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Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2007

done JCECE Engineering Solved Paper-2007

• question_answer1) A simple pendulum is made of a body which a hollow sphere is containing mercury suspended by means of a wire. If a little mercury is drained off, the period of pendulum will

A) remain unchanged

B) increase

C) decrease

D) become erratic

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• question_answer2) Two balloons are filled, one with pure $He$ gas and the other by air, respectively. If the pressure and temperature of these balloons are same then the number of molecules per unit volume is

A) more in the He filled balloon

B) same in both balloons

C) more in air filled balloon

D) in the ratio of$1:4$

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• question_answer3) Which of the following logic gates is a universal gate?

A) $OR$

B) $NOT$

C) $AND$

D) $NAND$

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• question_answer4) We consider a thermodynamic system. If $\Delta U$ represents the increase in its internal energy and $W$ the work done by the system, which of the following statements is true?

A) $\Delta U=-W$ in an adiabatic process

B) $\Delta U=W$ in an isothermal process

C) $\Delta U=-W$ in an isothermal process

D) $\Delta U=W$ in an adiabatic process

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• question_answer5) Aerofils are so designed that the speed of air

A) on top side is more than on lower side

B) on top side is less than on lower side

C) is same on both sides

D) is turbulent

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• question_answer6) According to Bernoulli's equation$\frac{P}{\rho g}+h+\frac{1}{2}\frac{{{v}^{2}}}{g}=$constant The terms $A,\,\,B$ and $C$ are generally called respectively:

A) gravitational head, pressure head and velocity head

B) gravity, gravitational head and velocity head

C) pressure head, gravitational head and velocity head

D) gravity, pressure and velocity head

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• question_answer7) The time of reverberation of a room $A$ is one second. What will be the time (in seconds) of reverberation of a room, having all the dimensions double of those of room$A?$

A) $2$

B) $4$

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

D) $1$

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• question_answer8) For sky wave propagation of $10\,\,MHz$ signal, what should be the minimum electron density in ionosphere?

A) $\tilde{\ }1.2\times {{10}^{12}}{{m}^{-3}}$

B) $\tilde{\ }{{10}^{6}}{{m}^{-3}}$

C) $\tilde{\ }{{10}^{14}}{{m}^{-3}}$

D) $\tilde{\ }{{10}^{22}}{{m}^{-3}}$

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• question_answer9) If the mass of moon is $\frac{M}{81}$, where $M$ is the mass of earth, find the distance of the point from the moon, where gravitational field due to earth and moon cancel each other. Given that distance between earth and moon is$60R$, where $R$ is the radius of earth.

A) $6R$

B) $8R$

C) $2R$

D) $4R$

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• question_answer10) $27$small drops each having charge $q$ and radius $r$ coalesce to from big drop. How many times charge and capacitance will become?

A) $3,\,\,27$

B) $27,\,\,3$

C) $27,\,\,27$

D) $3,\,\,3$

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• question_answer11) The magnetic moment has dimensions of

A) $[LA]$

B) $[{{L}^{2}}A]$

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

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

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• question_answer12) Which of the following circular rods, (given radius $r$ and length$l)$ each made of the same material and whose ends are maintained at the same temperature will conduct most heat?

A) $r=2{{r}_{0}};\,\,l=2{{l}_{0}}$

B) $r=2{{r}_{0}};\,\,l={{l}_{0}}$

C) $r={{r}_{0}};\,\,l={{l}_{0}}$

D) $r={{r}_{0}};\,\,l=2{{l}_{0}}$

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• question_answer13) For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

A) $2$

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

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

D) $\sqrt{2}$

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• question_answer14) The current in the given circuit is

A) $0.3\,\,A$

B) $0.1\,\,A$

C) $0.4\,\,A$

D) $0.2\,\,A$

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• question_answer15) Interference was observed in an interference chamber when air was present. Now, the chamber is evacuated and if the same light is used, a careful observation will show

A) no interference

B) interference with bright band

C) interference with dark bands

D) interference in which breadth of the fringe will be slightly increased

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• question_answer16) When a charged particle moving with velocity $\overset{\to }{\mathop{\mathbf{v}}}\,$is subjected to a magnetic field of induction$\overset{\to }{\mathop{\mathbf{B}}}\,$, the force on it is non-zero. This implies that

A) angle between $\overset{\to }{\mathop{\mathbf{v}}}\,$ and $\overset{\to }{\mathop{\mathbf{B}}}\,$ is necessarily${{90}^{o}}$

B) angle between $\overset{\to }{\mathop{\mathbf{v}}}\,$ and $\overset{\to }{\mathop{\mathbf{B}}}\,$ can have any value other than${{90}^{o}}$

C) angle between $\overset{\to }{\mathop{\mathbf{v}}}\,$ and $\overset{\to }{\mathop{\mathbf{B}}}\,$ can have any value other than zero and${{180}^{o}}$

D) angle between $\overset{\to }{\mathop{\mathbf{v}}}\,$ and $\overset{\to }{\mathop{\mathbf{B}}}\,$ is either zero or ${{180}^{o}}$

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• question_answer17) A particle moves along a straight line$OX$. At a time $t$ (in seconds) the distance $x$ (in metres) of the particle from $O$ is given by $x=40+12t-{{t}^{3}}$ How long would the particle travel before coming to rest?

A) $24\,\,m$

B) $40\,\,m$

C) $56\,\,m$

D) $16\,\,m$

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• question_answer18) Which one of the following statements is true?

A) Both light and sound waves in air are transverse

B) The sound waves in air are longitudinal while the light waves are transverse

C) Both light and sound waves in air are longitudinal

D) Both light and sound waves can travel in vacuum

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• question_answer19) When power is drawn from the secondary coil of the transformer, the dynamic resistance

A) increases

B) decreases

C) remains unchanged

D) changes erratically

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• question_answer20) A reference frame attached to the earth

A) is an inertial frame by definition

B) cannot be an inertial frame because earth is revolving round the sun

C) is an inertial frame because Newton's laws are applicable

D) is an inertial frame because the earth is rotating about its own axis

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• question_answer21) Pressure of an ideal gas is increased by keeping temperature constant. What is the effect on kinetic energy of molecules?

A) Increase

B) Decrease

C) No change

D) Can't be determined

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• question_answer22) What maximum frequency can be reflected from ionosphere?

A) $5\,\,MHz$

B) $6\,\,GHz$

C) $5\,\,kHz$

D) $500\,\,MHz$

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• question_answer23) A telescope has focal length of objective and eyepiece as $200\,\,cm$ and $5\,\,cm$ respectively. What is magnification of telescope?

A) $40$

B) $80$

C) $50$

D) $0.01$

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• question_answer24) A small disc of radius 2 cm is cut from a disc of radius 6 cm. If the distance between their centres is 3.2 cm, what is the shift in the centre of mass of the disc?

A) $40$

B) $80$

C) $50$

D) $0.01$

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• question_answer25) Which of the following is not a process involved in fabrication of$IC?$

A) Polymerization

B) Diffusion

C) Photolithography

D) Metallisation

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• question_answer26) Permanent magnet has properties retentively and coercively respectively

A) high-high

B) low-low

C) low-high

D) high-low

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• question_answer27) Hydrogen bomb is based upon

A) fission

B) fusion

C) chemical reaction

D) transmutation

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• question_answer28) What is not true for equipotential surface for uniform electric field?

A) Equipotential surface is flat

B) Equipotential surface is spherical

C) Electric lines are perpendicular to equipotential surface

D) Work done is zero

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• question_answer29) A closed organ pipe of length 20 cm is sounded with tuning fork in resonance. What is the frequency of tuning fork?$(v=332\,\,m/s)$

A) $300\,\,Hz$

B) $350\,\,Hz$

C) $375\,\,Hz$

D) $415\,\,Hz$

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• question_answer30) Two identical springs of spring constant $k$ are connected in series and parallel as shown in figure. A mass $M$ is suspended from them. The ratio of their frequencies of vertical oscillation will be

A) $2:1$

B) $1:2$

C) $4:1$

D) $1:4$

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• question_answer31) The area of the acceleration-displacement curve of a body gives

A) impulse

B) change in momentum per unit mass

C) change in $KE$ per unit mass

D) total change in energy

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• question_answer32) The speed of earth's rotation about its axis is$\omega$. Its speed is increased to $x$ times to make the effective acceleration due to gravity equal to zero at the equator. Then $x$ is

A) $1$

B) $8.5$

C) $17$

D) $34$

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• question_answer33) Hard $X-$rays for the study of fractures in bones should have a minimum wavelength of${{10}^{-11}}m$. The accelerating voltage for electrons in X-ray machine should be

A) $<124\,\,kV$

B) $>124\,\,kV$

C) between$60\,\,kV$and$70\,\,kV$

D) $=100\,\,kV$

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• question_answer34) In photoelectric effect, the electrons are ejected from metals if the incident light has a certain minimum

A) wavelength

B) frequency

C) amplitude

D) angle of incidence

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• question_answer35) A capacitor having capacitance with air, is filled with two dielectrics as shown. How many times capacitance will increase?

A) $12$

B) $6$

C) $8/3$

D) $3$

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• question_answer36) A leaf which contains only green pigments, is illuminated by a laser light of wavelength$0.6328\,\,\mu m$. It would appear to be

A) brown

B) black

C) red

D) green

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• question_answer37) The operation of a nuclear reactor is said to be critical, if the multiplication factor $(k)$ has a value

A) $1$

B) $1.5$

C) $2.1$

D) $2.5$

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• question_answer38) A galvanometer having a resistance of $8\Omega$ is shunted by a wire of resistance$2\Omega$. If the total current is $1\,\,A$, the part of it passing through the shunt will be

A) $0.25\,\,A$

B) $0.8\,\,A$

C) $0.2\,\,A$

D) $0.5\,\,A$

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• question_answer39) Flash light equipped with a new set of batteries, produces bright white light. As the batteries wear out

A) the light intensity gets reduced with no change in its colour

B) light colour changes first to yellow and then red with no change in intensity

C) it stops working suddenly while giving white light

D) colour changes to red and also intensity gets reduced

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• question_answer40) If alpha, beta and gamma rays carry same momentum, which has the longest wavelength?

A) Alpha rays

B) Beta rays

C) Gamma rays

D) None, all have same wavelength

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• question_answer41) An amplifier has a voltage gain${{A}_{v}}=1000$. The voltage gain in $dB$ is

A) $30\,\,dB$

B) $60\,\,dB$

C) $3\,\,dB$

D) $20\,\,dB$

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• question_answer42) When you make ice cubes, the entropy of water

A) does not change

B) increases

C) decreases

D) may either increase or decrease depending on the process used

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• question_answer43) Half-lives of two radioactive substances $A$ and $B$ are respectively $20\min$ and$40\min$. Initially the samples of $A$ and $B$ have equal number of nuclei. After $80\min$ the ratio of remaining number of $A$ and $B$ nuclei is

A) 1 : 16

B) 4 : 1

C) 1 : 4

D) 1 : 1

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• question_answer44) If equation of a sound wave is$y=0.0015\sin (62.8x+314t)$ then its wavelength will be

A) $0.1\,\,unit$

B) $2\,\,unit$

C) $0.3\,\,unit$

D) $0.2\,\,unit$

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• question_answer45) A projectile is thrown in the upward direction making an angle of ${{60}^{o}}$ with the horizontal direction with a velocity of$147\,\,m{{s}^{-1}}$. Then the time after which its inclination with the horizontal is ${{45}^{o}}$, is

A) $15\,\,s$

B) $10.98\,\,s$

C) $5.49\,\,s$

D) $2.745\,\,s$

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• question_answer46) A motor cycle is going on an over bridge of radius$R$. The driver maintains a constant speed. As the motor cycle is ascending on the overbridge, the normal force on it

A) increases

B) decreases

C) remains the same

D) fluctuates erratically

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• question_answer47) If we throw a body upwards with velocity of$4\,\,m/s$, at what height does its kinetic energy reduce to half of the initial value? (Take$g=10\,\,m{{s}^{-2}})$

A) $4\,\,m$

B) $2\,\,m$

C) $1\,\,m$

D) $0.4\,\,m$

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• question_answer48) Two glass plates are separated by water. If surface tension of water is $75$ $dynes/cm$ and area of each plate wetted by water is $8\,\,c{{m}^{2}}$ and the distance between the plates is $0.12\,\,mm$, then the force applied to separate the two plates is

A) ${{10}^{2}}dyne$

B) ${{10}^{4}}dyne$

C) ${{10}^{5}}dyne$

D) ${{10}^{6}}dyne$

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• question_answer49) Which of the following is true for rays coming from infinity?

A) Two images are formed

B) Continuous image is formed between focal points of upper and lower lens

C) One image is formed

D) None of the above

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• question_answer50) The north pole of a long horizontal bar magnet is being brought closer to a vertical conducting plane along the perpendicular direction. The direction of the induced current in the conducting plane will be

A) horizontal

B) vertical

C) clock wise

D) anti clock wise

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• question_answer51) Calcium carbide reacts with ${{H}_{2}}O$ to produce

A) Ethane

B) methane

C) ethylene

D) acetylene

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• question_answer52) Propyne and propene can be distinguished by

A) $dil.\,\,KMn{{O}_{4}}$

B) $conc.\,\,{{H}_{2}}S{{O}_{4}}$

C) $AgN{{O}_{3}}$ in ammonia

D) $B{{r}_{2}}$in$CC{{l}_{4}}$

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• question_answer53) Oxidation number of $Fe$ in $F{{e}_{2}}{{O}_{3}}$ is

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

B) $\frac{2}{6}$

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

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

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• question_answer54) Bauxite is an ore of

A) $Al$

B) $Ca$

C) $Cu$

D) $Ni$

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• question_answer55) The best source of vitamin $A$ is

A) beans

B) pulses

C) orange

D) carrot

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• question_answer56) Plaster of Paris is

A) $CaS{{O}_{4}}\cdot \frac{1}{2}{{H}_{2}}O$

B) $CaS{{O}_{4}}\cdot 2{{H}_{2}}O$

C) $CaS{{O}_{4}}\cdot {{H}_{2}}O$

D) $CaS{{O}_{4}}\cdot 4{{H}_{2}}O$

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• question_answer57) Penicillin is

A) analgesic

B) antipyretic

C) anti malarials

D) antibiotic

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• question_answer58) The most stable compound is

A) $LiF$

B) $LiCl$

C) $LiBr$

D) $Lil$

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• question_answer59) Heavy water is

A) $CaS{{O}_{4}}$

B) water contain$CaS{{O}_{4}},\,\,MgS{{O}_{4}}$

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

D) water contain$CaC{{O}_{3}}$

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• question_answer60) In the extraction of copper from its sulphide ore, the metal is formed by reduction of$C{{u}_{2}}O$ with

A) $FeS$

B) $CO$

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

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

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• question_answer61) $Ba{{O}_{2}}$ and ozone reacts to produce

A) $Ba$

B) $B{{a}_{2}}{{O}_{3}}$

C) $BaO$

D) $Ba{{(OH)}_{3}}$

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• question_answer62) Heisenberg uncertainty principle can be explained as

A) $\Delta x\ge \frac{\Delta p\times h}{4\pi }$

B) $\Delta x\times \Delta p\ge \frac{h}{4\pi }$

C) $\Delta x\times \Delta p\ge \frac{h}{\pi }$

D) $\Delta p\ge \frac{\pi h}{\Delta x}$

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• question_answer63) For decolourisarion of $1$ mole of $KMn{{O}_{4}}$, the moles of ${{H}_{2}}{{O}_{2}}$ required is

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

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

C) $\frac{5}{2}$

D) $\frac{7}{2}$

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• question_answer64) Bleaching powder is obtained by treating $C{{l}_{2}}$ with

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

B) $CaO$

C) $CaC{{O}_{3}}$

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

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• question_answer65) Magnalium contains

A) $Mg+Al$

B) $Mg+Cu$

C) $Mg+Fe$

D) $Mg+Mn$

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• question_answer66) The de-Broglie wave length of a panicle with mass $1\,\,kg$ and velocity $100\,\,m/s$ is

A) $6.6\times {{10}^{-33}}m$

B) $6.6\times {{10}^{-36}}m$

C) $3.3\times {{10}^{33}}m$

D) $3.3\times {{10}^{-36}}m$

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• question_answer67) The volume of a gas measured at ${{27}^{o}}C$ and $1\,\,atm$ pressure is$10\,\,L$. To reduce the volume to $2\,\,L$ at$1\,\,atm$. pressure, the temperature required is

A) $60\,\,K$

B) $75\,\,K$

C) $150\,\,K$

D) $225\,\,K$

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• question_answer68) Isotonic solutions have

A) same vapour pressure

B) same osmotic pressure

C) same boiling point

D) same temperature

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• question_answer69) Epsom salt is

A) $BaS{{O}_{4}}\cdot 2{{H}_{2}}O$

B) $CaS{{O}_{4}}\cdot {{H}_{2}}O$

C) $MgS{{O}_{4}}\cdot 2{{H}_{2}}O$

D) $MgS{{O}_{4}}\cdot 7{{H}_{2}}O$

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• question_answer70) Paracetamol is an

A) analgesic

B) antipyretic

C) both [a] and [b]

D) none of the above

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• question_answer71) The number of moles of oxygen obtained by the electrolytic decomposition of 108 g water is

A) $2.5$

B) $3$

C) $5$

D) $7.5$

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• question_answer72) The change in entropy for the fusion of $1$ mole of ice is $[mp$ of ice $=273\,\,K$, molar enthalpy of fusion for ice$=6.0\,\,kJ\,\,mo{{l}^{-1}}]$

A) $11.73\,\,J{{K}^{-1}}mo{{l}^{-1}}$

B) $18.84\,\,J{{K}^{-1}}mo{{l}^{-1}}$

C) $21.97\,\,J{{K}^{-1}}mo{{l}^{-1}}$

D) $24.47\,\,J{{K}^{-1}}mo{{l}^{-1}}$

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• question_answer73) Which does not give a precipitate with $AgN{{O}_{3}}$ solution?

A) $[Co{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}$

B) $[Co{{(N{{H}_{3}})}_{5}}Cl]C{{l}_{2}}$

C) $[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]Cl$

D) $[Co{{(N{{H}_{3}})}_{3}}C{{l}_{3}}]$

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• question_answer74) Total volume of atoms present in a face centred cubic unit cell of a metal is $(r$ is atomic radius)

A) $\frac{16}{3}\pi {{r}^{3}}$

B) $\frac{20}{3}\pi {{r}^{3}}$

C) $\frac{24}{3}\pi {{r}^{3}}$

D) $\frac{12}{3}\pi {{r}^{3}}$

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• question_answer75) Pure silicon doped with phosphorus is a

A) metallic conductor

B) insulator

C) $n-$type semiconductor

D) $p-$type semiconductor

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• question_answer76) Which of the following is a biodegradable polymer?

A) Cellulose

B) Polythene

C) Polyvinyl chloride

D) Nylon$6$

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• question_answer77) What is $X$ in the following nuclear reaction? $_{7}{{H}^{14}}{{+}_{1}}{{H}^{1}}{{\xrightarrow{{}}}_{8}}{{O}^{15}}+X$

A) $_{0}{{n}^{1}}$

B) $_{-1}{{e}^{0}}$

C) $_{+1}{{e}^{0}}$

D) $\gamma$

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• question_answer78) Solubility product of $PbC{{l}_{2}}$at$298\,\,K$is$1\times {{10}^{-6}}$. At this temperature solubility of $PbC{{l}_{2}}$ in $mol/L$ is

A) ${{(1\times {{10}^{-6}})}^{1/2}}$

B) ${{(1\times {{10}^{-6}})}^{1/3}}$

C) ${{(0.25\times {{10}^{-6}})}^{1/3}}$

D) ${{(0.25\times {{10}^{-6}})}^{1/2}}$

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• question_answer79) The $pH$ of a $0.001\,\,M$ solution of $HCl$ is

A) $0$

B) $3$

C) $5$

D) $10$

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• question_answer80) Gold number is associated with

A) amount of gold

B) protective colloids

C) purple of cassias

D) electrophoresis

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• question_answer81) Noble gases are used in discharge tubes to give different colours. Reddish-orange glow is due to

A) $Ar$

B) $Ne$

C) $Xe$

D) $Kr$

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• question_answer82) The set representing the correct order for first ionisation potential is

A) $K>Na>Li$

B) $Be>Mg>Ca$

C) $B>C>N$

D) $Ge>Si>C$

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• question_answer83) Dry ice is

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

B) solid camphor

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

D) solid$N{{O}_{2}}$

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• question_answer84) Methanol and ethanol are miscible in water due to

A) covalent character

B) hydrogen bonding character

C) oxygen bonding character

D) none of the above

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• question_answer85) Which of the following does not have optical isomer?

A) $[Co{{(N{{H}_{3}})}_{3}}C{{l}_{3}}]$

B) $[Co{{(en)}_{3}}]C{{l}_{2}}$

C) $[Co{{(en)}_{2}}C{{l}_{2}}]Cl$

D) $[Co(en){{(N{{H}_{3}})}_{2}}C{{l}_{2}}]Cl$

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• question_answer86) $IUPAC$name of the following, compound

A) $N,N-$dimethylcyclopropanecarboxamide

B) $N-$methylcyclopropanamide

C) cyclopropionamide

D) none of the above

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• question_answer87) The product of following reaction is$2C{{H}_{3}}MgBr+C{{H}_{2}}O\xrightarrow{{}}$

A) $C{{H}_{3}}OH$

B) ${{C}_{2}}{{H}_{5}}OH$

C) $C{{H}_{4}}$

D) ${{C}_{2}}{{H}_{6}}$

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• question_answer88) Freon used as refrigerant is

A) $C{{F}_{2}}=C{{F}_{2}}$

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

C) $CC{{l}_{2}}{{F}_{2}}$

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

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• question_answer89) Lucas reagent is

A) $anhy.\,\,ZnC{{l}_{2}}$and$N{{H}_{3}}$

B) $anhy.\,\,ZnC{{l}_{2}}$and$CaC{{l}_{2}}$

C) $anhy.\,\,ZnC{{l}_{2}}$and$conc.\,\,HCl$

D) $anhy.\,\,ZnC{{l}_{2}}$and$HCl$gas

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• question_answer90) The enzyme which can catalyse the conversion of glucose to ethanol is

A) zymase

B) in vertase

C) maltase

D) diastase

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• question_answer91) When dihydroxy acetone reacts with$HI{{O}_{4}}$, the product is/are

A) $HCHO$

B) $HCOOH$

C) $HCHO$and$HCOOH$

D) $HCHO$and$C{{O}_{2}}$

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• question_answer92) Which of the following does not reduce Fehling's solution?

A) Benzaldehyde

B) Formic acid

C) Glucose

D) Fructose

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• question_answer93) Sodium for mate on heating gives

A) oxalic acid and${{H}_{2}}$

B) sodium oxalate and${{H}_{2}}$

C) sodium oxalate

D) $C{{O}_{2}}$ and caustic soda

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• question_answer94) Reaction of ethyl for mate with excess of $C{{H}_{3}}Mgl$ followed by hydrolysis gives

A) $n-$propyl alcohol

B) isopropyl alcohol

C) acetaldehyde

D) acetone

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• question_answer95) Hydrolysis of phenyl isocyanide forms

A) benzoic acid

B) formic acid

C) acetic acid

D) none of these

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• question_answer96) Styrene can be purified by

A) simple distillation

B) fractional distillation

C) steam distillation

D) vacuum distillation

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• question_answer97) Which of the following is not reducing sugar?

A) Glucose

B) Fructose

C) Lactose

D) Sucrose

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• question_answer98) The monomer of teflon is:

A) $CHF=C{{H}_{2}}$

B) $C{{F}_{2}}=C{{F}_{2}}$

C) $CHCl=CHCl$

D) $CHF=CHCl$

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• question_answer99) The hybridisation state of carbon in fullerene is

A) $sp$

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

C) $s{{p}^{3}}$

D) $s{{p}^{3}}d$

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• question_answer100) A fruity smell is produced by the reaction of${{C}_{2}}{{H}_{5}}OH$ with

A) $C{{H}_{3}}COC{{H}_{3}}$

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

C) $PC{{l}_{5}}$

D) $C{{H}_{3}}CHO$

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• question_answer101) If$\left| \begin{matrix} a+x & a-x & a-x \\ a-x & a+x & a-x \\ a+x & -a-x & a-x \\ \end{matrix} \right|=0$, then$x$is equal to

A) $0,\,\,2a$

B) $a,\,\,2a$

C) $0,\,\,3a$

D) none of these

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• question_answer102) If the resultant of two forces $2p$ and $\sqrt{2}p$ is $\sqrt{10}p$, then the angle between them will be

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

B) $\pi$

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

D) $\frac{\pi }{4}$

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• question_answer103) When$y={{\sin }^{-1}}\left( \frac{2t}{1+{{t}^{2}}} \right)$,$x={{\tan }^{-1}}\left( \frac{2t}{1-{{t}^{2}}} \right)$ where$-1<t<1$, then$\frac{dy}{dx}$is equal to

A) $0$

B) $1$

C) $-1$

D) $\infty$

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• question_answer104) $\underset{x\to \infty }{\mathop{\lim }}\,\sqrt{\frac{x-\sin x}{x+{{\cos }^{2}}x}}$is equal to

A) $-1$

B) $0$

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

D) $1$

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• question_answer105) The least number of times a fair coin must be tossed so that the probability of getting at least one head in at least $0.8$ is:

A) $3$

B) $6$

C) $5$

D) none of these

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• question_answer106) If$\frac{dy}{dx}+y=2{{e}^{2x}}$, then$y$is equal to

A) $c{{e}^{-x}}+\frac{2}{3}{{e}^{2x}}$

B) $(1+x){{e}^{-x}}+\frac{2}{3}{{e}^{2x}}+c$

C) $c{{e}^{-x}}+\frac{2}{3}{{e}^{2x}}+c$

D) ${{e}^{-x}}+\frac{2}{3}{{e}^{2x}}+c$

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• question_answer107) A particle is projected under gravity$(g=9.81\,\,m/{{s}^{2}})$with a velocity of $29.43\,\,m/s$ at an elevation of${{30}^{o}}$. The time of flight in seconds to a height of $9.81\,\,m$ are

A) $1,\,\,2$

B) $5,\,\,1.5$

C) $1.5,\,\,2$

D) $2,\,\,3$

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• question_answer108) $\underset{x\to 1}{\mathop{\lim }}\,\frac{{{x}^{8}}-2x+1}{{{x}^{4}}-2x+1}$equals

A) $3$

B) $0$

C) $-3$

D) $1$

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• question_answer109) $\underset{x\to \frac{\pi }{6}}{\mathop{\lim }}\,\frac{\sin 2x}{\sin x}$is equal to

A) $\sqrt{3}$

B) $\frac{1}{\sqrt{3}}$

C) $2$

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

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• question_answer110) The position vectors of three points are $\widehat{\mathbf{i}},\,\,\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}$ and$\widehat{\mathbf{i}}+3\widehat{\mathbf{k}}$. The area of the triangle formed by these three points, is

A) $3\,\,sq\,\,unit$

B) $3\sqrt{3}sq\,\,unit$

C) $4\,\,sq\,\,unit$

D) $5\,\,sq\,\,unit$

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• question_answer111) $\int_{0}^{\pi /3}{\frac{\cos x+\sin x}{\sqrt{1+\sin 2x}}}dx$is equal to

A) $\frac{4\pi }{3}$

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

C) $\pi$

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

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• question_answer112) If $x,\,\,\,y$ are any two elements of a Boolean lattice, then $(x+y)\cdot (x+y')\cdot (x'+y)$ is equal to

A) $x+y$

B) $x\cdot y$

C) $x'+y$

D) $x\cdot y'$

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• question_answer113) Area of quadrilateral whose vertices are $(2,\,\,3)$ $(3,\,\,4),\,\,(4,\,\,5)$ and $(5,\,\,6)$ is equal to

A) $0$

B) $4$

C) $6$

D) none of these

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• question_answer114) In a triangle vertex angles are $A,\,\,\,B,\,\,\,C$ and side $BC$ are given. The area of $\Delta ABC$ is

A) $\frac{s(s-a)(s-b)(s-c)}{2}$

B) $\frac{{{b}^{2}}{{\sin }^{2}}\sin A}{\sin B}$

C) $ab\sin C$

D) $\frac{1}{2}\frac{{{a}^{2}}\sin B\sin C}{\sin A}$

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• question_answer115) $f(x)=\sin |x|$. Then $f(x)$ is not differentiable at

A) $x=0$ only

B) all$x$

C) multiples of$\pi$

D) multiples of$\frac{\pi }{2}$

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• question_answer116) Which of the following is a logical statement?

A) Are you going to chennai?

B) Shyam is a handsome boy.

C) Alas ! I were a king.

D) Sum of two irrational number is always irrational.

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• question_answer117) For a given integer$k$, in the interval $\left[ 2\pi k-\frac{\pi }{2},\,\,2\pi k+\frac{\pi }{2} \right]$the graph of $\sin x$ is

A) increasing from $-1$ to $1$

B) decreasing from $-1$ to $0$

C) decreasing from $0$ to $1$

D) none of the above

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• question_answer118) Coefficient of the term independent of $x$ in the expansion ${{\left( x+\frac{1}{{{x}^{2}}} \right)}^{6}}$ is equal to

A) 10

B) 15

C) 16

D) none of these

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• question_answer119) A particle starts from rest with uniform acceleration and acquires a velocity of $40\,\,m/s$ in$10\,\,s$. The displacement of the particle at the end of $10\,\,s$ is

A) $4\,\,m$

B) $200\,\,m$

C) $20\,\,m$

D) none of these

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• question_answer120) If$P(A)=P(B)=P(C)=\frac{1}{4},$ $P(AB)=P(CB)=0$and$P(A\cap C)=\frac{1}{8}$, then $P(A+B)$ is equal to

A) $\frac{5}{8}$

B) $\frac{37}{64}$

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

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

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• question_answer121) Angles $A,\,\,\,B$ and $C$ of a triangle are in $AP$ with common difference $15$ degree, then angle $A$ is equal to

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

B) ${{60}^{o}}$

C) ${{75}^{o}}$

D) ${{30}^{o}}$

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• question_answer122) Length of major axis of ellipse $9{{x}^{2}}+7{{y}^{2}}=63$ is

A) $3$

B) $9$

C) $6$

D) $2\sqrt{7}$

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• question_answer123) Area between curves$y={{x}^{2}},\,\,x={{y}^{2}}$is

A) $\frac{1}{9}sq\,\,unit$

B) $\frac{1}{3}sq\,\,unit$

C) $\frac{1}{\sqrt{3}}sq\,\,unit$

D) $\frac{2}{3}sq\,\,unit$

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• question_answer124) $\int{\log 2x\,\,dx}$is equal to

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

B) $x\log 2x-\frac{x}{2}+c$

C) ${{x}^{2}}\log 2x-\frac{x}{2}+c$

D) $x\log 2x-x+c$

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• question_answer125) $f(x)=\frac{1}{{{x}^{2}}}$,is

A) symmetric about $x-$axis

B) symmetric about $y-$axis

C) symmetric about $x$ and $y$ axes

D) none of the above

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• question_answer126) $1,\,\,\,2,\,\,\,3,\,\,\,4$ are four numbers. How many numbers can be made using all four numbers

A) $1$

B) $3$

C) $2$

D) $64$

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• question_answer127) $f(x)=\left\{ \begin{matrix} \frac{\sin 3x}{\sin x}, & x\ne 0 \\ k, & x=0 \\ \end{matrix} \right.$is continuous, if$k$is

A) $3$

B) $0$

C) $-3$

D) $-1$

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• question_answer128) If$y={{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)$, then$y'(0)$is

A) $1/2$

B) $0$

C) $1$

D) does not exist

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• question_answer129) The slope of the tangent at the point $(h,\,\,h)$ to the circle ${{x}^{2}}+{{y}^{2}}={{a}^{2}}$ is

A) $0$

B) $1$

C) $-1$

D) will depend on$h$

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• question_answer130) If$A=\left[ \begin{matrix} 0 & 1 \\ 0 & 0 \\ \end{matrix} \right],\,\,\,I$is the unit matrix of order$2$ and $a,\,\,\,b$are arbitary constants, then ${{(aI+bA)}^{2}}$ is equal to

A) ${{a}^{2}}I-abA$

B) ${{a}^{2}}I+2abA$

C) ${{a}^{2}}I+{{b}^{2}}A$

D) none of these

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• question_answer131) The value of$\tan {{1}^{o}}\tan {{2}^{o}}\tan {{3}^{o}}....tan{{89}^{o}}$is equal to

A) $-1$

B) $2$

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

D) $1$

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• question_answer132) Let $\alpha$ and $\beta$ be the roots of the equation ${{x}^{2}}+x+1=0$, then the equation whose roots are ${{\alpha }^{19}},\,\,{{\beta }^{7}}$, is

A) ${{x}^{2}}-x-1=0$

B) ${{x}^{2}}-x+1=0$

C) ${{x}^{2}}+x-1=0$

D) ${{x}^{2}}+x+1=0$

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• question_answer133) If sum of two unit vectors is also an unit vector, then the angle between the two vectors is

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

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

C) $\frac{\pi }{4}$

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

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• question_answer134) Distance from the point $(1,\,\,6,\,\,3)$ to the line $\overset{\to }{\mathop{\mathbf{r}}}\,=(\widehat{\mathbf{j}}+2\widehat{\mathbf{k}})+\lambda (\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}+3\widehat{\mathbf{k}})$is

A) $\sqrt{13}$

B) $13$

C) $2\sqrt{3}$

D) none of these

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• question_answer135) The value of $\int_{-\pi }^{\pi }{(1-{{x}^{2}})}\sin x{{\cos }^{2}}x\,\,\,dx$is

A) $0$

B) $\pi -\frac{{{\pi }^{3}}}{3}$

C) $2\pi -{{\pi }^{3}}$

D) $\frac{7}{2}-2{{\pi }^{3}}$

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• question_answer136) The equation of circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length$3a$, is

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

B) ${{x}^{2}}+{{y}^{2}}=16{{a}^{2}}$

C) ${{x}^{2}}+{{y}^{2}}=16{{a}^{2}}$

D) ${{x}^{2}}+{{y}^{2}}={{a}^{2}}$

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• question_answer137) The angle between the pair of tangents drawn to the ellipse $3{{x}^{2}}+2{{y}^{2}}=5$ from the point $(1,\,\,2)$ is

A) ${{\tan }^{-1}}\left( \frac{12}{5} \right)$

B) ${{\tan }^{-1}}(6\sqrt{5})$

C) ${{\tan }^{-1}}\left( \frac{12}{\sqrt{5}} \right)$

D) ${{\tan }^{-1}}(12\sqrt{5})$

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• question_answer138) The values of $x$ and $y$ such that $y$ satisfy the equation $(x,\,\,\,y\,\,\,\in$ real numbers)${{x}^{2}}-xy+{{y}^{2}}-4x-4y+16=0$is

A) $4,\,\,4$

B) $3,\,\,3$

C) $2,\,\,2$

D) none of these

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• question_answer139) The complex number $z=x+iy$ which satisfy the equation $\left| \frac{z-5i}{z+5i} \right|=1$ lies on

A) the axis of$x$

B) the straight line$y=5$

C) the circle passing through the origin

D) none of the above

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• question_answer140) $\left( 1+\cos \frac{\pi }{8} \right)\left( 1+\cos \frac{3\pi }{8} \right)\left( 1+\cos \frac{5\pi }{8} \right)$$\left( 1+\cos \frac{7\pi }{8} \right)$is equal to

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

B) $\cos \frac{\pi }{8}$

C) $\frac{1}{8}$

D) $\frac{1+\sqrt{2}}{2\sqrt{2}}$

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• question_answer141) If $a\le 0$, then one of the roots of${{x}^{2}}-2a|x-a|-3{{a}^{2}}=0$is

A) $(-1+\sqrt{6})a$

B) b)$(\sqrt{6}-1)a$

C) $a$

D) none of these

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• question_answer142) If the radius of the circumcircle of an isosceles triangle $PQR$ is equal to$PQ=PR$, then the angle $P$ is

A) $\frac{\pi }{6}$

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

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

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

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• question_answer143) If${{z}_{r}}=\cos \left( \frac{\pi }{{{2}^{r}}} \right)+i\sin \left( \frac{\pi }{{{2}^{r}}} \right),\,\,r=1,\,\,2,\,\,....$then${{z}_{1}},\,\,{{z}_{2}},\,\,{{z}_{3}}....$is equal to

A) $1$

B) $-i$

C) $i$

D) $-1$

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• question_answer144) The condition for which${{a}^{2}}{{x}^{4}}+b{{x}^{3}}+c{{x}^{2}}+dx+{{f}^{2}}$may be a perfect square, is

A) $4{{a}^{2}}c-{{b}^{2}}=8{{a}^{3}}f$

B) $4{{a}^{2}}c=8{{a}^{3}}f$

C) $2{{a}^{3}}c={{a}^{3}}f$

D) none of these

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• question_answer145) If$\tan (\cot x)=\cot (\tan x)$, then$\sin 2x$is equal to

A) $\frac{2}{(2n+1)\pi }$

B) $\frac{2}{(2n+1)\pi }$

C) $\frac{2}{n(n+1)\pi }$

D) $\frac{4}{n(n+1)\pi }$

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• question_answer146) Let$a,\,\,b,\,\,c$be real, if$a{{x}^{2}}+bx+c=0$has two real roots $\alpha$ and $\beta$, where$\alpha <-2$and$\beta >2$, then

A) $4-\frac{2b}{a}+\frac{c}{a}<0$

B) $4+\frac{2b}{a}-\frac{c}{a}<0$

C) $4-\frac{2b}{a}+\frac{c}{a}=0$

D) $4+\frac{2b}{a}+\frac{c}{a}=0$

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• question_answer147) The maximum value of ${{x}^{3}}-3x$ in the interval $[0,\,\,2]$ is

A) $-2$

B) $0$

C) $2$

D) $1$

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• question_answer148) $y$ intercept of line passes through $(2,\,\,2)$ and is perpendicular to the line$3x+y=3$, is

A) $\frac{1}{3}$

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

C) $1$

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

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• question_answer149) If $\alpha ,\,\,\beta ,\,\,\gamma$ be the angles which a line makes with the co-ordinates axes, then

A) ${{\sin }^{2}}\alpha +{{\cos }^{2}}\beta +{{\sin }^{2}}\gamma =1$

B) ${{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma =1$

C) ${{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1$

D) ${{\cos }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma =1$

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• question_answer150) The value of $x$ satisfying${{\sin }^{-1}}x+{{\sin }^{-1}}(1-x)={{\cos }^{-1}}x$ are

A) $0$

B) $1,\,\,-1$

C) $0,\,\,\frac{1}{2}$

D) none of these

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