# Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2003

### done CET - Karnataka Engineering Solved Paper-2003

• question_answer1) The dimensions of $\frac{a}{b}$ in the equation$P=\frac{a-{{t}^{2}}}{bx}$where P is pressure, $x$ is distance and t is time, are:

A) $\left[ {{M}^{2}}L{{T}^{-3}} \right]$

B) $\left[ M{{T}^{-2}} \right]$

C) $\left[ L{{T}^{-3}} \right]$

D) $\left[ M{{L}^{3}}{{T}^{-1}} \right]$

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• question_answer2) Three vectors satisfy the relation $\overrightarrow{A.}\overrightarrow{B}=0$ and $\overrightarrow{A.}\overrightarrow{C}=0,$then A is parallel to:

A) $\overrightarrow{C}$

B) $\overrightarrow{B}$

C) $\overrightarrow{B}\times \overrightarrow{C}$

D) $\overrightarrow{B}.\overrightarrow{C}$

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• question_answer3) A student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of $1\text{ }m{{s}^{-2}}$, the student starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of n, so that the student is able to catch the bus is:

A) $8\text{ }m{{s}^{-1}}$

B) $5\text{ }m{{s}^{-1}}$

C) $12\text{ }m{{s}^{-1}}$

D) $10\text{ }m{{s}^{-1}}$

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• question_answer4) For a given velocity, a projectile has the same range R for two angles of projection if ${{t}_{1}}$ and ${{t}_{2}}$ are the time of flight in the two cases, then:

A) ${{t}_{1}}{{t}_{2}}\propto R$

B) ${{t}_{1}}{{t}_{2}}\propto {{R}^{2}}$

C) ${{t}_{1}}{{t}_{2}}\propto \frac{1}{{{R}^{2}}}$

D) ${{t}_{1}}{{t}_{2}}\propto \frac{1}{R}$

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• question_answer5) Weight of a body of mass m decreases by 1% when it is raised to height h above the earths surface. If the body is taken to a depth h in a mine, change in its weight is:

A) 0.5% decrease

B) 2% decrease

C) 0.5% increase

D) 1% increase

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• question_answer6) The displacement time graph of a particle executing S.H.M. is as shown in the figure. The corresponding force-time graph of the particle is:

A) B) C) D) View Answer play_arrow
• question_answer7) Which of the following sets of concurrent forces maybe in equilibrium?

A) ${{F}_{1}}=3N,{{F}_{2}}=5N,\,{{F}_{3}}=1N$

B) (b ${{F}_{1}}=3N,{{F}_{2}}=5N,\,{{F}_{3}}=9N$

C) ${{F}_{1}}=3N,{{F}_{2}}=5N,\,{{F}_{1}}=6N$

D) ${{F}_{1}}=3N,{{F}_{2}}=5N,\,{{F}_{3}}=15N$

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• question_answer8) Youngs modulus of perfectly rigid body material is:

A) infinite

B) zero

C) $10\times {{10}^{10}}N/{{m}^{2}}$

D) $1\times {{10}^{10}}N/{{m}^{2}}$

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• question_answer9) An ideal monoatomic gas at ${{27}^{o}}C$ is compressed adiabatically to 8/27 times of its present volume. The increase in temperature of the gas is:

A) ${{375}^{o}}C$

B) ${{402}^{o}}C$

C) ${{175}^{o}}C$

D) ${{475}^{o}}C$

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• question_answer10) A sample of ideal monoatomic gas is taken round the cycle ABCA as shown in the figure. The work done during the cycle is: A) 3 PV

B) zero

C) 9 PV

D) 6 PV

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• question_answer11) A bucket full of hot water is kept in a room. It cools from ${{75}^{o}}C$ to ${{70}^{o}}C$ in ${{t}_{1}}$ minutes, from ${{70}^{o}}C$ to ${{65}^{o}}C$ in ${{t}_{2}}$ minutes and from ${{65}^{o}}C$to ${{60}^{o}}C$ in ${{t}_{3}}$ minutes. Then:

A) ${{t}_{1}}<{{t}_{2}}<{{t}_{3}}$

B) ${{t}_{1}}={{t}_{2}}={{t}_{3}}$

C) ${{t}_{1}}<{{t}_{2}}>{{t}_{3}}$

D) ${{t}_{1}}>{{t}_{2}}>{{t}_{3}}$

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• question_answer12) A fish, looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the surface of water, the radius of the circle in centimetre is:

A) $\frac{12\times 3}{\sqrt{5}}$

B) $12\times 3\times \sqrt{5}$

C) $\frac{12\times 3}{\sqrt{7}}$

D) $12\times 3\times \sqrt{7}$

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• question_answer13) A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and material are now added to P, as shown in the figure. The ray will suffer:

A) same deviation

B) greater deviation

C) total internal reflection

D) no deviation

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• question_answer14) The aperture of the objective lens of a telescope is made large so as to:

A) increase the resolving power of the telescope

B) increase the magnifying power of the telescope

C) to focus on distant objects

D) make image aberrationless

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• question_answer15) A lamp hanging 4 metres above the table is lowered by 1 metre. The illumination on the table:

A) decreased by 25%

B) increased by 25%

C) decreased by 66.7%

D) increased by 77.7%

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• question_answer16) The equation of a transverse wave travelling along positive $x$ axis with amplitude 0.2 m, velocity 360 m/sec and wavelength 60 m can be written as:

A) $y=0.2\sin \pi \left[ 6t+\frac{x}{60} \right]$

B) $y=0.2\sin \pi \left[ 6t-\frac{x}{60} \right]$

C) $y=0.2\sin 2\pi \left[ 6t-\frac{x}{60} \right]$

D) $y=0.2\sin 2\pi \left[ 6t+\frac{x}{60} \right]$

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• question_answer17) If ${{\upsilon }_{m}}$, is the velocity of sound in moist air, ${{\upsilon }_{d}}$is the velocity of sound in dry air, under identical conditions of pressure and temperature:

A) ${{\upsilon }_{d}}<{{\upsilon }_{d}}$

B) ${{\upsilon }_{m}}>{{\upsilon }_{d}}$

C) ${{\upsilon }_{m}}\,{{\upsilon }_{d}}=1$

D) ${{\upsilon }_{m}}={{\upsilon }_{d}}$

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• question_answer18) If T is the reverberation time of an auditorium of volume V, then

A) $T\propto {{V}^{2}}$

B) $T\propto V$

C) $T\propto \frac{1}{V}$

D) $T\propto \frac{1}{{{V}^{2}}}$

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• question_answer19) Two wires are fixed in a sonometer. Their tensions are in the ratio 8 : 1. The lengths are in the ratio 36 : 35. The diameters are in the ratio 4 : 1. Densities of the materials are in the ratio 1 : 2. If the higher frequency in the setting is 360 Hz, the beat frequency when the two wires are sounded together, is:

A) 8

B) 5

C) 10

D) 6

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• question_answer20) A sound source is moving towards stationary listener with $\frac{1}{10}$th of the speed of sound. The ratio of apparent to real frequency is:

A) ${{\left( \frac{9}{10} \right)}^{2}}$

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

C) $\frac{11}{10}$

D) ${{\left( \frac{11}{10} \right)}^{2}}$

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• question_answer21) If v is the speed of sound in air then the shortest length of the closed pipe which resonates to a frequency n, is:

A) $\frac{v}{2n}$

B) $\frac{v}{4n}$

C) $\frac{4n}{v}$

D) $\frac{2n}{v}$

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• question_answer22) Cavitation is a special application property exhibited only by:

A) ultrasonics

B) electromagnetic waves

C) audible sound

D) infrasonics

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• question_answer23) In Youngs double slit experiment, the fringe width is $\beta$, If the entire arrangement is placed in a liquid of refractive index n, the fringe width becomes:

A) $n\beta$

B) $\frac{\beta }{n+1}$

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

D) $\frac{\beta }{n}$

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• question_answer24) Yellow light is used in single slit diffraction experiment with slit width 0.6 mm. If yellow light is replaced by X-rays, then the pattern will reveal that:

A) no diffraction pattern

B) that the central maxima narrower

C) less number of fringes

D) more number of fringes

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• question_answer25) In an interference experiment, third bright fringe is obtained at a point on the screen with a light of 700 nm. What should be the wavelength of die light source in order to obtain 5th bright fringe at the same point?

A) 630 nm

B) 500 nm

C) 420 nm

D) 750 nm

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• question_answer26) If a ray of light in a denser medium enters into a rarer medium at an angle of incidence i, the angle of reflection and refraction are respectively r and r. If the reflected and refracted rays are at right angles to each other, the critical angle for the given pair of media is:

A) ${{\sin }^{-1}}\left( \tan r \right)$

B) ${{\sin }^{-1}}\left( \tan r \right)$

C) $ta{{n}^{-1}}\left( \sin i \right)$

D) $cot\left( \tan i \right)$

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• question_answer27) Waves that cannot be polarized are:

A) electromagnetic waves

B) light waves

C) longitudinal waves

D) transverse waves

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• question_answer28) The phenomenon of rotation of plane of plane polarized light is called:

A) Kerr effect

B) double refraction

C) optical activity

D) dichroism

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• question_answer29) As a result of interference of two coherent sources of light energy is:

A) redistributed and the distribution does not very with time

B) increased

C) redistributed and that distribution changes with time

D) decreased

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• question_answer30) There are ${{n}_{1}}$ photons of frequency ${{v}_{1}}$ in a beam of light. In an equally energetic beam there are ${{n}_{2}}$ photons of frequency ${{v}_{2}}$. Then the correct relation:

A) $\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{{{v}_{1}}}{{{v}_{2}}}$

B) $\frac{{{n}_{1}}}{{{n}_{2}}}=1$

C) $\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{{{v}_{2}}}{{{v}_{1}}}$

D) $\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{{{v}_{2}}^{2}}{{{v}_{1}}^{2}}$

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• question_answer31) A charge q is placed at the centre of the line joining two equal point charges each equal to Q. The system of 3 charges will be in equilibrium if q is equal to:

A) $+Q/4$

B) $-Q/2$

C) $+Q/2$

D) $-Q/4$

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• question_answer32) The inward and outward electric flux from a closed surface are respectively $8\times {{10}^{3}}$ and $4\times {{10}^{3}}$ units. Then the net charge inside the closed surface is:

A) $-4\times {{10}^{3}}$ coulomb

B) $4\times {{10}^{3}}$ coulomb

C) $\frac{-4\times {{10}^{3}}}{{{\varepsilon }_{0}}}$ coulomb

D) $-4\times {{10}^{3}}{{\varepsilon }_{0}}$coulomb

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• question_answer33) In the circuit as shown in the figure, the effective capacitance between A and B is: A) $2~\mu F$

B) $2~\mu F$

C) $8~\mu F$

D) $4~\mu F$

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• question_answer34) Capacitance of a parallel plate capacitor becomes $\frac{4}{3}$ times its original value, if a dielectric slab of thickness $t=d/2$ is inserted between the plates [d is the separation between the plates]. The dielectric constant of the slab is:

A) 4

B) 8

C) 2

D) 6

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• question_answer35) A charged particle of mass m and charge if is released from rest in an uniform electric field E neglecting the effect of gravity, the kinetic energy of the charged particle after t second is:

A) $\frac{2{{E}^{2}}{{t}^{2}}}{mq}$

B) $\frac{E{{q}^{2}}m}{2{{t}^{2}}}$

C) $\frac{Eqm}{t}$

D) $\frac{{{E}^{2}}{{q}^{2}}{{t}^{2}}}{2m}$

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• question_answer36) Two wires of the same dimensions but resistivities ${{\rho }_{1}}$ and ${{\rho }_{2}}$ are connected in series. The equivalent resistivity of the combination is:

A) $\frac{{{\rho }_{1}}+{{\rho }_{2}}}{2}$

B) ${{\rho }_{1}}+{{\rho }_{2}}$

C) $2\left( {{\rho }_{1}}+{{\rho }_{2}} \right)$

D) $\sqrt{{{\rho }_{1}}\,{{\rho }_{2}}}$

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• question_answer37) If a 30V, 90W bulb is to be worked in 120V line, the resistance to be connected in series with the bulb is:

A) $20~\,\Omega$

B) $10~\,\Omega$

C) $40~\,\Omega$

D) $30~\,\Omega$

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• question_answer38) The potential difference between me terminals of a cell in open circuit is 2.2 volt with resistance of 5 ohm across the terminals of a cell, the terminal potential difference is 1.8 volt. The internal resistance of the cell is:

A) $\frac{9}{10}$ ohm

B) $\frac{10}{9}$ ohm

C) $\frac{7}{12}$ ohm

D) $\frac{12}{7}$ ohm

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• question_answer39) Thirteen resistances each of resistance R ohm are connected in the circuit as shown in the figure. The effective resistance between A and B is: A) $\frac{4R}{3}\Omega$

B) $2R\Omega$

C) $R\Omega$

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

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• question_answer40) A group of N cells whose emf varies directly with the internal resistance as per the equation ${{E}_{N}}=1.5\,{{r}_{N}}$ are connected as shown in the figure above. The current I in the circuit is: A) 5.1 A

B) 0.51 A

C) 1.5 A

D) 0.15 A

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• question_answer41) The temperature coefficient of resistance of a wire is $0.00125/{{\,}^{o}}C$. Its resistance is 1 ohm at 300 K. Its resistance will be 2 ohm at:

A) 1127 K

B) 1400 K

C) 1154 K

D) 1100 K

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• question_answer42) A potentiometer has uniform potential gradient. The specific resistance of the material of the potentiometer wire is ${{10}^{-7}}$ ohm-metre and the current passing through it is 0.1 ampere, cross-section of the wire is 10 m. The potential gradient along the potentiometer wire is:

A) ${{10}^{-6}}V/m$

B) ${{10}^{-4}}V/m$

C) ${{10}^{-8}}V/m$

D) ${{10}^{-2}}V/m$

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• question_answer43) A fuse wire with radius 1 mm blows at 1.5 ampere. The radius of the fuse wire of the same material to blow at 3A will be:

A) ${{3}^{1/4}}mm$

B) ${{4}^{1/3}}mm$

C) ${{3}^{1/2}}mm$

D) ${{2}^{1/3}}mm$

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• question_answer44) A wire in the form of a circular loop of one turn carrying a current produces a magnetic field B at the centre. If the same wire is looped into a coil of two turns and carries the same current, the new value of magnetic induction at the centre is:

A) 3 B

B) 5 B

C) 4 B

D) 2 B

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• question_answer45) To send 10% of the main current through a moving coil galvanometer of resistance 99 ohm, the shunt required is:

A) 10 ohm

B) 9.9 ohm

C) 9 ohm

D) 11 ohm

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• question_answer46) The magnetic flux linked with a coil at any instant t is given by $\phi =5{{t}^{3}}-100t+300,$ the emf induced in the coil at $t=2$ second is:

A) 40 V

B) - 40 V

C) 300 V

D) 140 V

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• question_answer47) A charged particles moves along the line AB which lies in the same plane of a circular loop of conducting wire as shown in the figure. Then: A) no current will be induced in the loop

B) the current induced in the loop will change its direction as the charged particle passes by

C) the current induced will be anticlockwise

D) the current induced, will be clockwise

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• question_answer48) The time taken by A.C. of 50 Hz in reaching from zero to the maximum value is:

A) $50\times {{10}^{-3}}sec$

B) $5\times {{10}^{-3}}sec$

C) $1\times {{10}^{-3}}sec$

D) $2\times {{10}^{-3}}sec$

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• question_answer49) The ratio of the secondary to the primary turns in a transformer is 3 : 2 and the output power is P. Neglecting all power losses, the input power must be:

A) P/2

B) P

C) 2 P/3

D) 3 P/2

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• question_answer50) The material used for permanent magnet has:

A) low retentivity, high coercivity

B) high retentivity, low coercivity

C) high retentivity, high coercivity

D) low retentivity, low coercivity

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• question_answer51) A particle of mass M at rest decays into two masses ${{m}_{1}}$ and ${{m}_{2}}$ with non zero velocities. The ratio of de-Broglie wavelengths of the particles $\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}$ is:

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

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

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

D) $1:1$

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• question_answer52) For an electron in the second orbit of Bohrs hydrogen atom, the moment of linear momentum is:

A) $\pi h$

B) $2\pi h$

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

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

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• question_answer53) If elements with principal quantum number $n>4$were not allowed in nature, the number of possible elements would have been:

A) 32

B) 60

C) 64

D) 4

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• question_answer54) In photoelectric effect, the number of electrons ejected per second is:

A) proportional to the wavelength of light

B) proportional to the intensity of light

C) proportional to the work function of the metal

D) proportional to the frequency of light

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• question_answer55) Half life of a radioactive substance is 20 minutes. The time between 20% and 80% decay will be:

A) 40 minutes

B) 20 minutes

C) 25 minutes

D) 30 minutes

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• question_answer56) A hypothetical radioactive nucleus decays according to the following series $_{72}{{A}^{180}}\xrightarrow{\alpha }{{A}_{1}}\xrightarrow{{{\beta }^{-}}}{{A}_{2}}\xrightarrow{\alpha }{{A}_{3}}\xrightarrow{\gamma }{{A}_{4}}$ If the mass number and atomic number of A are respectively 180 and 72. Then the atomic number and mass number of A will respectively be:

A) 69, 171

B) 70, 172

C) 68, 172

D) 69, 172

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• question_answer57) Nucleus A is converted into C through the following reactions: $A\xrightarrow[{}]{{}}B+\alpha$ [$\alpha$ - alpha particle $B\xrightarrow[{}]{{}}C+2\beta$ $\beta$-electron] then:

A) A and B are isotopes

B) A and C are isobars

C) A and B are isobars

D) A and C are isotopes

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• question_answer58) If $m,\,{{m}_{n}}$ and ${{m}_{p}}$ are the masses of $_{Z}{{X}^{A}}$nucleus, neutron and proton respectively:

A) $m=\left( A-Z \right){{m}_{n}}+Z{{m}_{p}}$

B) $m<\left( A-Z \right){{m}_{n}}+Z{{m}_{p}}$

C) $m>\left( A-Z \right){{m}_{n}}+Z{{m}_{p}}$

D) $m=\left( A-Z \right){{m}_{p}}+Z{{m}_{n}}$

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• question_answer59) The electrical circuit used to get smooth D.C output from a rectifier circuit is called:

A) filter

B) oscillator

C) logic gates

D) amplifier

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• question_answer60) In the case of constants $\alpha$ and $\beta$ of a transistor:

A) $\alpha =\beta$

B) $\beta <1,\alpha >1$

C) $\alpha \beta =1$

D) $\beta >1,\alpha <1$

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• question_answer61) A colour less crystalline salt $x$ is soluble in dilute $HCl$. On adding $NaOH$ solution, it gives a white precipitate which is insoluble in excess of $NaOH$. $x$ is :

A) $A{{l}_{2}}{{(S{{O}_{4}})}_{3}}$

B) $ZnS{{O}_{4}}$

C) $MgS{{O}_{4}}$

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

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• question_answer62) Which metal is used to make alloy steel for armour plates, safes and helmets?

A) Al

B) Mn

C) Cr

D) Pb

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• question_answer63) lodoform test is not answered by:

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

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

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

D) $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}$

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• question_answer64) A gaseous carbon compound is soluble in dilute $HCl$. The solution on treating with $NaN{{O}_{2}}$ gives off nitrogen leaving behind a solution which smells of wood spirit. The carbon compound is:

A) $HCHO$

B) CO

C) ${{C}_{2}}{{H}_{5}}N{{H}_{2}}$

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

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• question_answer65) Which of the following statements is incorrect regarding benzyl chloride?

A) It gives white precipitate with alcoholic $AgN{{O}_{3}}$

B) It is an aromatic compound with substitution in the side chain

C) It undergoes nucleophilic substitution reaction

D) It is less reactive than vinyl chloride

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• question_answer66) Enthalpy of formation of HF and $HCl$ are -161 kJ and -92 kJ respectively. Which of the following statements is incorrect?

A) $HCl$ is more stable than HF

B) HF and $HCl$ arc exothermic compounds

C) The affinity of fluorine to hydrogen is greater than the affinity of chlorine to hydrogen

D) HF is more stable than $HCl$

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• question_answer67) Heat liberated with 100 ml of 1 N $NaOH$ is neutralised by 300 ml of IN $HCl$:

A) 11.56 kJ

B) 5.73 kJ

C) 22.92 kJ

D) 17.19 kJ

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• question_answer68) For a reaction $A+B\xrightarrow{{}}C+D$, if concentration of A is doubled without altering that of B, rate doubles. If concentration of B is increased nine times without altering that of A, rate triples. Order of the reaction is :

A) 2

B) 1

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

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

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• question_answer69) In Goldschmidt aluminothermic process, thermite contains :

A) 3 parts of $A{{l}_{2}}{{O}_{3}}$ and 4 parts of $Al$

B) 3 parts of $F{{e}_{2}}{{O}_{3}}$ and 2 parts of $Al$

C) 3 parts of $F{{e}_{2}}{{O}_{3}}$ and 1 part of $Al$

D) 1 part of $F{{e}_{2}}{{O}_{3}}$ and 1 part of $Al$

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• question_answer70) The structure of orthophosphoric acid is:

A) H-O-\overset{\begin{smallmatrix} O \\ \uparrow \end{smallmatrix}}{\mathop{\underset{\begin{align} & | \\ & O \\ & | \\ & H \\ \end{align}}{\mathop{P}}\,}}\,-O-H

B) O\leftarrow \overset{\begin{smallmatrix} O \\ | \end{smallmatrix}}{\mathop{\underset{\begin{align} & | \\ & O \\ & | \\ & H \\ \end{align}}{\mathop{P}}\,}}\,-O-H

C) $O\leftarrow \overset{\begin{smallmatrix} H \\ | \end{smallmatrix}}{\mathop{\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\mathop{P}}\,}}\,-O-H$

D) $H-OP=O$

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• question_answer71) A galvanic cell is constructed using the redox reaction, $\frac{1}{2}{{H}_{2}}(g)+AgCl(s){{H}^{+}}(aq)+C{{l}^{-}}$$(aq)+Ag(s)$it is represented as :

A) $Pt|{{H}_{2}}(g)|HCl(sol.n)|l\,AgN{{O}_{3}}(sol.n)|Ag$

B) $Ag|AgCl(s)|KCl(sol.n)|l\,HCl(sol.n)$$,\,{{H}_{2}}(g)|Pt$

C) $Pt|{{H}_{2}}(g)|KCl(sol.n)|l\,AgCl(s)\,l\,Ag$

D) $Pt|{{H}_{2}}(g)|HCl(sol.n)|l\,AgCl(s)\,l\,Ag$

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• question_answer72) Same amount of electric current is passed through solutions of $AgN{{O}_{3}}$ and $HCl$. If 1.08 g of silver is obtained in the first case, the amount of hydrogen liberated at S.T.P. in the second case is :

A) $224\,c{{m}^{3}}$

B) 1.008 g

C) $112\,c{{m}^{3}}$

D) $22400\,c{{m}^{3}}$

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• question_answer73) The flame colours of metal ions are due to:

A) Frenkel defect

B) Schottky defect

C) Metal deficiency defect

D) Metal excess defect

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• question_answer74) The order of reactivities of methyl halides in the formation of Grignard reagent is :

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

B) $C{{H}_{3}}Cl>C{{H}_{3}}Br>C{{H}_{3}}I$

C) $C{{H}_{3}}Br>C{{H}_{3}}CI>C{{H}_{3}}I$

D) $C{{H}_{3}}Br>C{{H}_{3}}I>C{{H}_{3}}Cl$

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• question_answer75) The reaction of an organic compound with ammonia followed by nitration of the product gives a powerful explosive, called RDX. The organic compound is :

A) phenol

B) toluene

C) glycerine

D) formaldehyde

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• question_answer76) A signature, written in carbon pencil weighs 1 mg. What is the number of carbon atoms present in the signature?

A) $5.02\times {{10}^{23}}$

B) $5.02\times {{10}^{20}}$

C) $6.02\times {{10}^{20}}$

D) $0.502\times {{10}^{20}}$

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• question_answer77) $N{{H}_{3}}$ and $HCl$ gas are introduced simultaneously from the two ends of a long tube. A white ring of $N{{H}_{4}}Cl$ appears first:

A) nearer to the $HCl$ end

B) at the centre of the tube

C) throughout the tube

D) nearer to the $N{{H}_{3}}$ end

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• question_answer78) A gas formed by the action of alcoholic $KOH$on ethyl iodide, decolourises alkaline $KMn{{O}_{4}}$. The gas is :

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

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

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

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

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• question_answer79) Which of the following is not a characteristic of chemisorption?

A) $\Delta H$is of the order of 400 kJ

B) Adsorption is irreversible

C) Adsorption may be multimolecular layer

D) Adsorption is specific

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• question_answer80) The concentration of electrolyte required to coagulate a given amount of $A{{s}_{2}}{{S}_{3}}$ sol. is minimum in the case of :

A) magnesium nitrate

B) potassium nitrate

C) potassium sulphate

D) aluminium nitrate

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• question_answer81) Identify the organic compound which, on heating with strong solution of $NaOH$, partly converted into an acid salt and partly into alcohol :

A) Benzyl alcohol

B) Acetaldehyde

C) Acetone

D) Benzaldehyde

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• question_answer82) The process by which synthesis of protein takes place based on the genetic information present in w-RNA is called :

A) translation

B) transcription

C) replication

D) messenger hypothesis

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• question_answer83) The enthalpies of formation of $A{{l}_{2}}{{O}_{3}}$ and $C{{r}_{2}}{{O}_{3}}$ are $-1596\text{ }kJ$ and $-1134kJ$ respectively. $\Delta H$ for the reaction, $2Al+C{{r}_{2}}{{O}_{3}}\xrightarrow{{}}2Cr+A{{l}_{2}}{{O}_{3}}$ is:

A) -2730 kJ

B) -462 kJ

C) -1365 kJ

D) +2730 kJ

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• question_answer84) The gaseous reaction $A+B2C+D+Q$ is most favoured at :

A) low temperature and high pressure

B) high temperature and high pressure

C) high temperature and low pressure

D) low temperature and low pressure

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• question_answer85) Temperature coefficient of a reaction is 2. When temperature is increased from ${{30}^{o}}C$ to${{100}^{o}}C$, rate of the reaction increases by :

A) 128 times

B) 100 times

C) 500 times

D) 250 times

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• question_answer86) The volume of water to be added to $\frac{N}{2}HCl$to prepare $500\,c{{m}^{3}}$ of $\frac{N}{10}$ solution is :

A) $450\text{ }c{{m}^{3}}$

B) $100\text{ }c{{m}^{3}}$

C) $45\text{ }c{{m}^{3}}$

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

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• question_answer87) The equivalent weight of a certain trivalent element is 20. Molecular, weight of its oxide is:

A) 152

B) 56

C) 168

D) 68

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• question_answer88) Identify the reaction that doesnt take place during the smelting process of copper extraction :

A) $2FeS+3{{O}_{2}}\xrightarrow{{}}2FeO+3S{{O}_{2}}\uparrow$

B) $C{{u}_{2}}O+FeS\xrightarrow{{}}C{{u}_{2}}S+FeO$

C) $2C{{u}_{2}}S+3{{O}_{2}}\xrightarrow{{}}2C{{u}_{2}}O+2S{{O}_{2}}\uparrow$

D) $FeO+Si{{O}_{2}}\xrightarrow{{}}FeSi{{O}_{3}}$

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• question_answer89) Pick out the complex compound in which the central metal atom obeys EAN rule strictly :

A) ${{K}_{4}}[Fe{{(CN)}_{6}}]$

B) ${{K}_{3}}[Fe{{(CN)}_{6}}]$

C) $[Cr{{({{H}_{2}}O)}_{6}}]C{{l}_{3}}$

D) $[Cu{{(N{{H}_{3}})}_{4}}]S{{O}_{4}}$

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• question_answer90) In a reversible reaction, the catalyst :

A) increases the activation energy of the backward reaction

B) increases the activation energy of the forward reaction

C) decreases the activation energy of both, forward and backward reaction

D) decreases the activation energy of forward reaction

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• question_answer91) Solubility product of a salt AB is $1\times {{10}^{-8}}$ in a solution in which concentration of A is ${{10}^{-3}}M$. The salt will precipitate when the concentration of B becomes more than :

A) ${{10}^{-4}}M$

B) ${{10}^{-7}}M$

C) ${{10}^{-6}}M$

D) ${{10}^{-5}}M$

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• question_answer92) The standard reduction potentials of Zn and Ag in water at 298 K are, $Z{{n}^{+2}}+2{{e}^{-}}Zn;$ ${{E}^{o}}=-0.76\,V$ and $A{{g}^{+}}+{{e}^{-}}Ag;$${{E}^{o}}=+0.80\,V$. Which of the following reactions take place?

A) $Z{{n}^{+2}}(aq)+2Ag(s)\xrightarrow{{}}2A{{g}^{+}}(aq)+Zn(s)$

B) $Zn(s)+2A{{g}^{+}}(aq)\xrightarrow{{}}Z{{n}^{+2}}(aq)+2Ag(s)$

C) $Z{{n}^{+2}}(aq)+A{{g}^{+}}(aq)\xrightarrow{{}}Zn(s)+Ag(s)$

D) $Zn(s)+Ag(s)\xrightarrow{{}}Z{{n}^{+2}}(aq)+A{{g}^{+}}(aq)$

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• question_answer93) The ratio of cationic radius to anionic radius in an ionic crystal is greater than 0.732. Its co-ordination number is :

A) 6

B) 8

C) 1

D) 4

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• question_answer94) Dacron is obtained by the condensation polymerization of :

A) Dimethyl terephthalate and ethylene glycol

B) Terephthalic acid and formaldehyde

C) Phenol and phthalic acid

D) Phenol and formaldehyde

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• question_answer95) 4-chloro-3, 5-dimethyl phenol is called :

A) Chloramphenicol

B) Paracetamol

C) Barbital

D) Dettol

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• question_answer96) The percentage s-character of the hybrid orbitals in methane, ethene and ethyne are respectively :

A) 25, 33, 50

B) 25, 50, 75

C) 50, 75, 100

D) 10, 20, 40

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• question_answer97) In the manufacture of sulphuric acid by contact process, Tyndall box is used to :

A) filter dust particles

B) remove impurities

C) convert $S{{O}_{2}}$ to $S{{O}_{3}}$

D) test the presence of dust particles

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• question_answer98) The pH value of gastric juice in human stomach is about 1.8 and in the small intestine it is about 7.8. The $p{{K}_{a}}$ value of aspirin is 3.5. Aspirin will be:

A) completely ionized in the small intestine and in the stomach

B) unionised in the small intestine and in the stomach

C) ionised in the small intestine and almost unionised in the stomach

D) ionised in the stomach and almost unionised in the small, intestine

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• question_answer99) The number of a and P particles emitted during the transformation of $_{90}T{{h}^{232}}$ to $_{82}P{{b}^{208}}$ are respectively :

A) 4, 2

B) 2, 2

C) 8, 6

D) 6, 4

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• question_answer100) When chlorine is passed through warm benzene in presence of the sunlight, the product obtained is :

A) Benzotrichloride

B) Chlorobenzene

C) Gammexane

D) D.D.T.

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• question_answer101) Ethyl benzoate reacts with $PC{{l}_{5}}$ to give :

A) ${{C}_{2}}{{H}_{5}}Cl+{{C}_{6}}{{H}_{5}}COCl+POC{{l}_{3}}+HCl$

B) ${{C}_{2}}{{H}_{5}}Cl+{{C}_{6}}{{H}_{5}}COCl+POC{{l}_{3}}$

C) $C{{H}_{3}}COCl+{{C}_{6}}{{H}_{5}}COCl+POC{{l}_{3}}$

D) ${{C}_{2}}{{H}_{5}}Cl+{{C}_{6}}{{H}_{5}}COOH+POC{{l}_{3}}$

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• question_answer102) Pick out the statement which is not relevant in the discussion of colloids :

A) Sodium aluminium silicate is used in the softening of hard water

B) Potash alum is used in shaving rounds and as a styptic in medicine

C) Artificial rain is caused by throwing electrified sand on the clouds from an aeroplane

D) Deltas are formed at a place where the river pours its water into the sea

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• question_answer103) A wooden box excavated from Indus valley had an activity of $1.18\times {{10}^{13}}$ disintegration per minute per gm. of carbon. What is the approximate age of this civilisation?

A) 4000 years

B) 5700 years

C) 8100 years

D) 6000 years

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• question_answer104) For a reaction if ${{K}_{p}}>{{K}_{c}}$, the forward reaction is favoured by :

A) low pressure

B) high pressure

C) high temperature

D) low temperature

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• question_answer105) In a lime kiln, to get higher yield of $C{{O}_{2}}$, the measure that can be taken is :

A) to remove CaO

B) to add more $CaC{{O}_{3}}$

C) to maintain high temperature

D) to pump out $C{{O}_{2}}$

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• question_answer106) What is the volume of 20 volume ${{H}_{2}}{{O}_{2}}$ required to get $5000\text{ }c{{m}^{3}}$ of oxygen at S.T.R?

A) $250\text{ }c{{m}^{3}}$

B) $50\text{ }c{{m}^{3}}$

C) $100\text{ }c{{m}^{3}}$

D) $125\text{ }c{{m}^{3}}$

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• question_answer107) The IUPAC name of ${{(C{{H}_{3}})}_{3}}C-CH=C{{H}_{2}}$ is:

A) 1, 1, l-trimethyl-2-propene

B) 3, 3, 3-trimethyl-2-propene

C) 2, 2-dimethyl-3-butene

D) 3, 3-dimethyl-l-butene

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• question_answer108) Railway wagon axles are made by heating iron rods embedded in charcoal powder. This process is known as:

A) Tempering

B) Case hardening

C) Sherardising

D) Annealing

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• question_answer109) Thomas slag is ...

A) $CaSi{{O}_{3}}$

B) $C{{a}_{3}}{{(P{{O}_{4}})}_{2}}$

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

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

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• question_answer110) Urea is preferred to ammonium sulphate as a nitrogenous fertilizer because :

A) it is more soluble in water

B) it is cheaper than ammonium sulphate

C) it is quite stable

D) it does not cause acidity in the soil

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• question_answer111) Two gas cylinders having same capacity have been filled with 44 g of ${{H}_{2}}$ and 44 g of $C{{O}_{2}}$respectively. If the pressure in $C{{O}_{2}}$ cylinder is 1 atmosphere at a particular temperature, the pressure in the hydrogen cylinder at the same temperature is :

A) 2 atmosphere

B) 1 atmosphere

C) 22 atmosphere

D) 44 atmosphere

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• question_answer112) Angular momentum of an electron in the nth orbit of hydrogen atom is given by :

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

B) $nh$

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

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

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• question_answer113) The element with atomic number 36 belongs to ......... block in the periodic table :

A) $p$

B) $s$

C) $f$

D) $d$

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• question_answer114) The function of $AlC{{l}_{3}}$ in Friedel-Crafts reaction is :

A) to absorb $HCl$

B) to absorb water

C) to produce nucleophiie

D) to produce electrophile

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• question_answer115) An important reaction of acetone is auto condensation in presence of concentrated sulphuric acid to give the aromatic compound ......

A) mesitylene

B) mesityl oxide

C) trioxan

D) phorone

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• question_answer116) Kinetic energy of one mole of an ideal gas at 300 K in kJ is :

A) 3.74

B) 348

C) 34.8

D) 3.48

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• question_answer117) The tripeptide hormone present in most living cells is :

A) glutathione

B) glutamine

C) oxytocin

D) ptyalin

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• question_answer118) Phenol$\xrightarrow{NaN{{O}_{2}}|{{H}_{2}}S{{O}_{4}}}B\xrightarrow{{{H}_{2}}O}C\xrightarrow{NaOH}D$name of the reaction is :

A) Liebermanns reaction

B) Phthalein fusion test

C) Reimer Tiemann reaction

D) Schotten-Baumann reaction

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• question_answer119) Energy is stored in our body in the form of:

A) ATP

B) ADP

C) Fats

D) Carbohydrates

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• question_answer120) An organic compound answers Molischs test as well as Benedicts test. But it does not answer Scliwanoffs test. Most probably, it is :

A) sucrose

B) protein

C) fructose

D) maltose

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• question_answer121) In Z, the set of all integers, the inverse of -7 w.r.t. *defined by $a*b=a+b+7$ for all $a,\,b\,\in Z$ is :

A) -14

B) 7

C) 14

D) -7

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• question_answer122) $(p\wedge \,\,\,\,\,\,\,p)\wedge (\sim p\wedge q)$is:

A) a tautology

B) a contradiction

C) tautology and contradiction

D) neither a tautology nor a contradiction

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• question_answer123) The number of words that can be formed out of the letters of the word ARTICLE so that the vowels occupy even places is :

A) 574

B) 36

C) 754

D) 144

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• question_answer124) In $\Delta \,ABC$ if $\left| \begin{matrix} 1 & a & b \\ 1 & c & a \\ 1 & b & c \\ \end{matrix} \right|=0$ then${{\sin }^{2}}A+{{\sin }^{2}}B+{{\sin }^{2}}C$ is equal to :

A) $\frac{4}{9}$

B) $\frac{9}{4}$

C) $3\sqrt{3}$

D) 1

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• question_answer125) 7th term of an A.P. is 40. Then the sum of first 13 terms is :

A) 520

B) 53

C) 2080

D) 1040

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• question_answer126) The coefficient of ${{x}^{32}}$in the expansion of${{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}$is:

A) $^{-15}{{C}_{3}}$

B) $^{15}{{C}_{4}}$

C) $^{-15}{{C}_{5}}$

D) $^{15}{{C}_{2}}$

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• question_answer127) Which of the following is a subgroup of$a=\text{ }\!\!\{\!\!\text{ }0,1,2,3,4,5\text{ }\!\!\}\!\!\text{ },$ under addition modules 6?

A) {0, 2}

B) {0, 1}

C) {0, 4}

D) {0, 3}

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• question_answer128) Assuming that the sums and products given below are defined which of the following is not true for matrices?

A) $AB=AC$ does not imply $B=C$

B) $A+B=B+A$

C) $(AB)=BA$

D) $AB=0$ implies $A=0$ or $B=0$

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• question_answer129) Inverse of the matrix $\left[ \begin{matrix} 1 & -2 \\ 3 & 4 \\ \end{matrix} \right]$ is :

A) $\frac{1}{10}\left[ \begin{matrix} 1 & -2 \\ 3 & 4 \\ \end{matrix} \right]$

B) $\frac{1}{10}\left[ \begin{matrix} 4 & 2 \\ -3 & 1 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} 4 & 2 \\ -3 & 1 \\ \end{matrix} \right]$

D) $\frac{1}{10}\left[ \begin{matrix} 4 & -2 \\ -3 & 1 \\ \end{matrix} \right]$

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• question_answer130) If the vectors $4\hat{i}+11\hat{j}+m\hat{k}$, $7\hat{i}+2\hat{j}+6\hat{k}$ and $i+5j+4k$ arc coplanar then m is equal to :

A) 0

B) 38

C) -10

D) 10

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• question_answer131) $\left| \begin{matrix} {{b}^{2}}{{c}^{2}} & bc & b+c \\ {{c}^{2}}{{a}^{2}} & ca & c+a \\ {{a}^{2}}{{b}^{2}} & ab & a+b \\ \end{matrix} \right|$ is equal to :

A) $\frac{1}{abc}(ab+bc+ca)$

B) $ab+bc+ca$

C) 0

D) $a+b+c$

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• question_answer132) In $\Delta \,ABC$ if $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$ then $\cos C$is equal to :

A) $\frac{5}{7}$

B) $\frac{7}{5}$

C) $\frac{16}{17}$

D) $\frac{17}{36}$

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• question_answer133) The value of $\frac{\tan {{70}^{o}}-\tan {{20}^{o}}}{\tan {{50}^{o}}}$ is equal to:

A) 2

B) 1

C) 0

D) 3

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• question_answer134) $\cos {{1}^{o}}+\cos {{2}^{o}}+\cos {{3}^{o}}+....+\cos {{180}^{o}}$ is equal to :

A) 1

B) 0

C) 2

D) -1

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• question_answer135) If $\left| \vec{a}\times \vec{b} \right|=4$ and $\left| \vec{a}\,.\,\vec{b} \right|=2$ then ${{\left| {\vec{a}} \right|}^{2}}{{\left| {\vec{b}} \right|}^{2}}$ is equal to :

A) 6

B) 2

C) 20

D) 8

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• question_answer136) $\underset{x\to 0}{\mathop{\lim }}\,\,\,\,{{(1-ax)}^{1/x}}$ is equal to :

A) ${{e}^{-a}}$

B) e

C) ${{e}^{a}}$

D) 1

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• question_answer137) Which of the following is not a proposition :

A) 3 is prime

B) $\sqrt{2}$ is irrational

C) Mathematics is interesting

D) 5 is an even integer

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• question_answer138) $\underset{n\to \infty }{\mathop{\lim }}\,\,{{({{3}^{n}}+{{4}^{n}})}^{1/n}}$ is equal to :

A) 4

B) 3

C) e

D) $\infty$

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• question_answer139) The distance between the directories of the hyperbola $x=8\sec \theta ,\,y=8\,\tan \theta$ is :

A) $8\sqrt{2}$

B) $16\sqrt{2}$

C) $4\sqrt{2}$

D) $6\sqrt{2}$

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• question_answer140) The general solution of the equation $\tan 2\theta \,.\,\tan \theta =1$ for $n\in z$ is, $\theta$ is equal to:

A) $(2n+1)\frac{\pi }{4}$

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

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

D) $\frac{1}{1}(2n+1)\frac{\pi }{3}$

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• question_answer141) $\sin \left( \frac{1}{2}{{\cos }^{-1}}\frac{4}{5} \right)$ is equal to :

A) $-\frac{1}{\sqrt{10}}$

B) $\frac{1}{\sqrt{10}}$

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

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

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• question_answer142) The angle between the vectors $\vec{a}+\vec{b}$ and $\vec{a}-\vec{b}$ when $a=(1,1,4)$ and $b=(1,-1,4)$is:

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

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

C) ${{15}^{o}}$

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

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• question_answer143) The angle between the lines in ${{x}^{2}}-xy-6{{y}^{2}}-7x+31y-18=0$ is :

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

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

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

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

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• question_answer144) The equation of line bisecting perpendicularly the segment joining the points (-4, 6) and (8,8) is :

A) $y=7$

B) $6x+y-19=0$

C) $x+2y-7=0$

D) $6x+2y-19=0$

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• question_answer145) If the distance of any point P from the points $A\,(a+b,\,\,a-b)$ and B $B\,(a-b,\,\,a+b)$ are equal then the locus of P is :

A) $ax+by=0$

B) $x-y=0$

C) $x+y=0$

D) $bx-ay=0$

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• question_answer146) If p is the length of the perpendicular from the origin on the line whose intercepts on the axes are a and b then :

A) ${{p}^{2}}={{a}^{2}}+{{b}^{2}}$

B) ${{p}^{2}}={{a}^{2}}-{{b}^{2}}$

C) $\frac{1}{{{p}^{2}}}=\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}$

D) $\frac{1}{{{p}^{2}}}=\frac{1}{{{a}^{2}}}-\frac{1}{{{b}^{2}}}$

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• question_answer147) If the slope of one of the lines given by $a{{x}^{2}}+2hxy+b{{y}^{2}}=0$ is 5 times the other then:

A) $5{{h}^{2}}=9ab$

B) $5{{h}^{2}}=ab$

C) ${{h}^{2}}=ab$

D) $9{{h}^{2}}=5ab$

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• question_answer148) $\int_{0}^{2\pi }{(\sin x+|\sin x|dx}$ is equal to :

A) 4

B) 0

C) 1

D) 8

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• question_answer149) $\int_{0}^{\pi }{\frac{x\,dx}{{{a}^{2}}{{\cos }^{2}}x+{{b}^{2}}{{\sin }^{2}}x}}$ is equal to :

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

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

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

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

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• question_answer150) The differential equation for which ${{\sin }^{-1}}x+{{\sin }^{-1}}y=c$ is given by :

A) $\sqrt{1-{{x}^{2}}}dy+\sqrt{1-{{y}^{2}}}\,dx=0$

B) $\sqrt{1-{{x}^{2}}}dx+\sqrt{1-{{y}^{2}}}\,dy=0$

C) $\sqrt{1-{{x}^{2}}}dx-\sqrt{1-{{y}^{2}}}\,dy=0$

D) $\sqrt{1-{{x}^{2}}}dy-\sqrt{1-{{y}^{2}}}\,dx=0$

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• question_answer151) The derivative of ${{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)$ w.r.t. ${{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)$is :

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

B) 1

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

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

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• question_answer152) If $x=a\,(\theta -\sin \theta ),\,y=a\,(1-\cos \theta )$ then $\frac{dy}{dx}$ is equal to :

A) $\cot \theta /2$

B) $\tan \theta /2$

C) $\frac{1}{2}\cos e{{c}^{2}}\frac{\theta }{2}$

D) $-\frac{1}{2}\cos e{{c}^{2}}\frac{\theta }{2}$

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• question_answer153) If $y=1-x+\frac{{{x}^{2}}}{2!}-\frac{{{x}^{3}}}{3!}+\frac{{{x}^{4}}}{4\,!}....$then $\frac{{{d}^{2}}y}{d{{x}^{2}}}$is equal to :

A) $-x$

B) $x$

C) $y$

D) $-y$

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• question_answer154) If $\sqrt{x}+\frac{1}{\sqrt{x}}=2\,\cos \theta$ then ${{x}^{6}}+{{x}^{-6}}$ is equal to:

A) $2\cos 12\theta$

B) $2\cos 6\,\theta$

C) $2\sin 3\,\theta$

D) $2\cos 3\,\theta$

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• question_answer155) The slope of the tangent to the curve$x=3{{t}^{2}}+1,\,y={{t}^{3}}-1$ at $x=1$ is :

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

B) 0

C) -2

D) $\infty$

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• question_answer156) Which of the following is a fourth root $\frac{1}{2}+\frac{\sqrt{3}}{2}$?

A) $cis\frac{\pi }{12}$

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

C) $cis\frac{\pi }{6}$

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

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• question_answer157) If $f(a)=2f(a)=1,\,g(a)=3,\,g(a)=-1$ then $\underset{x\to a}{\mathop{\lim }}\,\frac{f(a)\,g\,(x)-f(x)\,g\,(a)}{x-a}$ equal to :

A) 6

B) 1

C) -1

D) -5

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• question_answer158) The rate of change of the surface area of the sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to :

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

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

C) ${{r}^{2}}$

D) $r$

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• question_answer159) The amplitude of $\sin \frac{\pi }{5}+i\left( 1-\cos \frac{\pi }{5} \right)$ is :

A) $\frac{2\pi }{5}$

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

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

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

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• question_answer160) For the curve $xy={{c}^{2}}$ the subnormal at any point varies as :

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

B) ${{x}^{2}}$

C) ${{y}^{3}}$

D) $\infty$

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• question_answer161) The function $f(x)=\left| x \right|+\frac{\left| x \right|}{x}$ is :

A) discontinuous at origin because $\left| x \right|$ is discontinuous there

B) continuous at origin

C) discontinuous at origin because both $\left| x \right|$ and $\frac{\left| x \right|}{x}$ are discontinuous there

D) discontinuous at the origin because is discontinuous there.

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• question_answer162) $\int{{{e}^{x}}\left( \frac{1+\sin x}{1+\cos x} \right)dx}$ is equal to :

A) ${{e}^{x}}{{\sec }^{2}}\frac{x}{2}+C$

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

C) ${{e}^{x}}\sec \frac{x}{2}+C$

D) ${{e}^{x}}+\tan x+C$

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• question_answer163) $\int{\sqrt{1+\sin \left( \frac{x}{4} \right)}\,dx}$ is equal to :

A) $8\,\left( \sin \frac{x}{8}+\cos \frac{x}{8} \right)+C$

B) $8\,\left( \sin \frac{x}{8}-\cos \frac{x}{8} \right)+C$

C) $8\,\left( \cos \frac{x}{8}-\sin \frac{x}{8} \right)+C$

D) $8\,\left( \sin \frac{x}{8}-\cos \frac{x}{8} \right)+C$

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• question_answer164) $\int_{0}^{\infty }{\frac{x\,dx}{(1+x)\,(1+{{x}^{2}})}}$ is equal to :

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

B) 0

C) 1

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

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• question_answer165) If ${{I}_{n}}\int{{{(\log \,x)}^{n}}dx}$ then ${{I}_{n}}+n\,{{I}_{n-1}}$ is equal to :

A) ${{(x\,\log \,x)}^{n}}$

B) $x\,{{(\log \,x)}^{n}}$

C) $n\,{{(\log \,x)}^{n}}$

D) ${{(\log \,x)}^{n-1}}$

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• question_answer166) The area included between the parabolas$x=4y$ and $y=4x$ is (in square units) :

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

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

C) $\frac{16}{3}$

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

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• question_answer167) If ${{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=3\pi$ then$xy+yz+zx$ is equal to :

A) 1

B) 0

C) -3

D) 3

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• question_answer168) Which of the following is a group?

A) {1, 2, 4, 8} under multiplication

B) $\{0,\pm \,2,\pm \,4,\pm \,6\text{ }...\}$ under addition

C) $\{1,-1\}$ under addition

D) {0,1,2,3, 4} under multiplication module 5

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• question_answer169) If the circles ${{x}^{2}}+{{y}^{2}}+2gx+2fy=0$ and${{x}^{2}}+{{y}^{2}}+2gx+2fy=0$ touch each other then :

A) $ff=gg$

B) $fg=fg$

C) ${{(fg)}^{2}}={{(fg)}^{2}}$

D) $fg=fg$

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• question_answer170) The line $3x-2y=k$ meets the circle${{x}^{2}}+{{y}^{2}}=4{{r}^{2}}$ at only one point if k is equal to:

A) $52{{r}^{2}}$

B) $20{{r}^{2}}$

C) $\frac{20}{9}{{r}^{2}}$

D) $\frac{52}{9}{{r}^{2}}$

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• question_answer171) In three element group $\{e,a,b\}$ where e is the identity a b is equal to :

A) a

B) e

C) ab

D) b

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• question_answer172) The locus of a point which moves such that the difference of its distances from two fixed points is always a constant is :

A) a circle

B) a straight line

C) a hyperbola

D) an ellipse

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• question_answer173) The directrix of the parabola${{x}^{2}}-4x-8y+12=0$ is :

A) $y=0$

B) $x=1$

C) $y=-1$

D) $x=-1$

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• question_answer174) Which of the following is a point on the common chord of the circle${{x}^{2}}+{{y}^{2}}+2x-3y+6=0$ and${{x}^{2}}+{{y}^{2}}+x-8y-13=0$

A) (1, 4)

B) (1, -2)

C) (1, -4)

D) (1, 2)

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• question_answer175) The locus of the point of intersection of the perpendicular tangents to ellipse $\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1$ is:

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

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

C) ${{x}^{2}}+{{y}^{2}}=5$

D) ${{x}^{2}}+{{y}^{2}}=13$

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• question_answer176) The sum of the coefficients in the expansion of ${{(1+x-3{{x}^{2}})}^{3148}}$ is :

A) 8

B) 7

C) 1

D) -1

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• question_answer177) The relation $R=((1,1),\text{(}2,\,2\text{)},\,\text{(}3,\,\,3\text{)}\}$ on the set $\{1,2,3\}$ is :

A) symmetric only

B) reflexive only

C) an equivalence relation

D) transitive only

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• question_answer178) The least remainder when ${{17}^{30}}$ is divided by 5 is:

A) 2

B) 1

C) 4

D) 2

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• question_answer179) The limiting points of the co-axial system of circles ${{x}^{2}}+{{y}^{2}}+2\lambda y+4=0$ are :

A) $(0\pm 4)$

B) $(\pm 2,\,0)$

C) $(0,\pm 1)$

D) $(0,\pm 2)$

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• question_answer180) The maximum of $4{{\sin }^{2}}x+3{{\cos }^{2}}x$ is :

A) 4

B) 3

C) 7

D) 5

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