# Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2010

### done JCECE Engineering Solved Paper-2010

• question_answer1) At what angle must the two forces $(x+y)$ and $(x-y)$act so that the resultant may be

A) ${{\cos }^{-1}}\left[ -\frac{{{x}^{2}}+{{y}^{2}}}{2({{x}^{2}}-{{y}^{2}})} \right]$

B) ${{\cos }^{-1}}\left[ \frac{-2({{x}^{2}}-{{y}^{2}})}{{{x}^{2}}+{{y}^{2}}} \right]$

C) ${{\cos }^{-1}}\left[ -\frac{({{x}^{2}}+{{y}^{2}})}{({{x}^{2}}-{{y}^{2}})} \right]$

D) ${{\cos }^{-1}}\left[ -\frac{({{x}^{2}}-{{y}^{2}})}{({{x}^{2}}+{{y}^{2}})} \right]$

• question_answer2) A body starts from rest with uniform acceleration. If its velocity after n second is$v$, then its displacement in the last $2\,\,s$ is

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

B) $\frac{v(n+1)}{n}$

C) $\frac{v(n-1)}{n}$

D) $\frac{2v(n-1)}{n}$

• question_answer3) A wheel completes $2000$ revolutions to cover the $9.5\,\,km$ distance, then the diameter of the wheel is

A) $1.5\,\,m$

B) $1.5\,\,cm$

C) $7.5\,\,cm$

D) $7.5\,\,m$

• question_answer4) A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is

A) same everywhere

B) lower in front side

C) lower in rear side

D) lower in upper side

• question_answer5) A block $A$ weighing $100\,\,kg$ rests on a block $B$ and is tied with a horizontal string to the wall at$C$. Block $B$ weighs$200\,\,kg$. The coefficient of friction between $A$ and $B$ is $0.25$ and between $B$ and the surface is$\frac{1}{3}$. The horizontal force $P$ necessary to move the block $B$ should be$(g=10\,\,m/{{s}^{2}})$

A) $1150\,\,N$

B) $1250\,\,N$

C) $1300\,\,N$

D) $1420\,\,N$

• question_answer6) A boy and a man carry a uniform rod of length$L$, horizontally in such a way that boy gets $\frac{1}{4}th$ load. If the boy is at one end of the rod, the distance of the man from the other end is

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

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

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

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

• question_answer7) Two capillary of lengths $L$ and $2L$ and of radii $R$ and $2R$ are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary,$X=\frac{\pi p{{R}^{4}}}{8\eta L})$

A) $\frac{8}{9}X$

B) $\frac{9}{8}X$

C) $\frac{5}{7}X$

D) $\frac{7}{5}X$

• question_answer8) The molecules of a given mass of a gas have a $\text{rms}$ velocity of $200\,\,m/s$ at ${{27}^{o}}C$ and $1.0\times {{10}^{5}}\,\,N/{{m}^{2}}$ pressure. When the temperature is ${{127}^{o}}C$ and pressure is $0.5\times {{10}^{5}}N/{{m}^{2}}$, the $\text{rms}$ velocity in $m/s$ will

A) $\frac{100\sqrt{2}}{3}$

B) $100\sqrt{2}$

C) $\frac{400}{\sqrt{3}}$

D) None of these

• question_answer9) $3\,\,A$ of current is flowing in a linear conductor having a length of$40\,\,cm$. The conductor is placed in a magnetic field of strength $500$ gauss and makes an angle of ${{30}^{o}}$ with direction of the field. It experiences a force of magnitude

A) $3\times {{10}^{4}}N$

B) $3\times {{10}^{2}}N$

C) $3\times {{10}^{-2}}N$

D) $3\times {{10}^{-4}}N$

• question_answer10) A $50$ turn?s Circular coil has a radius of$3\,\,cm$, it is kept in a magnetic field acting normal to the area of the coil. The magnetic field $B$ increased from $0.10\,\,T$ to $0.35\,\,T$ in $2$ millisecond. The average induced $\text{emf}$ in the coil is

A) $1.77\,\,V$

B) $17.7\,\,V$

C) $177\,\,V$

D) $0.177\,\,V$

• question_answer11) In the circuit .shown in figure neglecting source resistance, the voltmeter and ammeter readings will be respectively

A) $0\,\,V,\,\,3\,\,A$

B) $150\,\,V,\,\,3\,\,A$

C) $150\,\,V,\,\,6\,\,A$

D) $0\,\,V,\,\,8\,\,A$

• question_answer12) Photon and electron are given energy$({{10}^{-2}}J)$. Wavelengths associated with photon and electron are ${{\lambda }_{ph}}$ and ${{\lambda }_{el}}$ then, correct statement will be

A) ${{\lambda }_{ph}}>{{\lambda }_{el}}$

B) ${{\lambda }_{ph}}<{{\lambda }_{el}}$

C) ${{\lambda }_{ph}}={{\lambda }_{el}}$

D) $\frac{{{\lambda }_{el}}}{{{\lambda }_{ph}}}=c$

• question_answer13) The wavelength of radiation emitted is${{\lambda }_{0}}$when an electron jumps from the third to the second orbit of hydrogen atom. For the electron jump from the fourth to the second orbit of hydrogen atom, the wavelength of radiation emitted will be

A) $\frac{16}{25}{{\lambda }_{0}}$

B) $\frac{20}{27}{{\lambda }_{0}}$

C) $\frac{27}{20}{{\lambda }_{0}}$

D) $\frac{25}{16}{{\lambda }_{0}}$

• question_answer14) Radius of $_{2}H{{e}^{4}}$ nucleus is $3$ fermi. The radius of $_{82}P{{b}^{206}}$ nucleus will be

A) $5$fermi

B) $6$Fermi

C) $11.16$ fermi

D) $8$ Fermi

• question_answer15) The contribution in the total current flowing through a semiconductor due to electrons and holes are $\frac{3}{4}$ and $\frac{1}{4}$ respectively. If the drift velocity of electrons is $\frac{5}{2}$ times that of holes at this temperature, then the ratio of concentration of electrons and holes is

A) $6:5$

B) $5:6$

C) $3:2$

D) $2:3$

• question_answer16) The attenuation in optical fibre is mainly due to

A) absorption

B) scattering

C) Neither absorption nor scattering

D) Both [a] and [b]

• question_answer17) An astronomical telescope has an angular magnification of magnitude $5$ for distant objects. The separation between the objective and the eye-piece is $36\,\,cm$ and the final image is formed at infinity. The focal length ${{f}_{o}}$ of the objective and the focal length ${{f}_{e}}$ of the eye-piece are

A) ${{f}_{o}}=45\,\,cm$and${{f}_{e}}=-9\,\,cm$

B) ${{f}_{o}}=-7.2\,\,cm$and${{f}_{e}}=5\,\,cm$

C) ${{f}_{o}}=50\,\,cm$and${{f}_{e}}=10\,\,cm$

D) ${{f}_{o}}=30\,\,cm$and${{f}_{e}}=6\,\,cm$

• question_answer18) A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of incident beam. At the first maximum of the diffraction pattern, the phase difference between the rays coming from the edges of the slit is

A) $0$

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

C) $\pi$

D) $2\pi$

• question_answer19) When the angle of incidence on a material is${{60}^{o}}$, the reflected light is completely polarized. The velocity of the refracted ray inside the material is (in$m{{s}^{-1}})$

A) $3\times {{10}^{8}}$

B) $\left[ \frac{3}{\sqrt{2}} \right]\times {{10}^{8}}$

C) $\sqrt{3}\times {{10}^{8}}$

D) $0.5\times {{10}^{8}}$

• question_answer20) Which of the following shows greenhouse effect?

A) Ultraviolet rays

B) Infrared rays

C) X-rays

D) None of these

• question_answer21) In Rutherford scattering experiment, what will be the correct angle for a scattering for an impact parameter$b=0$?

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

B) ${{270}^{o}}$

C) ${{0}^{o}}$

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

• question_answer22) A person sees his virtual image by holding a mirror very close to the face. When he moves the mirror away from his face, the image becomes inverted. What type of mirror he is using?

A) Plane mirror

B) Convex mirror

C) Concave mirror

D) None of these

• question_answer23) If a charged spherical conductor of radius $10\,\,cm$ has potential $V$ at a point distant $5\,\,cm$ from its centre, then the potential at a point distant $15\,\,cm$ from the centre will be

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

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

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

D) $3V$

• question_answer24) The equation of state of some gases can be expressed as$\left( p+\frac{a}{{{V}^{2}}} \right)(V-b)=RT$where, $p$ is the pressure, $V$ the volume, $T$ the absolute temperature and $a$ and $b$ are constants. The dimensional formula of $a$ is

A) $[M{{L}^{5}}{{T}^{-2}}]$

B) $[{{M}^{-1}}{{L}^{5}}{{T}^{-2}}]$

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

D) $[M{{L}^{-5}}{{T}^{-2}}]$

• question_answer25) A $16\,\,kg$ block moving on a frictionless horizontal surface with a velocity of $4\,\,m/s$ compresses an ideal spring and comes to rest. If the force constant of the spring be $100\,\,N/m,$ then the spring is compressed by

A) $1.6\,\,m$

B) $4\,\,m$

C) $6.1\,\,m$

D) $3.2\,\,m$

• question_answer26) A mass of $6\times {{10}^{24}}kg$ is to be compressed in a sphere in such a way that the escape velocity from the sphere is$3\times {{10}^{8}}m/s$. What should be the radius of the sphere?$(G=6.67\times {{10}^{-11}}N-{{m}^{2}}/k{{g}^{2}})$

A) $9\,\,km$

B) $9\,\,m$

C) $9\,\,cm$

D) $9\,\,mm$

• question_answer27) A wire of length $L$ and radius $r$ fixed at one end and a force $F$ applied to the other end produces an extension$l$. The extension produced in another wire of the same material of length $2L$ and radius $2r$ by a force$2F$, is

A) $l$

B) $2l$

C) $4l$

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

• question_answer28) Two trains are moving towards each other with speeds of $20\,\,m/s$ and $15\,\,m/s$ relative to the ground. The first train, sounds a whistle of frequency$600\,\,Hz$, the frequency of the whistle heard by a passenger in the second train before the train meets is (the speed of sound in air is$340\,\,m/s)$

A) $600\,\,Hz$

B) $585\,\,Hz$

C) $645\,\,Hz$

D) $666\,\,hz$

• question_answer29) Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is$25$. The intensities of the sources are in the ratio

A) $25:1$

B) $5:1$

C) $9:4$

D) $25:16$

• question_answer30) A microscope is focussed on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index $1.5$ is placed over a mark. How should the microscope be moved to get the mark again in focus?

A) $1\,\,cm$upward

B) $4.5\,\,cm$downward

C) $1\,\,cm$downward

D) $2\,\,cm$upward

• question_answer31) A thin lens made of glass of refractive index $\mu =1.5$ has a focal length equals to $12\,\,cm$ in air. It is now immersed in water$\left( \mu =\frac{4}{3} \right)$. Its new focal length is

A) $48\,\,cm$

B) $36\,\,cm$

C) $24\,\,cm$

D) $12\,\,cm$

• question_answer32) Air is pumped into an automobile tube upto a pressure of $200\,\,kPa$ in the morning when the air temperature is${{22}^{o}}C$. During the day, temperature rises to ${{42}^{o}}C$ and the tube expands by$2%$. The pressure of the air in the tube at this temperature, will be approximately

A) $212\,\,kPa$

B) $209\,\,kPa$

C) $206\,\,kPa$

D) $200\,\,kPa$

• question_answer33) A radioactive material decays by simultaneous emission of two particles with half-lives $1620\,\,yr$ and $810\,\,yr$ respectively. The time in year after which one-fourth of the material remains, is

A) $4860\,\,yr$

B) $3240\,\,yr$

C) $2340\,\,yr$

D) $1080\,\,yr$

• question_answer34) A stone dropped from a balloon which is at a height$h$, reaches the ground after $t$ second. From the same balloon, if two stones are thrown, one upwards and the other downwards, with the same velocity u and they reach the ground after ${{t}_{1}}$ and ${{t}_{2}}$ second respectively, then

A) $t={{t}_{1}}-{{t}_{2}}$

B) $t=\frac{{{t}_{1}}+{{t}_{2}}}{2}$

C) $t=\sqrt{{{t}_{1}}{{t}_{2}}}$

D) $t=\sqrt{t_{1}^{2}-t_{2}^{2}}$

• question_answer35) A shell at rest at the origin explodes into three fragments of masses $1\,kg,\,\,2\,kg$ and$m\,\,kg$. The $2\,\,kg$$\text{and}$$1\,\,kg$ pieces fly off with speeds of $12\,\,m/s$ along x-axis and $16\,\,m/s$ along y-axis respectively. If the $m\,\,kg$ piece flies off with a speed of$40\,\,m/s$, the total mass of the shell must be

A) $3.7\,\,kg$

B) $4\,\,kg$

C) $4.5\,\,kg$

D) $5\,\,kg$

• question_answer36) If a sphere is rolling, then the ratio of its rotational kinetic energy to the total kinetic energy is

A) $3.7\,\,kg$

B) $4\,\,kg$

C) $4.5\,\,kg$

D) $5\,\,kg$

• question_answer37) A body weighs w newton at the surface of the earth. Its weight at a height equals to half the radius of the earth, will be

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

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

C) $\frac{4w}{9}$

D) $\frac{8w}{27}$

• question_answer38) Apart of a long wire carrying a current $i$ is bent into a circle of radius $r$ as shown in figure. The net magnetic field at the centre $O$ of the circular loop is

A) $\frac{{{\mu }_{0}}I}{4r}$

B) $\frac{{{\mu }_{0}}I}{2r}$

C) $\frac{{{\mu }_{0}}I}{2\pi r}(\pi +1)$

D) $\frac{{{\mu }_{0}}I}{2\pi r}(\pi -1)$

• question_answer39) A $36\Omega$ galvanometer is shunted by resistance of$4\Omega$. The percentage of the total current, which passes through the galvanometer is

A) $8%$

B) $9%$

C) $10%$

D) $91%$

• question_answer40) A can filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. The time period for a revolution is about

A) $2\,\,s$

B) $4\,\,s$

C) $8\,\,s$

D) $10\,\,s$

• question_answer41) The centre of mass of three particles of masses $1\,\,kg,\,\,2\,\,kg$ and $3\,\,kg$ is at $(3,\,\,3,\,\,3)$ with reference to a fixed coordinate system. Where should a fourth particle of mass $4\,\,kg$ be placed, so that the centre of mass of the system of all particles shifts to a point$(1,\,\,1,\,\,1)?$

A) $(-1,\,\,-1,\,\,-1)$

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

C) $(2,\,\,2,\,\,2)$

D) $(1,\,\,1,\,\,1)$

• question_answer42) A pulley fixed to the ceiling carries a string with blocks of masses $m$ and $3m$ attached to its ends. The masses of string and pulley are negligible. When the system is released, the acceleration of centre of mass will be

A) $zero$

B) $-\frac{g}{4}$

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

D) $-\frac{g}{2}$

• question_answer43) A ray $PQ$ incident on the refracting face $BA$ is refracted in the prism $BAC$ as shown in the figure and emerges from the other refracting face $AC$ as$RS$, such that$AQ=AR$. If the angle of prism $A={{60}^{o}}$ and the refractive index of the material of prism is$\sqrt{3}$, then the angle of deviation of the ray is

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

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

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

D) None of these

• question_answer44) To get an output 1 from the circuit shown in the figure, the input must be

A) $A=0,\,\,B=1,\,\,C=0$

B) $A=1,\,\,B=0,\,\,C=0$

C) $A=1,\,\,B=0,\,\,C=1$

D) $A=1,\,\,B=1,\,\,C=0$

• question_answer45) Minimum number of $8\mu F$ and $250\,\,V$ capacitors are used to make a combination of $16\mu F$ and $1000\,\,V$ are

A) $4$

B) $32$

C) $8$

D) $3$

• question_answer46) Let ${{E}_{a}}$ be the electric field due to a dipole in its axial plane distant $l$ and let ${{E}_{q}}$ be the field in the equatorial plane distant$l'$, then the relation between ${{E}_{a}}$ and ${{E}_{q}}$ will be

A) ${{E}_{a}}=4{{E}_{q}}$

B) ${{E}_{q}}=2{{E}_{a}}$

C) ${{E}_{a}}=2{{E}_{q}}$

D) ${{E}_{q}}=3{{E}_{a}}$

• question_answer47) The current in the given circuit is-

A) $0.3\,\,A$

B) $0.4\,\,A$

C) $0.1\,\,A$

D) $0.2\,\,A$

• question_answer48) In the circuit shown below what will be the readings of the voltmeter and ammeter? (Total impedance of circuit$Z=100\Omega )$

A) $200\,\,V,\,\,1\,\,A$

B) $800\,\,V,\,\,2\,\,A$

C) $100\,\,V,\,\,2\,\,A$

D) $220\,\,V,\,\,2.2\,\,A$

• question_answer49) A ball of mass $10\,\,kg$ is moving with a velocity of$10\,\,m/s$. It strikes another ball of mass$5\,\,kg$, which is moving in the same direction with a velocity of$4\,\,m/s$. If the collision is elastic, then their velocities after collision will be respectively

A) $12\,\,m/s,\,\,6\,\,m/s$

B) $12\,\,m/s,\,\,25\,\,m/s$

C) $6\,\,m/s,\,\,12\,\,m/s$

D) $8\,\,m/s,\,\,20\,\,m/s$

• question_answer50) A hole is made at the bottom of the tank filled with water (density$1000kg/{{m}^{3}})$. If the total pressure at the bottom of the tank is $3$ atmosphere (1 atmosphere$=105N/{{m}^{2}})$, then the velocity of efflux is

A) $\sqrt{200}m/s$

B) $\sqrt{400}m/s$

C) $\sqrt{500}m/s$

D) $\sqrt{800}m/s$

• question_answer51) The $As{{F}_{5}}$ molecule is trigonal bipyramidal. The hybrid orbitals used by the $As$ atoms, for bonding are

A) ${{d}_{{{x}^{2}}-{{y}^{2}}}},\,\,{{d}_{{{z}^{2}}}},\,\,s,\,\,{{p}_{x}},\,\,{{p}_{y}}$

B) ${{d}_{xy}},\,\,s,\,\,{{p}_{x}},\,\,{{p}_{y}},\,\,{{p}_{z}}$

C) $s,\,\,{{p}_{x}},\,\,{{p}_{y}},\,\,{{p}_{z}},\,\,{{d}_{{{z}^{2}}}}$

D) ${{d}_{{{x}^{2}}-{{y}^{2}}}},\,\,s,\,\,{{p}_{x}},\,\,{{p}_{y}}$

• question_answer52) The low density of ice compared to water is due to

A) induced dipole-induced dipole interactions

B) dipole-induced dipole interactions

C) hydrogen bonding interactions

D) dipole-dipole interactions

A) ${{B}_{3}}{{H}_{3}}{{N}_{3}}$

B) $B{{H}_{3}}N{{H}_{3}}$

C) ${{B}_{3}}{{H}_{6}}{{N}_{3}}$

D) ${{H}_{3}}{{B}_{3}}{{N}_{6}}$

• question_answer54) Which of the following compounds will show metamerism?

A) $C{{H}_{3}}-CO-{{C}_{2}}{{H}_{5}}$

B) ${{C}_{2}}{{H}_{5}}-S-{{C}_{2}}{{H}_{5}}$

C) $C{{H}_{3}}-O-C{{H}_{3}}$

D) $C{{H}_{3}}-O-{{C}_{2}}{{H}_{5}}$

• question_answer55) Benzene on treatment with a mixture of conc. $HN{{O}_{3}}$ and conc. ${{H}_{2}}S{{O}_{4}}$at ${{100}^{o}}C$ gives

A) nitrobenzene

B) $m-$dinitrobenzene

C) $p-$dinitrobenzene

D) $o-$dinitrobenzene

• question_answer56) $0.765\,\,g$ of an acid gives $0.535\,\,g$ of $C{{O}_{2}}$ and $0.138\,\,g$ of. Then, the ratio of the percentage of carbon and hydrogen is

A) $19:2$

B) $18:11$

C) $20:17$

D) $1:7$

A) ${{(P{{h}_{3}}P)}_{3}}RhCl$

B) $K[PtC{{l}_{3}}({{C}_{2}}{{H}_{4}})]$

C) $[A{{l}_{2}}{{({{C}_{2}}{{H}_{6}})}_{6}}+TiC{{l}_{4}}]$

D) $[Fe{{({{C}_{2}}{{H}_{5}})}_{2}}]$

• question_answer58) $1\,\,L$ oxygen gas at $STP$ will weigh

A) $1.43\,\,g$

B) $2.24\,\,g$

C) $11.2\,\,g$

D) $22.4\,\,g$

• question_answer59) The $IUPAC$ name of the compound,${{C}_{2}}{{H}_{5}}-\underset{\begin{smallmatrix} || \\ C{{H}_{2}} \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}OH$is

A) 2-ethylprop-2-en-1-ol

B) 2-hydroxymethylbutan-1-ol

C) 2-methylenebutan-1-pl

D) 2-ethyl-3-hydroxyprop-1-ene

• question_answer60) The chemical name of vitamin ${{B}_{1}}$ is

A) ascorbic acid

B) riboflavin

C) pyridoxine

D) thiamine

• question_answer61) Glyptal polymer is obtained from glycol by reacting with

A) malonic acid

B) phthalic acid

C) maleic acid

D) terephthalic acid

• question_answer62) Molecular formula of Glauber's salt is

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

B) $CuS{{O}_{4}}\cdot 5{{H}_{2}}O$

C) $FeS{{O}_{4}}\cdot 7{{H}_{2}}O$

D) $N{{a}_{2}}S{{O}_{4}}\cdot 10{{H}_{2}}O$

• question_answer63) The size of colloidal particles is in between

A) ${{10}^{-7}}-{{10}^{-9}}cm$

B) ${{10}^{-9}}-{{10}^{-11}}cm$

C) ${{10}^{-5}}-{{10}^{-7}}cm$

D) ${{10}^{-2}}-{{10}^{-3}}cm$

• question_answer64) In the reaction,$S{{O}_{2}}+2{{H}_{2}}S\xrightarrow{{}}3S+2{{H}_{2}}O$ the substance oxidised is

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

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

C) $S$

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

• question_answer65) The emf of the cell$Ni|N{{i}^{2+}}(1.0\,\,M)||A{{u}^{3+}}(1.0\,\,M)|Au$is$[{{E}^{o}}(N{{i}^{2+}}/Ni)=-0.25\,\,V$and$(A{{u}^{3+}}/Au)=+1.5\,\,V]$

A) $2.00\,\,V$

B) $1.25\,\,V$

C) $-1.25\,\,V$

D) $1.75\,\,V$

• question_answer66) The heat of neutralisation is highest for the reaction between

A) $N{{H}_{4}}OH-C{{H}_{3}}COOH$

B) $HN{{O}_{3}}-N{{H}_{4}}OH$

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

D) $HCl-NaOH$

• question_answer67) An ideal gas expands in volume from $1\times {{10}^{-3}}{{m}^{3}}$to$1\times {{10}^{-2}}{{m}^{3}}$at $300\,\,K$ against a constant pressure of$1\times {{10}^{5}}N{{m}^{-2}}$. The work done is

A) $-900\,\,J$

B) $-900\,\,kJ$

C) $270\,\,kJ$

D) $900\,\,kJ$

• question_answer68) Which one of the following is correct?

A) $-\Delta G=\Delta H-T\Delta S$

B) $\Delta H=\Delta G-T\Delta S$

C) $\Delta S=\frac{1}{T}[\Delta G-\Delta H]$

D) $\Delta S=\frac{1}{T}[\Delta H-\Delta G]$

• question_answer69) The electronic configuration of element with atomic number $24$ is

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

B) $1{{s}^{2}},\,\,2{{s}^{2}}2{{p}^{6}},\,\,3{{s}^{2}}3{{p}^{6}}3{{d}^{10}}$

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

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

• question_answer70) In van der Waals' equation, of state of the gas law, the constant $'b'$ is a measure of

A) intermolecular repulsions

B) intermolecular attraction

C) volume occupied by the molecules

D) intermolecular collisions per unit volume

• question_answer71) If the radius of ${{K}^{+}}$and${{F}^{-}}$ are $133\,\,pm$ and $136\,\,pm$ respectively, the distance between ${{K}^{+}}$and ${{F}^{-}}$in $KF$ is

A) $269\,\,pm$

B) $134.5\,\,pm$

C) $136\,\,pm$

D) $3\,\,pm$

• question_answer72) The property of attracting electrons by the halogen atoms in a molecule is called

A) ionization potential

B) electron affinity

C) electronegativity

D) electronic attraction

• question_answer73) A reversible chemical reaction is having two reactants, in equilibrium. If the concentration of the reactants are doubled then the equilibrium constant will

A) be doubled

B) become one fourth

C) be halved

D) remain the same

• question_answer74) The strongest Bronsted base is

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

B) $ClO_{2}^{-}$

C) $ClO_{4}^{-}$

D) $Cl{{O}^{-}}$

• question_answer75) A solution contains $10\,\,mL$ $0.1\,\,N\,\,NaOH$ and NH$10\,\,mL\,\,0.05\,\,N\,\,{{H}_{2}}S{{O}_{4}}$, $pH$ of this solution is

A) less than$7$

B) $7$

C) zero

D) greater than$7$

• question_answer76) For which one of the following reactions${{K}_{p}}={{K}_{c}}$?

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

B) ${{N}_{2}}+{{O}_{2}}2NO$

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

D) $2S{{O}_{3}}2S{{O}_{2}}+{{O}_{2}}$

• question_answer77) What is the molarity of $0.2\,\,N\,\,N{{a}_{2}}C{{O}_{3}}$ solution?

A) $0.1\,\,M$

B) $0\,\,M$

C) $0.4\,\,M$

D) $0.2\,\,M$

• question_answer78) The order of a reaction with rate equal to $kC_{A}^{3/2}C_{B}^{-1/2}$is

A) $1$

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

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

D) $2$

• question_answer79) A simple method to remove peroxides from ethers is to treat them with an aqueous solution of

A) $KI$

B) $KCNS$

C) $N{{a}_{2}}{{S}_{2}}{{O}_{3}}$

D) $B{{r}_{2}}$

• question_answer80) Which of the following is the predominant product in the reaction of $HOBr$ with propene?

A) 2-bromo-1-propanol

B) 3-bromo-1-propanol

C) 2-bromo-2-propanol

D) 1-bromo-2-propanol

• question_answer81) Most stable carbonium ion is

A) ${{\overset{+}{\mathop{C}}\,}_{2}}{{H}_{5}}$

B) ${{(C{{H}_{3}})}_{3}}\overset{+}{\mathop{C}}\,$

C) ${{({{C}_{6}}{{H}_{5}})}_{3}}\overset{+}{\mathop{C}}\,$

D) ${{C}_{6}}{{H}_{5}}\overset{+}{\mathop{C}}\,{{H}_{2}}$

• question_answer82) In aqueous solutions, the basic strength of amines decreases in the order

A) $C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{2}}N{{H}_{2}}>{{(C{{H}_{3}})}_{3}}N$

B) ${{(C{{H}_{3}})}_{2}}NH>{{(C{{H}_{3}})}_{3}}N>C{{H}_{3}}N{{H}_{2}}$

C) ${{(C{{H}_{3}})}_{3}}N>{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}$

D) ${{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{3}}N$

• question_answer83) The most reactive compound towards formation of cyanohydrin on treatment with HCN followed by acidification is

A) benzaldehyde

B) $p-$nitrobenzaldehyde

C) phenylacetaldehyde

D) $p-$hydroxybenzaldehyde

• question_answer84) Producer gas is the mixture of

A) $CO+{{N}_{2}}$

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

C) $CO+$water vapour

D) ${{N}_{2}}+C{{H}_{4}}$

• question_answer85) What is the freezing point of a solution containing $8.1\,\,g\,\,HBr$ in $100\,\,g$ water assuming the acid to be $90%$ ionised? $({{k}_{f}}$ for water$=1.86\,\,K\,\,mo{{l}^{-1}})$

A) ${{0.85}^{o}}C$

B) $-{{3.53}^{o}}C$

C) ${{0}^{o}}C$

D) $-{{0.35}^{o}}C$

• question_answer86) Number of elements presents in the fifth period of Periodic Table is

A) $32$

B) $10$

C) $18$

D) $8$

• question_answer87) ${{[Sc({{H}_{2}}{{O}_{6}})]}^{3+}}$ion is

A) colourless and diamagnetic

B) coloured and octahedral

C) colourless and paramagnetic

D) coloured and paramagnetic

• question_answer88) Which one has the highest boiling point?

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

B) $Xe$

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

D) $He$

• question_answer89) Benzaldehyde reacts with ammonia to form

A) benzaldehyde ammonia

B) urotropine

C) hydrobenzamide

D) ammonium chloride

• question_answer90) Identify $Z$ in the sequence$C{{H}_{3}}COON{{H}_{4}}\xrightarrow{\Delta }X\xrightarrow[\Delta ]{{{P}_{2}}{{O}_{5}}}Y\xrightarrow{{{H}_{2}}O/{{H}^{+}}}Z$

A) $C{{H}_{3}}C{{H}_{2}}CON{{H}_{2}}$

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

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

D) ${{(C{{H}_{3}}CO)}_{2}}O$

• question_answer91) Acetic anhydride reacts with diethyl ether in the presence of anhydrous $AlC{{l}_{3}}$ to give

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

B) $C{{H}_{3}}C{{H}_{2}}COOC{{H}_{2}}C{{H}_{3}}$

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

D) $C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}$

• question_answer92) Denaturation of proteins leads to loss of its biological activity by

A) formation of amino acids

B) loss of primary structure

C) loss of both primary and secondary structures

D) loss of both secondary and tertiary structures

• question_answer93) The compound with highest boiling point

A) n-hexane

B) n-pentane

C) 2, 2-dimethylpropane

D) 2-methylbutane

• question_answer94) Which of the following statements concerning transition elements is false?

A) They are all metals

B) They easily form complex coordination compounds

C) Compounds containing their ions are mostly coloured

D) They show multiple oxidation states always differing by units of two

• question_answer95) In the manufacture of bromine from sea water, the mother liquor containing bromide is treated with

A) carbon dioxide

B) chlorine

C) iodine

D) sulphur dioxide

• question_answer96) A transition element X has the configuration $[Ar]{{d}^{4}}$ in its $+3$ oxidation state. It?s atomic number is

A) $25$

B) $26$

C) $22$

D) $19$

• question_answer97) The element with the electronic configuration as $[Ar]3{{d}^{10}}4{{s}^{2}}4{{p}^{3}}$ represents a

A) metal

B) non-metal

C) metalloid

D) transition element

• question_answer98) The number of moles of${{H}_{2}}$in$0.224$ hydrogen gas at$STP\,\,(273\,\,K,\,\,1\,\,atm)$, is

A) $0.1$

B) $0.01$

C) $0.001$

D) $1$

• question_answer99) The molecule which has zero dipole moment is

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

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

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

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

• question_answer100) Greenhouse effect is caused by

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

B) $CO$

C) $NO$

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

• question_answer101) If$y=\sin x$, then$\frac{{{d}^{2}}}{d{{y}^{2}}}({{\cos }^{7}}x)$is equal to

A) $7{{\cos }^{5}}x+35{{\cos }^{3}}x$

B) $7{{\cos }^{5}}x+35{{\cos }^{2}}x$

C) $-7{{\cos }^{5}}x+35{{\cos }^{2}}x$

D) None of the above

• question_answer102) The equation of ellipse whose axes are coincident with the coordinate axes and which touches the straight lines $3x-2y-20=0$ and$x+6y-20=0$, is

A) $\frac{{{x}^{2}}}{5}+\frac{{{y}^{2}}}{8}=1$

B) $\frac{{{x}^{2}}}{40}+\frac{{{y}^{2}}}{10}=10$

C) $\frac{{{x}^{2}}}{40}+\frac{{{y}^{2}}}{10}=1$

D) $\frac{{{x}^{2}}}{10}+\frac{{{y}^{2}}}{40}=1$

• question_answer103) The equation of the radical axis of the circles $2{{x}^{2}}+2{{y}^{2}}+14x-18y+15=0$and$4{{x}^{2}}+4{{y}^{2}}-3x-y+5=0$, is

A) $31x+35y-25=0$

B) $31x-35y+25=0$

C) $35x+31y-25=0$

D) $35x-31y+25=0$

• question_answer104) SS$\underset{x\to 1}{\mathop{\lim }}\,\frac{1+\log x-x}{1-2x+{{x}^{2}}}$is equal to

A) $1$

B) $-1$

C) $0$

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

• question_answer105) $\int_{0}^{\pi /2}{{{\cos }^{5}}\left( \frac{x}{2} \right)}\sin x\,\,dx$is equal to

A) $\frac{2}{7}\left( 1-\frac{1}{8\sqrt{2}} \right)$

B) $-\frac{4}{7}\left( 1-\frac{1}{8\sqrt{2}} \right)$

C) $\frac{4}{7}\left( 1-\frac{1}{8\sqrt{2}} \right)$

D) $-\frac{2}{7}\left( 1-\frac{1}{8\sqrt{2}} \right)$

• question_answer106) The area of the region bounded by the curve $y=\frac{{{a}^{3}}}{{{x}^{2}}+{{a}^{2}}}$and $x-axis$ is

A) $\pi {{a}^{2}}sq\,\,unit$

B) $2\pi {{a}^{2}}sq\,\,unit$

C) $3\pi {{a}^{2}}sq\,\,unit$

D) None of these

• question_answer107) If the constant forces$2\widehat{\mathbf{i}}-5\widehat{\mathbf{j}}+6\widehat{\mathbf{k}}$and $-\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}-\widehat{\mathbf{k}}$act on a particle due to which it is displaced from a point$A(4,\,\,-3,\,\,-2)$to a point$B(6,\,\,1,\,\,-3)$then the work done by the force is

A) $25\,\,unit$

B) $-15\,\,unit$

C) $9\,\,unit$

D) $-9\,\,unit$

• question_answer108) The equation of the line which passes through the point $(3,\,\,4)$ and the sum of its intercepts on the axes is$14$, is

A) $x+y=7$and$4x+3y=24$

B) $x+y=24$and$4x+3y=7$

C) $x-y=7$and$4x-3y=24$

D) None of the above

• question_answer109) If${{x}^{2}}-x+1=0$, then the value of$\sum\limits_{n=1}^{5}{{{\left( {{x}^{n}}+\frac{1}{{{x}^{n}}} \right)}^{2}}}$is

A) $8$

B) $10$

C) $12$

D) $14$

• question_answer110) Minimum value of${{4}^{x}}-{{4}^{1-x}},\,\,x\in R$is

A) $1$

B) $2$

C) $3$

D) $4$

• question_answer111) If $\alpha ,\,\,\beta$ are the roots of equation$8{{x}^{2}}-3x+27=0$, then the value of${{\left( \frac{{{\alpha }^{2}}}{\beta } \right)}^{1/3}}+{{\left( \frac{{{\beta }^{2}}}{\alpha } \right)}^{1/3}}$is

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

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

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

D) $4$

• question_answer112) There are four candidates for the post of a lecturer in Mathematics and one is to be selected by votes of $5$ men. The number of ways in which the votes can be given is

A) $1048$

B) $1072$

C) $1024$

D) $1064$

• question_answer113) The coefficient of ${{x}^{4}}$ in the expansion of${{(1+x+{{x}^{2}}+{{x}^{3}})}^{11}}$, is

A) $990$

B) $605$

C) $810$

D) None of these

• question_answer114) If the matrix$\left[ \begin{matrix} 0 & 2\beta & \gamma \\ \alpha & \beta & -\gamma \\ \alpha & -\beta & \gamma \\ \end{matrix} \right]$is orthogonal, then

A) $\alpha =\pm \frac{1}{\sqrt{2}}$

B) $\beta =\pm \frac{1}{\sqrt{6}}$

C) $\gamma =\pm \frac{1}{\sqrt{3}}$

D) All of these

• question_answer115) The sum of the series ${{\log }_{4}}2-{{\log }_{8}}2+{{\log }_{16}}2-....\infty$, is

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

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

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

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

• question_answer116) The range of the function$f(x)=\frac{x-2}{2-x}$, when$x\ne 2$is

A) $R$

B) $R-\{1\}$

C) $\{-1\}$

D) $R-\{-1\}$

• question_answer117) If $A$ and $B$ are two independent events such that $P(A)=\frac{1}{2}$ and $P(B)=\frac{1}{5},$ then which of the following is/are correct?

A) $P(A\cup B)=\frac{5}{3}$

B) $P\left( \frac{A}{B} \right)=\frac{1}{3}$

C) $P\left( \frac{A}{A\cup B} \right)=\frac{5}{6}$

D) All of these

• question_answer118) The probability of $A$ to fail in an examination is $\frac{1}{5}$ and that of $B$ is$\frac{3}{10}$, then the probability that either $A$ or $B$ fails is

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

B) $\frac{11}{25}$

C) $\frac{19}{50}$

D) None of these

• question_answer119) The value of $\cos y\cos \left( \frac{\pi }{2}-x \right)-\cos \left( \frac{\pi }{2}-y \right)\cos x$ $+\sin y\cos \left( \frac{\pi }{2}-x \right)+\cos x\sin \left( \frac{\pi }{2}-y \right)$is zero, if

A) $x=0$

B) $y=0$

C) $x=y$

D) None of these

• question_answer120) The value of$\sin [{{\cot }^{-1}}\{{{\cot }^{-1}}({{\cos }^{-1}}x)\}]$is equal to

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

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

C) $x$

D) None of these

• question_answer121) . The maximum value of $P=6x+8y$ subject to constraints$2x+y\le 30,\,\,x+2y\le 24$and$x\ge 0,\,\,y\ge 0$is

A) $90$

B) $120$

C) $96$

D) $240$

• question_answer122) With the help of trapezoidal rule for numerical integration and the following table.

 $x$ $0$ $0.25$ $0.50$ $0.75$ $1$ $f(x)$ $0$ $0.625$ $0.2500$ $0.5625$ $1$
The value of$\int_{0}^{1}{f(x)}\,\,dx$is

A) $0.35342$

B) $0.34375$

C) $0.34457$

D) $0.33334$

• question_answer123) If $B$ is an idempotent matrix and$A=I-B$, then

A) ${{A}^{2}}=A$

B) $AB=0$

C) $BA=0$

D) All of the above

• question_answer124) The coefficient of ${{x}^{20}}$ in the expansion of${{(1+{{x}^{2}})}^{40}}{{\left( {{x}^{2}}+2+\frac{1}{{{x}^{2}}} \right)}^{-5}}$, is

A) $^{30}{{C}_{10}}$

B) $^{30}{{C}_{25}}$

C) $1$

D) None of these

• question_answer125) For what values of$k\in R$, the expression $2{{x}^{2}}+kxy+3{{y}^{2}}-5y-2$ can be expressed as$({{a}_{1}}x+{{b}_{1}}y+{{c}_{1}})\cdot ({{a}_{2}}x+{{b}_{2}}y+{{c}_{2}})$?

A) $-3,\,\,-4$

B) $2,\,\,3$

C) $3,\,\,4$

D) $7,\,\,-7$

• question_answer126) If $a,\,\,\,b,\,\,\,c$ are the sides of a $\Delta \,\,ABC$ which are in$AP$, then $\cot \frac{C}{2}$ is equal to

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

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

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

D) $2\cot \frac{B}{2}$

• question_answer127) The continued product of the four values of ${{\left[ \cos \left( \frac{\pi }{3} \right)+i\sin \left( \frac{\pi }{3} \right) \right]}^{3/4}}$, is

A) $-1$

B) $1$

C) $2$

D) $-2$

• question_answer128) For the given line$3x-4y=8$, the points $(2,\,\,3)$ and $(-4,\,\,5)$ are on the

A) same side

B) opposite side

C) lie on the line

D) None of these

• question_answer129) The abscissae and ordinates of the points $A$ and $B$ are the roots of the equations${{x}^{2}}+2ax+b=0$and${{x}^{2}}+2cx+d=0$ respective, then the equation, of circle with $AB$ is diameter, is

A) ${{x}^{2}}+{{y}^{2}}+2ax+2cy+b+d=0$

B) ${{x}^{2}}+{{y}^{2}}-2ax-2cy-b-d=0$

C) ${{x}^{2}}+{{y}^{2}}+2ax+2cy-b-d=0$

D) ${{x}^{2}}+{{y}^{2}}-2ax-2cy+b+d=0$

• question_answer130) If $2x+y+k=0$is a normal to the parabola${{y}^{2}}=-8x$, then the value of $k$ is

A) $-16$

B) $-8$

C) $-24$

D) $24$

• question_answer131) The equation of tangent parallel to $y=x$ drawn to$\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1$, is

A) $x-y+1=0$

B) $x-y+2=0$

C) $x+y-1=0$

D) $x+y-2=0$

• question_answer132) The domain of the function$f(x)=\sqrt{3-x}+{{\cos }^{-1}}\left( \frac{3-2x}{5} \right)$, is

A) $[-1,\,\,3]$

B) $(-1,\,\,3]$

C) $[-1,\,\,3)$

D) None of these

• question_answer133) If $f(x)$ is differentiable in the interval $[2,\,\,5]$ where$f(2)=\frac{1}{5}$and$f(5)=\frac{1}{2}$, then there exist a number $c,\,\,2<c<5$ for which $f'(c)$ is equal to

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

B) $\frac{1}{5}$

C) $\frac{1}{10}$

D) None of these

• question_answer134) If the line $ax+by+c=0$is a normal to the curve$xy=1$, then

A) $a>0,\,\,b>0$

B) $a>0,\,\,b<0$

C) $a<0,\,\,b<0$

D) None of these

• question_answer135) $\int{{{\sec }^{3}}x}\,\,dx$is equal to

A) $\sec x\tan x+\log |\sec x+\tan x|+c$

B) $\frac{1}{2}\sec x\tan x+\frac{1}{2}\log |\sec x+\tan x|+c$

C) ${{\sec }^{3}}x\tan x+\log |{{\sec }^{3}}x+\tan x|+c$

D) None of the above

• question_answer136) The order and. degree of the differential equation${{\left( 1+3\frac{dy}{dx} \right)}^{2/3}}=4\left( \frac{{{d}^{3}}y}{d{{x}^{3}}} \right)$are

A) $1,\,\,\frac{2}{3}$

B) $3,\,\,1$

C) $3,\,\,3$

D) $1,\,\,2$

• question_answer137) If $\sin x$ is an integrating factor of the differential equation$\frac{dy}{dx}+Py=Q$, then $P$ can be

A) $\log \sin x$

B) $\cot x$

C) $\sin x$

D) $\log \cos x$

• question_answer138) Let$\overset{\to }{\mathop{\mathbf{a}}}\,=\widehat{\mathbf{i}}-\widehat{\mathbf{k}},\,\,\,\overset{\to }{\mathop{\mathbf{b}}}\,=x\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+(1-x)\widehat{\mathbf{k}}$and$\overset{\to }{\mathop{\mathbf{c}}}\,=y\widehat{\mathbf{i}}+x\widehat{\mathbf{j}}+(1+x-y)\widehat{\mathbf{k}}$. Then,$[\overrightarrow{\mathbf{a}}\overrightarrow{\mathbf{b}}\overrightarrow{\mathbf{c}}]$ depends on,

A) only$x$

B) only$y$

C) neither$x$nor$y$

D) both $x$ and$y$

• question_answer139) If the planes$\overset{\to }{\mathop{\mathbf{r}}}\,\cdot (2\widehat{\mathbf{i}}-\lambda \widehat{\mathbf{j}}+\widehat{\mathbf{k}})=3$and$\overset{\to }{\mathop{\mathbf{r}}}\,\cdot (4\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\mu \widehat{\mathbf{k}})=5$are parallel, then the value of $\lambda$ and $\mu$ are

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

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

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

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

• question_answer140) Two forces $P$ and $Q$ acting at a point have a resultant$R$. The resolved of $R$ in the direction of $P$ is a magnitude$Q$. Then, the angle between the forces and the magnitude of the resultant are

A) $\theta ={{\cos }^{-1}}\left( \frac{P-Q}{Q} \right),\,\,R=\sqrt{{{P}^{2}}-{{Q}^{2}}+2PQ}$

B) $\theta ={{\cos }^{-1}}\left( \frac{Q-P}{Q} \right),\,\,R=\sqrt{{{Q}^{2}}-{{P}^{2}}+2PQ}$

C) $\theta ={{\cos }^{-1}}\left( \frac{P-Q}{P} \right),\,\,R=\sqrt{2{{P}^{2}}-{{Q}^{2}}+2PQ}$

D) None of the above

• question_answer141) A point is moving in a straight line with uniform acceleration describes $a$ and $b$ feet in successive intervals of ${{t}_{1}}$ and ${{t}_{2}}$ seconds. Then, the acceleration is

A) $\frac{2(b{{t}_{1}}-a{{t}_{2}})}{{{t}_{1}}{{t}_{2}}({{t}_{1}}+{{t}_{2}})}$

B) $\frac{b{{t}_{2}}-a{{t}_{1}}}{{{t}_{1}}{{t}_{2}}({{t}_{1}}+{{t}_{2}})}$

C) $\frac{b{{t}_{2}}-a{{t}_{1}}}{2{{t}_{1}}{{t}_{2}}({{t}_{1}}+{{t}_{2}})}$

D) None of these

• question_answer142) If$2f(x)+3f\left( \frac{1}{x} \right)=\frac{1}{x}-2,\,\,x\ne 0$, then$\int_{1}^{2}{f(x)}\,\,dx$equal to

A) $-\frac{2}{5}\log 2+\frac{1}{2}$

B) $-\frac{2}{5}\log 2-\frac{1}{2}$

C) $\frac{2}{5}\log 2+\frac{1}{2}$

D) None of these

• question_answer143) The maximum value of the function $y=x{{(x-1)}^{2}}$, is

A) $0$

B) $\frac{4}{27}$

C) $-4$

D) None of these

• question_answer144) $\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{x}}{\sqrt{4-\sqrt{x}}-\sqrt{x}}$is equal to

A) $0$

B) $1$

C) $-1$

D) does not exist

• question_answer145) If$\frac{d}{dx}\left( \frac{1+{{x}^{4}}+{{x}^{8}}}{1+{{x}^{2}}+{{x}^{4}}} \right)=a{{x}^{3}}+bx$, then

A) $a=4,\,\,b=2$

B) $a=4,\,\,b=-2$

C) $a=-2,\,\,b=4$

D) None of these

• question_answer146) If$y={{x}^{n-1}}\log x$, then${{x}^{2}}{{y}_{2}}+(3-2n)x{{y}_{1}}$is equal to

A) $-{{(n-1)}^{2}}y$

B) ${{(n-1)}^{2}}y$

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

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

• question_answer147) The length of latusrectum of the ellipse$2{{x}^{2}}+{{y}^{2}}-8x+2y+7=0$, is

A) $\sqrt{2}$

B) $2$

C) $8$

D) None of these

• question_answer148) The angle between the pair of tangents from the point $\left( 1,\,\,\frac{1}{2} \right)$ to the circle${{x}^{2}}+{{y}^{2}}+4x+2y-4=0$, is

A) ${{\cos }^{-1}}\left( \frac{4}{5} \right)$

B) ${{\sin }^{-1}}\left( \frac{4}{5} \right)$

C) ${{\tan }^{-1}}\left( \frac{4}{5} \right)$

D) None of these

• question_answer149) The value of$\cos \left( \frac{\pi }{7} \right)\cos \left( \frac{4\pi }{7} \right)\cos \left( \frac{5\pi }{7} \right)$is equal to

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

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

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

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

• question_answer150) The vertical poles, $AB$ of length $2\,\,m$ and $CD$ of length $20\,\,m$ are erected with base $B$ and $D$ respectively. It is given that distance between the poles is more than $20\,\,m$ and $(\angle ACB)=\frac{2}{77}$, then distance between the poles is

A) $68\,\,m$

B) $24\,\,m$

C) $72\,\,m$

D) None of these