question_answer2) A ship of mass \[3\times {{10}^{7}}kg,\] initially at rest, is pulled by a force of \[5\times {{10}^{4}}N\] through a distance of 3 m. Assuming that the resistance due to water is negligible, the speed of the ship is
question_answer4) An object is placed on the surface of a smooth inclined plane of inclination 8. It takes time t to reach the bottom. If the same object is allowed to slide down a rough inclined plane of inclination\[\theta ,\] it takes time \[nt\] to reach the bottom, where n is a number greater than 1. The coefficient of friction µ is given by
question_answer5) A 500 kg horse pulls a can of mass 1500 kg along a level road with an acceleration of \[1\,m/{{s}^{2}}\]. If the coefficient of sliding friction is 0.2, then the horizontal force exerted by the earth on the horse is
question_answer6) A spring is held compressed so that its stored energy is 2.4 J. its ends are in contact with masses 1 g and 48 g placed on a functionless table. When the spring is released, the heavier mass wilt acquire a speed of
question_answer7) Two simple pendulums first of bob mass \[{{M}_{1}}\] and length \[{{L}_{1}},\] second of bob mass \[{{M}_{2}}\] and length \[{{L}_{2}}.\,{{M}_{1}}={{M}_{2}}\] and \[{{L}_{1}}=2{{L}_{2}}\]. If the vibrational energy of both is same. Then which of the following is correct?
question_answer9) A body of mass m is situated on the earth in the gravitational field of sun. For the body to escape from die gravitation pull of the solar system the body must be imparted an escape velocity of (assume earth to be stationary)
question_answer10) Find the lifting force of a 4 kg cork life belt in sea water, if the densitites of cork and sea water are \[0.2\,\times {{10}^{3}}kg/{{m}^{3}}\] and \[1.03\,\times {{10}^{3}}kg/{{m}^{3}}\] respectively.
question_answer13) Two sound waves, each of amplitude A and frequency \[\omega ,\] superpose at a point with phase difference of \[\frac{\pi }{2}.\] The amplitude and frequency of the resultant wave are respectively
question_answer14) A source emits electromagnetic waves of wavelength 3 m. One beam reaches the observer directly and other after reflection from a water surface, travelling 1.5 m extra distance and with intensity reduced to (1/4) as compared to intensity due to direct beam alone. The resultant intensity will be
question_answer15) 15. A square of side 3, cm is located at a distance 25 cm from a concave mirror of focal length 10 cm. The centre of square is at the axis of the mirror and the plane is normal to axis of mirror. The area enclosed by the image of the square is
question_answer16) A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal
question_answer18) A proton enters a magnetic field of flux density \[1.5\,Wb/{{m}^{2}}\] with a speed of \[2\times {{10}^{7}}\,m/s\] at angle of 30° with the field. The force on a proton will be
question_answer19) Two long straight wires are set parallel to each other at separation rand each carries a current in the same direction. The strength of the magnetic field at any point midway between the two wires is
question_answer20) The work done in turning a magnet of magnetic moment At by an angle of 90° from the meridian is n times the corresponding work done to turn it through an angle of 60°
question_answer21) An inductive coil has a resistance of 100\[\Omega \] When an AC signal of frequency 1000 Hz is applied to the coil, the voltage leads the current by \[45{}^\circ \]. The inductance of the coil is
question_answer24) Light of two different frequencies whose photons have energies 1 eV and 2.5 eV successively illuminate a metal of work function 0.5 eV. The ratio of the maximum speeds of the emitted electrons will be
question_answer25) An electron Jumps from the first excited state to the ground State of hydrogen atom. Whit will be the percentage change in the speed of electron?
question_answer26) The mutual inductance of a pair of coils, each of N rums, is M henry If a current of i ampere in one of the coils is brought to zero in t second, the emf induced per turn in the other coil, in volt will be
question_answer27) A body falls from rest. In the last second of its fall it covers half of the total distance. If g is \[9.8\,\,m/{{s}^{2}},\] then the total time of its fall is (in second)
question_answer28) A force\[\mathbf{\vec{F}}=a\mathbf{\vec{i}}+3\mathbf{\vec{j}}+\mathbf{6\vec{k}}\] is acting at a point \[\mathbf{\vec{r}}=\mathbf{2\vec{i}}+\mathbf{6\vec{j}}+\mathbf{12\vec{k}}.\] The value of a for which angular momentum is conserved is
question_answer29) A wooden block is floating in a liquid 50% of its volume inside the liquid when the vessel is stationary. Percentage of volume immersed when the vessel moves upwards with an acceleration\[a=g/3\] is
question_answer30) Two resistors 400\[\Omega \] and 800\[\Omega \]are connected in series with a 6 V battery- The potential difference measured by voltmeter of 10\[k\Omega \] across \[400\,\Omega \] resistor is
question_answer31) An astronomical telescope in normal adjustment receives light from a distant source S the tube length is now decreased slightly, then
A)
no image will be formed
doneclear
B)
a virtual image of S will be formed at a finite distance
doneclear
C)
a large, real image of S will be formed behind the eye-piece, far away from it
doneclear
D)
a small, real image of S will be formed behind the eye-piece close to it
question_answer32) The potential difference in volt across the resistance R., in the circuit shown in figure, is \[({{R}_{1}}=15\,\Omega ,\,{{R}_{2}}=15\,\Omega ,\,{{R}_{3}}=30\,\Omega ,\,{{R}_{4}}=35\,\Omega )\]
question_answer33) The ratio of molecular masses of two radioactive substances is 3/2 and the ratio of their decay constants is 4/3, Then, the ratio of their initial activities per mole will be
question_answer35) A person is at a distance x from a bus when the bus begins 10 move with a constant acceleration a. What is the minimum velocity with which [he person should run towards the bus so as to catch it?
question_answer36) A car is travelling with linear velocity v on a circular road of radius r. If it is increasing its speed at die rate of \[a\,m/{{s}^{2}},\] then the resultant acceleration will be
question_answer37) A body of mass 10 kg at rest explodes into two pieces of masses 7 kg and 3 kg. If the total increase in kinetic energy due to explosion is 1680 J, the magnitude of their relative velocity in m/s, after explosion is
question_answer38) The moment of inertia of a body about a given axis is \[1.2\,\,kg\,{{m}^{2}}\]. Initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of \[25\,rad/{{s}^{2}}\] must be applied about that axis for a duration of
question_answer39) Steel and aluminium wires have equal resistances and masses. Which of die wires is longer and how many times? (Given, densities of steel and aluminium are \[7.8\,\times {{10}^{3}}\,kg\,{{m}^{-3}}\] and \[2.7\times {{10}^{3}}\,kg\,{{m}^{-3}}\] and their resistivities are \[0.15\,\mu \Omega .m\] and\[0.028\,\mu \Omega -m\] respectively)
question_answer40) Two cells of emfs \[{{E}_{1}}\] and\[{{E}_{2}}({{E}_{1}}>{{E}_{2}})\] are connected as shown in figure. When a potentiometer is connected between A and B, the balancing length of the potentiometer wire is 300 cm. On connecting the same potentiometer between A and C, the balancing length is 100 on. The ratio\[\frac{{{E}_{1}}}{{{E}_{2}}}\]is
question_answer41) In hydrogen atom the electron is making \[6.6\,\times {{10}^{15}}\,rev/s\] around the nucleus of radius \[0.53\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. The magnetic field produced at the centre of the orbit is nearly
question_answer43) The energy difference between the first two levels of hydrogen atom is 10.2eV. For another element of atomic number 10 and mass number 20, this will be
question_answer44) The following equation represents induced transmutation \[_{4}B{{e}^{9}}{{+}_{2}}H{{e}^{4}}{{\xrightarrow{{}}}_{6}}{{C}^{12}}+X\] In this equation, X represents
question_answer45) The masses of neutron and proton are 1.0087 and 1.0073 amu respectively- If the neutrons and protons combine to form helium nucleus of mass 4.0015 amu the binding energy of the helium nucleus will be
question_answer46) The activity of a radioactive sample is measured as 9750 count/min at t=0 and 975 count/min at t =5min. The decay constant is nearly
question_answer47) Light of wavelength \[\lambda ,\] strikes a photoelectric surface and electrons are ejected with an energy E. Iff is to be increased to exactly twice its original value, the wavelength changes to\[\lambda ;\] where
A)
\[\lambda \]is less than \[\frac{\lambda }{2}\]
doneclear
B)
\[\lambda \]is greater than\[\frac{\lambda }{2}\]
doneclear
C)
\[\lambda \] is greater than \[\frac{\lambda }{2}\] but less than \[\lambda ,\]
doneclear
D)
\[\lambda \] is exactly equal to\[\frac{\lambda }{2}\]
question_answer48) Three point masses, each of mass m are placed at the corners of an equilateral triangle of side The moment of inertia of this system about, an axis along one side of the triangle is
question_answer49) A pipe opened at both ends produces a note of frequency \[{{f}_{1.}}\] When the pipe is kept with \[\frac{3}{4}\]th of its length in water, it produces a note of frequency \[{{f}_{2.}}\] The ratio \[\frac{{{f}_{1}}}{{{f}_{2}}}\] is of
question_answer50) A solenoid is 1.5 m long and its inner diameter is 4.0 cm. It has 3 layers of windings of 1000 turns each and carries a current of 2.0A. The magnetic flux for a cross-section of the solenoid is nearly
question_answer54) A saturated solution of \[\text{A}{{\text{g}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\]is \[\text{2}\text{.5}\times {{10}^{-2}}\,M.\] The value of its solubility product is
question_answer55) The enthalpies of combustion of carbon and carbon monoxide are \[~-393.5\] and \[-283\text{ kJ mo}{{\text{l}}^{-1}}\]respectively. The enthalpy of formation of carbon monoxide per mole is
question_answer59) A metal has bcc structure and the edge length of its unit cell is \[\text{3}\text{.04}\overset{\text{o}}{\mathop{\text{A}}}\,\text{.}\] The volume of the unit cell in \[\text{c}{{\text{m}}^{\text{3}}}\]will be
question_answer77) The equilibrium constant for a reaction, \[{{N}_{2}}(g)+{{O}_{2}}(g)\rightleftharpoons 2NO(g)\] is \[4\times {{10}^{-4}}\] at \[\text{2000}\,\text{K}\text{.}\] In the presence of catalyst, the equilibrium is attained 10 times faster. The equilibrium constant in presence of catalyst at 2000 K is
question_answer78) Consider the following \[{{\text{E}}^{\text{o}}}\]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, \[Sn(s)+2F{{e}^{3+}}(aq)\xrightarrow{{}}2F{{e}^{2+}}(aq)+S{{n}^{2+}}(aq)\]is
question_answer79) The relationship between the values of osmotic pressure of 0.1 M solutions of \[\text{KN}{{\text{O}}_{\text{3}}}\text{(}{{\text{p}}_{\text{1}}}\text{)}\]and \[C{{H}_{3}}COOH({{p}_{2}})\]is
question_answer80) Volume of \[\text{0}\text{.6 M NaOH}\]required to neutralize \[\text{30}\,\text{c}{{\text{m}}^{\text{3}}}\]of \[\text{0}\text{.4}\,\text{M}\,\text{HCl}\]is
question_answer86) The IUPAC name of \[C{{H}_{3}}-\underset{OH}{\mathop{\underset{|}{\mathop{CH}}\,}}\,-C{{H}_{2}}-\underset{OH}{\overset{C{{H}_{3}}}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-C{{H}_{3}}\]is
question_answer87) The order of decreasing stability of the carbanions is \[{{(C{{H}_{3}})}_{3}}\bar{C}(1),{{(C{{H}_{3}})}_{2}}\bar{C}H(2),C{{H}_{3}}\bar{C}{{H}_{2}}(3),\]\[{{C}_{6}}{{H}_{5}}\bar{C}{{H}_{2}}(4)\]
question_answer88) Which set of products is expected on reductive ozonolysis of the following diolefin? \[C{{H}_{3}}CH=\overset{C{{H}_{3}}}{\mathop{\overset{|}{\mathop{C}}\,}}\,-CH=C{{H}_{2}}\]
question_answer101) If \[{{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}\theta d\theta ,}\] where n is a positive integer, then \[n({{I}_{n-1}}+{{I}_{n+1}})\]is equal to
question_answer103) The set of points of discontinuity of the function \[f(x),\]where\[f(x)=\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{(2\sin x)}^{2n}}}{{{3}^{n}}-{{(2\cos x)}^{2n}}}\]is
A)
R
doneclear
B)
\[\left\{ n\pi \mp \frac{\pi }{3},n\in I \right\}\]
doneclear
C)
\[\left\{ n\pi \pm \frac{\pi }{6},n\in I \right\}\]
question_answer104) The derivative of \[\cos e{{c}^{-1}}\left( \frac{1}{2{{x}^{2}}-1} \right)\] with respect to \[\sqrt{1-{{x}^{2}}}\]at \[x=\frac{1}{2}\]is
question_answer108) Observe the following statements: (i) The circle \[{{x}^{2}}+{{y}^{2}}-6x-4y-7=0\] touches y-axis (ii) The circle \[{{x}^{2}}+\text{ }{{y}^{2}}+6x+4y-7=0\] touches \[x-\]axis Then, which of the following statements is/are correct?
question_answer109) The line \[x+y=a\]meets the axes of X and Y at A and B respectively. \[A\Delta AMN\]is inscribed in the \[\text{ }\!\!\Delta\!\!\text{ }\,\text{O}\,\text{A}\,\text{B,}\] O being the origin, with right angle at N. M and N lie on OB and AB respectively. If the area of the \[\Delta AMN\]is \[\frac{3}{8}\] of the area of the \[\Delta OAB,\] then\[\frac{AN}{BN}\] is equal to
question_answer110) The intercept made by a line on y-axis is double to the intercept made by it on x-axis and if it passes through\[(1,2),\]then its equation is
question_answer113) If the vectors \[\vec{a}=\hat{i}+a\hat{j}+{{a}^{2}}\hat{k},\vec{b}=\hat{i}+b\hat{j}+{{b}^{2}}\hat{k},\]\[\vec{c}=\hat{i}+c\hat{j}+{{c}^{2}}\hat{k}\]are three non-coplanar vectors and \[\left| \begin{matrix} a & {{a}^{2}} & 1+{{a}^{3}} \\ b & {{b}^{2}} & 1+{{b}^{3}} \\ c & {{c}^{2}} & 1+{{c}^{3}} \\ \end{matrix} \right|=0,\] then the value of aback is
question_answer115) The value of \[\left( 1+\cos \frac{\pi }{8} \right)\left( 1+\cos \frac{3\pi }{8} \right)\]\[\left( 1+\cos \frac{5\pi }{8} \right)\left( 1+\cos \frac{7\pi }{8} \right)\] is equal to
question_answer116) If the probability of A to fail in an examination is \[\frac{1}{5}\]and that of B is \[\frac{3}{10},\] then the probability that either A or B fails, is
question_answer121) The ninth term in the expansion of\[{{[{{3}^{{{\log }_{3}}\sqrt{{{25}^{x-1}}+7}}}+{{3}^{-\frac{1}{8}{{\log }_{3}}({{5}^{x-1}}+1)}}]}^{10}}\]is equal to 180, then \[x\]is equal to
question_answer123) The coefficient of x in the quadratic equation \[a{{x}^{2}}+bx+c=0\]was wrongly taken as 17 in place of 13 and its roots were found to be - 2 and - 15, the actual roots of the equation are
question_answer124) It is given that \[\sum\limits_{r=1}^{\infty }{\frac{1}{{{(2r-1)}^{2}}}}=\frac{{{\pi }^{2}}}{8},\]then\[\sum\limits_{r=1}^{\infty }{\frac{1}{{{r}^{2}}}}\]is equal to
question_answer130) A man on the top of a cliff 100 m high, observe the angles of depression of two points on the opposite sides of the cliff as \[\text{3}{{\text{0}}^{\text{o}}}\] and \[\text{6}{{\text{0}}^{\text{o}}}\] respectively. Then, the distance between the two points is equal to
question_answer132) The vector equation of a plane through the point \[(2\hat{i}-\hat{j}-4\hat{k})\] and parallel to the plane \[\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})-7=0\]is
question_answer133) The equation\[{{x}^{3}}-3x+4=0\] has only one real root. What is its first approximate value as obtained by the method of false position in\[(-3,-2)?\]
question_answer134) An oil company required 13000, 20000 and 15000 barrels of high grade, medium grade and low grade oil respectively. Refinery A produces 100, 300 and 200 barrels per day of high grade, medium grade and low grade oil respectively. While, refinery B produces 200, 400 and 100 barrels per day of high grade, medium grade and low grade oil respectively. If refinery A costs Rs 400 per day and refinery B costs Rs 300 per day to operate, then the days should each be run to minimize costs, while satisfying requirements are
question_answer136) If A and B are two events such that\[P(A\cup B)=\frac{5}{6},P(A\cap B)=\frac{1}{3},P(\bar{B})=\frac{1}{2},\] then the events A and B are
question_answer137) If \[P(x,y,z)\]is a point on the line segment joining Q (2, 2, 4) and R (3, 5, 6) such that the projections of \[\overrightarrow{\text{OP}}\]on the axes are\[\frac{13}{5},\frac{19}{5},\frac{26}{5}\] respectively, then P divides QR in the ratio
question_answer138) The vector \[\vec{c}\] is perpendicular to the vectors\[\vec{a}=(2,-3,1),\vec{b}=(1,-2,3)\] and satisfies the condition \[\vec{c}.(\hat{i}+2\hat{j}-7\hat{k})=10.\]Then, \[\vec{c}\] is equal to
question_answer139) Consider the differential equation \[y=px+\sqrt{{{a}^{2}}{{p}^{2}}+{{b}^{2}}},\]where\[p=\frac{dy}{dx}.\]The order and degree of the differential equation are
question_answer145) The normal chord at a point t on the parabola \[{{y}^{2}}=4ax\]subtends a right angle at the vertex. Then,\[{{t}^{2}}\] is equal to
question_answer146) The equation of a circle of radius 5 which lies within the circle \[{{x}^{2}}+{{y}^{2}}+14x+10y-26=0\]and touches it at the point \[(-1,3)\] is
question_answer147) The sum of the series \[\left[ 1+\left( \frac{1}{2}+\frac{1}{3} \right).\frac{1}{4}+\left( \frac{1}{4}+\frac{1}{5} \right).\frac{1}{{{4}^{2}}}+\left( \frac{1}{6}+\frac{1}{7} \right)\frac{1}{{{4}^{3}}}+...\infty \right]\]is equal to
question_answer149) A line is drawn through a fixed point \[(h,k)\] cutting the coordinate axes at P and Q respectively. The rectangle OPRQ is completed. Find the equation of locus of R.