Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2010
done CET - Karnataka Engineering Solved Paper-2010 Total Questions - 179
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
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
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?
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
doneclear
B)
\[i\] approaches \[\frac{E}{r}\], V approaches zero
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
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
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, \[{{n}_{w}}=\frac{4}{3}\].
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
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
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
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 \[330\text{ }m{{s}^{-1}}\])
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
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
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 \[{{Q}_{1}}={{Q}_{2}}\]
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
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.
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?
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).
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
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B)
Radius of the planet is half as that of earth, but the mass is the same as that of earth
doneclear
C)
Both the mass and radius of the planet are twice as that of earth
doneclear
D)
Mass of the planet is half as that of earth, but radius is same as that of earth
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
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
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
doneclear
B)
Brightness of the bulbs \[{{B}_{1}}\] and \[{{B}_{2}}\]increase
doneclear
C)
Brightness of the bulb \[{{B}_{1}}\] decreases and \[{{B}_{2}}\]increases
doneclear
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
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
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
doneclear
B)
current is induced in the loop in the clockwise direction
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)
\[4\,m{{s}^{-1}}\]
doneclear
B)
\[2\,m{{s}^{-1}}\]
doneclear
C)
\[2\,m{{s}^{-1}}\] in the opposite direction of the train
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
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
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
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
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
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
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
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
doneclear
B)
\[\frac{5}{16},\] but into the plane of the paper
doneclear
C)
\[\frac{7}{16},\] but out of 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
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
doneclear
B)
depends on the nature of the metal and also on the intensity of incident radiation
doneclear
C)
is same for all metals and independent of the intensity of the incident radiation
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
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
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
doneclear
B)
Fusion of two nuclei of mass number lying in the range of \[51<A<100\] will release energy
doneclear
C)
Fusion of two nuclei of mass number lying in the range of \[1<A<50\] will release energy
doneclear
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_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
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
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
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\[=0.53\overset{o}{\mathop{A}}\,\]).
question_answer56)
PQ and RS are long parallel conductorsseparated 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
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
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
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
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B)
the number of turns in the inductance coil is increased
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C)
separation between the plates of the capacitor is increased
doneclear
D)
a dielectric is introduced into the gap between the plates of the capacitor
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
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
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
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
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
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
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?
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
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
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
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
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
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
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
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
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
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.
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
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
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
doneclear
B)
Silver chromate gets precipitated first
doneclear
C)
Silver chloride gets precipitated first
doneclear
D)
Both silver chromate and silver chloride start precipitating simultaneously
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
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
question_answer125)
If \[\vec{a},\vec{b}\]and \[\vec{c}\] are unit vectors, such that \[\vec{a}+\vec{b}+\vec{c}=\vec{0},\]then\[3\vec{a}.\vec{b}+2\,\vec{b}.\vec{c}+\vec{c}.\vec{a}\]
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
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
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
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
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
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
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
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
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
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
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
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
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
question_answer178)
For the curve \[4{{x}^{5}}=5{{y}^{4}},\] the ratio of thecube of the subtangent at a point on the curve the square of the subnormal at the same point is