question_answer2) The displacement-time graph of two moving particles make angles of \[{{30}^{o}}\] and \[{{45}^{o}}\] with the X-axis. The ratio of their velocities is
question_answer3) Block A of mass of 2 kg is placed over block B of mass 8 kg. The combination is placed over a rough horizontal surface. Coefficient of friction between B and the floor is 0.5. Coefficient of friction between blocks A and B is 0.4. A horizontal force of 10 N is applied on block B. The force of friction between blocks A and B is \[(g=10\,m{{s}^{-2}})\]
question_answer4) The height y and the distance \[x\] along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by \[y=8\text{ }t5\text{ }{{t}^{2}}m\] and \[x=6t\text{ }m\], where t is in seconds. The velocity with which the projectile is projected is
question_answer5) A body of mass 5 kg is thrown vertically up with a kinetic energy of 490 J. The height at which the kinetic energy of the body becomes half of the original value is (acceleration due to gravity \[=9.8\text{ }m{{s}^{-2}}\])
question_answer6) A solid sphere of mass m rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is v. The kinetic energy of the sphere at the bottom is
question_answer8) The following four wires of length L and radius r are made of the same material. Which of these will have the largest extension, when the same tension is applied?
question_answer9) The resultant of two forces acting at an angle of \[{{120}^{o}}\] is 10 kg-wt and is perpendicular to one of the forces. That force is
question_answer10) Eight equal drops of water are falling through air with a steady velocity of \[10\text{ }cm\text{ }{{s}^{-1}}\]. If the drops combine to form a single drop big in size, then the terminal velocity of this big drop is
question_answer12) A perfect gas at \[{{27}^{o}}C\] is heated at constant pressure so as to double its volume. The increase in temperature of the gas will be
question_answer13) Three identical rods A, B and C are placed end to end. A temperature difference is maintained between the free ends of A and C. The thermal conductivity of B is thrice that of C and half of that of A. The effective thermal conductivity of the system will be (\[{{K}_{A}}\]a is the thermal conductivity of rod A)
question_answer14) The quantities of heat required to raise the temperatures of two copper spheres of radii \[{{r}_{1}}\] and \[{{r}_{2}}\] \[({{r}_{1}}=1.5\text{ }{{r}_{2}})\] through 1 K are in the ratio
question_answer15) Which one of the following is\[{{v}_{m}}\].T graph for perfectly black body? \[{{v}_{m}}\] is the frequency of radiation with maximum intensity. T is the absolute temperature.
question_answer16) A particle executing a simple harmonic motion has a period of 6 s. The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is
question_answer17) The equation of a wave is given by\[y=10\sin \left( \frac{2\pi }{45}t+\alpha \right).\]If the displacement is 5 cm at \[t=0\], then the total phase at \[t=7.5\text{ }s\]is
question_answer18) Two tuning forks A and B, produce notes of frequencies 258 Hz and 262 Hz. An unknown note sounded with A produces certain beats. When the same note is sounded with B, the beat frequency gets doubled. The unknown frequency is
question_answer19) A wire under tension vibrates with a fundamental frequency of 600 Hz. If the length of the wire is doubled, the radius is halved and the wire is made to vibrate under one - ninth the tension. Then the fundamental frequency will become
question_answer21) Wavelength of given light waves in air and in a medium are \[6000\overset{o}{\mathop{A}}\,\]and \[4000\overset{o}{\mathop{A}}\,\] respectively. The critical angle is
question_answer22) The time required for the light to pass through a glass slab (refractive index = 1.5) of thickness 4 mm is (\[c=3\times {{10}^{8}}m{{s}^{-1}}\] speed of light in free space)
question_answer23) A prism having refractive index 1.414 and refracting angle \[{{30}^{o}}\] has one of the refracting surfaces silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is
question_answer24) A plano convex lens has a maximum thickness of 6 cm. When placed on a horizontal table with the curved surface in contact with the table surface, the apparent depth of the bottommost point of the lens is found to be 4 cm. If the lens is inverted such that the plane face of the lens is in contact with the surface of the table, the apparent depth of the centre of the plane face is found to be \[\left( \frac{17}{4} \right)\]cm. The radius of curvature of the lens is
question_answer25) Two thin lenses have a combined power of +9 D. When they are separated by a distance of 20 cm, their equivalent power becomes +\[+\frac{27}{5}D\]. Their individual powers (in dioptre) are
question_answer27) Two monochromatic light waves of amplitudes 3 A and 2 A interfering at a point have a phase difference of \[{{60}^{o}}\]. The intensity at that point will be proportional to
question_answer29) A parallel beam of light of wavelength 6000 A gets diffracted by a single slit of width 0.3 mm. The angular position of the first minima of diffracted light is
question_answer31) Two identical charged spheres of material density p, suspended from the same point by inextensible strings of equal length make an angle 6 between the strings. When suspended in a liquid of density o the angle 9 remains the same. The dielectric constant K of the liquid is
question_answer32) The electric field at a point due to an electric dipole, on an axis inclined at an angle\[\theta \left( <{{90}^{0}} \right)\] to the dipole axis, is perpendicular to the dipole axis, if the angle \[\theta \]is
question_answer35) A conductor wire having \[{{10}^{29}}\] free electrons 1 \[{{m}^{3}}\] carries a current of 20A. If the cross-section of the wire is \[1\text{ }m{{m}^{2}}\], then the drift velocity of electrons will be \[(e=1.6\times {{10}^{-19}})\]
question_answer37) The voltage V and current \[I\] graph for a conductor at two different temperatures \[{{T}_{1}}\]and \[{{T}_{2}}\] and shown in the figure. The relation between \[{{T}_{1}}\] and \[{{T}_{2}}\] is
question_answer39) The torque required to hold a small circular coil of 10 turns, area \[1\text{ }mm2\] and carrying a current of \[\left( \frac{21}{44} \right)\]A in the middle of a long solenoid of \[{{10}^{3}}\] turns/m carrying a current of 2.5 A, with its axis perpendicular to the axis of the solenoid is
question_answer40) A particle of charge e and mass m moves with a velocity v in a magnetic field B applied perpendicular to the motion of the particle. The radius r of its path in the field is
question_answer41) A neutron, a proton, an electron and an \[\alpha \]-particle enter a region of uniform magnetic field with the same velocities. The magnetic field is perpendicular and directed into the plane of the paper. The tracks of the particles are labelled in the figure. The electron follows the track.
question_answer42) The deflection in a moving coil galvanometer is reduced to half when it is shunted with a \[40\,\Omega \] coil. The resistance of the galvanometer is
question_answer43) A current of \[\left( \frac{2}{\sqrt{3}} \right)A\], produces a deflection of \[{{60}^{o}}\] in a tangent galvanometer. The reduction factor is
question_answer44) In an AC circuit, V and \[I\] are given by \[V=150\sin \left( 150t \right)\] volt and \[I=150\sin \left( 150t+\frac{\pi }{3} \right)\] amp. The power dissipated in the circuit is
question_answer49) The photoelectric threshold wavelength for silver is \[{{\lambda }_{0}}\]. The energy of the electron ejected from the surface of silver by an incident wavelength \[\lambda \left( \lambda <{{\lambda }_{0}} \right)\] will be
question_answer51) When an electron jumps from the orbit \[n=2\]to \[n=4\], then wavelength of the radiations absorbed will be (R is Rydberg's constant)
question_answer52) The thermonuclear reaction of hydrogen inside the stars is taking place by a cycle of operations. The particular element which acts as a catalyst is
question_answer54) The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half-life of the radioactive sample is
question_answer57) In the case of forward biasing of a p-n junction diode, which one of the following figures correctly depicts the direction of conventional current (indicated by an arrow mark)?
question_answer58) An electron of mass me and a proton of mass \[{{m}_{p}}\] are moving with the same speed. The ratio of their de-Broglie's wavelengths \[{{\lambda }_{e}}/{{\lambda }_{p}}\]is
question_answer60) If the scattering intensity of a liquid is 8 units at a wavelength of 500 nm, then the scattering intensity at a wavelength of 400 nm will be approximately
question_answer68) Generally, the first ionization energy increases along a period. But there are some exceptions. The one which is not an exception is
question_answer70) Increasing order of carbon-carbon bond length for the following is \[\underset{(A)}{\mathop{{{C}_{2}}{{H}_{4}}}}\,\] \[\underset{(B)}{\mathop{{{C}_{2}}{{H}_{2}}}}\,\] \[\underset{(C)}{\mathop{{{C}_{6}}{{H}_{6}}}}\,\] \[\underset{(D)}{\mathop{{{C}_{2}}{{H}_{6}}}}\,\]
question_answer71) A mixture of \[CaC{{l}_{2}}\] and \[NaCl\] weighing 4.44 g is treated with sodium carbonate solution to precipitate all the calcium 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 is (atomic mass of \[Ca=40\])
question_answer72) \[50\text{ }c{{m}^{3}}\] of \[0.2\text{ }N\text{ }HCl\] is titrated against\[0.1\text{ }N\text{ }NaOH\] solution. The titration was discontinued after adding \[50\text{ }c{{m}^{3}}\] of \[NaOH\]. The remaining titration is completed by adding \[0.5\text{ }N\text{ }KOH\]. The volume of \[KOH\]required for completing the titration is
question_answer73) The rms velocity of hydrogen is \[\sqrt{7}\] times the rms velocity of nitrogen. If T is the temperature of the gas, which of the following is true?
question_answer75) The amount of heat evolved when \[500\text{ }c{{m}^{3}}\] of \[M\text{ }HCl\] is mixed with \[200\text{ }c{{m}^{3}}\] of \[0.2\text{ }M\text{ }NaOH\] is
question_answer76) The enthalpy of vaporization of benzene is +35.3 kJ/mol at its boiling point, \[{{80}^{o}}C\]. The entropy change in the transition of vapour to liquid at its boiling point is
question_answer78) 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_answer80) 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?
question_answer84) 1.2 g of organic compound of Kjeldahlization liberates ammonia which consumes \[30\,\,c{{m}^{3}}\]of\[1\text{ }N\text{ }HCl\]. The percentage of nitrogen in the organic compound is
question_answer87) 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 still left in the lead layer is approximately
question_answer92) Excess of silver nitrate solution is added to 100 mL of 0.01 M pentaaqua chloro chromium (III) chloride solution. The mass of silver chloride obtained in grams is [Atomic mass of silver is 108].
question_answer93) The following data were obtained during the first order decomposition of \[2A\,(g)\to B\,(g)+C\,(s)\] at a constant volume and at a particular temperature
question_answer95) The activation energy of a reaction at a given temperature is found to be \[2.303\text{ }RT\text{ }J\text{ }mo{{l}^{-1}}\]. The ratio of rate constant to the Arrhenius factor is
question_answer97) A buffer solution contains 0.1 mole of sodium acetate dissolved in \[1000\text{ }c{{m}^{3}}\] 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
question_answer98) \[{{H}_{2}}S\] is passed into one \[n{{m}^{3}}\] of a solution containing 0.1 mole of \[Z{{n}^{2+}}\] and 0.01 mole of \[C{{u}^{2+}}\] till the sulphide ion concentration reaches to \[8.1\times {{10}^{-19}}\] moles. Which one of the following statements is true? [\[{{K}_{sp}}\] of \[ZnS\] and \[CuS\] are \[3\times {{10}^{-22}}\] and\[8\times {{10}^{-36}}\] respectively.]
question_answer101) The standard emf of a galvanic cell involving 2 moles of electrons in its redox reaction is 0.59 V. The equilibrium constant for the redox reaction of the cell is
question_answer102) 9.65 C of electric current is passed through fused alhydrous \[MgC{{l}_{2}}\]. The magnesium metal thus obtained is completely converted into a Grignard reagent. The number of moles of Grignard reagent obtained is
question_answer103) The empirical formula of a non-electrolyte is\[C{{H}_{2}}O\]. A solution containing 3 g of the compound exerts the same osmotic pressure as that of 0.05 M glucose solution. The molecular formula of the compound is
question_answer107) Which one of the nitrogen atoms in\[{{H}_{2}}\underset{I}{\mathop{N}}\,-\underset{II}{\mathop{N}}\,H-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-\underset{III}{\mathop{N}}\,{{H}_{2}}\] is the most nudeophilic?
A)
III
doneclear
B)
I
doneclear
C)
II
doneclear
D)
All three nitrogen atoms are equally strong nudeophilic centres
question_answer110) Which one of the following is an intermediate in the reaction of benzene with \[C{{H}_{3}}Cl\] in the presence of anhydrous \[AlC{{l}_{3}}\]?
question_answer112) Following is the substitution reaction in which \[-CN\] replaces \[-Cl\]. \[R-Cl+\underset{(alcoholic)}{\mathop{KCN}}\,\xrightarrow[\Delta ]{}R-CN+KCl\] To obtain propanenitrile, \[R-Cl\] should be
question_answer122) The sum of the first \[n\]terms of \[\frac{{{1}^{2}}}{1}+\frac{{{1}^{2}}+{{2}^{2}}}{1+2}+\frac{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}{1+2+3}+....\]is
question_answer123) If \[n\]is an odd positive integer and \[{{(1+x+{{x}^{2}}+{{x}^{3}})}^{n}}=\sum\limits_{r=0}^{3n}{{{a}_{r}}{{x}^{r}}},\]then \[{{a}_{0}}-{{a}_{1}}+{{a}_{2}}-{{a}_{3}}+...-{{a}_{3n}}\]is equal to
question_answer125) If \[\alpha ,\beta \]and \[\gamma \]are roots of \[{{x}^{3}}-2x+1=0,\]then the value of \[\sum{\left( \frac{1}{\alpha +\beta -\gamma } \right)}\]is
question_answer129) . Angles of elevation of the top of a tower from three point (collinear) A, Band C on a road leading to the foot of the tower are \[{{30}^{o}},{{45}^{o}}\]and \[{{60}^{o}}\]respectively. The ration of AB to BC is
question_answer135) If \[f(x)=\left\{ \begin{matrix} \frac{\log x}{x-1}, & if\,x\ne 1 \\ \,\,k\,\,\,\,\,\,\,\,\,\,\,, & if\,x=1 \\ \end{matrix} \right.\]is continuous at \[x=1,\]then the value of k is
question_answer141) If a, b and c are non-coplanar, then the value of \[a.\left\{ \frac{b\times c}{3b.(c\times a)} \right\}-b\left\{ \frac{c\times a}{2c.(a\times b)} \right\}\]is
question_answer142) If \[2i+3j,i+j+k\]and \[\lambda i+4j+2k\]taken in an order are coterminous edges of a parallelepiped of volume 2 cu units, then value of \[\lambda \]is
question_answer146) On the set of all non-zero reals, an operation is defined as \[a*b=\frac{3ab}{2}.\]in this group, a solution of \[({{2}^{*}}x)*{{3}^{-1}}={{4}^{-1}}\]is
question_answer147) \[G=\left\{ \left[ \begin{matrix} x & x \\ x & x \\ \end{matrix} \right],x\,\text{is}\,\text{a}\,\text{non}-\text{zero}\,\text{real}\,\text{number} \right\}\]is a group with respect to matrix multiplication. In this group, the inverse of \[\left[ \begin{matrix} \frac{1}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{3} \\ \end{matrix} \right]\]is
question_answer150) The centre of a circle which cuts \[{{x}^{2}}+{{y}^{2}}-1=0,\]\[{{x}^{2}}+{{y}^{2}}-3y+2=0\]and \[{{x}^{2}}+\]\[{{y}^{2}}+x+y-3=0\]orthogonally is
question_answer153) If the foci of \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{4}=1\]and \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{9}=1\]coincide, then the value of a is
question_answer159) If\[\omega \]is an imaginary cube root of unity, then the value of \[(1-\omega +{{\omega }^{2}}).(1-{{\omega }^{2}}+{{\omega }^{4}}).(1-{{\omega }^{4}}+{{\omega }^{8}})....\](\[2n\]factors) is
question_answer161) If \[\sqrt{r}=a{{e}^{\theta \cot \alpha }}\]where a and \[\alpha \]are real numbers, then \[\frac{{{d}^{2}}r}{d{{\theta }^{2}}}-4r{{\cot }^{2}}\alpha \]is
question_answer166) Area of a triangle formed by tangent and normal to the curve \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{v}^{2}}}=1\]at \[P\left( \frac{a}{\sqrt{2}},\frac{b}{\sqrt{2}} \right)\]with the x-axis is
question_answer177) If P is a point on \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]with foci S and s?, then the maximum value of \[\Delta SPS'\]is