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# Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2013

### done J and K - CET Engineering Solved Paper-2013

• question_answer1) Which of the following physical quantity unit is not a fundamental unit?

A) Length

B) Mass

C) Magnetic field

D) Current

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• question_answer2) The dimensional formula of electric potential is

A) $M{{L}^{2}}{{T}^{-3}}{{A}^{-1}}$

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

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

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

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• question_answer3) The motion of a particle in straight line is an example of

A) constant velocity motion

B) uniformly accelerated motion

C) non-uniformly accelerated motion

D) zero velocity motion

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• question_answer4) The velocity vector of the motion described by the position vector of a particle, $r=2t\,\,\hat{i}+{{t}^{2}}\hat{j}$is given by

A) $V=2i+2t\,\hat{j}$

B) $V=2t\,\,\hat{i}+2t\,\hat{j}$

C) $V=t\,\,\hat{i}+{{t}^{2}}\,\hat{j}$

D) $V=2\,\,\hat{i}+{{t}^{2}}\,\hat{j}$

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• question_answer5) The velocity-time graph of particle comes out to be a non-linear curve. The motion is

A) uniform velocity motion

B) uniformly accelerated motion

C) non-uniform accelerated motion

D) nothing can be said about the motion

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• question_answer6) A projectile is thrown with initial velocity ${{\upsilon }_{0}}$ and angle ${{30}^{o}}$ with the horizontal. If it remains in the air for $1\text{ }s,$ what was its initial velocity?

A) $19.6\text{ }m/s$

B) $9.8\text{ }m/s$

C) $4.9\text{ }m/s$

D) $1\text{ }m/s$

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• question_answer7) Newton's second law of motion is

A) $F=dp/dt$

B) $F=mv$

C) $~F=m{{v}^{2}}$

D) $~F={{m}^{2}}v$

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• question_answer8) The centripetal force is given by the expression

A) $\frac{M{{V}^{2}}}{R}$

B) $\frac{{{M}^{2}}V}{R}$

C) $\frac{Mv}{{{R}^{2}}}$

D) $\frac{Mv}{R}$

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• question_answer9) Uniform circular motion is an example of

A) constant speed motion

B) constant velocity motion

C) non-accelerated motion

D) zero accelerated motion

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• question_answer10) The scalar product of two vectors $A=2\hat{i}+2\hat{j}-\hat{k}$ and $B=-\hat{j}+\hat{k},$ is given by

A) $A.B=3$

B) $A.B=4$

C) $A.B=-4$

D) $A.B=-3$

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• question_answer11) The linear momentum is conserved in

A) elastic collisions

B) inelastic collisions

C) Both 1 and 2

D) Neither 1 nor 2

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• question_answer12) The power (P) of an engine lifting a mass of $100\text{ }kg$up to a height of $10\text{ }m$in $1\text{ }min$is

A) $P=163.3\,\,W$

B) $P=9800\text{ }W$

C) $P=10000\text{ }W$

D) $P=5000\,\,W$

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• question_answer13) The conservation of angular momentum demands that

A) the external force on the system must be zero

B) the external torque on the system must be zero

C) both the external force as well as the external torque must be zero

D) neither of them must be zero

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• question_answer14) The moment of inertia (J) and the angular momentum (L) are related by the expression

A) $I=L\omega$

B) $L=I\omega$

C) $L={{I}^{2}}\omega$

D) $\omega =LI$ where (0 is the angular velocity.

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• question_answer15) The moment of inertia (J) of a sphere of radius R and mass M is given by

A) $I=M{{R}^{2}}$

B) $I=(1/2)M{{R}^{2}}$

C) $I=(4/3)M{{R}^{2}}$

D) $I=(2/5)M{{R}^{2}}$

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• question_answer16) The universal law of gravitation is the force law known also as the

A) triangular law

B) square law

C) inverse square law

D) parallelogram law

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• question_answer17) The value of acceleration due to gravity at the surface of earth

A) is maximum at the poles

B) is maximum at the equator

C) remains constant everywhere on the surface of the earth

D) is maximum at the international timeline

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• question_answer18) The escape velocity of a particle from the surface of the earth is given by

A) ${{(g/R)}^{1/2}}$

B) ${{(2\,gR)}^{1/2}}$

C) ${{(3\,\,gR)}^{1/2}}$

D) ${{(\,gR/2)}^{2}}$

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• question_answer19) The Young's modulus of a rope of $10\text{ }m$ length and having diameter of $2\text{ }cm$is $200\times {{10}^{11}}\,dyne/c{{m}^{2}}$. If the elongation produced in the rope is $1\text{ }cm,$ the force applied on the rope is

A) $6.28\times {{10}^{5}}\,\,N$

B) $6.28\times {{10}^{4}}\,\,N$

C) $6.28\times {{10}^{4}}\text{ }dyne$

D) $6.28\times {{10}^{5}}\text{ }dyne$

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• question_answer20) "The pressure exerted at any point in an enclosed fluid is transmitted equally in all directions". This is known as

A) Archimedes 'principle

B) Law of floatation

C) Pascal?s law

D) Bernoulli principal

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• question_answer21) There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to

A) $\sqrt{h}$

B) $h$

C) ${{h}^{3/2}}$

D) ${{h}^{2}}$

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• question_answer22) The zeroth law of thermodynamics for three systems A, B and C in contact demands that

A) A and B are in thermal equilibrium

B) B and C are in thermal equilibrium

C) A and C are in thermal equilibrium

D) A B and C are in thermal equilibrium

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• question_answer23) The efficiency of a Carnot engine kept at the temperatures of ${{27}^{o}}C$ and ${{127}^{o}}C$ is

A) $20%$

B) $25%$

C) $30%$

D) $40%$

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• question_answer24) The average pressure of an ideal gas is

A) $p=(1/3)mnV_{av}^{2}$

B) $p=(1/3)mn{{V}_{av}}$

C) $p=(1/4)mnV_{av}^{2}$

D) $p=(1/3)mn{{V}_{av}}$ where symbols have their usual meanings.

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• question_answer25) According to equipartition law of energy each particle in a system of particles have thermal energy E equal to

A) $E={{k}_{B}}T$

B) $E=(1/2){{k}_{B}}T$

C) $E=3\,\,{{k}_{B}}T$

D) $E=(3/2)\,\,{{k}_{B}}T$

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• question_answer26) The velocity of sound in a gas is $1300\text{ }m/s$at STP and specific heat at constant pressure is $6.84\,cal\,{{K}^{-1}}\,mo{{l}^{-1}}$. The rms velocity at STP is $(R=1.98\,cal\,\,{{K}^{-1}}\,mo{{l}^{-1}})$

A) $1300\text{ }m/s$

B) $2600\text{ }m/s$

C) $1898\text{ }m/s$

D) $650\text{ }m/s$

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• question_answer27) The time period of a simple pendulum of length $9.8\text{ }m$is

A) $0.159\,\,s$

B) $3.14\,\,s$

C) $6.5\,\,s$

D) $6.28\text{ }s$

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• question_answer28) The displacement, velocity and acceleration in a simple harmonic motion are related as the

A) displacement, velocity and acceleration all act in the same direction

B) displacement and velocity act in the same direction but acceleration in the opposite direction

C) Velocity and acceleration are parallel and both are perpendicular to the displacement

D) displacement and acceleration are antiparallel and both perpendicular to the velocity

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• question_answer29) The beats are the examples of

A) simple harmonic motion

B) interference of two or more waves having same amplitude but slightly different frequencies in the same direction

C) interference of two or more waves having different amplitude but same frequencies in the same direction

D) interference of two or more waves having same amplitude out slightly different frequencies in the perpendicular direction

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• question_answer30) The fundamental frequency of an open pipe of length $1\text{ }m,$ if the speed of sound in air is $340\text{ }m/s$is

A) $340\text{ }Hz$

B) $170\text{ }Hz$

C) $680\text{ }Hz$

D) $85\text{ }Hz$

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• question_answer31) A whistle with frequency $1020\text{ }Hz$is blown at a station. A man travelling in train moving towards the station at $30\text{ }m/s$hears the sound of the whistle. If the speed of sound is $340\text{ }m/s,$ the apparent frequency heard by him is

A) $1020\text{ }Hz$

B) $1110\text{ }Hz$

C) $2040\text{ }Hz$

D) $610\text{ }Hz$

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• question_answer32) An electric charge does not have which of hte following properties?

A) Total charge conservation

B) Quantization of charge

C) Two type of charge

D) Circular line of force

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• question_answer33) The net electric force on a charge of $+3\mu C$ at the mid-point on the line joining two charges of magnitude $+2\mu C$ and $-2\mu C$ separated by the distance of $6mm,$is

A) $6000\,N$

B) $500\,N$

C) $60\,N$

D) zero

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• question_answer34) A hollow sphere of radius $0.1\text{ }m$ has a charge of $5\times {{10}^{-8}}C.$. The potential at a distance of $5\text{ }cm$from the centre of the sphere is $=\left( \frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{9}}\,\,N{{m}^{2}}\,\,{{C}^{-2}} \right)$

A) $4000\,V$

B) $4500\,V$

C) $5000\,V$

D) $6000\,V$

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• question_answer35) A parallel plate capacitor of capacitance 5 microfarad is charged to $120\text{ }V$and then connected to another uncharged capacitor. If the potential falls to $40\text{ }V,$ and capacitance of the second capacitor is

A) 5 microfarad

B) 10 microfarad

C) 15 microfarad

D) 20 microfarad

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• question_answer36) Two identical capacitors are first connected in series and then in parallel. The ratio of equivalent capacitance is

A) $1:1$

B) $1:2$

C) $1:3$

D) $1:4$

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• question_answer37) An electron revolves in a circle at the rate of 1019 rounds per second. The equivalent current is $(e=1.6\times {{10}^{-19}}C)$

A) $1.0\,\,A$

B) $1.6\,\,A$

C) $2.0\text{ }A$

D) $2.6\text{ }A~$

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• question_answer38) A silver wire of radius $0.1\text{ }cm$carries a current of$2A$. If the charge density in silver is $5.86\times {{10}^{28}}{{m}^{-3}},$ the drift velocity is

A) $0.2\times {{10}^{-3}}m/s$

B) $0.4\times {{10}^{-4}}\text{ }m/s$

C) $0.68\times {{10}^{-4}}\text{ }m/s$

D) $7\times {{10}^{-4}}\text{ }m/s$

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• question_answer39) A $1\,m$ long wire of diameter of $0.31\text{ }mm$ has a resistance of $4.2\Omega$. If it is replaced by another wire of same material of length $1.5\text{ }m$and diameter $0.155\text{ }mm,$ the resistance of wire is

A) $25.2\text{ }\Omega$

B) $0.6\text{ }\Omega$

C) $26.7\text{ }\Omega$

D) $\text{0}\text{.8 }\Omega$

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• question_answer40) 24 cells of emf $1.5\text{ }V$each having internal resistance of $1\text{ }ohm$are connected to an external resistance of$1.5\text{ }ohms$. To get maximum current

A) all cells are connected in series combination

B) all cells are connected in parallel combination

C) 4 cells in each row are connected in series and6 such rows are connected in parallel

D) 6 cells in each row are connected in series and 4 such rows are connected in parallel

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• question_answer41) The temperature coefficient of the resistance of a wire is$0.00125\text{ }per{{\text{ }}^{o}}C$. At $300\text{ K}$its resistance is $1\Omega$. The resistance of wire will be $2\,\,\Omega ,$ at

A) $1154\,\,K$

B) $1100\,\,K$

C) $1400\text{ }K$

D) $1127\,\,K$

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• question_answer42) A long straight wire is carrying a current of$12\text{ }A$334. The magnetic field at a distance of $8\text{ }cm$is $({{\mu }_{0}}=4\pi \times {{10}^{-7}}\,\,N/{{A}^{2}})$

A) $2\times {{10}^{-4}}Wb/{{m}^{2}}$

B) $3\times {{10}^{-5}}\text{ }Wb/{{m}^{2}}$

C) $4\times {{10}^{-4}}Wb/{{m}^{2}}$

D) $4\times {{10}^{-5}}\text{ }Wb/{{m}^{2}}$

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• question_answer43) The magnetic field at a point on the axis of a long solenoid having 5 turns per cm length when a current of $0.8\,A$flows through it is

A) $5.024\times {{10}^{-8}}\text{ }Wb/{{m}^{2}}$

B) $6.024\times {{10}^{-8}}\text{ }Wb/{{m}^{2}}$

C) $7.024\times {{10}^{-8}}\text{ }Wb/{{m}^{2}}$

D) $8.024\times {{10}^{-8}}\text{ }Wb/{{m}^{2}}$

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• question_answer44) Two straight wires each $10\text{ }cm$long are parallel to one another and separated by$2\text{ }cm$. When the current flowing in them is $30\text{ }A$and $40\text{ }A$respectively, the force experienced by either of the wires is

A) $1.2\times {{10}^{-3}}N$

B) $12\times {{10}^{-3}}N$

C) $11.2\times {{10}^{-3}}\text{ }N$

D) $10.2\times {{10}^{-3}}\text{ }N$

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• question_answer45) The horizontal and vertical components of earth's magnetic field at a place are $0.3\text{ }G$ and$0.52\text{ }G$. The earth's magnetic field and the angle of dip are

A) $0.3\text{ }G$and $\delta ={{30}^{o}}$

B) $0.4\text{ }G$and $\delta ={{40}^{o}}$

C) $0.5\text{ }G$and $\delta ={{50}^{o}}$

D) $0.6\text{ }G$and $\delta ={{60}^{o}}$

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• question_answer46) A bar magnet of pole strength $10\text{ }Am$is cut into two equal parts breadthwise. The pole strength of each magnet is

A) $5\text{ }Am$

B) $~10\text{ }Am$

C) $15\text{ }Am$

D) $20\text{ }Am$

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• question_answer47) A conductor of length $5\text{ }cm$is moved parallel to itself with a speed of $2\text{ }m/s,$ perpendicular to a uniform magnetic field of${{10}^{-3}}\text{ }Wb/{{m}^{3}}$. The induced e.m.f. generated is

A) $2\times {{10}^{-3}}V$

B) $1\times {{10}^{-3}}V$

C) $1\times {{10}^{-4}}V$

D) $2\times {{10}^{-4}}V$

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• question_answer48) The induced emf in a coil of $10\text{ }H$inductance in which current varies from $9\text{ }A$to $4\text{ }A$in $0.2\,\,s$ is

A) $200\,\,V$

B) $250\,\,V$

C) $300\,\,V$

D) $350\,\,V$

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• question_answer49) The alternating current in a circuit is given by $I=50\,\,\sin \,\,314t$. The peak value and frequency of the current are

A) ${{I}_{0}}=25\,\,A$and $f=100\,\,Hz$

B) ${{I}_{0}}=50\,\,Hz$ and $f=50\,Hz$

C) ${{I}_{0}}=50A$ and $f=100\,\,Hz$

D) ${{\text{I}}_{0}}=25A$and $f=50\,\,Hz$

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• question_answer50) A 5$50\text{ }Hz$ AC signal is applied in a circuit of inductance of $(1/\pi )H$ and resistance $2100\,\Omega$The impedance offered by the circuit is

A) $1500\text{ }\Omega$

B) $1700\,\,\Omega$

C) $2102\,\Omega$

D) $2500\,\,\Omega$

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• question_answer51) If the alternating current $I={{I}_{1}}\,\,\cos \,\,\,\omega t+{{I}_{2}}\,\,\sin \,\,\omega t$(of then the rms current is given by

A) $\frac{{{I}_{1}}+{{I}_{2}}}{\sqrt{2}}$

B) $\frac{|{{I}_{1}}+{{I}_{2}}|}{\sqrt{2}}$

C) $\sqrt{\left( \frac{I_{1}^{2}+I_{2}^{2}}{2} \right)}$

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

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• question_answer52) The transverse nature of electromagnetic waves is proved by which of the following?

A) Interference phenomena

B) Diffraction phenomena

C) Dispersion phenomena

D) Polarization phenomena

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• question_answer53) Which component of electromagnetic spectrum have maximum wavelength?

A) Radio waves

B) Visible spectrum

C) Gamma rays

D) X-rays

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• question_answer54) An object is 8 cm high. It is desired to form a real image $4\text{ }cm$high at $60\text{ }cm$from the mirror. The type of mirror needed with the focal length is

A) convex mirror with focal length $f=40\text{ }cm$

B) convex mirror with focal length $f=20\text{ }cm$

C) concave mirror with focal length $f=-40\text{ }cm$

D) concave mirror with focal length $f=-20\text{ }cm$

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• question_answer55) When an object is placed $40\text{ }cm$from a diverging lens, its virtual image is formed $20\text{ }cm$from the lens. The focal length and power of lens are

A) $F=-20cm,\,P=-5\,D$

B) $F=-40cm,\,P=-5\,D$

C) $F=-40cm,\,P=-2.5\,D$

D) $F=-20\,cm,\,P=-2.5\,D$

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• question_answer56) A magnifying glass of focal length $5\text{ }cm$is used to view an object by a person whose smallest distance of distinct vision is$25\text{ }cm$. If he holds the glass close to eye, the magnification is

A) $5$

B) $6$

C) $2.5$

D) $3$

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• question_answer57) A person has a minimum distance of distinct vision as$50\text{ }cm$. The power of lenses required to read a book at a distance of $25\text{ }cm$is

A) $3\,\,D$

B) $1\,\,D$

C) $2\,\,D$

D) $4\,\,D$

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• question_answer58) If two slits in Young's experiment are $0.4\text{ }mm$apart and fringe width on a screen $200\text{ }cm$away is $2\text{ }mm$the wavelength of light illuminating the slits is

A) $500\text{ }nm$

B) $600\text{ }nm$

C) $400\text{ }nm$

D) $300\text{ }nm$

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• question_answer59) Electric field strength due to a diple at a point on the axial line of dipole is

A) from positive charge to negative charge

B) from negative charge to positive charge

C) along the equatorial line

D) at an angle to axial line

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• question_answer60) The distance of moon form the earth is $3.8\times {{10}^{5}}\text{ }km$. Supposing that the eye is most sensitive to the light of wavelength $550\text{ }nm,$ the separation of two points on the moon that can be resolved by a $500\text{ }cm$telescope is

A) $50\,\,m$

B) $55\,\,m$

C) $51\text{ }m$

D) $60\,\,m$

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• question_answer61) Unpolarized light falls on two polarizing sheets placed one on top of other. If the intensity of transmitted light is one fourth of the incident light, the angle between them is

A) ${{35}^{o}}$

B) ${{40}^{o}}$

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

D) ${{50}^{o}}$

E) Not available

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• question_answer62) The Brewster's law is given by the expression

A) $\mu =\frac{\sin \,i}{\sin \,r}$

B) $\mu =\tan \,{{\theta }^{o}}$

C) $\mu =\cos \theta$

D) $\mu =sin\theta$

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• question_answer63) Einstein's photoelectric equation is

A) ${{E}_{\max }}=hv-\phi$

B) $E=m{{c}^{2}}$

C) ${{E}^{2}}={{p}^{2}}{{c}^{2}}+m_{0}^{2}{{c}^{4}}$

D) $E=\left( \frac{1}{2} \right)m{{v}^{2}}$

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• question_answer64) The Davission-Germer experiment is the direct evidence of

A) particle nature of electrons

B) wave nature of electrons

C) wave nature of light

D) particle nature of light

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• question_answer65) The Rutherford scattering experiment porves that an atom consists of

A) a sphere of positive charge in which electrons are embedded like seeds of water-melon

B) a sphere of negative charge in which protons are embedded like seeds of water-melon

C) a sphere of electron cloud in which the positive charge in placed at the centre of the sphere

D) a sphere of neutral charge

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• question_answer66) According to Bohr model of hydrogen atom, only those orbits are permissible which satisfy the condition

A) $mv=nh$

B) $\frac{m{{v}^{2}}}{r}=n\left( \frac{h}{2\pi } \right)$

C) $mvr=n\left( \frac{h}{2\pi } \right)$

D) $mv{{r}^{2}}=n\left( \frac{h}{2\pi } \right)$

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• question_answer67) The radioactive decay of thorium $(A=232,\,\,Z=90)$ releases six alpha and four beta particles. The atomic number and mass number of the final product is

A) $Z=80,\,\,A=207$

B) $Z=82,\,\,A=208$

C) $Z=92,\,\,A=209$

D) $Z=90,\,\,A=207$

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• question_answer68) Polonium has a half-life of $140$ days. If we take $20\,\,g$of polonium initially then the amount of it that remains after 280 days is

A) $2.5\,\,g$

B) $5\,\,g$

C) $10\text{ }g$

D) $15\text{ }g$

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• question_answer69) Based on the band theory of conductors, insulators and semi-conductors, the forbidden gap is smallest in

A) conductors

B) insulators

C) semi-conductors

D) All of these

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• question_answer70) Based on the I-V characteristics of the diode, we can classify diode as

A) bi-directional device

B) ohmic device

C) non-ohmic device

D) passive element

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• question_answer71) The Boolean expression for the XOR gate is

A) $Y=A+B$

B) $Y=A.B$

C) $Y=AB=BA$

D) $Y=A\oplus B$

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• question_answer72) Which of the following logic gates are also known as the Universal gates?

A) AND, OR. NOT gate

B) XOR, XNOR gate

C) NAND, NOR gate

D) All logic gates

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• question_answer73) The length of antenna (L) required to propagate a signal of wavelength $\lambda$ is given as

A) $L=\frac{\lambda }{2}$

B) $L=2\lambda$

C) $L=\frac{\lambda }{3}$

D) $L=\frac{\lambda }{4}$

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• question_answer74) The modulation is the process in which the

A) modulating signal is sent by antenna in the air

B) carrier signal is sent by the antenna in the air

C) modulated signal formed by the mixing of modulating signal with the carrier signal is sent by the antenna

D) modulated signal formed by the mixing of modulating signal with the carrier signal is received by a receiver antenna

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• question_answer75) The demodulator or detector circuit consists of a

A) resistor

B) transistor

C) diode

D) capacitor

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• question_answer76) Which of the following would contain the same number of atoms as 20 g of calcium? [At. masses:$Ca=40,Mg=24,C=12$]

A) 24 g of magnesium

B) 12 got carbon

C) 24 got carbon

D) 12 g of magnesium

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• question_answer77) 100 mL of $\text{N}{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$is mixed with 100 mL of $\text{1 M NaOH}$solution. The resulting solution will be

A) highly acidic

B) neutral

C) highly basic

D) slightly acidic

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• question_answer78) The bond order of$\text{N}_{\text{2}}^{\text{+}}$on the basis of molecular orbital theory is [Atomic number of$\text{N}\,\text{=}\,\text{7}$]

A) 3

B) 2.5

C) 2

D) 1.5

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• question_answer79) What is the total number of electrons that can have the values $n=2,l=1,s=1/2$in the electronic configuration$1{{s}^{2}}2{{s}^{2}}2{{p}^{3}}$

A) 1

B) 3

C) 5

D) 7

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• question_answer80) Calculate the wavelength associated with an electron moving with a velocity of ${{10}^{6}}\,m/s$(mass of electron $=9.1\times {{10}^{-31}}\,kg,$$h=6.6\times {{10}^{-34}}\,kg\,{{m}^{2}}\,{{s}^{-1}}$)

A) $6.2\times {{10}^{-8}}\,m$

B) $7.25\times {{10}^{-8}}\,m$

C) $6.25\,\overset{\text{o}}{\mathop{\text{A}}}\,$

D) None of the above

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• question_answer81) Which of the following pairs is not correctly matched?

A) Hund's rule In orbitals of equivalent energy electron spins remain unpaired if possible

B) Pauli's exclusion No two electrons can principle have all the four quantum numbers identical

C) Zeeman effect The effect of magnetic field on the atomatic spectra

D) Uncertainty It is impossible to principle determine the position of an electron

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• question_answer82) The orbital diagram in which Aufbau principle is violated is

A)

B)

C)

D)

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• question_answer83) The ${{[\text{OH}]}^{-}}$in a solution is $1\,\text{mol}\,{{\text{L}}^{-1}}.$ The pH of the solution is

A) 1

B) 0

C) 14

D) ${{10}^{-14}}$

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• question_answer84) The solubility of $\text{Fe(OH}{{\text{)}}_{\text{3}}}$is $x\,\text{mol}\,{{\text{L}}^{-1}}.$Its${{K}_{sp}}$ would be

A) $9{{x}^{3}}$

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

C) $27{{x}^{4}}$

D) $9{{x}^{4}}$

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• question_answer85) In which of the following reactions, increase in pressure will favour the forward reaction?

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

B) $2NO(g)+{{O}_{2}}(g)\rightleftharpoons 2N{{O}_{2}}(g)$

C) $C(s)+{{H}_{2}}O(g)\rightleftharpoons CO(g)+{{H}_{2}}(g)$

D) $2HI(g)\rightleftharpoons {{H}_{2}}(g)+{{I}_{2}}(g)$

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• question_answer86) Which of the following is a Lewis acid?

A) $BF_{4}^{-}$

B) $O{{H}^{-}}$

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

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

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• question_answer87) According to collision theory of chemical reactions rates of the reaction increase with increase in the temperature of a reaction because of

A) increase in the velocity of the reacting molecules

B) increase in the number of collisions

C) increase in the number of molecules having the activation energy (threshold energy)

D) None of the above

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• question_answer88) Consider the reaction, $2{{N}_{2}}O{{}_{5}}(g)\xrightarrow{{}}4N{{O}_{2}}(g)+{{O}_{2}}(g)$ The rate law for this reaction is rate$=k[{{N}_{2}}{{O}_{5}}].$ Which of the following statements is true regarding the above reaction?

A) Its order is 1 and molecularity is 1

B) Its order is 1 and molecularity is 2

C) Its order is 2 and molecularity is 2

D) Its order is 2 and molecularity is 1

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• question_answer89) A catalyst is a substance which

A) increases the rate of forward reaction in reversible reaction

B) increases the rate of both forward and backward reaction in a reversible reaction

C) does not influence a reversible reaction

D) increases the rate of backward reaction in a reversible reaction.

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• question_answer90) Which of the following solutions will have the highest boiling point?

A) 1 M glucose solution

B) 1 M sodium nitrate solution

C) 1 M barium chloride solution

D) 1 M aluminium chloride solution

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• question_answer91) Which of the following is a colligative property?

A) Lowering of vapour pressure

B) Osmotic pressure

C) Boiling point

D) Change in entropy

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• question_answer92) van't Hoff factor for $\text{Ca(N}{{\text{O}}_{\text{3}}}{{\text{)}}_{\text{2}}}$is

A) 1

B) 2

C) 3

D) 4

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• question_answer93) What will be the freezing point of 1% solution of glucose in water, given that molal depression constant for water is $1.84\,\text{K}\,\text{mo}{{\text{l}}^{-}}$

A) 272.898 K

B) $~0.102{{\,}^{o}}C$

C) 273 K

D) $108{{\,}^{o}}C$

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• question_answer94) If$\Delta H$and$\Delta S$are positive for a reaction, the reaction will be spontaneous only when

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

B) $T\Delta S>\Delta H$

C) $T\Delta S<\Delta H$

D) $T\Delta S$is negative

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• question_answer95) Calculate the enthalpy change for the reaction, ${{C}_{2}}{{H}_{4}}(g)+{{H}_{2}}(g)\xrightarrow{{}}{{C}_{2}}{{H}_{6}}(g)$ using the data given below ${{C}_{2}}{{H}_{4}}(g)+3{{O}_{2}}(g)\xrightarrow{{}}2C{{O}_{2}}(g)+2{{H}_{2}}O(l)$ $\Delta H=-1415\,kJ$ ${{C}_{2}}{{H}_{6}}(g)+\frac{7}{2}{{O}_{2}}(g)\xrightarrow{{}}2C{{O}_{2}}(g)+3{{H}_{2}}O$ $\Delta H=-1566\,kJ$ ${{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l);\Delta H=-286\,kJ$

A) $-437\,kJ$

B) $135\,kJ$

C) $-135\,kJ$

D) None of these

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• question_answer96) In thermodynamics, a quantity whose value simply depends upon the initial and final state of the system is called

A) a thermodynamic quantity

B) a state function

C) an adiabatic quantity

D) a path function

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• question_answer97) All naturally occurring processes proceed spontaneously in a direction which leads to

A) increase in enthalpy of system

B) decrease in entropy of system

C) decrease in free energy of system

D) increase in free energy of system

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• question_answer98) When an electrolytic solution conducts electricity, the current is carried by

A) the electrons

B) cations and anions

C) neutral molecules

D) the atoms of the electrolyte

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• question_answer99) An electrochemical cell has two half cell reactions as, ${{A}^{2+}}+2{{e}^{-}}\xrightarrow{{}}A;$ $E_{{{A}^{2+}}/A}^{o}=0.34\,V$ $X\xrightarrow{{}}{{X}^{2+}}+2{{e}^{-}};$ $E_{{{x}^{2}}/x}^{0}=-2.37\,V$ The cell voltage will be

A) $2.71\,V$

B) $2.03\,V$

C) $-2.71\,V$

D) $-2.03\,V$

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• question_answer100) In the electrolysis of dilute ?[2804 using platinum electrode

A) ${{\text{H}}_{\text{2}}}$is liberated at cathode

B) ${{\text{O}}_{\text{2}}}$is produced at cathode

C) $\text{C}{{\text{l}}_{\text{2}}}$ is obtained at cathode

D) $\text{N}{{\text{H}}_{\text{3}}}$ is produced at anode

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• question_answer101) When a solution of sodium hydroxide is added to acetic acid solution, the conductivity of the resulting solution will

A) increase

B) remain unchanged

C) decrease

D) become zero

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• question_answer102) The behaviour of a real gas approaches ideal behaviour at

A) low temperature, low pressure

B) high temperature, high pressure

C) low temperature, high pressure

D) high temperature, low pressure

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• question_answer103) Which of the following is not the postulate of the kinetic theory of gases?

A) Gas molecules are in a permanent state of random motion

B) Pressure of gas is due to molecular impacts on the walls

C) The molecules are perfectly elastic

D) The molecular collisions are elastic

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• question_answer104) When a cation leaves its normal position in the crystal and moves to some interstitial space, the defect in the crystal is known as

A) Schottky defect

B) F-centre

C) Frenkel defect

D) non-stoichiometric defect

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• question_answer105) Fog is a colloidal system of

A) gas in liquid

B) liquid in gas

C) gas in gas

D) gas in solid

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• question_answer106) The purification of a colloidal solution could be done by

A) sedimentation

B) ultrafiltration

C) filtration

D) precipitation

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• question_answer107) Bakelite is a product of the reaction between

A) formaldehyde and NaOH .

B) aniline and urea

C) phenol and methanol

D) phenol and chloroform

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• question_answer108) How does electron affinity change when we move from left to right in a period in the Periodic Table?

A) It increases

B) It decreases

C) It remains unchanged

D) It first increases and then decreases

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• question_answer109) Which of the following statements is not correct?

A) lonisation energy increases on going down a group in the Periodic Table

B) Among alkaline earth metals, reducing character increases down the group

C) Fluorine is the most electronegative element

D) Metallic character increases on going down a group in the Periodic Table

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• question_answer110) Which of the following species has a trigonal planar shape?

A) $_{.}^{.}CH_{3}^{-}$

B) $CH_{3}^{+}$

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

D) $Si{{H}_{4}}$

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• question_answer111) Which of the following will have maximum dipole moment?

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

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

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

D) $PC{{l}_{3}}$

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• question_answer112) Which of the following forces is the strongest?

A) Hydrogen bonding

B) Dipole-dipole forces

C) van der Waals' forces

D) Coordinate bonding

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• question_answer113) Which of the following statements is correct?

A) $s{{p}^{3}}-$ hybrid orbitals have equal s and p character

B) The bond angle decreases with the decrease of s character of a hybridized orbital

C) Resonance decreases the stability of a molecule

D) Resonance is due to delocalization of sigma electrons

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• question_answer114) Which of the following is the correct order of increasing oxidising character of oxoacids of chlorine?

A) $HCl{{O}_{3}}<HCl{{O}_{4}}<HCl{{O}_{2}}<HClO$

B) $~HCl{{O}_{4}}<HCl{{O}_{3}}<HCl{{O}_{2}}<HClO$

C) $~HClO<HCl{{O}_{4}}<HCl{{O}_{3}}<HCl{{O}_{2}}$

D) $HClO<HCl{{O}_{2}}<HCl{{O}_{3}}<HCl{{O}_{4}}$

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• question_answer115) Which of the following oxides of group 16 has the highest boiling point?

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

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

C) ${{H}_{2}}Se$

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

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• question_answer116) The +1 oxidation state of thallium is more stable than its +3 oxidation state because of

A) its atomic size

B) its ionization potential

C) inert pair effect

D) diagonal relationship

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• question_answer117) Which of the following statements is false regarding alkali metals?

A) Alkali metals are soft and can be cut with the help of knife

B) Alkali metals do not occur in free state in nature

C) Alkali metals are highly electropositive elements

D) Alkali metal hydrides are covalent in character

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• question_answer118) Among the following outermost configurations of transition metals, which shows the highest oxidation state?

A) $~3{{d}^{3}}4{{s}^{2}}$

B) $~3{{d}^{5}}\text{ }4{{s}^{1}}$

C) $3{{d}^{5}}\text{ }4{{s}^{2}}$

D) $3{{d}^{2}}\text{ }4{{s}^{2}}$

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• question_answer119) The tendency of transition metals to form stable complexes is due to their

A) low ionization energies

B) variable oxidation states

C) strong electropositive nature

D) high charge/size ratio and vacant d orbitals

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• question_answer120) The transition metal ions are generally paramagnetic in nature because

A) they have coloured salts

B) they have one or more unpaired cf-electrons

C) they have one or more paired s-electrons

D) they are reducing agents

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• question_answer121) The most common oxidation state of lanthanides is

A) $+\,4$

B) $+\text{ }3$

C) $+\,6$

D) $+\,2$

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• question_answer122) Specify the coordination number of cobalt in $[Co(CN)({{H}_{2}}O){{(en)}^{2}}]{{~}^{2+}}$

A) 6

B) 4

C) 0

D) 3

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• question_answer123) Which of the following complexes is square planar and diamagnetic?

A) ${{[NiC{{l}_{4}}]}^{2-}}$

B) ${{[NI{{(CN)}_{4}}]}^{2-}}$

C) ${{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}$

D) ${{[CuC{{l}_{4}}]}^{2-}}$

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• question_answer124) Which type of isomerism is exhibited by$[Pt{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]?$

A) Coordination isomerism

B) Linkage isomerism

C) Optical isomerism

D) Geometrical isomerism

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• question_answer125) Ethylene diamine tetraacetate ion is a

A) unidentate ligand

B) bidentate ligand

C) pentadentate ligand

D) hexadentate ligand

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• question_answer126) Which of the following is an ore of zinc?

A) Galena

B) Pyrolusite

C) Sphaterite

D) Magnetite

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• question_answer127) The impurities associated with the ore after mining are collectively called

A) flux

B) slag

C) minerals

D) gangue

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• question_answer128) During extraction of iron, the iron obtained at the bottom of blast furnace is known as

A) steel

B) wrought iron

C) cast iron

D) None of these

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• question_answer129) Select the molecule which has only one $\pi -$bond

A) $CH\equiv CH$

B) $C{{H}_{2}}=CH-CHO$

C) $C{{H}_{3}}-CH=C{{H}_{2}}$

D) $C{{H}_{3}}-CH=CH-COOH$

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• question_answer130) Which of the following groups is ortho and para directing?

A) $-COCl$

B) $-CHO$

C) $-OH$

D) $-COC{{H}_{3}}$

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• question_answer131) Amongst the given cations, the most stable carbonium ion is

A) ${{\,}^{+}}C{{H}_{3}}$

B) ${{(C{{H}_{3}})}_{3}}{{C}^{+}}$

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

D) ${{(C{{H}_{3}})}_{2}}\overset{+}{\mathop{C}}\,H$

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• question_answer132) The hybridization of carbon atoms in C?C single bond of$HC=C-CH=C{{H}_{2}}$ is

A) $s{{p}^{3}}-s{{p}^{2}}$

B) $s{{p}^{2}}-s{{p}^{3}}$

C) $sp-s{{p}^{2}}$

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

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• question_answer133) The number of optical isomers of the compound$C{{H}_{3}}CHBrCHBrCOOH$is

A) 0

B) 1

C) 3

D) 4

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• question_answer134) Electrolysis of an aqueous solution of sodium ethanoate gives

A) methane

B) ethane

C) butane

D) methyl ethanoate

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• question_answer135) Which of the following compounds will exhibit cis-trans (geometrical) isomerism?

A) 2-butene

B) 2-butyne

C) 2-butanol

D) 1-butanol

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• question_answer136) The reaction given below is an example of which of the following? $2C{{H}_{3}}Br+2Na\xrightarrow{\text{dry}\,\text{ether}}{{C}_{2}}{{H}_{6}}+2NaBr$

A) Reimer-Tiemann reaction

B) Wurtz reaction

C) Hoffman bromamide reaction

D) Aldol condensation

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• question_answer137) Chlorobenzene can be prepared by reacting aniline with

A) hydrochloric acid in the presence of nitrous acid

B) cuprous chloride in the presence of aluminium chloride

C) chlorine in the presence of aluminium chloride

D) nitrous acid followed by heating with cuprous chloride

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• question_answer138) Phenol on treatment with cone. $\text{HN}{{\text{O}}_{\text{3}}}$gives

A) o-nitrophenol

B) p-nitrophenol

C) o-and p-nitrophenol

D) 2, 4, 6-trinitrophenol

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• question_answer139) Which of the following compounds will be formed when methoxy benzene is reacted with HBr?

A) Phenol and bromomethane

B) Methanol and bromobenzene

C) Phenol and methanol

D) Bromobenzene and bromomethane

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• question_answer140) When ethanol and${{\text{I}}_{\text{2}}}$are heated in the presence of$\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\text{,}$the yellow crystals obtained are of

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

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

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

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

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• question_answer141) Identify B in the following series of reaction $C{{H}_{3}}CHO\xrightarrow{C{{H}_{3}}MgX}A\xrightarrow{HOH}B$

A) 2-propanol

B) 1-propanol

C) ethanol

D) None of these

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• question_answer142) Which of the following compounds has maximum acidic character?

A) Dichloroacetic acid

B) Acetic acid

C) Trichloroacetic ucid

D) Triflouoroacetic acid

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• question_answer143) Among the following, the least reactive aldehyde is

A) $HCHO$

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

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

D) ${{C}_{2}}{{H}_{5}}CHO$

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• question_answer144) Propanal on reaction with lithium aluminium hydride gives

A) 1-propanol

B) 2-propanol

C) ethanol

D) butanol

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• question_answer145) Idenitfy Z in the following sequence $C{{H}_{3}}C{{H}_{2}}I\xrightarrow{KCN}X\xrightarrow{{{H}_{3}}{{O}^{+}}/{{H}_{2}}O}Y$ $\xrightarrow[\Delta ]{{{H}_{3}}{{O}^{+}}/{{H}_{2}}O}Z$

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

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

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

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

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• question_answer146) Treatment of aniline with bromine water produces

A) 2,4,6-tribromoaniline

B) a mixture of ortho and para bromoaniline

C) bromobenzene

D) N-bromoaniline

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• question_answer147) ${{C}_{6}}{{H}_{5}}COCl\xrightarrow{N{{H}_{3}}}X\xrightarrow{{{P}_{2}}{{O}_{5}}}Y\xrightarrow[{{H}_{2}}]{Ni}Z$ The end product in the above sequence of reactions is

A) benzole acid

B) aniline

C) benzyl amine

D) benzonitrile

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• question_answer148) Which of the following is least reactive to nitration?

A) Benzene

B) Nitrobenzene

C) Chlorobenzene

D) Aniline

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• question_answer149) Nucleic acids are polymers of

A) nucleotides

B) nucleosides

C) nuclei of heavy metals

D) proteins

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• question_answer150) Which of the following enzymes helps in digestion of proteins?

A) Invertase

B) Trypsin

C) Tryosinase

D) Urease

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• question_answer151) The value of$\cos \left( \frac{3\pi }{2}+x \right)\,\cos \,(2\pi +x)\left\{ \cot \left( \frac{3\pi }{2}-x \right)+\cot \,(2\pi +x) \right\}$is

A) $0$

B) $1$

C) $cos\text{ }x$

D) $sin\text{ }x$

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• question_answer152) If $\sin B=3\sin (2A+B),$ then $2\tan A+\tan (A+B)$ is equal to

A) $0$

B) $-2$

C) $1$

D) $1$

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• question_answer153) If $\theta =\frac{\pi }{{{2}^{n}}+1},$ then the value of ${{2}^{n}}\cos \theta \,\cos \,2\theta \,\cos \,{{2}^{2}}\theta .....\cos {{2}^{n-1}}\theta$ is

A) $\sin \theta$

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

C) $0$

D) $1$

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• question_answer154) Using the principal values, the value of ${{\sin }^{-1}}\left\{ \sin \frac{5\pi }{6} \right\}+{{\tan }^{-1}}\left\{ \tan \frac{\pi }{6} \right\}$is equal to

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

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

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

D) $\frac{5\pi }{6}$

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• question_answer155) Find the value of ${{\cos }^{-1}}\left( \frac{4}{5} \right)+{{\tan }^{-1}}\left( \frac{3}{5} \right)$.

A) ${{\tan }^{-1}}\left( \frac{7}{10} \right)$

B) ${{\tan }^{-1}}\left( \frac{27}{11} \right)$

C) ${{\sin }^{-1}}\left( \frac{7}{5} \right)$

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

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• question_answer156) If $X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right]$ and $X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right]$, then X is equal to

A) $\left[ \begin{matrix} 5 & 0 \\ 0 & 4 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 7 & 0 \\ 1 & 5 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} 5 & 0 \\ 1 & 4 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} 7 & 1 \\ 0 & 4 \\ \end{matrix} \right]$

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• question_answer157) If $\left| \begin{matrix} x+7 & 5 \\ x+-3 & 3 \\ \end{matrix} \right|=26,$ then x is equal to

A) $1$

B) $3$

C) $5$

D) $7$

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• question_answer158) The value of $\left| \begin{matrix} {{a}^{2}} & 2ab & {{b}^{2}} \\ {{b}^{2}} & {{a}^{2}} & 2ab \\ 2ab & {{b}^{2}} & {{a}^{2}} \\ \end{matrix} \right|$ is

A) ${{({{a}^{2}}+{{b}^{2}})}^{3}}$

B) ${{({{a}^{3}}+{{b}^{3}})}^{2}}$

C) ${{({{a}^{4}}+{{b}^{4}})}^{2}}$

D) ${{({{a}^{2}}+{{b}^{2}})}^{4}}$

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• question_answer159) If $A=\left[ \begin{matrix} 3 & -4 \\ 1 & -1 \\ \end{matrix} \right],$ then $(A-A')$ is equal to (where, A 'is transpose of matrix A)

A) null matrix

B) identity matrix

C) symmetric

D) skew-symmetric

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• question_answer160) If ${{A}^{-1}}=\left[ \begin{matrix} 5 & -2 \\ -7 & 3 \\ \end{matrix} \right]$ and ${{B}^{-1}}=\frac{1}{2}\left[ \begin{matrix} 9 & -7 \\ -8 & 6 \\ \end{matrix} \right],$ then ${{(AB)}^{-1}}$ is equal to

A) $\left[ \begin{matrix} 47 & -39/2 \\ -41 & 17 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 94 & -82 \\ -39 & 34 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} -47 & 46 \\ 39/2 & -17 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} -47 & 39/2 \\ 46 & -17 \\ \end{matrix} \right]$

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• question_answer161) The value of $\underset{x\to 1}{\mathop{\lim }}\,\frac{x-1}{{{\log }_{e}}x}$ is

A) $1$

B) $0$

C) Not defined

D) $-1$

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• question_answer162) $\underset{x\to 0}{\mathop{\lim }}\,\,{{\left\{ \tan \left( \frac{\pi }{4}+x \right) \right\}}^{1/x}}$is equal to

A) $e$

B) ${{e}^{2}}$

C) $1/e$

D) $1/{{e}^{2}}$

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• question_answer163) The value of $\underset{n\to \infty }{\mathop{\lim }}\,\,\,\left\{ \frac{1+2+3+....+n}{n+2}-\frac{n}{2} \right\}$ is

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

B) $1$

C) $-1$

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

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• question_answer164) If $y=1+\frac{x}{1!}+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{3}}}{3!}.....,$then $\frac{dy}{dx}$ is equal to

A) ${{e}^{x}}$

B) $\sin \,x$

C) $y$

D) $x$

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• question_answer165) The value of $\frac{d}{dx}({{x}^{n}}\,{{\log }_{a}}\,x{{e}^{x}})$ is

A) ${{e}^{x}}\,{{\log }_{a}}\,x+\frac{{{x}^{n-1}}}{{{\log }_{e}}\,a}$

B) ${{e}^{x}}{{x}^{n-1}}\,\left\{ x{{\log }_{a}}\,x+\frac{1}{{{\log }_{e}}\,a}+n\,{{\log }_{a}}x \right\}$

C) $n{{x}^{n-1}}\,{{\log }_{a}}\,x{{e}^{x}}$

D) ${{x}^{n}}\,{{\log }_{a}}x.{{e}^{x}}$

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• question_answer166) The interval in which the function $f(x)=\sin x-\cos x,\,\,\,\,0\le x\le 2\pi$ is strictly decreasing, is

A) $0<x<\frac{3\pi }{4}$

B) $\frac{7\pi }{4}<x<2\pi$

C) $\frac{3\pi }{4}<x<\frac{7\pi }{4}$

D) $0<x<\frac{7\pi }{4}$

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• question_answer167) The slope of normal to the curve $y={{x}^{3}}+2x+6$ which is parallel to line $x+14y+4=0$ is

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

B) $-\frac{1}{14}$

C) $-4$

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

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• question_answer168) The approximate value of ${{(0.009)}^{1/3}}$ is

A) $0.2$

B) $0.2083$

C) $0.0032$

D) $0.0083$

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• question_answer169) If $\left\{ \begin{matrix} \frac{(1-\cos \,4x)}{{{x}^{2}}}, & if & x<0 \\ a, & if & x=0, \\ \frac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4}, & if & x>0 \\ \end{matrix} \right.$then $f(x)$ is continuous at $x=0,$ for a

A) $4$

B) $\sqrt{32}$

C) $8$

D) $16$

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• question_answer170) The value of $\int_{0}^{\pi /2}{\frac{dx}{1+\tan x}}$ is

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

B) $0$

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

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

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• question_answer171) Evaluate $\int{\frac{3x-2}{(x+3){{(x+1)}^{2}}}}\,dx.$

A) $\frac{11}{4}\log \,[|x+1|\,|x+3|]+\frac{5}{2(x+1)}+C$

B) $\frac{11}{4}\log \,\left| \frac{x+3}{x+1} \right|+\frac{1}{x+1}+C$

C) $\frac{11}{4}\log \,|x+2|+\frac{5}{2}(x+3)+\frac{1}{x+1}+C$

D) $\frac{11}{4}\log \,\left| \frac{x+1}{x+3} \right|+\frac{5}{2(x+1)}+C$

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• question_answer172) The general solution of the linear differential equation $\frac{dy}{dx}+\sec \,x.\,y=\tan x$ $\left( 0\le x\le \frac{\pi }{2} \right)$is

A) $y=-x\,{{(\sec x+\tan x)}^{-1}}+\frac{C}{\sec x+\tan x}+1$

B) $y=x+\frac{C}{\sec x+\tan x}+\frac{1}{\tan x}$

C) $y=\frac{x+1}{\sec x+\tan x}+C$

D) $y=x+\sec x-\tan \,x+C$

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• question_answer173) On solving the differential equation ${{x}^{2}}y\,dx-({{x}^{3}}+{{y}^{2}})dy=0,$the value of $\log \,y$ is

A) $\frac{{{x}^{3}}}{3{{y}^{3}}}+C$

B) $\frac{{{x}^{2}}}{{{y}^{2}}}+C$

C) $\frac{{{x}^{2}}}{3{{y}^{3}}}+C$

D) $\frac{{{x}^{3}}}{{{x}^{3}}+{{y}^{3}}}+C$

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• question_answer174) The value of $\int{\frac{2+\sin x}{1+\cos x}}\,{{e}^{x/2}}dx$ is

A) $2.{{e}^{x/2}}\,\tan \frac{x}{2}+C$

B) ${{e}^{x/2}}\,\tan \,x+C$

C) $\frac{1}{2}{{e}^{x/2}}\,\sin x+C$

D) $\frac{1}{2}\,\,{{e}^{x/2}}\,\sin \frac{x}{2}+C$

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• question_answer175) On evaluation, the value of $\int_{0}^{4}{f(x)\,\,dx,}$where $f(x)=\left\{ \begin{matrix} |x-2|+2, & x\le 2 \\ {{x}^{2}}-2, & x>2 \\ \end{matrix} \right.$ is

A) $\frac{56}{3}$

B) $\frac{60}{3}$

C) $\frac{66}{3}$

D) $\frac{62}{3}$

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• question_answer176) The particular solution of the differential equation $\frac{dy}{dx}+y\,\cot \,x=2x+{{x}^{2}}\,\cot \,x,$such that $y(\pi /2)=0$ is

A) $y=\frac{{{\pi }^{2}}}{4\,\cos \,x},(x\ne 0)$

B) $y={{x}^{2}}-\frac{\pi }{2}\tan x$

C) $y=\frac{2x}{\sin x}+\frac{1}{{{x}^{2}}},(x\ne 0)$

D) $y={{x}^{2}}-\frac{{{\pi }^{2}}}{4\sin x}(\sin x\ne 0)$

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• question_answer177) The differential equation corresponding to the equation${{y}^{2}}=a(b-{{x}^{2}})$ where a, b are constants is

A) ${{y}^{2}}\frac{{{d}^{2}}y}{d{{x}^{2}}}=a\left( b-\frac{dy}{dx}+x \right)$

B) $xy\frac{{{d}^{2}}y}{d{{x}^{2}}}+x{{\left( \frac{dy}{dx} \right)}^{2}}-y\frac{dy}{dx}=0$

C) $y{{\left( \frac{dy}{dx} \right)}^{2}}-x\frac{dy}{dx}+1=0$

D) None of the above

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• question_answer178) The area bounded by the circle ${{x}^{2}}+{{y}^{2}}=16$ and the line $y=x$in the first quadrant is

A) $4\pi \,\,\,sq\,units$

B) $8\pi \,\,\,sq\,units$

C) $2\pi \,\,\,sq\,units$

D) $\pi \,\,\,sq\,units$

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• question_answer179) The focal distance of the point $(x,y)$ from the ellipse $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\,\,\,\,a>b$ is

A) $a\pm \sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}y$

B) $b\pm \sqrt{1-\frac{{{a}^{2}}}{{{b}^{2}}}}y$

C) $a\pm \sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}\,x$

D) $b\pm \sqrt{1-\frac{{{a}^{2}}}{{{b}^{2}}}}\,x$

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• question_answer180) The lines $3x+y-14=0$ $\lambda x-2y=0$ $3x-8y+4=0$ are concurrent. Then, the value of $\lambda$ is

A) $1$

B) $2$

C) $3$

D) $4$

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• question_answer181) The equation of a straight line which cuts off intercept on X-axis which is twice that on y-axis and is at a unit distance from . origin is given by

A) $x+y=0$

B) $x+2y\pm \sqrt{2}=0$

C) $x+2y\pm \sqrt{5}=0$

D) $x+\sqrt{5}y\pm 2=0$

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• question_answer182) The equation of a straight line upon which the length of the perpendicular from the origin is 5 and slope of this perpendicular is $3/4$ is

A) $2x+5y\pm 16=0$

B) $4x+3y\pm 25=0$

C) $4x+3y\pm 5=0$

D) $2x+5y\pm 4=0$

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• question_answer183) The radius of the circle ${{(x\,\cos \theta +y\sin \theta -a)}^{2}}+(x\,\sin \theta -y\cos \theta )={{k}^{2}}$ is

A) ${{a}^{2}}+{{b}^{2}}-{{k}^{2}}$

B) $a\,sin\,\theta -b\,\cos \,\theta$

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

D) $k$

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• question_answer184) The locus of a point which moves in a plane such that its distance from a fixed point in the plane is always equal to its distance from a fixed straight line in the same plane represents

A) a circle

B) a parabola

C) a hyperbola

D) an ellipse

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• question_answer185) The eccentricity of the ellipse $25{{x}^{2}}+9{{y}^{2}}-150x-90y+225=0$is

A) $\frac{4}{5}$

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

C) $\frac{4}{15}$

D) $\frac{9}{5}$

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• question_answer186) The mean deviation from the median is

A) equal to that measured from another value

B) maximum, if all observations are positive

C) greater than that measured from any other value

D) less than measured from any other value

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• question_answer187) The variance of the data

 $x:1$ $a$ ${{a}^{2}}$ ?.. ${{a}^{n}}$ $f{{:}^{n}}{{C}_{0}}$ $^{n}{{C}_{1}}$ $^{n}{{C}_{2}}$ ?.. $^{n}{{C}_{n}}$

A) ${{\left( \frac{1+{{a}^{2}}}{2} \right)}^{n}}-{{\left( \frac{1+a}{2} \right)}^{2n}}$

B) ${{\left( \frac{1+{{a}^{2}}}{2} \right)}^{2n}}-{{\left( \frac{1+a}{2} \right)}^{n}}$

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

D) ${{\left( \frac{1+a}{2} \right)}^{n}}-{{\left( \frac{1+{{a}^{2n}}}{2} \right)}^{n}}$

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• question_answer188) An analysis of the weekly wages paid to workers in two firms A and B, belonging to the same industry gives the following results

 Firm A Firm B Number of wage earners $586$ $648$ Average of weekly wages Rs. $52.5$ Rs. $47.5$ Variance of the distribution of wages $100$ $121$
Then, which firm pays out larger amount and which shows greater variability, respectively?

A) $A,\,B$

B) $B,\,A$

C) $B,\,B$

D) $A,\,A$

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• question_answer189) If the standard deviation of a variable X is $\sigma ,$ then the standard deviation of variable $\frac{aX+b}{c}$is

A) $a\sigma$

B) $\frac{a}{c}\sigma$

C) $\left| \frac{a}{c} \right|\sigma$

D) $\frac{a\sigma +b}{c}$

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• question_answer190) A bag contains 50 tickets numbered 1, 2, 3, ...,50 of which five are drawn at random and arranged in ascending order of magnitude $({{x}_{1}}<{{x}_{2}}<{{x}_{3}}<{{x}_{4}}<{{x}_{5}}),$ then the probability that ${{x}_{3}}=30$ is

A) $\frac{^{29}{{C}_{2}}{{\times }^{20}}{{C}_{2}}}{^{50}{{C}_{5}}}$

B) $\frac{^{30}{{C}_{1}}{{\times }^{29}}{{C}_{1}}}{^{50}{{C}_{5}}}$

C) $\frac{^{5}{{C}_{1}}{{\times }^{50}}{{C}_{2}}}{^{50}{{C}_{5}}}$

D) $\frac{^{50}{{C}_{2}}{{\times }^{29}}{{C}_{1}}}{^{50}{{C}_{5}}}$

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• question_answer191) If S is the sample space and $P(A)=\frac{1}{3}\,P(B)$and $S=A\cup B,$ where A and B are two mutually exclusive events, then $P(A)$ is equal to

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

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

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

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

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• question_answer192) Five persons entered the lift cabin on the ground floor of an eight floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floors is

A) $\frac{^{7}{{P}_{5}}}{{{7}^{5}}}$

B) $\frac{{{7}^{5}}}{^{7}{{P}_{5}}}$

C) $\frac{6}{^{6}{{P}_{5}}}$

D) $\frac{^{5}{{P}_{5}}}{{{5}^{5}}}$

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• question_answer193) In a three dimensional space the equation ${{x}^{2}}-5x+6=0$represents

A) points

B) planes

C) curves

D) None of these

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• question_answer194) If $(3,\,4,-1)$ and $(-1,\,2,3)$ be end points of the diameter of a sphere, then the radius of the sphere is

A) $2$

B) $3$

C) $6$

D) $7$

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• question_answer195) If the position vector a of a point $(12,\,\,n)$ is such that $|a|=13,$ then the value of $\pi$ is

A) $\pm \,\,3$

B) $\pm \,\,4$

C) $\pm \,\,5$

D) $\pm \,\,6$

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• question_answer196) The following lines are $r=(\hat{i}+\hat{j})+\lambda (\hat{i}+2\hat{j}-\hat{k}),$ and $r=(\hat{i}+\hat{j})+\mu (-\hat{i}+\hat{j}-2\hat{k})$

A) collinear

B) skew-lines

C) coplanar lines

D) parallel lines

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• question_answer197) The position vector of a point R which divides the line joining $P(6,\,3,-2)$and $Q(3,1,-4)$Q(3,1, - 4) in the ratio $2:1$ externally is

A) $\hat{i}+3\hat{j}-2\hat{k}$

B) $3\hat{i}-\hat{k}$

C) $-\hat{j}-6\hat{k}$

D) $2\hat{i}-\hat{j}$

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• question_answer198) If $a=\hat{i}+2\hat{j}-3\hat{k}$ and $b=2\hat{i}+4\hat{j}+9\hat{k},$ then the unit vector parallel to $a+b$ is

A) $\frac{1}{6}\,5\hat{i}-\hat{k}$

B) $\frac{1}{\sqrt{35}}(5\hat{i}+3\hat{j}-\hat{k})$

C) $\frac{1}{5}(3\hat{j}-5\hat{k})$

D) $3\hat{i}+6\hat{j}-6\hat{k}$

E) None of these

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• question_answer199) The angle between the lines $\frac{x-5}{-3}=\frac{y+3}{-4}=\frac{z-7}{0},\,\frac{x}{1}=\frac{y-1}{-2}=\frac{z-6}{2}$is

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

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

C) ${{\cos }^{-1}}\left( \frac{1}{3} \right)$

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

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• question_answer200) If $|a|=2,\,\,|b|=5$ and $|a\times b|=8,$ then $a\,.\,b$ is equal to

A) $3$

B) $4$

C) $5$

D) $6$

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• question_answer201) Suppose ${{A}_{1}},{{A}_{2}}.....,{{A}_{30}}$are thirty sets each with five elements and ${{B}_{1}},{{B}_{2}}.....,{{B}_{n}}$ are 'n' sets each with three elements. Let $\underset{i=1}{\mathop{\overset{30}{\mathop{\cup }}\,}}\,\,\,{{A}_{i}}=\underset{j=1}{\mathop{\overset{n}{\mathop{\cup }}\,}}\,\,\,\,{{B}_{j}}=S.$ Assume that each element of S belongs to exactly 10 of ${{A}_{i}}s$ and exactly 9 of ${{B}_{j}}s,$then the value of x is

A) $90$

B) $15$

C) $9$

D) 45

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• question_answer202) A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples, then the value of x is

A) $39\le x\le 63$

B) $63$

C) $39$

D) $139\ge x$

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• question_answer203) The cartesian product $A\times A$ has 9 elements among which are found $(-1,0)$ and $(0,1),$ then set A is equal to

A) $\{1,\,\,0\}$

B) $\{1,\,\,-1,\,\,\,0\}$

C) $\{\,0,\,\,-1\}$

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

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• question_answer204) If $S=\{(a,\,b):b=|a-1|,a\in Z$ and $|a|<3\},$ where Z denotes the set of integers. Then, the range set of S is

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

B) $\{-1,\,2,\,3,\,1\}$

C) $\{0,\,1,\,2,\,3,\,4\}$

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

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• question_answer205) Pisa relation from $\{11,\,12,\,13\}$to $\{8,\,10,\,12\}$ defined by $y=x-3$. Then, ${{R}^{-1}}$ is

A) $\{(8,\,11),\,(10,13)\}$

B) $\{(11,\,8),\,(13,10)\}$

C) $\{(10,\,13),\,(8,11),\,(12,\,10)\}$

D) None of the above

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• question_answer206) The quotient of the identity function by the reciprocal function is given by

A) ${{x}^{2}}\,\forall \,\,x\,\in \,R$ (set of real numbers)

B) $\frac{1}{{{x}^{2}}}\,\,\forall \,\,x\in R-\{0\}$

C) ${{x}^{2}}\,\,\forall \,\,x\in R-\{0\}$

D) None of the above

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• question_answer207) Which of the following is not a function?

A) $\{(x,y):\,x,\,y\,\in R,{{x}^{2}}=y\}$

B) $\{(x,y):\,x,\,y\,\in R,{{y}^{2}}=x\}$

C) $\{(x,y):\,x,\,y\,\in R,x={{y}^{3}}\}$

D) $\{(x,y):\,x,\,y\,\in R,y={{x}^{3}}\}$

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• question_answer208) If $(1+i)\,(2i+1)\,(1+3i)....(1+ni)=x+iy,$ then $2.5.10....(1+{{n}^{2}})$ is equal to

A) $1$

B) $i$

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

D) $1+{{n}^{2}}$

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• question_answer209) The value of $|{{z}_{1}}|=|{{z}_{2}}|=...=|{{z}_{n}}|=1,$ then $|{{z}_{1}}+{{z}_{2}}+{{z}_{3}}+....+{{z}_{n}}|$ is (where, ${{z}_{1}}$ is complex number with $i=1$ to n)

A) $\left| \frac{1}{{{z}_{1}}+{{z}_{2}}+{{z}_{3}}+....+{{z}_{n}}} \right|$

B) $\left| \frac{1}{{{z}_{1}}}+\frac{1}{{{z}_{2}}}+\frac{1}{{{z}_{3}}}+...+\frac{1}{{{z}_{n}}} \right|$

C) $\left| \frac{1}{{{z}_{1}}{{z}_{2}}}+\frac{1}{{{z}_{3}}{{z}_{4}}}+....+\frac{1}{{{z}_{n-1}}{{z}_{n}}} \right|$

D) $1$

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• question_answer210) The non-zero solutions of the equation ${{z}^{2}}+|z|=0,$ where z is a complex number, are

A) $\pm \,\,1$

B) $\pm \,\,i$

C) $1\pm \,\,i$

D) $\pm \,\,1\pm i$

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• question_answer211) Which of the following shaded regions represents the solution set of in equation $|x-y|\ge 1$

A)

B)

C)

D)

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• question_answer212) The values of x for which $-11\le 4x-3\le 13$is

A) $-4\le x\le 5$

B) $-2\le x\le 4$

C) $-8\le x\le 16$

D) $-11\le x\le 10$

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• question_answer213) The solution set of the following linear in equations $x-2y\ge 0;\,\,\,2x-y\le -2;\,\,x\ge 0,y\ge 0$is given by

A) $[1,\,\,2]$

B) Null set

C) $x\ge 1$

D) Set of real numbers

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• question_answer214) For the given LPP (Linear Programming Problem) max $z=5x+3y$ $2x+y\le 12$ $3x+2y\le 20$ $x\ge 0,\,y\ge 0$ the optimal solution set is

A) $(0,\,\,0)$

B) $(6,\,\,0)$

C) $(4,\,\,4)$

D) $(0,\,\,10)$

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• question_answer215) A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains atleast 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin content of 1 kg food is given below

 Food Vitamin A Vitamin B Vitamin C x 1 2 3 y 2 2 1
$1\text{ }kg$of food X costs $Rs.\text{ }16$and $1\text{ }kg$ of food Y costs $Rs.\text{ }20$. Find the least cost of the mixture which will produce the required diet.

A) $Rs.\,100$

B) $Rs.\,98$

C) $Rs.\,116$

D) $Rs.\,112$

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• question_answer216) Which of the following is a purely imaginary term of the sequence $8-6i,$ $7-4i,\,6-2i,...$?

A) 9th term

B) 2nd term

C) 4th term

D) 8 term

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• question_answer217) If ${{S}_{n}}$ denotes the sum of first n terms of AP $<{{a}_{n}}>,$such that $\frac{{{S}_{m}}}{{{S}_{n}}}=\frac{{{m}^{2}}}{{{n}^{2}}},$ then $\frac{{{a}_{m}}}{{{a}_{n}}}$ is equal to

A) $\frac{2m+1}{2n+1}$

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

C) $\frac{m-1}{n-1}$

D) $\frac{m+1}{n+1}$

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• question_answer218) The sum of all possible products of the first n natural numbers taken two by two is

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

B) $\frac{n(n+1)(n+2)}{6}$

C) $\frac{n({{n}^{2}}-1)(3n+2)}{12}$

D) $2{{n}^{3}}+3{{n}^{2}}-1$

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• question_answer219) How many four digit numbers are there with distinct digits?

A) $5040$

B) $4536$

C) $30240$

D) $5274$

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• question_answer220) If $^{n}{{C}_{r}}{{+}^{n}}{{C}_{r+1}}{{=}^{n+1}}{{C}_{x}},$then x is equal to

A) $r$

B) $r-1$

C) $n$

D) $r+1$

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• question_answer221) The coefficient of the term independent of x in the expansion $\left( \frac{x+1}{{{x}^{2/3}}-{{x}^{1/3}}+1}-\frac{x-1}{x-{{x}^{1/2}}} \right)$is

A) $8064$

B) $210$

C) $-546$

D) $5040$

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• question_answer222) There are 12 points in a plane. The number of straight lines joining any two of them, when 3 of them are collinear, is

A) $60$

B) $63$

C) $64$

D) $65$

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• question_answer223) Which of the following is the correct principle of Mathematical induction?

A) Let $P(n)$ be a statement such that n be any integer and $P(1)$ is true. Also. $P(m)$ is true for m, any natural number, then $P(n)$ is true for all integers n

B) Let $P(n)$ be a statement involving natural number n such that $P(1)$ is true and$P(m)$ is true whenever $P(n)$ is true for every $n\ge m,$then $P(n)$ is true for all $n\in N$ (set of natural numbers)

C) Let$P(n)$ be a statement where $n\in N$such that$P(1)$ is true and $P(n),\,P(n+1)$also holds, then $P(n)$ is true $\forall n\in N$

D) Let $P(n)$ be a statement involving the natural number n, such trial P(1) is true and s$P(m+1)$ is true for all $n\le m$Then, $P(n)$ is true for all $n\in N$

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• question_answer224) If $x>0$and ${{\cot }^{-1}}\,(x+2)=\frac{\pi }{12},$ then the value of x is

A) $2\sqrt{3}$

B) $\sqrt{3}$

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

D) $\sqrt{3}-1$

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• question_answer225) If $\cot \,\theta (1+\sin \theta )=4m$ and $\cot \theta (1-\sin \theta )=4n,$ then ${{({{m}^{2}}-{{n}^{2}})}^{2}}$is equal to

A) $mn$

B) $\tan \theta$

C) $1$

D) $\frac{m+n}{4}$

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