question_answer2) A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement \[x\]is proportional to:
question_answer3) A ball is released from the top of a tower of height h m. It takes T s to reach the ground. What is the position of the ball in 773 s?
question_answer4) A projectile can have the same range R for two angles of projection. If\[{{T}_{1}}\]and\[{{T}_{2}}\]be the times of flights in the two cases, then the product of the two times of flights is directly proportional to
question_answer5) An automobile travelling with a speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, ie., 120 km/h, the stopping distance will be:
question_answer6) A machine gun fires a bullet of mass 40 g with velocity\[1200\text{ }m{{s}^{-1}}\]. The man holding it, can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
question_answer7) Two masses\[{{m}_{1}}=5\,kg\]and\[{{m}_{2}}=4.8\text{ }kg\] tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift is free to move? \[(g=9.8m/{{s}^{2}})\]
question_answer8) A block rests on a rough inclined plane making an angle of\[30{}^\circ \]with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block Jin kg) is (take\[g=10\text{ }m/{{s}^{2}})\]
question_answer9) A force\[\overrightarrow{F}=(5\hat{i}+3\text{ }\hat{j}+2\hat{k})N\]is applied over a particle which displaces it from its origin to the point\[\overrightarrow{r}=(2\hat{i}-\hat{j})m\]. The work done on the particle in joules is
question_answer10) A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane, it follows that
question_answer11) A ball is thrown from a point with a speed\[{{v}_{0}}\]at an angle of projection\[\theta \]. From the same point and at the same instant, a person starts running with a constant speed\[\frac{{{v}_{0}}}{2}\]to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?
question_answer12) One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively\[{{I}_{A}}\]and\[{{I}_{B}}\]such that
question_answer13) A satellite of mass m revolves around the earth of radius R at a height\[x\]from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is
question_answer15) If g is the acceleration due to gravity on the earths surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is
question_answer16) Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to
question_answer19) The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is\[{{t}_{0}}\]in air. Neglecting frictional force of water and given that the density of the bob is \[(4/3)\times 1000kg/{{m}^{3}}\]. What relationship between\[t\]and\[{{t}_{0}}\]is true?
question_answer21) The displacement y of a particle in a medium can be expressed as \[y={{10}^{-6}}\sin \left( 100t+20x+\frac{\pi }{4} \right)m,\]where t is in second and x in metre. The speed of the wave is
question_answer22) A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency\[{{\omega }_{0}}\]. An external force F(t) proportional to\[\cos \omega t(\omega \ne {{\omega }_{0}})\]is applied to the oscillator. The time displacement of the oscillator will be proportional to
question_answer23) One mole of ideal monoatomic gas\[(\gamma =5/3)\].is mixed with one mole of diatomic gas\[(\gamma =7/5)\]. What is\[\gamma \]for the mixture? \[\gamma \] denotes the ratio of specific heat at constant pressure, to that at constant volume:
question_answer24) If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously, will be
question_answer27) The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness\[x\]and\[4x,\]respectively are\[{{T}_{2}}\]and\[{{T}_{1}}({{T}_{2}}>{{T}_{1}})\]. The rate of heat transfer through the slab, in a steady state is \[\left( \frac{A({{T}_{2}}-{{T}_{1}})K}{x} \right)f,\]with\[f\]equals to
question_answer28) A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now, this lens has been .used to form the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object?
question_answer30) An electromagnetic wave of frequency \[v=3.0\text{ }MHz\]passes from vacuum into a dielectric medium with permittivity\[\varepsilon =4.0\]. Then
A)
wavelength is doubled and the frequency remains unchanged
doneclear
B)
wavelength is doubled and frequency becomes half
doneclear
C)
wavelength is halved, and frequency remains unchanged
question_answer31) Two spherical conductors B and C having equal radii and carrying equal charges in them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged, is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is
question_answer32) A charged particle q is shot towards another charged particle Q which is fixed, with a speed v. It approaches Q upto a closest distance r and then returns. If q was given a speed 2v, the closest distance of approach would be
question_answer34) The resistance of the series combination of two resistances is S. When they are joined in parallel, the total resistance is P. If\[S=nP,\]then the minimum possible value of n is
question_answer35) An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 4/3 and 2/3, then the ratio of the currents passing through the wire will be
question_answer36) In a metre bridge experiment, null point is obtained at 20 cm from one end of the wire when resistance\[X\]is balanced against another resistance Y. If\[X<Y,\]then where will be the new position of the null point from the same end, if one decides to balance a resistance of\[4X\]against\[Y\]?
question_answer39) The thermo-emf of a thermocouple varies with the temperature\[\theta \]of the hot junction as\[E=a\theta +b{{\theta }^{2}}\]in volts where the ratio a/b is\[700{}^\circ C\]. If the cold junction is kept at\[0{}^\circ C,\] then the neutral temperature is
A)
\[700{}^\circ C\]
doneclear
B)
\[350{}^\circ C\]
doneclear
C)
\[1400{}^\circ C\]
doneclear
D)
no neutral temperature is possible for this thermocouple
question_answer40) The electrochemical equivalent of metal is \[3.3\times {{10}^{-7}}\]kg per coulomb. The mass of the metal liberated at the cathode when a 3 A current is passed for 2 s, will be
question_answer41) A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of the coil will be
question_answer42) The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is\[5\mu T\]. What will be its value at the centre of the loop?
question_answer43) Two long conductors, separated by a distance d carry currents\[{{I}_{1}}\]and\[{{I}_{2}}\]in the same direction. They exert a force F on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to 3 d. The new value of the force between them is
question_answer44) The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2 s. The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be:
question_answer46) In an LCR series ac circuit, the voltage across each of the components. L, C and R is 50 V. The voltage across the LC combination will be
question_answer47) In an LCR circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to
question_answer48) A metal conductor of length 1m rotates vertically about one of its ends at angular velocity 5 radians per second. If the horizontal component of earths magnetic field is\[0.2\times {{10}^{-4}}T,\]then the emf developed between the two ends of the conductor is
question_answer49) The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately
question_answer50) A charged oil drop is suspended in uniform field of \[3\times {{10}^{4}}V/m\]so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge\[=9.9\times {{10}^{-15}}kg\]and\[=10m/{{s}^{2}}\])
question_answer51) A nucleus disintegrates into two nuclear parts which have their velocities in the ratio\[2:1\]. The ratio of their nuclear sizes will be
question_answer52) The binding energy per nucleon of deuteron \[(_{1}^{2}H)\]and helium nucleus\[(_{2}^{4}He)\]is 1.1 MeV and 7 MeV respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is
question_answer53) An\[\alpha -\]particle of energy 5 MeV is scattered through\[180{}^\circ \]by a fixed uranium nucleus. The distance of the closest approach is of the order of
question_answer60) As the temperature is raised from\[20{}^\circ C\]to\[40{}^\circ C\],the average kinetic energy of neon atoms changes by a factor of which of the following?
question_answer65) To neutralise completely 20 mL of 0.1M aqueous solution of phosphorous acid \[({{H}_{3}}P{{O}_{3}}),\]the volume of 0.1M aqueous KOH solution required is
question_answer66) For which of the following parameters the structural isomers\[{{C}_{2}}{{H}_{5}}OH\]and\[C{{H}_{3}}OC{{H}_{3}}\] would be expected to have the same values? (Assume ideal behaviour)
A)
Heat of vaporization
doneclear
B)
Vapour pressure at the same temperature
doneclear
C)
Boiling points
doneclear
D)
Gaseous densities at the same temperature and pressure
question_answer68) An ideal gas expands in volume from \[1\times {{10}^{-3}}{{m}^{3}}\]to\[1\times {{10}^{-2}}{{m}^{3}}\]at 300K against a constant pressure of\[1\times {{10}^{5}}N{{m}^{-2}}\]. The work done is
question_answer69) In a first order reaction, the concentration of the reactant, decreases from 0.8 M to 0.4 M in 15 min. The time taken for the concentration to change from 0.1 M to 0.025 M is
question_answer71) The rate equation for the reaction\[2A+B\to C\] is found to be rate\[=k[A]\,[B]\] The correct statement in relation to this reaction is that the
A)
unit of k must be \[{{s}^{-1}}\]
doneclear
B)
\[{{t}_{1/2}}\]is a constant
doneclear
C)
rate of formation of C is twice the rate of, disappearance of A
doneclear
D)
value of k is independent of the initial concentrations of A and B
question_answer72) Consider the following\[E{}^\circ \]values \[E_{F{{e}^{3+}}/F{{e}^{2+}}}^{o}=+0.77\,V\] \[E_{S{{n}^{2+}}/Sn}^{o}=-0.14\,V\] Under standard conditions the potential for the reaction \[Sn(s)+2F{{e}^{3+}}(aq)\to 2F{{e}^{2+}}(aq)+S{{n}^{2+}}(aq)\]is
question_answer73) The molar solubility (in\[mol\text{ }{{L}^{-1}}\]) of a sparingly soluble salt\[M\,{{X}_{4}}\]is s. The corresponding solubility product is\[{{K}_{sp}}\]. s is given in terms of. \[{{K}_{sp}}\]by the relation
question_answer74) The standard emf of a cell, involving one electron change is found to be 0.591 V at\[25{}^\circ C\]. The equilibrium constant of the reaction is \[(F=96,500\text{ }C\text{ }mo{{l}^{-1}})\]
question_answer75) The enthalpies of combustion of carbon and carbon monoxide are\[-393.5\]and\[-283k\text{ }J\] \[mo{{l}^{-1}}\]respectively. The enthalpy of formation of carbon monoxide per mole is
question_answer82) Aluminium chloride exists as dimer,\[A{{l}_{2}}C{{l}_{6}}\]in solid state as well as in solution of non-polar solvents such as benzene. When dissolved in water, it gives
question_answer83) The soldiers of Napolean army while at Alps during freezing winter suffered a serious problem as regards to the tin buttons of their uniforms. White metallic tin buttons got converted to grey powder. This transformation is related to
A)
a change in the crystalline structure of tin
doneclear
B)
an interaction with nitrogen of the air at very low temperatures
doneclear
C)
a change in the partial pressure of oxygen in the air
doneclear
D)
an interaction with water vapour contained in the humid air
question_answer84) Excess of\[KI\]reacts with\[CuS{{O}_{4}}\]solution and then\[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\]solution is added to it. Which of the statements is incorrect for this reaction?
question_answer87) Co-ordination compounds have great importance in biological systems. In this context which of the following statements is incorrect?
A)
Chlorophylls are green pigments in plants and contain calcium
doneclear
B)
Haemoglobin is the red pigment of blood and contains iron
doneclear
C)
Cyanocobalamin is vitamin\[{{B}_{12}}\]and contains cobalt
question_answer90) Consider the following nuclear reactions: \[_{92}^{238}M\to _{y}^{x}N+2_{2}^{4}He;_{y}^{x}N\to _{B}^{A}L+2{{\beta }^{+}}\] The number of neutrons in the element L is
question_answer92) The ammonia evolved from the treatment of 0.30g of an organic compound for the estimation of nitrogen was passed in 10s) ml, of M sulphuric acid. The excess of acid required 20 mL of 0.5 M sodium hydroxide solution for complete neutralization. The organic compound is
question_answer99) Consider the acidity of the carboxylic acids \[PhCOOH\] \[o-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\] \[p-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\] \[m-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\] Which of the following order is correct?
question_answer109) Insulin production and its action in human body are responsible for the level of diabetes. This compound belongs to which of the following categories?
question_answer123) If one root of the equation\[{{x}^{2}}+px+12=0\]is 4, while the equation\[{{x}^{2}}+px+q=0\]has equal roots, then the value of q is
question_answer124) The coefficient of the middle term in the binomial expansion in powers of\[x\]of\[{{(1+ax)}^{4}}\] and of\[{{(1-ax)}^{6}}\]is the same, if a equals:
A)
\[-\frac{5}{3}\]
doneclear
B)
\[\frac{10}{3}\]
doneclear
C)
\[-\frac{3}{10}\]
doneclear
D)
\[\frac{3}{5}\] The coefficient of\[x\]in the middle term of expansion of\[{{(1+\alpha x)}^{4}}{{=}^{4}}{{C}_{2}}.{{\alpha }^{2}}\] The coefficient of x in the middle term of the expansion of\[{{(1-\alpha x)}^{6}}{{=}^{6}}{{C}_{3}}{{(-\alpha )}^{3}}\] According to question, \[^{4}{{C}_{2}}{{\alpha }^{2}}{{=}^{6}}{{C}_{3}}{{(-\alpha )}^{3}}\] \[\Rightarrow \] \[\frac{4!}{2!2!}{{\alpha }^{2}}=-\frac{6!}{3!3!}{{\alpha }^{3}}\] \[\Rightarrow \] \[6{{\alpha }^{2}}=-20{{\alpha }^{3}}\] \[\Rightarrow \] \[\alpha =-\frac{6}{20}\] \[\Rightarrow \] \[\alpha =-\frac{3}{10}\]
question_answer126) If\[{{s}_{n}}=\sum\limits_{r=0}^{n}{\frac{1}{^{n}{{C}_{r}}}}\]and\[{{t}_{n}}=\sum\limits_{r=0}^{n}{\frac{r}{^{n}{{C}_{r}}}},\]then\[\frac{{{t}_{n}}}{{{s}_{n}}}\]is equal to
question_answer127) Let\[{{T}_{r}}\]be the rth term of an A P whose first term is a and common difference is d. If for some positive integers\[m,n,m\ne n,{{T}_{m}}=\frac{1}{n}\]and \[{{T}_{n}}=\frac{1}{m},\]then\[a-d\]equals
question_answer128) The sum of the first n terms of the series\[{{1}^{2}}+{{2.2}^{2}}+{{3}^{2}}+{{2.4}^{2}}+{{5}^{2}}+{{2.6}^{2}}+...\]is \[\frac{n{{(n+1)}^{2}}}{2}\]when n is even. When n is odd the sum is
question_answer131) If\[u=\sqrt{{{a}^{2}}{{\cos }^{2}}\theta +{{b}^{2}}{{\sin }^{2}}\theta }\]\[+\sqrt{{{a}^{2}}{{\sin }^{2}}\theta +{{b}^{2}}{{\cos }^{2}}\theta },\]then the difference between the maximum and minimum values of\[{{u}^{2}}\]is given by
question_answer132) The sides of a triangle are\[\sin \alpha ,\cos \alpha \]and\[\sqrt{1+\sin \alpha \cos \alpha }\]for some\[0<\alpha <\frac{\pi }{2}\]. Then the greatest angle of the triangle is
question_answer135) if\[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( 1+\frac{a}{x}+\frac{b}{{{x}^{2}}} \right)}^{2x}}={{e}^{2}},\]then the values of a and b are
question_answer139) A function\[y=f(x)\]as a second order derivative\[f=6(x-1)\]. If its graph passes through the point (2, 1) and at that point the tangent to the graph is\[y=3x-5,\]then the function is
question_answer151) Let\[A(2,-3)\]and\[B(-2,1)\]be vertices of a triangle ABC. If the centroid of this triangle moves on the line\[2x+3y=1,\]then the locus of the vertex C is the line:
question_answer152) The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is\[-1,\]is
question_answer155) If a circle passes through the point (a, b) and cuts the circle\[{{x}^{2}}+{{y}^{2}}=4\]orthogonally, then, the locus of its centre is
question_answer156) If the lines\[2x+3y+1=0\]and\[3x-y-4=0\] lie along diameters of a circle of circumference\[10\pi ,\]then the equation of the circle is
question_answer158) If\[a\ne 0\]and the line\[2bx+3cy+4d=0\]passes through the points of intersection of the parabolas\[{{y}^{2}}=4ax\]and\[{{x}^{2}}=4ay,\]then
question_answer159) The eccentricity of an ellipse with its centre at the origin, is\[\frac{1}{2}\]. If one of the directrices is \[x=4,\]then the equation of the elapse is:
question_answer160) A line makes the same angle. 9 with each of the\[x\]and z axis. If the angle P, which it makes with y-axis, is such that\[si{{n}^{2}}\beta =3\text{ }si{{n}^{2}}\theta ,\]then\[{{\cos }^{2}}\theta \]equals
question_answer162) A line with direction cosines proportional to 2,1, 2 meets each of the lines\[x=y+a=z\]and \[x+a=2y=2z\]. The co-ordinates of each of the points of intersection are given by
question_answer163) If the straight lines\[x=1+s,y=-3-\lambda s,\]\[z=1+\lambda s\]and\[x=\frac{t}{2},y=1+t,z=2-t,\]with parameters s and t respectively, are co-planar, then\[\lambda \]equals
question_answer164) Let\[\overrightarrow{a},\overrightarrow{d}\]and\[\overrightarrow{c}\]be three non-zero vectors such that no two of these are collinear. If the vector\[\overrightarrow{a}+2\overrightarrow{b}\]is collinear with\[\overrightarrow{c}\]and\[\overrightarrow{b}+3\overrightarrow{c}\]is collinear with\[\overrightarrow{a}\] (\[\lambda \]being some non-zero scalar), then\[\overrightarrow{a}+2\overrightarrow{b}+6\overrightarrow{c}\]equals
question_answer165) A particle is acted upon by constant forces\[4\hat{i}+\hat{j}-3\hat{k}\] and\[3\hat{i}+\hat{j}-\hat{k}\] which displace it from a point\[\hat{i}+2\hat{j}+3\hat{k}\]to the point\[5\hat{i}+4\hat{j}+\hat{k}\]. The work done in standard units by the forces is given by
question_answer166) If\[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\]are non-coplanar vectors and\[\lambda \]is a real number, then the vectors\[\overrightarrow{a}+2\overrightarrow{b}+3\overrightarrow{c},\]and\[\lambda \overrightarrow{b}+4\overrightarrow{c}\]and\[(2\lambda -1)\overrightarrow{c}\]are non-coplanar for
question_answer167) Let\[\overrightarrow{u},\overrightarrow{v},\overrightarrow{w}\]be such that\[|\overrightarrow{u}|=1,|\overrightarrow{v}|=2,\]\[|\overrightarrow{w}|=3.\] If the projection\[\overrightarrow{v}\]long\[\overrightarrow{u}\]is equal to that of\[\overrightarrow{w}\] along\[\overrightarrow{u}\]and\[\overrightarrow{v},\overrightarrow{w}\]are perpendicular to each other, then\[|\overrightarrow{u}-\overrightarrow{v}+\overrightarrow{w}|\]equals:
question_answer169) With two forces acting at a point, the maximum effect is obtained when their resultant is 4N. If they act at right angles, then their resultant is 3N. Then the forces are
question_answer170) In a right angle\[\Delta ABC,\text{ }\angle A=90{}^\circ \]and sides a, b, c are respectively, 5 cm, 4 cm and 3 cm. If a force F has moments 0, 9 and 16 in N cm unit respectively about vertices A, B and C, the magnitude of F is