A ball of radius r and density falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is \[\eta \] the value of h is given by
A satellite moves round the earth in a circular orbit of radius R making one revolution per day. A second satellite moving in a circular orbit, moves round the earth once in 8 days. The radius of the orbit of the second satellite is
The ratio of electrostatic and gravitational forces acting between electron and proton separated by a distance\[5 \times 1{{0}^{-}}^{11}\,m\], will be (Charge on electron \[= 1.6 \times 1{{0}^{-}}^{19}C\], mass of electron \[= 9.1 \times 1{{0}^{-}}^{31}kg\], mass of proton \[=1.6\times 10\,kg\], \[\operatorname{G}=6.7\times 1{{0}^{-11}}\,N{{m}^{2}}/k{{g}^{2}}\])
Five identical metal plates each of area A are held parallel to each other with successive separation d as shown in figure. The effective capacitance of the system between points P and Q is
A cylindrical solid of length L and radius a is having varying resistivity given by \[\rho ={{\rho }_{0}}x\], where \[{{\rho }_{0}}\] is a positive constant and x is measured from left end of solid. The cell shown in the figure is having emf V and negligible internal resistance. The electric field as a function of x is best described by
A particle starts from the origin at \[\operatorname{t} = 0\] and moves in the x-y plane with constant acceleration 'a' in the y direction. Its equation of motion is\[\operatorname{y} = b{{x}^{2}}\]. The x-component of its velocity is
The wavelength of red light from He-Ne laser is 633 nm in air but 474 nm in the aqueous humor inside the eye ball. Then the speed of red light through the aqueous humor is
When a \[{{\operatorname{U}}^{238}}\] nucleus originally at rest, decays by emitting an alpha particle having a speed ?u?, the recoil speed of the residual nucleus is
A Camot engine whose low temperature reservoir is at\[7{}^\circ C\]has an efficiency of\[50%\]. It is desired to increase the efficiency to\[70%\]. By how many degrees should the temperature of the high temperature reservoir be increased?
A gas in container A is in thermal equilibrium with another gas in container B. Both contain equal masses of the two gases in the respective containers. Which of the following can be true?
The oscillation of a body on a smooth horizontal surface is represented by the equation,\[\operatorname{X}= A cos \left( \omega \,t \right)\] where \[X=\text{ }displacement\text{ }at\text{ }time\text{ }t\] \[\omega =frequency\text{ }of\text{ }oscillation\]Which one of the following graphs shows correctly the variation of ?a? with ?t??
Two loudspeakers M and A are located 20 m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car is initially at a point P, 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/hr along the perpendicular bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q. Let n(t) represent the beat frequency measured by a person sitting in the car at time t. Let n, n and n be the beat frequencies measured at locatons P, Q and R, respectively. The speed of sound in air is 330ms"1. Which of the following statement (s) is (are) true regarding the sound heard by the person
A)
\[{{n}_{p}}={{n}_{R}}=nQ\]
doneclear
B)
The rate of change in beat frequency is minimum when the car passes through Q
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C)
The plot below represents schematically the variation of beat frequency with time
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D)
The plot below represents schematically the variation of beat frequency with time
The voltage time \[\left( V-t \right)\] graph for triangular wave having peak value \[{{V}_{0}}\] is as shown in figure. The rms value of V in time interval from \[t\text{ }=\text{ }0\] to T/4 is \[\frac{{{V}_{0}}}{\sqrt{x}}\] then find the value of x.
An EM wave from air enters a medium. The electric fields are \[{{\vec{E}}_{1}}={{E}_{01}}\hat{x}\,cos\,\,\left[ 2\pi \nu \left( \frac{z}{c}-t \right) \right]\] in air and \[{{\vec{E}}_{2}}={{E}_{02}}\hat{x}\,cos\,\left[ k(2z-ct) \right]\] in medium, where the wave number k and frequency v refer to their values in air. The medium is nonmagnetic. If \[{{\in }_{{{r}_{1}}}}and{{\in }_{{{r}_{2}}}}\] refer to relative permittivity?s of air and medium respectively, which of the following options is correct?
Electrons in a certain energy level \[n\text{ }=\text{ }{{n}_{1}}\], can emit 3 spectral lines. When they are in another energy level, \[n\text{ }=\text{ }{{n}_{2}}\]. They can emit 6 spectral lines. The orbital speed of the electrons in the two orbits are in the ratio of
Two parallel conducting plates 5mm apart are held horizontally one above the other. The upper plate is maintained at a positive potential of 15 kV while the lower plate is earthed. If a small oil drop of relative density 0.92 and of radius \[5\text{ }\mu m\] remains stationary between the plates, if the charge on the drop is Xe then find the value of x.
The limbs of a manometer consist two uniform capillary tubes of radii \[7.2\times {{10}^{-}}^{4}\] and \[14\times {{10}^{-\,4}}m\]. Find out the correct pressure difference (in Pa) if the level of the liquid in narrower tube stands 0.2 m above that in the broader tube. (Density of liquid: \[1{{0}^{3}}kg/{{m}^{3}}\], Surface tension: \[72 \times 1{{0}^{-3}}N/m\])
A monochromatic light ray is incident on the refracting face of a prism of angle\[75{}^\circ \]. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the prism is \[\sqrt{2}\], then determine the angle of incidence on the first face of the prism.
A clock which keeps correct time at \[25{}^\circ C\] has a pendulum made of brass whose coefficient of linear expansion is 0.000019. How many seconds a day will it gain if the temperature fall to \[0{}^\circ C\]?
An equiconvex lens of focal length 10 cm (in air) and R. I. 3/2 is put at a small opening on a tube of length 1m fully filled with liquid of R. 1.4/3. A concave mirror of radius of curvature 20 cm is cut into two halves \[{{M}_{1}}\,and\,{{M}_{\text{2}}}\] and placed at the end of the tube. \[{{M}_{1}}\,and\,{{M}_{\text{2}}}\] are placed such that their principal axes AB and CD respectively are separated by 1mm each from the principal axis of the lens. A slit S placed in air illuminates the lens with light of frequency\[7.5 \times 1{{0}^{14}}Hz\]. The light reflected from \[{{M}_{1}}\,and\,{{M}_{2}}\] forms interference pattern on the left end EF of the tube. O is an opaque substance to cover the hole left by\[{{M}_{1}}\,\,and\,\,{{M}_{2}}\]. Width of the fringes on EF is\[\left( x \times 10 \right)\mu m\]. Find the value of x in metre.
A complex of a certain metal ion has a magnetic moment of\[4.90BM\]. Another complex of the same metal ion in the same oxidation state has \[2.8\text{ }BM\]magnetic moment. The central metal ion could be which of the following?
Plot of Z (compressibility factor) versus pressure (p) for a few gases are given below: Select the INCORRECT statement.
A)
If \[b>a/RT,\]the initial slope is positive, and the size effect (i,e, 'b' factor) will dominate the behaviour of the gas.
doneclear
B)
If \[b<a/RT,\]the initial slope is negative, and the effect of the attractive forces (i,e, 'a' factor) will dominate the behavior of the gas.
doneclear
C)
At \[0{}^\circ C,\] the effect of attractive forces dominates the behaviour of \[C{{H}_{4}}\] and \[C{{O}_{2}}\] while the molecular size effect dominates the behaviour of \[{{H}_{2}}\]
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D)
If temperature is low enough, the term \[a/RT\]will be smaller than 'b" and so the initial slope of Z versus p will be positive. As the temperature rises,\[a/RT\].becomes larger. At a sufficiently high temperature it becomes more than 'b' and the initial slope of Z versus p becomes negative
\[B{{I}_{3}}\] is symmetrical planar molecule, all the \[(B-I)\] bonds lie at \[120{}^\circ \] of each other. The distance between the I atoms is\[3.54\overset{o}{\mathop{A}}\,\]. The radius of covalently bonded I atom is\[1.33\overset{o}{\mathop{A}}\,\]. Covalent radius of boron atom is
One mole of an ideal gas undergoes a reversible Carnot cycle with \[{{V}_{1}}=10L,\], \[{{V}_{2}}=20L\] and \[{{T}_{1}}=400K,\] Let \[{{T}_{2}}=300K,\]\[{{C}_{v,m}}=(3/2)R\,\,\Delta H\] and \[\Delta V\]for isothermal reversible compression are respectively,
In \[BeO\](Zinc blende structure), \[M{{g}^{2+}}\] is introduced in available tetrahedral voids. If the ions are removed from a single body diagonal after doping, the molecular formula of the unit cell is
The reaction: \[OC{{l}^{\Theta }}+{{I}^{^{\Theta }}}\xrightarrow{\overset{^{\Theta }}{\mathop{O}}\,H}+C{{l}^{^{\Theta }}}\] Takes place in the following steps:
\[0.5g\]of fuming sulphuric acid \[({{H}_{2}}S{{O}_{4}}+S{{O}_{3}}),\]called oleum, is diluted with water. This solution completely neutralised by \[26.7mL\] of \[0.4\text{ }M\]\[NaOH\]. The percentage of free \[S{{O}_{3}}\] in the sample solution is ______.
A current strength of \[0.1\text{ }A\]is passed for \[96.5\text{ }s\]through \[100\text{ }mL\]of a solution of \[0.05\text{ }M\text{ }KCl\text{ }pH\]of the final solution is ______.
For a reversible reaction, \[A+BC\] \[\left( \frac{dx}{dt} \right)=2.0\times {{10}^{3}}L\,mo{{l}^{-1}}\,{{s}^{-1}},\] \[[A][B]-(1.0\times {{10}^{2}}{{s}^{-1}})[C]\] where x is the amount of 'A' dissociated. The value of equilibrium constant (K) is
In an experiment, addition of \[5.0\text{ }mL,\] of \[0.006\text{ }M\]\[BaC{{l}_{2}}\] to \[10.0\text{ }mL\]of arsenic sulphide sol just causes the complete coagulation in\[34\text{ }h\]. The flocculating value of the effective ion is______.
If R be a relation from set A to B defined by \[xRy\Rightarrow \left( x-y \right)\] is positive then R is. If \[A=\left\{ 4,3 \right\},\text{ }B=\left\{ 2,3,4 \right\}-\]
If the extremities of a line segment of lengths \[\ell \], moves in two fixed perpendicular straight lines, then the locus of that point which divides this line segment in the ratio 1 : 2, is-
P is a variable point on the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] whose vertex is A(a, 0). The locus a b of the middle point of AP is-
If V be the volume of a tetrahedron and V be the volume of another tetrahedron formed by the centroids of the previous tetrahedron, if V = KV; then K is equal to
If \[A\left( cos\alpha ,\text{ }sin\alpha \right),B\left( sin\alpha ,-cos\alpha \right),C\left( 1,2 \right)\] are the vertices of a \[\Delta ABC\], then as \[\alpha \] varies the locus of its centroid is -
A line passes through (2, 2) and makes a triangle of axes 9 square units with co-ordinate axis in 1st Quadrant, the sum of all possible slopes of line is-
Find the value of \[\underset{x\to 0}{\mathop{\lim }}\,\left( \left[ \frac{100x}{\sin x} \right]+\left[ \frac{99\,\sin x}{x} \right] \right)\] (where [.] represents the greatest integral function).
If \[f\left( x \right)\] be a continuous function defined for\[1\le x\le 3,(x)\in Q\forall x\in [1,3],f(2)=10\], then find value of f(1.8) (where Q is a set of all rational numbers).
Function \[f\left( x \right)={{x}^{3}}+6{{x}^{2}}+\left( 9+2k \right)x+1\forall x\in R\]is strictly increasing function if \[k>\lambda \] then find\[\lambda \].