question_answer4) An electron starting from rest has a velocity\[v\] that increases linearly with time t as\[v=kt,\] where\[k=2\text{ }m{{s}^{-2}}\]. The distance covered by electron in first 3 s is
question_answer5) The excess of pressure inside a drop of soap solution is pj and that inside a soap bubble of same radius is\[{{p}_{b}}\]. The correct relation between \[{{p}_{d}}\]and\[{{p}_{b,}}\]is given by
question_answer6) Two vectors A and B are such that,\[A+B=C\] and\[{{A}^{2}}+{{B}^{2}}={{C}^{2}}\]. If 9 is the angle between positive directions of A and B, then
question_answer7) Let two satellites X and Y revolves around a planet P in circular orbits of radii 4R and R respectively. If the speed of the satellite X is 3v, then the speed of satellite Y will be
question_answer8) A bimetallic strip is made of two strips A and B having coefficient of linear expansion as\[{{\alpha }_{A}}\]and da. If\[{{\alpha }_{A}}>{{\alpha }_{B}},\] which one of the following describes the behaviour of the metallic strip when heated?
A)
Strip will bend only when \[\frac{{{\alpha }_{A}}+{{\alpha }_{B}}}{2}>({{\alpha }_{A}}-{{\alpha }_{B}})\]
question_answer9) An electron accelerated through a potential difference of V volts has a wavelength\[\lambda \] associated with it. Mass of proton is nearly 2000 times that of an electron. In order to have the same wavelength\[\lambda \]for the proton, it must be accelerated through a potential difference of
question_answer10) Two points charges of\[+3C\]and\[+9C\]repel each other with a force of 27 N. If charges of\[-3C\] are given to each of these charges, then the new force of interaction will be
question_answer11) In Young's double slit experiment the 7th maximum with wavelength\[{{\lambda }_{1}}\]is at a distance\[{{d}_{1}}\]and that with wavelength\[{{\lambda }_{2}}\]is at distance\[{{d}_{2}}.\]Then, \[{{d}_{1}}/{{d}_{2}}=\]
question_answer12) The plates of a parallel air capacitor are 2 cm apart. If a slab of dielectric constant 5 and thickness 1 cm is placed between its plates, then to keep the capacitance of the capacitor unchanged. The plates of the capacitor should moved by a distance of
question_answer13) If\[W\]units of works is required to turn a magnetic needle through\[60{}^\circ \]when it is lying parallel to a magnetic field, then amount of torque needed to maintain needle in this position will be
question_answer14) If two stars radiates maximum energy at wavelengths\[316\times {{10}^{-7}}m\]and\[4.8\times {{10}^{-7}}m\] respectively, then ratio of their temperatures T/T? will be
question_answer15) The diameter of the moon is\[3.5\times {{10}^{3}}\]km and its distance from the earth is\[3.8\times {{10}^{5}}\]km seen by a telescope having focal lengths of the objective and eye piece as 4 m and 10 cm respectively, the diameter of image of the moon will be approximately
question_answer17) If a constant volume gas thermometer records a pressure of 20 kPa at tripple point of water and pressure of 14.3 kPa at the dry ice, then the temperature of dry ice will be
question_answer18) Two discs have same mass and thickness but are made, up of different materials having different densities. Which one of them will have larger moment of inertia?
A)
Both disc have same moment of inertia
doneclear
B)
disc having less density have larger moment of inertia
doneclear
C)
disc having more density have larger moment of inertia
question_answer19) If a resistor of\[30\,\Omega ,\]is bent in the form of a circle as shown in figure, then the effective resistance' between points X and Y will be
question_answer20) A radioactive nuclide decays to form a stable nuclide. If the half-life of nuclide is 3 min, then what fraction of its 1 g will remain radioactive after 9 min?
question_answer21) If an\[\alpha -\]particle of energy 10 MeV is deflected back when its distance from the nucleus is \[4\times {{10}^{-14}}m,\]then the atomic number of the atom is
question_answer23) A bus starts from rest with an acceleration\[1\,m{{s}^{-2}}\]. A man who is 48 m behind the bus starts with a uniform velocity of\[10\text{ }m{{s}^{-1}}\]. Then the minimum rime after which the man will reach the bus
question_answer26) A particle describes a horizontal circle on the smooth surface of an inverted cone. If the height of the plane of the circle above the vertex is 9.8 cm, then the speed of the particle will be (Take\[g=9.8\text{ }m/{{s}^{2}}\])
question_answer28) If two vessels of different materials identical in size and wall thickness are filled with equal quantities of ice at\[0{}^\circ C\]and ice melts completely in 10 and 25 min respectively, then the ratio of coefficients of thermal conductivies of the materials of the vessels will be
question_answer29) The stress for elastic limit of a material is\[3.5\times {{10}^{8}}N-{{m}^{-2}}\]. The minimum diameter of a rod made of this material which can support 500 N load without exceeding elastic limit will be
question_answer30) A ray of light passing through a prism having\[\mu =\sqrt{2}\]suffers minimum deviation. If the angle of incidence is double the angle of refraction within the prism, then the angle of the prism is
question_answer31) A drop of olive oil is introduced in a mixture of alcohol and water. The density of the mixture is same as that of olive oil. The upward thrust on the drop is
question_answer32) A Carnot engine whose low temperature reservoir is at\[7{}^\circ C\]has an efficiency of 50%. If the efficiency of heat engine is to be increased more by 10% then the temperature of high temperature reservoir should be increased by
question_answer33) An AC source of frequency 50 Hz is connected to 50 mH inductor and a bulb. To get the maximum brightness from the bulb, what should be the capacitance of a capacitor connected in series with the circuit?
question_answer34) Two long straight wires are connected by a circular section that has a radius r as shown in figure. All segments of the wire lie in the same place and carry steady current I. The magnetic field at centre O of the circular segment will be
question_answer35) If two wires made of tinned copper having identical cross-section but different lengths \[{{l}_{1}}\]and\[{{l}_{2}}\]respectively are used as fuse wires, then the fuses will melt at same value of current in both of them
question_answer36) A wave is represented by \[y=a\cos (\omega t+kx+\phi )\] where\[\omega ,\phi \]and\[\phi \]are three constants. The dimensions of\[\omega ,k\]and\[\phi \]are respectively
question_answer37) Two blocks of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] are placed in contact with each other on a rough horizontal surface having coefficient of friction\[\mu \]as shown in figure. The minimum horizontal force F required to move the block\[{{m}_{1}}\]
question_answer38) A ball of mass m moving with a velocity\[\mu \]collides head-on with another ball of mass m initially at rest. If the coefficient of restitution be e, then the ratio of the final and initial velocities of the first ball is
question_answer39) If\[{{I}_{A}},{{K}_{A}}\]and\[{{I}_{B}},{{K}_{B}}\]are the moments of interia and kinetic energies of two freely rotating bodies A and B respectively, such that\[{{I}_{A}}>{{I}_{B}}\]and their angular mements are equal, then
question_answer40) The angular frequency and the amplitude of a simple pendulum are\[\omega \]and a respectively. If the pendulum is displaced through a distance\[x\] from the mean position then the ratio of its kinetic energy (K) and potential energy (U) will be
question_answer42) End product of the following reaction is\[C{{H}_{3}}C{{H}_{2}}COOH\xrightarrow[red\,P]{C{{l}_{2}}}\xrightarrow[{}]{Alcoholic\text{ }KOH}\]
question_answer48) In which of the following pairs are both the ions coloured in aqueous solution? (At. no. : Sc = 21, Ti = 22, Ni = 28, Cu = 29, Co =27)
question_answer52) The standard emf of the cell \[Zn+C{{u}^{2+}}\xrightarrow[{}]{{}}Cu+Z{{n}^{2+}}\]is 1.10 at\[25{}^\circ C\]. The emf of the cell when\[0.1\text{ }M\,C{{u}^{2+}}\]and\[0.1\text{ }M\,Z{{n}^{2+}}\]solution are used will be
question_answer53) Given: The mass of electron is\[9.11\times {{10}^{-31}}kg\]and Planck constant is\[6.626\times {{10}^{-34}}Js,\]the uncertainty involved in the measurement of velocity within a distance of\[0.1\overset{o}{\mathop{\text{A}}}\,\]is
question_answer54) If \[E_{F{{e}^{2+}}/Fe}^{o}=-0.441V\] and \[E_{F{{e}^{3+}}/F{{e}^{2+}}}^{o}=0.771V\]the standard emf of the reaction \[Fe+3F{{e}^{3+}}\xrightarrow[{}]{{}}3F{{e}^{2+}}\]will be
question_answer55) The enthalpy of combustion of\[{{H}_{2}},\]cyclohexene\[({{C}_{6}}{{H}_{10}})\]and cyclohexane\[({{C}_{6}}{{H}_{12}})\]are\[-241,~-3800\] and\[-3920\text{ }kJ\]per mol respectively. Heat of hydrogenation of cyclohexene is
question_answer59) For the following cell with hydrogen electrodes at two different pressures\[{{p}_{1}}\]and\[{{p}_{2}},\]emf is given by \[\underset{{{p}_{1}}}{\mathop{pt({{H}_{2}})}}\,|\underset{1M}{\mathop{{{H}^{+}}(aq)}}\,|\underset{{{p}_{2}}}{\mathop{Pt({{H}_{2}})}}\,\]
question_answer60) Consider the following two reactions, \[A\xrightarrow[{}]{{}}\]Product; \[-\frac{d[A]}{dt}={{k}_{1}}{{[A]}^{0}}\] \[B\xrightarrow[{}]{{}}\]Product; \[-\frac{d[B]}{dt}={{k}_{2}}[B]\] \[{{k}_{1}}\]and\[{{k}_{2}}\]are expressed in terms of molarity (mol\[{{L}^{-1}}\]) and time\[({{s}^{-1}})\]as
question_answer61) \[CsBr\]crystallises in a body centred cubic lattice. The unit cell length is 436.6 pm. Given that the atomic mass of Cs = 133 u and that of Br = 80 u and Avogadro number being \[6.0.2\times {{10}^{23}}mo{{l}^{-1}},\] the density of\[CsBr\]is
question_answer63) During the process of digestion, the proteins present in food materials are hydrolysed to amino acids. The two enzymes involved in the process Proteins \[\xrightarrow[{}]{Enzyme(A)}\]Polypeptides are respectively
question_answer65) A metal M forms water soluble MS 04 and inert MO. MO in aqueous solution forms insoluble \[M{{(OH)}_{2}}\]which is soluble in\[NaOH\]. Metal M is
question_answer66) In an organic compound of molar mass 108g \[mo{{l}^{-1}},C,H\]and N atoms are present in 9 : 1: 3.5 by weight. Molecular formula can be
question_answer70) For an aqueous solution, freezing point is\[-0.186{}^\circ C\]. Elevation of the boiling point of the same solution is (\[{{K}_{f}}=1.86{}^\circ mo{{l}^{-1}}kg\]and\[{{K}_{b}}=0.512{}^\circ mo{{l}^{-1}}kg\])
question_answer74) A carbonyl compound reacts with hydrogen cyanide to form cyanbhydrin which on hydrolysis forms a racemic mixture of a\[\alpha -\]ydroxy acid. The carbonyl compound is
question_answer84) If one root of the equation\[lx+mx+n=0\]is\[\frac{9}{2}\] \[(l,m\]and n are positive integers) and\[\frac{m}{4n}=\frac{l}{m},\]then\[l+n\]is equal to
question_answer85) If\[\alpha \]and\[\beta \]are the roots of the equation \[a{{x}^{2}}+bx+c=0,\]then\[\frac{\alpha }{\alpha \beta +b}+\frac{\beta }{a\alpha +b}\]is equal to
question_answer86) If\[{{H}_{1}}\]and\[{{H}_{2}}\]are two harmonic means between two positive numbers a and\[b(a\ne b),\]and G are the arithmetic and geometric means between a and b, then\[\frac{{{H}_{2}}+{{H}_{1}}}{{{H}_{2}}{{H}_{1}}}\]is
question_answer87) Let\[{{S}_{n}}=\frac{1}{{{1}^{3}}}+\frac{1+2}{{{1}^{3}}+{{2}^{3}}}+...+\]\[\frac{1+2+....+n}{{{1}^{3}}+{{2}^{3}}+...+{{n}^{3}}},n=1,2,3,.....\]Then\[{{S}_{n}}\]is not greater than
question_answer89) If\[p(n):2+4+6+....+(2n),n\in N,\]then\[p(k)=k(k+1)+2\]implies\[p(k+1)=\] \[(k+1)(k+2)+2\]is true for all\[k\in N\]. So, statement\[p(n)=n(n+1)+2\]is true for
question_answer91) If A and B are square matrices of size\[n\times n\]such that\[{{A}^{2}}-{{B}^{2}}=(A\text{ }B)(A+B)\]then which of the following will be always true?
question_answer97) The\[x-\]axis, y-axis and a line passing through the point A(6, 0) form a\[\Delta ABC\]. If\[\angle A=30{}^\circ ,\] then the area of the triangle (in sq unit) is
question_answer98) The equation of perpendicular bisectors of sides AB and AC of a\[\Delta ABC\]are\[x-y+5=0\]and\[x+2y=0,\]respectively. If the coordinates of vertex A are\[(1,-2),\]the equation of BC is
question_answer99) If two chords having lengths\[{{a}^{2}}-1\]and\[3(a+1),\]where a is a constant of a circle bisect each other, then the radius of the circle is
question_answer101) The equation of the plane passing through the mid-point of the line of join of the points (1, 2, 3) and (3, 4, 5) and perpendicular to it, is
question_answer102) The direction cosines\[l,m\]and n of two lines are connected by the relation\[l+m+n=0,\text{ }lm=0,\]then the angle between them is