# Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2010

### done CET - Karnataka Engineering Solved Paper-2010

• question_answer1) All capacitors used in the diagram are identical and each is of capacitance C. Then the effective capacitance between the point A and B is

A) 1.5 C

B) 6 C

C) C

D) 3 C

• question_answer2) Two identical conducting balls A and B have positive charges ${{q}_{1}}$ and ${{q}_{2}}$ respectively but ${{q}_{1}}\ne {{q}_{2}}.$ The balls are brought together so that they touch each other and then kept in their original positions. The force between them is

A) less than that before the balls touched

B) greater than that before the balls touched

C) same as that before the balls touched

D) zero

• question_answer3)   Red light of wavelength 625 nm is incident normally on an optical diffraction grating with $2\times {{10}^{5}}$ lines/m. Including central principal maxima, how many maxima may be observed on a screen which is far from the grating?

A) 15

B) 17

C) 8

D) 16

• question_answer4) A battery of emf E has an internal resistance r. A variable resistance R is connected to the terminals of the battery. A current; is drawn from the battery. V is the terminal potential difference. If R alone is gradually reduced to zero, which of the following best describes $i$and V?

A) $i$approaches zero, V approaches E

B) $i$ approaches $\frac{E}{r}$, V approaches zero

C) $i$ approaches $\frac{E}{r}$, V approaches E

D) $i$ approaches infinity, V approaches E

• question_answer5) Three voltmeters A, B and C having resistances R, 1.5R and 3 R respectively are used in a circuit as shown. When a potential difference is applied between X and Y, the readings of the voltmeters are ${{V}_{1}},\text{ }{{V}_{2}}$, and ${{V}_{3}}$respectively. Then

A) ${{V}_{1}}={{V}_{2}}={{V}_{3}}$

B) ${{V}_{1}}<{{V}_{2}}={{V}_{3}}$

C) ${{V}_{1}}>{{V}_{2}}>{{V}_{3}}$

D) ${{V}_{1}}>{{V}_{2}}={{V}_{3}}$

• question_answer6) A point object O is placed in front of a glass rod having spherical end of radius of curvature 30 cm. The image would be formed at

A) 30 cm left

B) infinity

C) 1 cm to the right

D) 18 cm to the left

• question_answer7) A, B and C are the parallel sided transparent media of refractive indices ${{n}_{1}},{{n}_{2}}$ and ${{n}_{3}}$respectively. They are arranged as shown in the figure. A ray is incident at an angle $i$ on the surface of separation of A and B which is as shown in the figure. After the refraction into the medium B, the ray grazes the surface of separation of the madia B and C. Then, $\sin i$ equals to

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

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

C) $\frac{{{n}_{2}}}{{{n}_{3}}}$

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

• question_answer8) A boat has green light of wavelength $\lambda =500\,nm$ on the mast. What wavelength would be measured and what colour would be observed for this light as seen by a diver submerged in water by the side of the boat? Given, ${{n}_{w}}=\frac{4}{3}$.

A) Green of wavelength 376 nm

B) Red of wavelength 665 nm

C) Green of wavelength 500 nm

D) Blue of wavelength 376 nm

• question_answer9) Two beams of red and violet colours are made to pass separately through a prism of $A={{60}^{o}}$. In the minimum deviation position, the angle of refraction inside the prism will be

A) greater for red colour

B) equal but not ${{30}^{o}}$ for both the colours

C) greater for violet colour

D) ${{30}^{o}}$ for both the colours

• question_answer10) A plano-convex lens is made of refractive index of 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is

A) 400 cm

B)   200 cm

C)   100 cm

D)   50 cm

• question_answer11) Two simple harmonic motions are represented by ${{y}_{1}}=5[\sin 2\pi t+\sqrt{3}\cos 2\pi t]$and ${{y}_{2}}=5\sin \left( 2\pi t+\frac{\pi }{4} \right)$ The ratio of their amplitudes is

A) $1:1$

B) $2:1$

C) $1:3$

D) $\sqrt{3}:1$

• question_answer12) A bat flies at a steady speed of $4\text{ }m{{s}^{-1}}$ emitting a sound of $f=90\times {{10}^{3}}Hz$. It is flying horizontally towards a vertical wall. The frequency of the reflected sound as detected by the bat will be (take velocity of sound in air is $330\text{ }m{{s}^{-1}}$)

A) $88.1\times {{10}^{3}}Hz$

B) $87.1\times {{10}^{3}}Hz$

C) $92.1\times {{10}^{3}}Hz$

D) $89.1\times {{10}^{3}}Hz$

• question_answer13) A closed organ pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then the number of beats produced per second while vibrating in the fundamental mode is

A) 2

B) 6

C) 8

D) 7

• question_answer14) A uniform wire of length L, diameter D and density $\rho$ is stretched under a tension T. The correct relation between, its fundamental frequency $f$, the length L and the diameter D is

A) $f\propto \frac{1}{LD}$

B) $f\propto \frac{1}{L\sqrt{D}}$

C) $f\propto \frac{1}{{{D}^{2}}}$

D) $f\propto \frac{1}{L{{D}^{2}}}$

• question_answer15) Two small spheres of masses ${{M}_{1}}$ and ${{M}_{2}}$are suspended by weightless insulating threads of lengths ${{L}_{1}}$ and ${{L}_{2}}$. The spheres carry charges ${{Q}_{1}}$ and ${{Q}_{2}}$ respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of ${{\theta }_{1}}$ and ${{\theta }_{2}}$ as shown. Which one of the following conditions is essential, if ${{\theta }_{1}}={{\theta }_{2}}$?

A) ${{M}_{1}}\ne {{M}_{2}},$ but ${{Q}_{1}}={{Q}_{2}}$

B) ${{M}_{1}}={{M}_{2}}$

C) ${{Q}_{1}}={{Q}_{2}}$

D) ${{L}_{1}}={{L}_{2}}$

• question_answer16) The wavelength of the light used in Young's double slit experiment is $\lambda$. The intensity at a point on the screen is $I$, where the path difference is $\frac{\lambda }{6}$. If ${{I}_{0}}$ denotes the maximum intensity, then the ratio of $I$ and ${{I}_{0}}$ is

A) 0.866

B) 0.5

C) 0.707

D) 0.75

• question_answer17) What is the minimum thickness of a thin film required for constructive interference in the reflected light from it? Given, the refractive index of the film = 1.5, wavelength of the light incident on the film = 600 nm.

A) 100 nm

B) 300 nm

C) 50 nm

D) 200 nm

• question_answer18) There is a uniform electric field of intensity E which is as shown. How many labelled points have the same electric potential as the fully shaded point?

A) 2

B) 3

C) 8

D) 11

• question_answer19) Critical angle for certain medium is $si{{n}^{-1}}(0.6)$. The polarizing angle of that medium is

A) $ta{{n}^{-1}}[1.5]$

B) ${{\sin }^{-1}}[0.8]$

C) ${{\tan }^{-1}}[1.6667]$

D) ${{\tan }^{-1}}[0.6667]$

• question_answer20) The speed of electromagnetic wave in vacuum depends upon the source of radiation

A) increases as we move from $\gamma$-rays to radio waves

B) decreases as we move from $\gamma$-rays to radio waves

C) is same for all of them

D) None of the above

• question_answer21) The moment of inertia of a circular disc of radius 2 m and mass 1 kg about an axis passing through the centre of mass but perpendicular to the plane of the disc is$2\text{ }kg\text{ }{{m}^{2}}$. Its moment of inertia about an axis parallel to this axis but passing through the edge of the disc is (see the given figure).

A) $8\text{ }kg\text{ }{{m}^{2}}$

B) $4\text{ }kg\text{ }{{m}^{2}}$

C) $10\text{ }kg\text{ }{{m}^{2}}$

D) $6\text{ }kg\text{ }{{m}^{2}}$

• question_answer22) An astronaut on a strange planet finds that acceleration due to gravity is twice as that on the surface of earth. Which of the following could explain this?

A) Both the mass and radius of the planet are half as that of earth

B) Radius of the planet is half as that of earth, but the mass is the same as that of earth

C) Both the mass and radius of the planet are twice as that of earth

D) Mass of the planet is half as that of earth, but radius is same as that of earth

• question_answer23) Which of the following substances has the highest elasticity?

A) Sponge

B) Steel

C) Rubber

D) Copper

• question_answer24) Three liquids of equal masses are taken in three identical cubical vessels A, B and C. Their densities are ${{\rho }_{A}},{{\rho }_{B}}$ and ${{\rho }_{C}}$respectively but ${{\rho }_{A}}<{{\rho }_{B}}<{{\rho }_{C}}.$ The force exerted by the liquid on the base of the cubical vessel is

A) maximum in vessel C

B) minimum in vessel C

C) the same in all the vessels

D) maximum in vessel A

• question_answer25) Water is in streamline flows along a horizontal pipe with non-uniform cross-section. At a point in the pipe where the area of cross section is $10\text{ }c{{m}^{2}}$, the velocity of water is $1\text{ }m{{s}^{-1}}$ and the pressure is 2000 Pa. The pressure at another point where the cross sectional area is $5\text{ }c{{m}^{2}}$ is

A) 4000 Pa

B) 2000 Pa

C) 1000 Pa

D) 500 Pa

• question_answer26) In the circuit given here, the points A, B and C are 70 V, zero, 10 V respectively. Then

A) the point D will be at a potential of 60 V

B) the point D will be at a potential of 20 V

C) currents in the paths AD, DB and DC are in the ratio of $1:2:3$

D)  currents in the paths AB, DB and DC are in the ratio of $3:2:1$

• question_answer27) ${{B}_{1}},{{B}_{2}}$ and ${{B}_{3}}$ are the three identical bulbs connected to a battery of steady emf with key K closed. What happens to the brightness of the bulbs ${{B}_{1}}$ and ${{B}_{2}}$ when the key is opened?

A) Brightness of the bulb ${{B}_{1}}$ increases and that of ${{B}_{2}}$ decreases

B) Brightness of the bulbs ${{B}_{1}}$ and ${{B}_{2}}$increase

C) Brightness of the bulb ${{B}_{1}}$ decreases and ${{B}_{2}}$increases

D) Brightness of the bulbs ${{B}_{1}}$ and ${{B}_{2}}$decrease

• question_answer28) Magnetic field at the centre of a circular coil of radius R due to $i$ flowing through it is B. The magnetic field at a point along the axis at distance R from the centre is

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

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

C) $\frac{B}{\sqrt{8}}$

D) $\sqrt{8}B$

• question_answer29) Two thick wires and two thin wires, all of same material and same length, form a square in three different ways P, Q and R as shown in the figure. With correct connections shown, the magnetic field due to the current flow, at the centre of the loop will be zero in case of

A) Q and R

B) P only

C) P and Q

D) P and R

• question_answer30) There is a uniform magnetic field directed perpendicular and into the plane of the paper. An irregular shaped conducting loop is slowly changing into a circular loop in the plane of the paper. Then

A) current is induced in the loop in the anticlockwise direction

B) current is induced in the loop in the clockwise direction

C) AC is induced in the loop

D) no current is induced in the loop

• question_answer31) The dimensions of resistance are same as those of..... .where h is the Planck's constant, e is the charge.

A) $\frac{{{h}^{2}}}{{{e}^{2}}}$

B) $\frac{{{h}^{2}}}{e}$

C) $\frac{h}{{{e}^{2}}}$

D) $\frac{h}{e}$

• question_answer32) A train is moving slowly on a straight track with a constant speed of $2\text{ }m{{s}^{-1}}$. A passenger in that train starts walking at a steady speed of $2\text{ }m{{s}^{-1}}$ to the back of the train in the opposite direction of the motion of the train. So to an observer standing on the platform directly in front of that passenger, the velocity of the passenger appears to be

A) $4\,m{{s}^{-1}}$

B) $2\,m{{s}^{-1}}$

C) $2\,m{{s}^{-1}}$ in the opposite direction of the train

D) zero

• question_answer33) A ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards right as shown relative to its initial position with respect to the table, the ball

A) Both (1) and (2)

B) only (3)

C) only (1)

D) only (2)

• question_answer34) A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position X are respected by

A)

B)

C)

D)

• question_answer35) If the linear momentum of a body is increased by 50%, then the kinetic energy of that body increases by

A) 100%

B) 125%

C) 225%

D) 25%

• question_answer36) The temperature of a gas contained in a closed vessel of constant volume increases by ${{1}^{o}}C$ when the pressure of the gas is increased by 1%. The initial temperature of the gas is

A) 100 K

B) ${{273}^{o}}C$

C) ${{100}^{o}}C$

D) 200 K

• question_answer37) A motorboat covers a given distance in 6 h moving downstream on a river. It covers the same distance in 10 h moving upstream. The time it takes to cover the same distance in still water is

A) 9 h

B) 7.5 h

C) 6.5 h

D) 8 h

• question_answer38) Two slabs are of the thicknesses ${{d}_{1}}$ and ${{d}_{2}}$. Their thermal conductivities are ${{K}_{1}}$ and ${{K}_{2}}$ respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures ${{\theta }_{1}}$ and ${{\theta }_{2}}$. Assume ${{\theta }_{1}}>{{\theta }_{2}}$. The temperature $\theta$ of their common junction is

A)   $\frac{{{K}_{1}}{{\theta }_{1}}+{{K}_{2}}{{\theta }_{2}}}{{{\theta }_{1}}+{{\theta }_{2}}}$

B)   $\frac{{{K}_{1}}{{\theta }_{1}}{{d}_{1}}+{{K}_{2}}{{\theta }_{2}}{{d}_{2}}}{{{K}_{1}}{{d}_{2}}+{{K}_{2}}{{d}_{1}}}$

C)   $\frac{{{K}_{1}}{{\theta }_{1}}{{d}_{2}}+{{K}_{2}}{{\theta }_{2}}{{d}_{1}}}{{{K}_{1}}{{d}_{2}}+{{K}_{2}}{{d}_{1}}}$

D)   $\frac{{{K}_{1}}{{\theta }_{1}}+{{K}_{2}}{{\theta }_{2}}}{{{K}_{1}}+{{K}_{2}}}$

• question_answer39) Hot water cools from ${{60}^{o}}C$ to ${{50}^{o}}C$ in the first 10 min and to ${{42}^{o}}C$ in the next 10 min. Then the temperature of the surroundings is

A) ${{20}^{o}}C$

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

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

D) ${{10}^{o}}C$

• question_answer40) The efficiency of Carnot's heat heat engine is 0.5 when the temperature of the source is ${{T}_{1}}$that of sink is ${{T}_{2}}$. The efficiency of source. Carnot's heat engine is also 0.5. The temperatures of source and second engine are respectively

A) $2{{T}_{1}},2{{T}_{2}}$

B) $2{{T}_{1}},\frac{{{T}_{2}}}{2}$

C) ${{T}_{1}}+5,\,{{T}_{2}}-5$

D) ${{T}_{1}}+10,\,{{T}_{2}}-10$

• question_answer41) A current $i$ is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure. The magnetic field at the centre of the loop is $\frac{{{\mu }_{0}}i}{R}$ times

A)   $\frac{5}{16},$ but out of the plane of the paper

B)   $\frac{5}{16},$ but into the plane of the paper

C)   $\frac{7}{16},$ but out of the plane of the paper

D)   $\frac{7}{16},$ but into the plane of the paper

• question_answer42) An ideal choke draws a current of 8 A when connected to an AC supply of 100 V, 50 Hz. A pure resistor draws a current of 10 A when connected to the same source. The ideal choke and the resistor are connected in series and then connected to the AC source of 150 V, 40 Hz. The current in the circuit becomes

A)   $\frac{15}{\sqrt{2}}A$

B)   8 A

C)   18 A

D)   10 A

• question_answer43) The spectrum of an oil flame is an example for

A) line emission spectrum

B) continuous emission spectrum

C) line absorption spectrum

D) band emission spectrum

• question_answer44) According to Einstein's photoelectric equation, the graph of KE of the photoelectron emitted from the metal versus the frequency of the incident radiation gives a straight line graph, whose slope

A) depends on the intensity of the incident radiation

B) depends on the nature of the metal and also on the intensity of incident radiation

C) is same for all metals and independent of the intensity of the incident radiation

D) depends on the nature of the metal

• question_answer45) An electron is moving in an orbit of a hydrogen atom from which there can be a maximum of six transition. An electron is moving in an orbit of another hydrogen atom from which there can be a maximum of three transition. The ratio of the velocities of the electron in these two orbits is

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

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

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

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

• question_answer46) ${{v}_{1}}$ is the frequency of the series limit of Lyman series, ${{v}_{2}}$ is the frequency of the first line of Lyman series and ${{v}_{3}}$ is the frequency of the series limit of the Balmer series. Then

A) ${{v}_{1}}-{{v}_{2}}={{v}_{3}}$

B) ${{v}_{1}}={{v}_{2}}-{{v}_{3}}$

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

D) $\frac{1}{{{v}_{1}}}=\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{3}}}$

• question_answer47) Assume the graph of specific binding energy versus mass number is as shown in the figure. Using this graph, select the correct choice from the following.

A)   Fusion of two nuclei of mass number lying in the range of $100<A<200$ will release energy

B)   Fusion of two nuclei of mass number lying in the range of $51<A<100$ will release energy

C)   Fusion of two nuclei of mass number lying in the range of $1<A<50$ will release energy

D) Fission of the nucleus of mass number lying in the rang of $100<A<200$ will release energy when broken into two fragments

• question_answer48) Pick out the correct statement from the following.

A) Energy released per unit mass of the reactant is less in case of fusion reaction

B) Packing fraction may be positive or may be negative

C) $P{{u}^{239}}$ is not suitable for a fission reaction

D) For stable nucleus, the specific binding energy is low

• question_answer49) A radioactive sample ${{S}_{1}}$ having the activity ${{A}_{1}}$ has twice the number of nuclei as another sample ${{S}_{2}}$ of activity ${{A}_{2}}$. If ${{A}_{2}}=2{{A}_{1}}$, then the ratio of half-life of ${{S}_{1}}$ to the half-life of ${{S}_{2}}$ is

A) 4

B) 2

C) 0.25

D) 0.75

• question_answer50) When a neutron is disintegrated to give a $\beta$-particle,

A) a neutrino alone is emitted

B) a proton and neutrino are emitted

C) a proton alone is emitted

D) a proton and an antineutrino are emitted

• question_answer51) The forbidden energy gap in Ge is 0.72 eV, Given, $hc=12400\text{ }eV-\overset{o}{\mathop{A}}\,$. The maximum wavelength of radiation that will generate electron hole pair is

A) $172220\,\,\overset{\text{o}}{\mathop{\text{A}}}\,$

B)   $172.2\,\,\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $17222\,\,\overset{\text{o}}{\mathop{\text{A}}}\,$

D) $1722\,\,\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer52) In a p-n junction diode not connected to any circuit

A) the potential is the same everywhere

B) the p-type side has a higher potential than the n-type side

C) there is an electric field at the junction  directed from the n-type side to p-type side

D) there is an electric field at the junction directed from the p-type side to n-type side

• question_answer53) In a given direction, the intensities of the scattered light by a scattering substance for two beams of light are in the ratio of $256:81$. The ratio of the frequency of the first beam to the frequency of the second beam is

A) $64:127$

B) $1:2$

C) $64:27$

D) None of these

• question_answer54) Identify the logic operation performed by the circuit given here.

A) OR

B) NOR

C) NOT

D) NAND

• question_answer55) The de-Broglie wavelength of the electron in the ground state of the hydrogen atom is ...... (radius of the first orbit of hydrogen atom$=0.53\overset{o}{\mathop{A}}\,$).

A) $1.67\overset{o}{\mathop{A}}\,$

B) $3.33\overset{o}{\mathop{A}}\,$

C) $1.06\overset{o}{\mathop{A}}\,$

D) $0.53\overset{o}{\mathop{A}}\,$

• question_answer56) PQ and RS are long parallel conductors   separated by certain distance. M is the midpoint between them (see the figure). The net magnetic field at M is B. Now, the current 2 A is switched off. The field at M now becomes

A) 2 B

B) B

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

D) 35

• question_answer57) An electron enters the space between the plates of a charged capacitor as shown. The charge density on the plate is $\sigma$. Electric intensity in the space between the plates is A uniform magnetic field B also exists in the space perpendicular to the direction of E. The electron moves perpendicular to both $\overrightarrow{E}$ and $\overrightarrow{B}$ without any change in direction. The time taken by the electron to travel a distance l in the space is

A) $\frac{\sigma l}{{{\varepsilon }_{0}}B}$

B) $\frac{\sigma B}{{{\varepsilon }_{0}}l}$

C) $\frac{{{\varepsilon }_{0}}lB}{\sigma B}$

D) $\frac{{{\varepsilon }_{0}}l}{\sigma B}$

• question_answer58) In a series resonant R-L-C circuit, the voltage across R is 100 V and the value of $R=1000\,\Omega$. The capacitance of the capacitor is $2\times {{10}^{-6}}F$; angular frequency of AC is $200\text{ }rad\text{ }{{s}^{-1}}$. Then the potential difference across the inductance coil is

A) 100 V

B) 40 V

C) 250 V

D) 400 V

• question_answer59) A capacitor and an inductance coil are connected in separate AC circuits with a bulb glowing in both the circuits. The bulb glows more brightly when

A) an iron rod is introduced into the inductance coil

B) the number of turns in the inductance coil is increased

C) separation between the plates of the capacitor is increased

D) a dielectric is introduced into the gap between the plates of the capacitor

• question_answer60) A charge +Q is moving upwards vertically. It enters a magnetic field directed to north. The force on the charge will be towards

A) north

B) south

C) east

D) west

• question_answer61) In the electrolytic refining of zinc

A) graphite is at the anode

B) the impure metal is at the cathode

C) the metal ion get reduced at the anode

D) acidified zinc sulphate is the electrolyte

• question_answer62) The wave number of the spectral line in the emission spectrum of hydrogen will be equal to $\frac{8}{9}$ times the Rydberg's constant if the electron jumps from

A) $n=3$ to $n=1$

B) $n=10$ to $n=1$

C) $n=9$ to $n=1$

D) $n=2$ to $n=1$

• question_answer63) Consider the following gaseous equilibria with equilibrium constants ${{K}_{1}}$and ${{K}_{2}}$ respectively. $S{{O}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)S{{O}_{3}}(g)$ $2S{{O}_{3}}(g)2S{{O}_{2}}(g)+{{O}_{2}}(g)$ The equilibrium constants are related as

A) $K_{1}^{2}=\frac{1}{{{K}_{2}}}$

B) $2{{K}_{1}}=K_{2}^{2}$

C) ${{K}_{2}}=\frac{2}{K_{1}^{2}}$

D) $K_{2}^{2}=\frac{1}{{{K}_{1}}}$

• question_answer64) Enthalpy of vaporization of benzene is $+\,\,35.3\,kJ\,\,mo{{l}^{-1}}$ at its boiling point, ${{80}^{o}}C$. The entropy change in the transition of the vapour to liquid at its boiling point in $[J{{K}^{-1}}mo{{l}^{-1}}]$ is

A) -441

B) -100

C) +441

D) +100

• question_answer65) Which one of the following conversions involve change in both hybridisation and shape?

A)   $C{{H}_{4}}\xrightarrow{{}}{{C}_{2}}{{H}_{6}}$

B)   $N{{H}_{3}}\xrightarrow{{}}NH_{4}^{+}$

C)   $B{{F}_{3}}\xrightarrow{{}}BF_{4}^{-}$

D)   ${{H}_{2}}O\xrightarrow{{}}{{H}_{3}}{{O}^{+}}$

• question_answer66) In chromite ore, the oxidation number of iron, and chromium are respectively

A)   + 3, + 2

B) + 3, + 6

C) + 2, + 6

D) + 2, + 3

• question_answer67) For the reversible reaction. $A\,(s)+B(g)C\,(g)+D(g);$$\Delta {{G}^{o}}=-350\,\,kJ$ Which one of the following statements is true?

A) The entropy change is negative

B) Equilibrium constant is greater than one

C) The reaction should be instantaneous

D) The reaction is thermodynamically not feasible

• question_answer68) Out of the compounds below the vapour pressure of at a particular temperature is

A) higher than that of

B) lower than that of

C) higher or lower than, depending on the size of the vessel

D) same as that of

• question_answer69) The amount of heat evolved when $500\text{ }c{{m}^{3}}$ of $0.1\text{ }M\,HCl$ is mixed with $200\text{ }c{{m}^{3}}$ of $0.2\text{ }NaOH$ is

A) 2.292 kJ

B) 1.292kJ

C) 0.292 kJ

D) 3.392 kJ

• question_answer70) During the adsorption of krypton on activated charcoal at low temperature

A) $\Delta H>0$ and $\Delta S<0$

B) $\Delta H<0$ and $\Delta S<0$

C) $\Delta H>0$ and $\Delta S>0$

D) $\Delta H<0$ and $\Delta S>0$

• question_answer71) The set of quantum numbers for the outermost electron for copper in its ground state is

A) $4,\,\,1,\,\,1,+\frac{1}{2}$

B) $3,\,\,2,\,\,2,+\frac{1}{2}$

C) $4,\,\,0,\,\,0,+\frac{1}{2}$

D) $4,\,\,2,\,\,2,+\frac{1}{2}$

A) (ii) and (iii)

B) (i), (ii) and (iv)

C) (i), (ii) and (iii)

D) (i) and (iv)

• question_answer73) Which one of these is not true for benzene?

A) It forms only one type of mono substituted product

B) There are three carbon-carbon single bonds and three carbon-carbon double bonds

C) The heat of hydrogenation of benzene is less than the theoretical value

D) The bond angle between the carbon-carbon bonds is ${{120}^{o}}$

• question_answer74) A mixture of $CaC{{l}_{2}}$ and $NaCl$ weighing 4.44 g is treated with sodium carbonate solution to precipitate all the $C{{a}^{2+}}$ ions as calcium carbonate. The calcium carbonate so obtained is heated strongly to get 0.56 g of CaO. The percentage of $NaCl$ in the mixture (atomic mass of $Ca=40$) is

A) 75

B) 30.6

C) 25

D) 69.4

• question_answer75) For one mole of an ideal gas, increasing the temperature from ${{10}^{o}}C$ to ${{20}^{o}}C$

A) increases the average kinetic energy by two times

B) increases the rms velocity by $\sqrt{2}$ times

C) increases the rms velocity by two times

D) increases both the average kinetic energy and rms velocity, but not significantly

• question_answer76) Generally, the first ionization energy increases along a period. But there are some exceptions. One which is not an exception is

A) N and O

B) Na and Mg

C) Mg and Al

D) Be and B

• question_answer77) $50\,\,c{{m}^{3}}$ of $0.2\text{ }N\,HCl$ is titrated against $0.1\text{ }N\,NaOH$ solution. The titration is discontinued after adding $50\,\,c{{m}^{3}}$ of $NaOH$. The remaining titration is completed by adding $0.5\text{ }N\,KOH$. The volume of $KOH$required for completing the titration is

A) $12\,\,c{{m}^{3}}$

B) $10\,\,c{{m}^{3}}$

C) $25\,\,c{{m}^{3}}$

D) $10.5\,\,c{{m}^{3}}$

• question_answer78) In which one of the following, does the given amount of chlorine exert the least pressure in a vessel of capacity $1\,\,d{{m}^{3}}$ at 273 K?

A) 0.0355 g

B) 0.071 g

C) $6.023\times {{20}^{21}}$molecules

D) 0.02 mol

• question_answer79) Based on the first law of thermodynamics, which one of the following is correct?

A) For an isochoric process $=\Delta E=-q$

B) For an adiabatic process $=\Delta E=-w$

C) For an isothermal process $=q=+w$

D) For a cyclic process $q=-w$

• question_answer80) For alkali metals, which one of the following trends is incorrect?

A) Hydration energy: $Li>Na>K>Rb$

B) Ionization energy: $Li>Na>K>Rb$

C) Density: $Li<Na<K<Rb$

D) Atomic size: $Li<Na<K<Rb$

• question_answer81) 1 g of silver gets distributed between $10\,\,c{{m}^{3}}$of molten zinc and $100\,\,c{{m}^{3}}$ of molten lead at${{800}^{o}}C$. The percentage of silver in the zinc layer is approximately

A) 89

B) 91

C) 97

D) 94

• question_answer82) One mole of an organic compound A with the formula ${{C}_{3}}{{H}_{8}}O$ reacts completely with two moles of HI to form X and Y. When Y is boiled with aqueous alkali it forms Z. Z answers the iodoform test. The compound A is

A) propan-2-ol

B) propan-1-ol

C) ethoxyethane

D) methoxyethane

• question_answer83)   The IUPAC name of ${{K}_{2}}[Ni{{(CN)}_{4}}]$ is

A) potassium tetracyanonickelate (II)

B) potassium tetracyanatonickelate (III)

C) potassium tetracyanatonickelate (II)

D) potassium tetracyanonickelate (III)

• question_answer84) The spin only magnetic moment of $M{{n}^{4+}}$ ion is nearly

A) 3 BM

B) 6 BM

C) 4 BM

D) 5 BM

• question_answer85) In Kjeldahl’s method, ammonia from 5 g of food neutralizes $30\,c{{m}^{3}}$ of 0.1 N acid. The percentage of nitrogen in the food is

A) 8.4

B)   8.4

C)   16.8

D)   1.68

• question_answer86) Carbon can reduce ferric oxide to iron at a temperature above 983 K because

A) carbon monoxide formed is thermodynamically less stable than ferric oxide

B) carbon has a higher affinity towards oxidation than iron

C) free energy change for the formation of carbon dioxide is less negative than that for ferric oxide

D) iron has a higher affinity towards oxygen than carbon

• question_answer87) An oxygen containing organic compound upon oxidation forms a carboxylic acid as the only organic product with its molecular mass higher by 14 units. The organic compound is

A) an aldehyde

B) a primary alcohol

C) a secondary alcohol

D) acetone

• question_answer88) The compound obtained when acetaldehyde reacts with dilute aqueous sodium hydroxide exhibits

A) geometrical isomerism

B) optical isomerism

C) neither optical nor geometrical isomerism

D) both optical and geometrical isomerism

• question_answer89) The activation energy for a reaction at the temperature TK was found to be$2.303\text{ }RT\text{ }J\text{ }mo{{l}^{-1}}$. The ratio of the rate constant to Arrhenius factor is

A) ${{10}^{-1}}$

B) ${{10}^{-2}}$

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

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

• question_answer90) A dibromo derivative of an alkane reacts with sodium metal to form an alicyclic hydrocarbon. The derivative is

A) 1,1-dibromopropane

B) 2, 2-dibromobutane

C) 1, 2-dibromoethane

D) 1, 4-dibromobutane

• question_answer91) Time required for 100 per cent completion of a zero order reaction is

A) $\frac{2k}{a}$

B) $\frac{a}{2k}$

C) $\frac{a}{k}$

D) $ak$

• question_answer92) 0.023 g of sodium metal is reacted with $100\text{ }c{{m}^{3}}$ of water. The pH of the resulting solution is

A) 10

B) 11

C) 9

D) 12

• question_answer93) Which one of the following is wrongly matched?

A) ${{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}$       - Square planar

B) $[Ni{{(CO)}_{4}}]$                         - Neutral ligand

C) $[Fe{{(C{{N}_{6}})}^{3-}}]$                       - $s{{p}^{3}}{{d}^{2}}$

D) ${{[Co{{(en)}_{3}}]}^{3+}}$      - Follows EAN rule

• question_answer94) Which one of the following conformations of cyclohexane is the least stable?

A) Half-chair

B) Boat

C) Twisted-boat

D) Chair

• question_answer95) Which one of the following is a molecular crystal?

A) Rock salt

B) Quartz

C) Dry ice

D) Diamond

• question_answer96) A buffer solution contains 0.1 mole of sodium acetate in $1000\,\,c{{m}^{3}}$ of 0.1 M acetic acid. To the above buffer solution, 0.1 mole of sodium acetate is further added and dissolved. The pH of the resulting buffer is equal to

A) $p{{K}_{a}}-\log \,2$

B) $p{{K}_{a}}$

C) $p{{K}_{a}}+\,2$

D) $p{{K}_{a}}+\log \,2$

• question_answer97) Which one of the following has the most nucleophilic nitrogen?

A)

B)

C)

D)

• question_answer98) Chloroacetic acid is a stronger acid than acetic acid. This can be explained using

A) -M effect

B) -I effect

C) + M effect

D) +I effect

• question_answer99) The correct sequence of reactions to convert p-nitrophenol into quinol involves

A) reduction, diazotization and hydrolysis

B) hydrolysis, diazotization and reduction

C) hydrolysis, reduction and diazotization

D) diazotization, reduction and hydrolysis

• question_answer100) $C{{H}_{3}}C{{H}_{2}}Br\xrightarrow[\Delta ]{aq.\,KOH}a=\xrightarrow[\Delta ]{KMn{{O}_{4}}/{{H}^{+}}}$$B\xrightarrow[\Delta ]{N{{H}_{3}}}C\xrightarrow[alkali]{B{{r}_{2}}}D,'D'$ is

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

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

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

D) $CHB{{r}_{3}}$

• question_answer101) The letter ‘D’ in D-glucose signifies

A) configuration at all chiral carbons

B) dextrorotatory

C) that it is a monosaccharide

D) configuration at a particular chiral carbon

• question_answer102) Reaction of methyl bromide with aqueous sodium hydroxide involves

A) racemization

B) ${{S}_{N}}1$ mechanism

C) retention of configuration

D) ${{S}_{N}}2$ mechanism

• question_answer103) 9.65 C of electric current is passed through fused anhydrous magnesium chloride. The magnesium metal thus, obtained is completely converted into a Grignard reagent. The number of moles of the Grignard reagent obtained is

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

B) $1\times {{10}^{-4}}$

C) $5\times {{10}^{-5}}$

D) $1\times {{10}^{-5}}$

• question_answer104) Which one of the following does not involve coagulation?

A) Formation of delta regions

B) Peptization

C) Treatment of drinking water by potash alum

D) Clotting of blood by the use of ferric chloride

• question_answer105)   In alkaline medium, alanine exists predominantly as

A)   anion

B)     Zwitterion

C)   cation

D)   covalent form

• question_answer106) The standard emf of galvanic cell involving 3 moles of electrons in its redox reaction is 0.59 V. The equilibrium constant for the reaction of the cell is

A)   ${{10}^{25}}$

B)   ${{10}^{20}}$

C)   ${{10}^{15}}$

D)   ${{10}^{30}}$

• question_answer107)   Benzaldehyde and acetone can be best distinguished using

A)   Fehling's solution

B)   Sodium hydroxide solution

C)   2, 4-DNP

D)   Tollen's reagent

• question_answer108)   Which one of the following statements is true?

A)   Saponification of oil yields a diol

B)   Drying of oil involves hydrolysis

C)   Addition of antioxidant to oil minimizes rancidity

D)   Refining of oil involves hydrogenation

• question_answer109)   The following data is obtained during the first order thermal decomposition of $2A(g)\xrightarrow{{}}B(g)+C(s)$at constant volume and temperature.

 S.N. Time Total pressure in Pascal 1. At the end of 10 min 300 2. After completion 200
The rate constant in ${{\min }^{-1}}$ is

A)   0.0693

B)   6.93

C)   0.00693

D)     69.3

• question_answer110) Phenol $\xrightarrow{X}$ forms a tribromo derivative. ‘’X’’ is

A) bromine in benzene

B) bromine in water

C) potassium bromide solution

D) bromine in carbon tetrachloride at ${{0}^{o}}C$

• question_answer111) The correct sequence of steps involved in the mechanism of Cannizaro’s reaction is

A) nucleophilic attack, transfer of ${{H}^{-}}$and transfer of ${{H}^{+}}$

B) transfer of ${{H}^{-}}$, transfer of ${{H}^{+}}$ and nucleophilic attack

C) transfer if ${{H}^{+}}$ nucleophilic attack and transfer of ${{H}^{-}}$

D) electrophilic attack by $O{{H}^{-}}$, transfer of${{H}^{+}}$ and transfer of ${{H}^{-}}$

• question_answer112) Which one of the following is an example for homogeneous catalysis?

A) Manufacture of sulphuric acid by Contact process

B) Manufacture of ammonia by Habeas process

C) Hydrolysis of sucrose in presence of dilute hydrochloric acid

D) Hydrogenation of oil

• question_answer113) The empirical formula of a non-electrolyte is $C{{H}_{2}}O$. A solution containing 6 g of the compound exerts the same osmotic pressure as that of 0.05 M glucose solution at the same temperature. The molecular formula of the compound is

A)   ${{C}_{2}}{{H}_{4}}{{O}_{2}}$

B)   ${{C}_{3}}{{H}_{6}}{{O}_{3}}$

C)   ${{C}_{5}}{{H}_{10}}{{O}_{5}}$

D)   ${{C}_{4}}{{H}_{8}}{{O}_{4}}$

• question_answer114)   A white crystalline salt A reacts with dilute $HCl$ to liberate a suffocating gas B and also forms a yellow precipitate. The gas B turns potassium dichromate acidified with dilute ${{H}_{2}}S{{O}_{4}}$ to a green coloured solution C. A, B and C are respectively

A) $N{{a}_{2}}S{{O}_{3}},\,S{{O}_{2}}\,\,C{{r}_{2}}{{(S{{O}_{4}})}_{3}}$

B) $N{{a}_{2}}{{S}_{2}}{{O}_{3}},\,S{{O}_{2}}\,\,C{{r}_{2}}{{(S{{O}_{4}})}_{3}}$

C) $N{{a}_{2}}S,\,\,S{{O}_{2}},\,\,\,C{{r}_{2}}{{(S{{O}_{4}})}_{3}}$

D) $N{{a}_{2}}S{{O}_{4}},\,\,S{{O}_{2}},\,C{{r}_{2}}{{(S{{O}_{4}})}_{3}}$

• question_answer115) Molecules of a noble gas do not possess vibrational energy because a noble gas

A) is monoatomic

B) is chemically inert

C) has completely filled shells

D) is diamagnetic

• question_answer116) $1\,\,d{{m}^{3}}$ solution containing ${{10}^{-5}}$ moles each of $C{{l}^{-}}$ ions and $CrO_{4}^{2-}$ ions is treated with ${{10}^{-4}}$ moles of silver nitrate. Which one of the following observations is made? $[{{K}_{sp}}A{{g}_{2}}Cr{{O}_{4}}=4\times {{10}^{-12}}]$

A) Precipitation does not occur

B) Silver chromate gets precipitated first

C) Silver chloride gets precipitated first

D) Both silver chromate and silver chloride start precipitating simultaneously

• question_answer117) pH value of which one of the following is not equal to one?

A) $0.1\text{ }M\text{ }HN{{O}_{3}}$

B) $0.05\text{ }M\text{ }{{H}_{2}}S{{O}_{4}}$

C) $0.1\text{ }M\text{ }C{{H}_{3}}COOH$

D) $50\,\,c{{m}^{3}}$of $0.4\,\,M$$HCl+50\,\,c{{m}^{3}}$of $0.2\,M\,NaOH$

• question_answer118)   ${{E}_{1}},\,{{E}_{2}},{{E}_{3}}$ are the emf values of the three galvanic cells respectively.

 (i) $Zn|Zn_{1M}^{2+}||Cu_{0.1M}^{2+}|Cu$ (ii) $Zn|Zn_{1M}^{2+}||Cu_{1M}^{2+}|Cu$ (iii) $Zn|Zn_{0.1\,M}^{2+}||Cu_{1M}^{2+}|Cu$
Which one of the following is true?

A) ${{E}_{2}}>{{E}_{3}}>{{E}_{1}}$

B) ${{E}_{3}}>{{E}_{2}}>{{E}_{1}}$

C) ${{E}_{1}}>{{E}_{2}}>{{E}_{3}}$

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

• question_answer119)   The IUPAC name of is

A)   2-methyl-3-bromohexanal

B)   - 3-bromo-2-methylbutanal

C)   2-methyl-3-bromobutanal

D)   3-bromo-2-methylpentanal

• question_answer120) Which one of the following forms propane nitrile as the major product?

A) Ethyl bromide + alcoholic $KCN$

B) Propyl bromide + alcoholic $KCN$

C) Propyl bromide + alcoholic $AgCN$

D) Ethyl bromide + alcoholic $AgCN$

• question_answer121) If then ${{A}^{2}}+xA+I=0$  for $(x,y)$ is

A)   $(-4,1)$

B)   $(-1,3)$

C)   $(4,-1)$

D)   $(1,3)$

• question_answer122) The constant term of the polynomial is

A) 0

B) 2

C) -1

D) 1

• question_answer123) If $\vec{a},\vec{b}$ and $\vec{c}$ are non-zero coplanar vectors, then $[2\vec{a}-\vec{b}3\vec{b}-\vec{c}4\vec{c}-\vec{a}]$ is

A) $25$

B) $0$

C) $27$

D) $9$

• question_answer124) A space vector makes the angles ${{150}^{o}}$ and ${{60}^{o}}$ with the positive direction of x-and y-axes. The angle made by the vector with the positive direction z-axis is

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

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

C) ${{180}^{o}}$

D) ${{120}^{o}}$

• question_answer125) If $\vec{a},\vec{b}$and $\vec{c}$ are unit vectors, such that $\vec{a}+\vec{b}+\vec{c}=\vec{0},$then  $3\vec{a}.\vec{b}+2\,\vec{b}.\vec{c}+\vec{c}.\vec{a}$

A) -1

B) 1

C) -3

D) 3

• question_answer126) If $a>b>c,$ ${{\sec }^{-1}}\frac{a+b}{a-b}=2{{\sin }^{-1}}x,$ then x is

A) $-\sqrt{\frac{b}{a+b}}$

B) $\sqrt{\frac{b}{a+b}}$

C) $-\sqrt{\frac{a}{a+b}}$

D) $\sqrt{\frac{a}{a+b}}$

• question_answer127) If $x\ne n\pi ,$ $x\ne (2n+1)\frac{\pi }{2},$ $n\in Z,$ then $\frac{{{\sin }^{-1}}(\cos x)+{{\cos }^{-1}}(\sin x)}{{{\tan }^{-1}}(\cot x)+{{\cot }^{-1}}(\tan x)}$ is

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

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

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

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

• question_answer128) The general solution $1+{{\sin }^{2}}3\sin x.\cos x,\tan x\ne \frac{1}{2},$is

A) $2n\pi +\frac{\pi }{4},n\in Z$

B) $2n\pi -\frac{\pi }{4},n\in Z$

C) $n\pi -\frac{\pi }{4},n\in Z$

D) $n\pi +\frac{\pi }{4},n\in Z$

• question_answer129) The least positive integer n, for which $\frac{{{(1+i)}^{n}}}{{{(1-i)}^{n-2}}}$ is positive, is

A) 3

B) 4

C) 1

D) 2

• question_answer130) If $x+iy={{(-1+i\sqrt{3})}^{2010}},$ then x is

A) $-{{2}^{2010}}$

B) ${{2}^{2010}}$

C) $1$

D) $-1$

• question_answer131) $(\sin \theta +\cos \theta )\,(\tan \theta +cot\theta )$ is equal to

A) $\sin \theta \,\cos \theta$

B) $1$

C) $\sec \theta +\text{cosec}\theta$

D) $\sec \theta \,\,\text{cosec}\theta$

• question_answer132) This sides of a triangle are $6+2\sqrt{3},4\sqrt{3}$ and $\sqrt{24}.$ the tangent of the smallest angle of the triangle is

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

B) $\sqrt{2}-1$

C) $\sqrt{3}$

D) $1$

• question_answer133) A simple graph contains 24 edges. Degree of each vertex is 3. The number of vertices is

A) 8

B) 12

C) 21

D) 16

• question_answer134) $\underset{x\to \infty }{\mathop{\lim }}\,\,n\,\sin \frac{2\pi }{3n}.\cos \frac{2\pi }{3n}$ is

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

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

C) $1$

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

• question_answer135) The function $f(x)=[x],$  where [x] denotes the greatest integer not greater than x, is

A) continuous for all non-integral values of x

B) continuous only at positive integral values of x

C) continuous for all real values of x

D) continuous only at rational values of x

• question_answer136) The greatest value of x satisfying $~21=385$(mod x) and $587=167$ (mod x) is

A) $156$

B) $32$

C) $28$

D) $56$

• question_answer137) The number $({{49}^{2}}-4)({{49}^{3}}-49)$ is divisible by

A) $7!$

B) $9!$

C) $6!$

D) $5!$

• question_answer138) The least positive integer x satisfying${{2}^{2010}}\equiv 3x$(mod 5) is

A) 3

B) 4

C) 1

D) 2

• question_answer139) If A and B are two square matrices of the same order such that $AB=B$and $BA=A,$ then ${{A}^{2}}+{{B}^{2}}$is always equal to

A) $I$

B) $A+B$

C) $2AB$

D) $2BA$

• question_answer140) If A is a $3\times 3$ non-singular matrix and if $|A|=3,$then $|{{(2A)}^{-1}}|$ is

A) $24$

B) $3$

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

D) $\frac{1}{24}$

• question_answer141) If   $a,-a,$ b   are   the   roots   of ${{x}^{3}}-5{{x}^{2}}-x+5=0,$  then b is a root of

A) ${{x}^{2}}+3x-20=0$

B) ${{x}^{2}}-5x+10=0$

C) ${{x}^{2}}-3x-10=0$

D)   ${{x}^{2}}+5x-30=0$

• question_answer142) In the binomial expansion of ${{(1+x)}^{15}},$ the coefficients of ${{x}^{r}}$ and ${{x}^{r+3}}$ are equal. Then, r is

A) $8$

B) $7$

C) $4$

D) $6$

• question_answer143) The   nth   term   of   the   series $1+3+7+13+21+.....$ is 9901. The value of n is

A) $100$

B) $90$

C) $900$

D) $99$

• question_answer144) If $\frac{1}{(3-5x)(2+3x)}=\frac{A}{3-5x}+\frac{B}{2+3x},$  then $A:B$ is

A) $2:3$

B) $5:3$

C) $3:5$

D) $3:2$

• question_answer145) If $\hat{i},\hat{j},\hat{k}$ are unit vectors along the positive direction of x, y and z-axes, then a false statement in the following is

A) $\Sigma \hat{i}\times (\hat{j}+\hat{k})=\vec{0}$

B) $\Sigma \hat{i}\times (\hat{j}\times \hat{k})=\vec{0}$

C) $\Sigma \,\hat{i}.(\hat{j}\times \hat{k})=\vec{0}$

D) $\Sigma \,\hat{i}.(\hat{j}+\hat{k})=\vec{0}$

• question_answer146) In P(X), the power set of a non-empty set X, an binary operation * is defined by$A\,*\,B=A\cup B,\forall A,B\in P(x)$ under *, a true statement is

A) identity law is not satisfied

B) inverse law is not satisfied

C) commutative law is not satisfied

D) associative law is not satisfied

• question_answer147) The inverse of 2010 in the group ${{Q}^{+}}$ of all positive rational under the binary operation * defined by $a*b=\frac{ab}{2010},\forall \,a,b\in {{Q}^{+}},$ is

A) $2009$

B) $2011$

C) $1$

D) $2010$

• question_answer148) If the three function $f(x),g(x)$ and $h(x)$ are such that $h(x)=f(x).g(x)$ and $f'(x).g'(x)=c$ where c is constant, then

A) $h'=(x).h''(x)$

B) $\frac{h(x)}{h''(x)}$

C) $\frac{h''(x)}{h(x)}$

D) $\frac{h(x)}{h'(x)}$

• question_answer149) The derivative of ${{e}^{ax}}\,\,\cos \,bx$with respect x is $r{{e}^{ax}}\,\,\cos \,bx\,\,{{\tan }^{-1}}\frac{b}{a}.$ When $a>0,b>0,$then value of r, is

A) $\sqrt{{{a}^{2}}+{{b}^{2}}}$

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

C) $ab$

D) $a+b$

• question_answer150) The chord of the circle ${{x}^{2}}+{{y}^{2}}-4x=0$ which is bisected at $(1,0)$ is perpendicular to the line

A) $y=x$

B) $x+y=0$

C) $x=1$

D) $y=1$

• question_answer151) In $\Delta ABC,$if $a=2,b={{\tan }^{-1}}\frac{1}{2}$ and $C={{\tan }^{-1}}\frac{1}{3},$ then (A, b) equals

A) $\frac{3\pi }{4},\frac{2}{\sqrt{5}}$

B) $\frac{\pi }{4},\frac{2\sqrt{2}}{\sqrt{5}}$

C) $\frac{3\pi }{4},\frac{2\sqrt{2}}{\sqrt{5}}$

D) $\frac{\pi }{4},\frac{2}{\sqrt{5}}$

• question_answer152) The straight line $2x+3y-k=0,$ $k>0$ cuts the x and y-axes at A and B. The area of $\Delta OAB,$, where 0 is the origin, is $12\text{ }sq$unit.    The equation of the circle having AB as diameter is

A) ${{x}^{2}}+{{y}^{2}}-6x-4y=0$

B) ${{x}^{2}}+{{y}^{2}}+4x-6y=0$

C) ${{x}^{2}}+{{y}^{2}}-6x+4y=0$

D) ${{x}^{2}}+{{y}^{2}}-4x-6y=0$

• question_answer153) Let $P(x,y)$ be the mid point of the line joining $(1,0)$ to a point on the curve Then, locus of P is symmetrical about

A)   $y-axis$

B)   $x-axis$

C)   $x=1$

D)   $y=1$

• question_answer154) The function $f(x)=|x-2|+x$ is

A) differentiable at both $x=2$ and $x=0$

B) differentiable at $x=2$ but not at $x=0$

C) continuous at $x=2$but not at $x=0$

D) continuous at both $x=2$ and $x=0$

• question_answer155) Let R be an equivalence relation defined on a set containing 6 elements. The minimum number or ordered pairs that R should contain is

A) $12$

B) $6$

C) $64$

D) $36$

• question_answer156) The line joining $A(2,-7)$ and $B(6,5)$ is divided into 4 equal parts by the points P, Q and R such that$AQ=RP=QB$. The mid-point of PR is

A) $(4,12)$

B) $(-8,1)$

C) $(4,-1)$

D) $(8,-2)$

• question_answer157) Let $P\equiv (-1,0),$ $Q\equiv (0,0)$ and $R=(3,3)$ be three points. The equation of the bisector of the angle PQR is

A) $x-\sqrt{3}y=0$

B) $\sqrt{3}x-y=0$

C) $x+\sqrt{3}y=0$

D) $\sqrt{3}x+y=0$

• question_answer158) If m is the slope of one of the lines represented by $a{{x}^{2}}+2hxy+b{{y}^{2}}=0,$then ${{(h+bm)}^{2}}$ is equal to

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

B) ${{(a-b)}^{2}}$

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

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

• question_answer159) $\cos {{12}^{o}}\,\cot {{102}^{o}}+\cot {{102}^{o}}\,\cot {{66}^{o}}$$+\cot {{66}^{o}}\,\cot {{12}^{o}}$ is

A) $-2$

B) $1$

C) $-1$

D) $2$

• question_answer160) A wire of length $20\text{ }cm$is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is

A) $20\text{ }sq\text{ }cm$

B) $25\text{ }sq\text{ }cm$

C) $10\,\,sq\,\,cm$

D) $30\,\,sq\,\,cm$

• question_answer161) Two circles centred at $(2,3)$ and $(5,6)$ intersect each other. If the radii are equal, the equation of the common chord is

A) $x+y+1=0$

B) $x-y+1=0$

C) $x+y-8=0$

D) $x-y-8=0$

• question_answer162) Equation of the circle centred at $(4,3)$ touching the circle ${{x}^{2}}+{{y}^{2}}=1$externally, is

A) ${{x}^{2}}+{{y}^{2}}-8x-6y+9=0$

B) ${{x}^{2}}+{{y}^{2}}+8x+6y+9=0$

C) ${{x}^{2}}+{{y}^{2}}+8x-6y+9=0$

D) ${{x}^{2}}+{{y}^{2}}-8x6y+9=0$

• question_answer163) The points $(1,0),$ $(0,1),$ $(0,0)$  and $(2k,3k),k\ne 0$  are concyclic, if k is

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

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

C) $-\frac{5}{13}$

D) $\frac{5}{13}$

• question_answer164) The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola ${{x}^{2}}=-\text{ }8y$ is

A) $x=2$

B) $x=-2$

C) $y=2$

D) $y=-2$

• question_answer165) The condition for the line $y=mx+c$to be a normal to the parabola ${{y}^{2}}=4ax$ is

A) $c=-2am-a{{m}^{3}}$

B) $c=-\frac{a}{m}$

C) $c=\frac{a}{m}$

D) $c=2am+a{{m}^{3}}$

• question_answer166) The eccentric angle of the point $(2,\sqrt{3})$  lying on $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{4}=1$ is

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

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

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

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

• question_answer167) The distance of the focus of ${{x}^{2}}-{{y}^{2}}=4,$form the directrix which is nearer to it, is

A) $4\sqrt{2}$

B) $8\sqrt{2}$

C) $2\sqrt{2}$

D) $\sqrt{2}$

• question_answer168) If $\int{f(x)\,\sin x.\cos x\,dx}$$=\frac{1}{2({{b}^{2}}-{{a}^{2}})}\log f(x)+c,$where c is the constant of integration, then $f(x)$ is

A) $\frac{2}{ab\,\,\cos \,\,2x}$

B) $\frac{2}{({{b}^{2}}-{{a}^{2}})\,\cos \,2x}$

C) $\frac{2}{ab\,\sin \,2x}$

D) $\frac{2}{({{b}^{2}}-{{a}^{2}})\,\sin \,2x}$

• question_answer169) If  $\int{\frac{\sqrt{x}}{x(x+1)}}\,dx=k\,{{\tan }^{-1}}m,$then $(k,m)$ is

A) $(2,x)$

B) $(1,x)$

C) $(1,\sqrt{x})$

D) $(2,\sqrt{x})$

• question_answer170) $\int_{0}^{\pi /4}{\frac{\sin \,x+\cos x}{3+\sin 2x}}dx$ is

A) $\frac{1}{4}\log 3$

B) $\log 3$

C) $\frac{1}{2\log \,3}$

D) $2\log 3$

• question_answer171) $\int_{0}^{1}{x{{(1-x)}^{3/2}}}dx$ is

A) $-\frac{2}{35}$

B) $\frac{4}{35}$

C)   $\frac{24}{35}$

D) $-\frac{8}{35}$

• question_answer172) The area bounded by the curve $y=\left\{ \begin{matrix} {{x}^{2}}, & x<0 \\ x, & x\ge 0 \\ \end{matrix} \right.$ and the line $y=4,$ is

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

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

C) $\frac{40}{3}$

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

• question_answer173) The order and degree of the differential equation   $y=\frac{dp}{dx}x=\sqrt{{{a}^{2}}{{p}^{2}}+{{b}^{2}}},$where  $p=\frac{dy}{dx}$ (here a and b are arbitrary constants) respectively are

A) $2,2$

B) $1,1$

C) $1,2$

D) $2,1$

• question_answer174) The general solution of the differential equation $2x\frac{dy}{dx}-y=3$ is a family of

A) hyperbolas

B) parabolas

C) straight lines

D) circles

• question_answer175) If $x=a\,{{\cos }^{3}}\theta$and $y=a\,{{\sin }^{3}}\,\theta ,$ then $\frac{dy}{dx}$ is

A) $\sqrt[3]{\frac{y}{x}}$

B) $\sqrt[3]{\frac{x}{y}}$

C) $-\sqrt[3]{\frac{x}{y}}$

D) $-\sqrt[3]{\frac{y}{x}}$

• question_answer176) If $y={{\tan }^{-1}}\sqrt{{{x}^{2}}-1},$  then the ratio $\frac{{{d}^{2}}y}{d{{x}^{2}}}:\frac{dy}{dx}$ is

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

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

C)   $\frac{1+2{{x}^{2}}}{x({{x}^{2}}+1)}$

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

• question_answer177) P is the point of contact of the tangent form the origin to the curve$y=lo{{g}_{e}}\text{ }x$. The length of the perpendicular drawn form the origin to the normal at P is

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

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

C) $2\sqrt{{{e}^{2}}+1}$

D) $\sqrt{{{e}^{2}}+1}$

• question_answer178) For the curve $4{{x}^{5}}=5{{y}^{4}},$ the ratio of the    cube of the subtangent at a point on the curve the square of the subnormal at the same point is

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

B) $\frac{{{5}^{4}}}{4}$

C) $\frac{{{4}^{4}}}{{{5}^{4}}}$

D) ${{\left( \frac{5}{4} \right)}^{4}}$

• question_answer179) The set of real values of x for which $f(x)=\frac{x}{\log \,x}$is increasing, is

A) $\{x:x\ge e\}$

B) empty

C) $\{x:x<e\}$

D) $\{1\}$

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