question_answer3) An unpolarised beam of intensity \[{{I}_{0}}\] is incident on a pair of nicols making an angle of \[{{60}^{o}}\] with each other. The intensity of light emerging from the pair is:
question_answer5) A cyclist starts from the centre 0 of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference and returns to the centre along O as shown in the figure. If the round trip takes 10 min, the net displacement and average speed of the cyclist (in meters and kilometre per hour) are:
question_answer7) A beam of light of wavelength 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first dark fringes on either side of the central bright fringe is:
question_answer9) A battery of emf 10 V and internal resistance \[3\,\Omega \] is connected to a resistor. The current in the circuit is 0.5 A. The terminal voltage of the battery when the circuit is closed is:
question_answer10) A galvanometer coil has a resistance of 15 \[\Omega \] and gives full scale deflection for a current of 4 mA. To convert it to an ammeter of range 0 to 6 A:
A)
\[10\,m\,\,\Omega \] resistance is to be connected in parallel to the galvanometer
doneclear
B)
\[10\,m\,\,\Omega \] resistance is to be connected in series with the galvanometer
doneclear
C)
\[0.1\,\,\,\Omega \] resistance is to be connected in parallel to the galvanometer
doneclear
D)
\[0.1\,\,\,\Omega \] resistance is to be connected in series with the galvanometer
question_answer11) The electron dirft speed is small and the charge of the electron is also small but still, we obtain large current in a conductor. This is due to:
A)
the conducting property of the conductor
doneclear
B)
the resistance of the conductor is small
doneclear
C)
the electron number density of the conductor is small
doneclear
D)
the electron number density of the conductor is enormous
question_answer12) A straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid air by a uniform horizontal magnetic field B. The magnitude of B (in tesia) is: (assume \[g=9.8\text{ }m{{s}^{-2}}\])
question_answer15) A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be?
question_answer17) The top of the atmosphere is about 400 kv with respect to the surface of the earth corresponding to an electric field that decreases with altitude. Near the surface the earth, the field is about \[100\,\,V{{m}^{-1}}\] do not get an electric shock as we step out of our house into the open house because (assume the house to be a steel cage so that there is no field inside)
A)
there is a potential difference between our body and the ground
doneclear
B)
\[100\,\,V{{m}^{-1}}\] is not a high electric field so that we do not feel the shock
doneclear
C)
our body and the ground forms a equipotential surface
question_answer19) When light of wavelength 300 nm falls on a photoelectric emitter, photoelectrons are liberated. For another emitter, light of wavelength 600 nm is sufficient for liberating photoelectrons. The ratio of the work function of the two emitters is:
question_answer21) If \[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\] are the wavelengths of the first members of the Lyman and Paschen series respectively, then \[{{\lambda }_{1}}:{{\lambda }_{2}}\] is:
question_answer22) Activity of a radioactive sample decreases to \[{{(1/3)}^{rd}}\] of its original value in 3 days. Then, in 9 days its activity will become:
question_answer26) A transparent cube of 0.21 m edge contains a small air bubble. Its apparent distance when viewed through one face of the cube is 0.10 m and when viewed from the opposite face is 0.04 m. The actual distance of the bubble from the second face of the cube is:
question_answer27) White light is incident on one of the refracting surfaces of a prism of angle \[{{5}^{o}}\]. If the refractring indices for red and blue colours are 1.641 and 1.659 respectively, the angular separation between these two colours when they emerge out of the prism is:
question_answer28) For a given lens, the magnification was found to be twice as large as when the object was 0.15 m distant from it as when the distance was 0.2 m. The focal length of the lens is:
question_answer30) A thin prism \[{{P}_{1}}\] with angle \[{{4}^{o}}\] made from a glass of refractive index 1.54 is combined with another thin prism \[{{P}_{2}}\] made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism \[{{P}_{2}}\]is:
question_answer31) If white light is used in the Newtons rings experiment, the colour observed in the reflected light is complementary to that observed in the transmitted light through the same point. This is due to:
A)
\[{{90}^{o}}\] change of phase in one of the reflected waves
doneclear
B)
\[{{180}^{o}}\] change of phase in one of the reflected waves
doneclear
C)
\[{{145}^{o}}\] change of phase in one of the reflected waves
doneclear
D)
\[{{45}^{o}}\] change of phase in one the reflected waves
question_answer32) Specific rotation of sugar solution is \[0.5\text{ }deg\text{ }{{m}^{2}}/kg.\text{ }200\text{ }kg{{m}^{-3}}\] of impure sugar solution is taken in a sample polarimeter tube of length 20 cm and optical rotation is found to be \[{{19}^{o}}\]. The percentage of purity of sugar is:
question_answer33) A simple pendulum has a length \[l\] and the mass of the bob is m. The bob is given a charge q coulomb. The pendulum is suspended between the vertical plates of a charged parallel plate capacitor. If E is the electric field strength between the plates, the time period of the pendulum is given by:
question_answer34) A gang capacitor is formed by interlocking a number of plates as, shown in figure. The distance between the consecutive plates is 0.885 cm and the overlapping area of the plates is \[5\text{ }c{{m}^{2}}\]. The capacity of the unit is:
question_answer35) A satellite in a circular orbit of radius R has a period of 4 h. Another satellite with orbital radius 3 R around the same planet will have a period (in hours):
question_answer38) A monoatomic gas is suddenly compressed to \[{{(1/8)}^{th}}\] of its initial volume adiabatically The ratio of its final pressure to the initial pressure is: (Given the ratio of the specific heats of the given gas to be 5/3)
question_answer39) A Carnot engine takes heat from a reservoir at \[{{627}^{o}}C\] and rejects heat to a sink at \[{{27}^{o}}C\]. Its efficiency will be:
question_answer40) A 30 V, 90 W lamp is to be operated on a 120 V DC line. For proper glow, a resistor of ...... \[\Omega \] should be connected in series with the lamp.
question_answer41) A battery consists of a variable number (n) of identical cells, each having an internal resistance r connected in series. The terminals of the battery are short-circuited. A graph of current \[(I)\] in the circuit versus the number of cells will be as shown in figure:
question_answer42) A tuning fork A produces 4 beats/s with another tuning fork B of frequency 320 Hz. On filing one of the prongs of A, 4 beats/s are again heard when sounded with the same fork B. Then, the frequency of the fork A before filing is:
question_answer45) The equation of a simple harmonic wave is given by \[y=5\sin \frac{\pi }{2}\left( 100t-x \right)\] where \[x\]- and y are in metre and time is in second. The period of the wave in second will be:
question_answer48) A rectangular vessel when full of water, takes 10 min to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water?
question_answer50) In a LCR series circuit, the potential difference between the terminals of the inductance is 60 V between the terminals of the capacitor is 30 V and that across the resistance is 40 V Then, supply voltage will be equal to:
question_answer52) A solenoid 1.5m long and 0.4 cm in diameter possesses 10 turns per cm length. A current of 5 A falls through it. The magnetic field at the axis inside the solenoid is:
question_answer53) A wire PQR is bent as shown in figure and is placed in a region of uniform magnetic field B. The length of \[PQ=QR=l.\text{ }A\] current \[I\]ampere flows through the wire as shown. The magnitude of the force on PQ and Q.R will be:
question_answer55) A current of 6 A enters one comer P of an equilateral triangle PQR having 3 wires of resistances \[2\Omega \] each and leaves by the comer R. Then the current \[{{I}_{1}}\] and \[{{I}_{2}}\] are:
question_answer57) Maxium velocity of the photoelectrons emitted by a metal surface is \[1.2\times {{10}^{6}}m{{s}^{-1}}\]. Assuming the specific charge of the electron to be \[1.8\times {{10}^{11}}C\text{ }k{{g}^{-1}}\], the value of the stopping potential in volt will be:
question_answer60) If \[{{r}_{1}}\] and \[{{r}_{2}}\] are the radii of the atomic nuclei of mass numbers 64 and 125 respectively, then the ratio \[({{r}_{1}}/{{r}_{2}})\] is:
question_answer62) The atomic number of Ni and Cu are 28 and 29 respectively. The electronic configuration. \[1{{s}^{2}},2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}3{{d}^{10}}\] represents :
question_answer68) The decomposition of a certain mass of \[CaC{{O}_{3}}\] gave \[11.2\text{ }d{{m}^{3}}\] of \[C{{O}_{2}}\] gas at STR The mass of KOH required to completely neutralise the gas is :
question_answer70) 0.06 mole of \[KN{{O}_{3}}\] solid is added to \[100\,c{{m}^{3}}\]of water at 298K. The enthalpy of \[KN{{O}_{3}}\]aqueous solution is \[35.8\text{ }kJ\text{ }rno{{l}^{-1}}\]. After the solute is dissolved the temperature of the solution will be:
question_answer71) 4 moles each of \[S{{O}_{2}}\] and \[{{O}_{2}}\] gases are allowed to react to form \[S{{O}_{3}}\] in a closed vessel. At equilibrium 25% of \[{{O}_{2}}\] is used up. The total number of moles of all the gases at equilibrium is :
question_answer86) The concentration of a reactant X decreases from 0.1 M to 0.005 M in 40 minute. If the reaction follows 1 order kinetics, the rate of the reaction when the concentration of X is M will be :
question_answer89) When a quantity of electricity is passed through \[CuS{{O}_{4}}\]solution, 0.16 g of copper gets deposited. If the same quantity of electricity is passed through acidulated water, then the volume of \[{{H}_{2}}\] liberated at STP will be : [given: atomic weight of \[Cu=64\]]
question_answer90) Solubility product of a salt AB is \[1\times {{10}^{-8}}{{M}^{2}}\]solution in which the concentration of \[{{A}^{+}}\] ions is \[{{10}^{-3}}M\]. The salt will precipitate when the concentration of B- ions is kept:
question_answer91) Which one of the following condition will increase the voltage of the cell represented by the equation? \[Cu(s)+2A{{g}^{+}}(aq)C{{u}^{2+}}(aq)+2Ag(s)\]
A)
Increase in the dimension of Cu electrode
doneclear
B)
Increase in the dimension of Ag electrode
doneclear
C)
Increase in the concentration of \[C{{u}^{2+}}\]ions
doneclear
D)
Increase in the concentration of \[A{{g}^{+}}\] ions
question_answer93) The mass of glucose that should be dissolved in 50 g of water in order to produce the same lowering of vapour pressure as is produced by dissolving 1 g of urea in the same quantity of water is :
question_answer94) Osmotic pressure observed when benzoic acid is dissolved in benzene is less than that expected from theoretical considerations. This is because :
question_answer97) For a reversible reaction: \[X(g)+3Y(g)2Z(g);\,\,\Delta H=-40\,kJ\], the standard entropies of X, Y and Z are 60, 40 and \[50\,\,J{{K}^{-1}}\,mo{{l}^{-1}}\] respectively. The temperature at which the above reaction attains equilibrium is about:
question_answer115) The formula mass of Mohrs salt is 392. The iron present in it is oxidised by \[KMn{{O}_{4}}\] in acid medium. The equivalent mass of Mohrs salt is:
question_answer119) For a reaction \[A+B\xrightarrow{{}}C+D\] if the concentration of A is doubled without alteming the concentration of B, the rate gets doubled. If the concentration of B is increased by nine times without alteming the concentration of A, the rate gets tripled. The order of the reaction is :
question_answer122) If \[\alpha ,\,\beta \] and \[\gamma \] are the. roots, of the equation\[{{x}^{3}}-8x+8=0\], then \[\sum \,\,{{\alpha }^{2}}\] and \[\sum \frac{1}{\alpha \beta }\] are respectively :
question_answer127) If the distance between the foci and the distance between the directories of the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] are in the ratio \[3:2\], then \[a:b\] is :
question_answer128) The ellipse \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{\mathbf{2}}}}{16}=1\] and the hyperbola\[\frac{{{x}^{2}}}{25}-\frac{{{y}^{\mathbf{2}}}}{16}=1\] have in common :
question_answer131) If the length of the tangent from any point on the circle \[{{(x-3)}^{2}}+{{(y+2)}^{2}}=5{{r}^{2}}\] to the circle \[{{(x-3)}^{2}}+{{(y+2)}^{2}}={{r}^{2}}\] is 16 unit, then the area between the two circles in sq unit is:
question_answer132) The circles \[a{{x}^{2}}+a{{y}^{2}}+2{{g}_{1}}x+2{{f}_{1}}y+{{c}_{1}}=0\] and \[b{{x}^{2}}+b{{y}^{2}}+2{{g}_{2}}x+2{{f}_{2}}y+{{c}_{2}}=0\](\[a\ne 0\] and \[b\ne 0\]) cut orthogonally if:
question_answer133) The equation of the common tangent of the two touching circles, \[{{y}^{2}}+{{x}^{2}}-6x-12y+37=0\] and\[{{x}^{2}}+{{y}^{2}}-6y+7=0\] is :
question_answer141) From an aeroplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the aeroplane are observed to be \[{{30}^{o}}\] and \[{{60}^{o}}\] respectively. The height at which the aeroplane is flying in km is :
question_answer144) If \[a>b>0\], then the value of\[{{\tan }^{-1}}\left( \frac{a}{b} \right)+{{\tan }^{-1}}\left( \frac{a+b}{a-b} \right)\] depends on :
question_answer151) In the group G = {1,5,7,11} under multiplication modulo 12, the solution of\[{{7}^{-1}}{{\otimes }_{12}}\,(x\,{{\otimes }_{12}}11)=5\] is equals :
question_answer153) If \[\vec{p}=\hat{i}=+\hat{j},\vec{q}=4k-\text{ }\hat{j}\] and \[\vec{r}=\hat{i}+\hat{k}\] then the unit vector in the direction of \[3\vec{p}+\vec{q}-2\vec{r}\] is:
question_answer154) If a and b are the two vectors such that \[|\vec{a}|=3\sqrt{3},\,|\vec{b}|=4\] and \[|\vec{a}+\vec{b}|=\sqrt{7}\], then the angle between a and b is:
question_answer156) If the area of the parallelogram with \[\vec{a}\] and \[\vec{b}\]as two adjacent sides is 15 sq unit, then the area of the parallelogram having, \[3\vec{a}+2\vec{b}\] and \[\vec{a}+3\vec{b}\] as two adjacent sides in sq unit is :
question_answer157) The locus of the point which moves such that the ratio of its distance from two fixed point in the plane is always a constant \[k\,(<1)\] is :
question_answer161) If the curve \[y=2{{x}^{3}}+a{{x}^{2}}+bx+c\] passes through the origin and the tangents drawn to it at \[x=-1\] and \[x=2\] are parallel to the x-axis, then the values of a, b and c are respectively:
question_answer163) The tangent and the normal drawn to the curve \[y={{x}^{2}}-x+4\] at P(1, 4) cut the x-axis at A and B respectively. If the length of the sub tangent drawn to the curve at P is equal to the length of the subnormal, then the area of the triangle PAB in sq unit is :
question_answer166) The complex number \[\frac{(-\sqrt{3}+3i)\,(1-i)}{(3+\sqrt{3}\,i)\,(i)\,(\sqrt{3}+\sqrt{3}i)}\] when represented in the Argand diagram is :
question_answer172) If \[{{I}_{1}}=\int_{0}^{\pi /2}{x\sin x\,dx}\] and \[{{I}_{2}}=\int_{0}^{\pi /2}{x\cos x\,dx}\], then which one of the following is true?
question_answer173) If \[f(x)\] is defined [-2,2] by \[f(x)=4{{x}^{3}}-3x+1\] and\[g(x)=\frac{f(-x)-f(x)}{{{x}^{2}}+3}\],then \[\int_{-2}^{2}{g\,(x)\,dx}\] is equal to :
question_answer175) The solution of the differential equation \[{{e}^{-x}}(y+1)\,dy+({{\cos }^{2}}x+\sin 2x)y\,dx=0\]subjected to the condition that \[y=1\] when\[x=0\] is :
question_answer177) If \[f(x)\] and \[g(x)\] are two functions with\[g(x)=x-\frac{1}{x}\] and \[fog(x)={{x}^{3}}-\frac{1}{{{x}^{3}}}\], then \[f(x)\] is:
question_answer180) If \[f(x)\] is a function such that\[f(x)+f(x)=0\] and \[g(x)={{[f(x)]}^{2}}+{{[f(x)]}^{2}}\] and \[g(3)=3\] then\[g(8)\] is equal to :