $\tan \theta /2$

D) $\frac{1}{1-\cos \theta }$

• question_answer137) The equation of tangent at $(-4,-4)$ on the curve${{x}^{2}}=-4y$ is:

A) $2x+y+4=0$

B) $2x-y-12=0$

C) $2x+y-4=0$

D) $2x-y+4=0$

• question_answer138) The value of=$\int_{0}^{\pi /2}{\log \tan x\,dx}$ is:

A) $\infty$

B) $\pi$

C) zero

D) 1

• question_answer139) The value of$\int_{{}}^{{}}{\frac{dx}{{{(x-5)}^{2}}}}$is:

A) $\frac{1}{x-5}+c$

B) $-\frac{1}{x-5}+c$

C) $\frac{2}{(x+5)}+c$

D) none of these

• question_answer140) The angle between the curves ${{y}^{2}}=x$ and ${{x}^{2}}=y$at $(1,1)$is:

A) ${{\tan }^{-1}}(3/4)$

B) ${{\tan }^{-1}}(4/5)$

C) ${{\tan }^{-1}}(2/3)$

D) none of these

• question_answer141) The length of sub tangent to the curve ${{x}^{2}}{{y}^{2}}={{a}^{4}}$ at the point $(-a,a)$ is:

A) 3a

B) 2a

C) 4a

D) a

• question_answer142) The abscissae of the points, where the tangent to curve $y={{x}^{3}}-3{{x}^{2}}-9x+5$is parallel to $x-$axis, are:

A) $x=0$and 0

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

C) $~x=-1$ and 3

D) none of these

• question_answer143) The general solution of the differential equation $\frac{dy}{dx}=\frac{{{x}^{2}}}{{{y}^{2}}}$ is:

A) ${{x}^{3}}-{{y}^{3}}=c$

B) ${{x}^{3}}+{{y}^{3}}=c$

C) ${{x}^{2}}+{{y}^{2}}=c$

D) ${{x}^{2}}-{{y}^{2}}=c$

• question_answer144) The modulus and amplitude of $\frac{1+i}{1-i}$ are:

A) $1$and $\frac{\pi }{4}$

B) $\sqrt{2}$and$\frac{\pi }{3}$

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

D) $-1$and $-\pi /2$

• question_answer145) Equation of the parabola with its vertex at $(2,1)$ and focus is $(-1,1)$

A) $4{{x}^{2}}+{{y}^{2}}-4xy+8x+46y-71=0$

B) $3{{x}^{2}}+2{{y}^{2}}-7xy+3x++9y-15=0$

C) $2{{x}^{2}}+3{{y}^{2}}-5xy+9x+7y-14=0$

D) none of these

• question_answer146) The length of transverse axis of the hyperbola $3{{x}^{2}}-4{{y}^{2}}=32$ is:

A) $\frac{8\sqrt{2}}{\sqrt{3}}$

B) $\frac{16\sqrt{2}}{\sqrt{3}}$

C) $\frac{64}{3}$

D) $\frac{3}{32}$

• question_answer147) If $\cos \theta =-1/2$and ${{0}^{o}}<\theta <{{360}^{o}},$ then the value of $\theta$ are:

A) $~{{120}^{o}}$ and ${{300}^{o}}$

B) $~{{60}^{o}}$ and ${{120}^{o}}$

C) ${{120}^{o}}$and ${{240}^{o}}$

D) $~{{60}^{o}}$ and$~{{240}^{o}}$

• question_answer148) The value of $\left| \begin{matrix} 41 & 42 & 43 \\ 44 & 45 & 46 \\ 47 & 48 & 49 \\ \end{matrix} \right|$is equal to:

A) 2

B) 4

C) zero

D) 1

• question_answer149) If $a\vec{i}+6\vec{j}-\vec{k}$and $7\vec{i}-3\vec{j}+17\vec{k}$are perpendicular vectors, then the value of a is equal to:

A) 5

B) 7

C) 4

D) 3/2

• question_answer150) If A and B are square matrices and ${{A}^{-1}}$and${{B}^{-1}}$of the same order exist, then ${{(AB)}^{-1}}=1$

A) $A{{B}^{-1}}$

B) ${{A}^{-1}}B$

C) ${{A}^{-1}}{{B}^{-1}}$

D) ${{B}^{-1}}{{A}^{-1}}$

• question_answer151) If $\vec{a}$and $\vec{b}$are unit vectors and $\theta$is the angle between then $|\vec{a}-\vec{b}|\,=$

A) $2\sin \theta$

B) $2\cos \theta$

C) $2\sin \theta /2$

D) $2\cos \theta /2$

• question_answer152) If${{\text{H}}_{\text{1}}}$and ${{\text{H}}_{2}}$are two sub groups G, then identify the correct statement:

A) neither ${{H}_{1}}\cup {{H}_{2}}$nor ${{H}_{1}}\cap {{H}_{2}}$is a sub group

B) nothing can be said about ${{H}_{1}}\cup {{H}_{2}}$and ${{H}_{1}}\cap {{H}_{2}}$

C) ${{H}_{1}}\cap {{H}_{2}}$ is a sub group

D) ${{H}_{1}}\cup {{H}_{2}}$is a sub group

• question_answer153) The circle ${{x}^{2}}+{{y}^{2}}-3x-4y+2=0$cut $x-$axis at:

A) $(2,0),(-3,0)$

B) $(3,0),(4,0)$

C) $(1,0),(-1,0)$

D) $(1,0),(2,0)$

• question_answer154) The two circles ${{x}^{2}}+{{y}^{2}}-2x+6y+6=0$and ${{x}^{2}}+{{y}^{2}}-5x+6y+15=0$

A) intersect

B) are concentric

C) touch internally

D) touch externally

• question_answer155) The vertex of the parabola${{(y-2)}^{2}}=16(x-1)$is:

A) $(2,1)$

B) $(1,-2)$

C) $(-1,2)$

D) $(1,2)$

• question_answer156) The unit vector perpendicular to the vectors$\vec{i}-\vec{j}+\vec{k}$and $2\vec{i}+3\vec{j}-\vec{k}$is:

A) $\frac{-2i+3\vec{j}+5\vec{k}}{\sqrt{30}}$

B) $\frac{-2i+5\vec{j}+6\vec{k}}{\sqrt{38}}$

C) $\frac{-2\vec{i}+3\vec{j}+5\vec{k}}{\sqrt{38}}$

D) none of these

• question_answer157) In a group G, the elements $a,b,c,c,d\in G$the ${{(abc)}^{-1}}$is:

A) ${{c}^{-1}}{{b}^{-1}}{{a}^{-1}}$

B) ${{b}^{-1}}{{c}^{-1}}{{d}^{-1}}$

C) ${{a}^{-1}}{{b}^{-1}}{{c}^{-1}}$

D) ${{b}^{-1}}{{c}^{-1}}{{a}^{-1}}$

• question_answer158) If ${{\,}^{15}}{{C}_{3r}}={{\,}^{15}}{{C}_{r+3,}}$then r is equal to:

A) 2

B) 4

C) 3

D) 6

• question_answer159) The equation$2{{x}^{2}}+4x-k{{y}^{2}}+4x+2y-1=0$represents a pair of lines. The value of $k$ is:

A) $-5/3$

B) $+\,5/3$

C) $1/3$

D) $-1/3$

• question_answer160) The equation$12{{x}^{2}}+7xy+a{{y}^{2}}+13x-y+3=0$represents a pair of perpendicular lines. Then the value of a is:

A) $7/2$

B) $-19$

C) $-12$

D) $12$

• question_answer161) $\sqrt{2+\sqrt{2+\sqrt{2}}}+...\infty$is equal to:

A) $-1$

B) $\sqrt{2}$

C) 2

D) $1/2$

• question_answer162) If sixth term of a H.P is$\frac{1}{61}$ and its tenth term is$\frac{1}{105},$ then first term of that H.P. is:

A) 1/38

B) 1/39

C) 1/6

D) 1/17

• question_answer163) Let $f:R\to R$ be defined by $f(x)=3x+4.$Then ${{f}^{-1}}(x)$is:

A) $\frac{x+4}{3}$

B) $\frac{x}{3}-4$

C) $3x+4$

D) none of these

• question_answer164) Let S be a finite set containing n elements. Then the total number of binary operations on S is:

A) ${{n}^{n}}$

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

C) ${{n}^{{{n}^{2}}}}$

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

• question_answer165) If z lies on $|z|=1,$then 2/z lies on:

A) a circle

B) a ellipse

C) a straight line

D) a parabola

• question_answer166) If $x,l,z$are in A.P. and $x,2,z$are in G.P. the $x,4,z$are in:

A) A.P.

B) G.P.

C) H.P.

D) none of these

• question_answer167) The roots of the equation $\log 2({{x}^{2}}-4x+5)=(x-2)$ are:

A) $4,5$

B) $2,-3$

C) $~2,3$

D) $3,5$

• question_answer168) The number of ways in which 8 distinct toys can be distributed among 5 children is:

A) ${{5}^{8}}$

B) ${{8}^{5}}$

C) ${{\,}^{8}}{{P}_{5}}$

D) $40$

• question_answer169) in the expansion of ${{\left( {{x}^{3}}-\frac{1}{{{x}^{2}}} \right)}^{15}},$ the constant term is:

A) ${{\,}^{15}}{{C}_{9}}$

B) zero

C) $-{{\,}^{15}}{{C}_{9}}$

D) 1

• question_answer170) The sum of the series ${{\log }_{4}}2-{{\log }_{8}}2+{{\log }_{16}}2...$is:

A) ${{e}^{2}}$

B) ${{\log }_{e}}2+1$

C) ${{\log }_{e}}3-2$

D) $1-{{\log }_{e}}2$

• question_answer171) A root of the equation$\left| \begin{matrix} 0 & x+a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \\ \end{matrix} \right|=0$is:

A) $a$

B) $b$

C) zero

D) 1

• question_answer172) If the lines $x+2ay+a=0,$$x+3by+b=0$and$x+4cy+c=0$are concurrent, then a, b and c are in:

A) A.P.

B) G.P.

C) H.P.

D) none of these

• question_answer173) The domain of definition of the function $f(x)=\sqrt{{{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right)}$is:

A) $[1,4]$

B) $(1,4)$

C) $(0,5)$

D) $(0,5]$

• question_answer174) $\underset{x\to 0}{\mathop{\lim }}\,\frac{(1-\cos 2x)\sin 5x}{{{x}^{2}}\sin 3x}$is equal to?

A) 10/3

B) 3/10

C) 6/5

D) 5/6

• question_answer175) $\int_{0}^{1}{\frac{{{\tan }^{-1}}x}{1+{{x}^{2}}}dx}$ is equal to:

A) $\pi /4$

B) ${{\pi }^{2}}/32$

C) 1

D) none of these

• question_answer176) The equation${{\sin }^{2}}\theta =\frac{{{x}^{2}}+{{y}^{2}}}{2xy},$ possible if:

A) $~x=y$

B) $x=-y$

C) $2x=y$

D) none of these

• question_answer177) In a group (G, *) for some a of $G,{{a}^{2}}=e,$where e is the identity. Then:

A) $a=\sqrt{e}$

B) $a={{a}^{-1}}$

C) $a=e$

D) none of these

• question_answer178) In a group$G=\{0,1,2,3,4,5\}$under addition modulo$6,{{(2+{{3}^{-1}}+4)}^{-1}}=$

A) zero

B) 2

C) 3

D) 5

• question_answer179) $\int_{{}}^{{}}{\frac{\cos 2\pi }{\cos \pi }}\,dx$is equal to:

A) $2\sin x+\log (\sec x-\tan x)+c$

B) $2\sin x-\log (\sec x-\tan x)+c$

C) $2\sin x+\log (\sec x+\tan x)+c$

D) $2\sin -\log (\sec x+\tan x)+c$

• question_answer180) $\int_{{}}^{{}}{\frac{x+\sin x}{1+\cos x}}\,dx$is equal to:

A) $x\tan x/2+c$

B) $\cot x/2+c$

C) $\log (1+\cos x)+c$

D) $\log (x+\sin x)+c$