A particle moves in a straight line with retardation proportional to square of its displacement. Its loss of kinetic energy for any displacement x is proportional to
Two particles of masses\[3\,kg\]and 2 kg are moving with velocities\[{{\vec{v}}_{1}}=2\hat{i}\]and\[{{\vec{v}}_{2}}=3\hat{j},\] respectively. The first particle of mass 3 kg has an acceleration of\[{{\vec{a}}_{1}}=2\hat{i}+2\hat{j}\]while acceleration of the second particle is zero. The centre of mass of these two particles follow a
A river is flowing from west to east direction with velocity v. A swimmer standing at the south bank wants to cross the river in order to reach a point just in front of the starting point. If the swimmer can swim at a speed of u w.r.t. the river flow, the angle with the north direction, required to swim is equal to
The radioactivity of a sample is\[{{R}_{1}}\]at time\[{{t}_{1}}\] and \[{{R}_{2}}\]at time \[{{t}_{2}}.\]Mean life of the specimen is T. The number of atoms that have disintegrated in the time interval \[({{t}_{2}}-{{t}_{1}})\]is
A spherical cavity is made in solid sphere of radius R. The mass of the sphere before the cavity was eked out was M. The gravitational field intensity at the center of the sphere due to remaining mass is
A particle of mass m is under the influence of a force F which varies with the displacement \[x\] according to the relation \[F=-kx+{{F}_{0}}\] which k and \[{{F}_{0}}\] are constants. The particle when disturbed will oscillate
A)
about \[x=0,\]with\[\omega \ne \sqrt{k/m}\]
doneclear
B)
about\[x=0,\]with \[\omega =\sqrt{k/m}\]
doneclear
C)
about \[x={{F}_{0}}/k\]with \[\omega =\sqrt{k/m}\]
doneclear
D)
about \[x={{F}_{0}}/k\]with \[\omega \ne \sqrt{k/m}\]
The figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current through the battery (i) just after the switch is closed and (ii) a long time later, keeping greatest first.
Typical magnetization curves (hysteresis loops) for four materials are shown in the following figures. Which one is the best suitable for core of a moving coil galvanometer? [H and\[I\]are magnetizing field intensity and intensity of magnetization, respectively]
Two identical long, solid cylinders are used to conduct heat from temperature\[{{T}_{1}}\]to temperature\[{{T}_{2}}.\]Originally the cylinders are connected in series and the rate of heat transfer is H. If the cylinders are connected in parallel, then the rate of heat transfer would be
A disc of mass M and radius R is performing pure rolling motion in \[X-Y\]plane as shown in figure. The magnitude of angular momentum of the disc about O is
A thin rod of length \[l\]and mass m is suspended from one of its ends. It is set into oscillation about a horizontal axis which is passing through the suspension point. Its angular speed is\[\omega \]while passing through its mean position. How high will the center of mass rise from the lowest position?
The energy emitted per seconds by a black body at \[27{{\,}^{o}}C\]is\[\text{ }\!\!~\!\!\text{ 10 J}\text{.}\] If the temperature of the black body is increased to \[327{{\,}^{o}}C,\] the energy emitted per second will be
A system is shown in given figure. The surface on which the blocks are placed is smooth. If the two blocks are displaced by small amount, then determine the time period of oscillation of resulting motion of two blocks.
A string of length 1.5 m with its two ends clamped is vibrating in the fundamental mode. The amplitude at the center of the string is 4 mm. The minimum distance, between two points having amplitude 2 mm, is
A planoconvex lens\[\left( \mu =\frac{3}{2} \right)\] has radius of curvature \[R=10\text{ }cm,\]and is placed at a distance of b from a concave lens of focal length 20 cm as shown. At what distance should a point object be placed from planoconvex lens, so that position of the final image is independent of b?
In YDSE, how many maxima can be obtained on a screen (including central maxima) on both sides of the central maxima if \[d=\frac{5\lambda }{2},\]where \[\lambda \] is the wavelength of light?
A 40 kg slab rests on a frictionless floor as shown in the figure. A 10 kg block rests on the top of the slab. The static coefficient of friction between the block and slab is 0.60 while the kinetic friction is 0.40. The 10 kg block is acted upon by a horizontal force 100 N. If \[g=9.8\,m/{{s}^{2}},\]the resulting acceleration of the slab will be
Two tuning forks P and Q are vibrated together. The number of beats produced are represented by the straight line OA in the following graph. After loading Q with wax again these are vibrated together and the beats produced are represented by the line OB. If the frequency of P is 341 Hz, the frequency of Q will be
A solution containing one mole per litre of each \[Cu{{(N{{O}_{3}})}_{2}};AgN{{O}_{3}};H{{g}_{2}}{{(N{{O}_{3}})}_{2}};Mg{{(N{{O}_{3}})}_{2}}\]is being electrolysed using inert electrodes. The values of standard electrode potentials (reduction potentials in volts are \[Ag/A{{g}^{+}}=0.80\]\[V,2Hg/H{{g}_{2}}^{++}=0.79\,V,\]\[Cu/C{{u}^{++}}=+\,0.24\,V,\,Mg/\]\[M{{g}^{++}}=-2.37\,V.\] With increasing voltage, the sequence of deposition of metals on the cathode will be
The ionization energy of \[\text{H}{{\text{e}}^{\text{+}}}\]is \[\text{19}\text{.6}\times {{10}^{-18}}\text{J}\]\[\text{ato}{{\text{m}}^{-1}}\]The energy of the first stationary state of \[\text{L}{{\text{i}}^{\text{+2}}}\]will be
In \[{{\text{P}}_{\text{4}}}{{\text{O}}_{\text{6}}}\]and\[{{\text{P}}_{\text{4}}}{{\text{O}}_{10}},\]the number of oxygen atoms bonded to each phosphorus atoms are, respectively
8 litres of \[{{H}_{2}}\]and 6 litres of \[\text{C}{{\text{l}}_{\text{2}}}\]are allowed to react to maximum possible extent. Find out the final volume of reaction mixture. Suppose P and T remains constant throughout the course of reaction.
What is the mass of sodium bromate solution necessary to prepare \[\text{85}\text{.5}\,\text{c}{{\text{m}}^{3}}\]of \[\text{0}\text{.672 N}\]solution when the half-cell reaction is \[\text{Br}{{\text{O}}^{-}}_{3}+6{{H}^{+}}+6e\to B{{r}^{-}}+3{{H}_{2}}O?\]
A compound XY crystallizes in BCC lattice with unit cell-edge length of 480 pm. If the radius of \[{{Y}^{-}}\]is 225 pm, then the radius of \[{{X}^{+}}\] is
A tangent drawn on the curve obtained by plotting concentration of product \[(mole\,{{L}^{-1}})\] of a first order reaction vs. time (min) at the point corresponding to time 20 minutes makes an angle of \[{{30}^{o}}\] with concentration axis. Hence, the rate of formations of product after 20 minutes will be
Which gas will be evolved out when \[[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}+{{(C{{H}_{3}})}_{2}}CHN{{H}_{2}}]\] is treated with sodium nitrite and\[\text{HCl}\,\text{?}\]
\[{{\text{I}}_{\text{2}}}\]and\[\text{B}{{\text{r}}_{\text{2}}}\]are added to a solution containing\[{{\text{I}}^{-}}\] and \[\text{B}{{\text{r}}^{-}}.\]What reaction would occur if \[E_{{{I}_{2}}/{{I}^{-}}}^{o}=+\,0.54\,V\]and \[E_{B{{r}_{2}}/B{{r}^{-}}}^{o}=+1.09\,V?\]
The total pressure of a sample of methane collected over water is 735 torr at\[\text{29}{{\,}^{\text{o}}}\text{C}\text{.}\] The aqueous tension at \[\text{29}{{\,}^{\text{o}}}\text{C}\text{.}\] pressure exerted by dry methane?
Assertion: The solid \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]is ionic.
Reason: In solid state\[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]exists as \[{{\text{ }\!\![\!\!\text{ N}{{\text{O}}_{3}}\text{ }\!\!]\!\!\text{ }}^{+}}{{[N{{O}_{2}}]}^{-}}\]
A)
If both assertion and reason are true, and reason is the correct explanation of assertion.
doneclear
B)
If both assertion and reason are true but reason is not the correct explanation of assertion.
Number of ways in which 7 green bottles and 8 blue bottles can be arranged in a row if exactly 1 pair of green bottles is side by side, is (assume all bottles to be alike except for the colour)
A biased coin with probability \[-p(0<p<1)\]of falling tails is tossed until a tail appears for the first time. If the probability that tail comes in odd number of trials is 2/3, then p equals
The values of\[\theta \]and\[\lambda \]in the following equations\[\sin \theta x-\cos \theta y+(\lambda +1)z=0;\] \[\cos \theta x+\sin \theta y-\lambda z=0;\] \[\lambda x+(\lambda +1)y+\cos \theta z=0\] have non trivial solution, are
The equation \[{{x}^{2}}+bx+c=0\]has distinct roots. If 2 is subtracted from each root, the results are the reciprocal of the original roots. Value of\[{{b}^{2}}+{{c}^{2}}\] is
The area bounded by the curve \[y=f(x),\]the co- ordinate axes and the line \[x=x{{ & }_{1}}\]is given by \[{{x}_{1}}{{e}^{{{x}_{1}}}}.\]Therefore, \[f(x)\]equals
Tangents drawn from point of intersection A of circles \[{{x}^{2}}+{{y}^{2}}=4\]and \[{{(x-\sqrt{3})}^{2}}+\]\[{{(y-3)}^{2}}=4\] cut the line joining their centres at B and C. Triangle BAG is
The value of a for the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1(a>b),\]if the extremities of the latus-rectum of the ellipse having positive ordinate lies on the parabola \[{{x}^{2}}=-2(y-2),\]is
If the curves \[{{x}^{2}}-{{y}^{2}}=4\]and \[xy=\sqrt{5}\]intersect at points A and 5, then the possible number of point(s) C on the curve \[{{x}^{2}}-{{y}^{2}}=4\]such that triangle ABC is equilateral is
The distance of two points P and Q on the parabola \[{{y}^{2}}=4ax\]from the focus S are 3 and 12. Then the distance of the point of intersection of the tangents at P and Q from the focus S is
The real value of a for which the value of \[m\] satisfying the equation \[({{a}^{2}}-1){{m}^{2}}-(2a-3)m\,+a=0\]gives the slope of a line parallel to the\[y-\]axis is
Let ABC be a triangle with \[\angle B={{90}^{o}}\]and AD be the bisector of \[\angle A\]with D on BC. If \[AC=6\text{ }cm\]and the area of the triangle ADC is \[10\text{ }c{{m}^{2}},\] then the length of BD in cm is equal to
Let \[\hat{a}\] and \[\hat{c}\] be unit vectors at an angle \[\frac{\pi }{3}\] with each other. If \[\left( \hat{a}\times (\hat{b}\,\times \hat{c}) \right).(\hat{a}\times \hat{c})=5\] then the value of \[[\hat{a}\hat{b}\hat{c}]\] is