The moment of inertia of a uniform disc about an axis passing through its centre and perpendicular to its plane is 1 kg \[{{m}^{2}}\]. It is rotating with an angular velocity 100 rad \[{{s}^{-1}}\]. Another identical disc is gently placed on it so that their centres coincide. Now these two discs together continue to rotate about the same axis. Then the loss in kinetic energy in kilojoules is
An ideal gas is taken through a cyclic thermodynamic process through four steps. The amount of heat involved in these steps are \[{{Q}_{1}}=5960J,{{Q}_{2}}=-5585J,{{Q}_{3}}=-2980J\] and \[{{Q}_{4}}=3645J\] respectively. The corresponding quantities of work involved are \[{{W}_{1}}=2200J,{{W}_{2}}=-825J,\]\[{{W}_{3}}=-1100J\] and \[{{W}_{4}}\] respectively. Find the value of \[{{W}_{4}}.\]. What is the efficiency of the cycle?
A magnetic flux through a stationary loop with a resistance R varies during the time interval \[\tau \]as \[\phi =at(\tau -t)\]. What is the amount of heat generated in the loop during that time?
A block of mass \[{{m}_{1}}\] lies on a smooth horizontal table and is connected to another freely hanging block of mass \[{{m}_{2}}\] by a light inextensible string passing over a smooth fixed pulley situated at the edge of the table as shown in the figure. Initially the system is at rest with \[{{m}_{1}}\] at a distance d from the pulley. The time taken for \[{{m}_{1}}\] to reach the pulley is
Two identical charged spheres suspended from a common point by two massless strings of length \[l\] are initially a distance d(d < < \[l\]) apart because of their mutual repulsion. The spheres begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance x between them
A stone of mass 2 kg is projected upward with kinetic energy of 98 J. The height at which the kinetic energy of the stone becomes half its original value, is given by
In a series LCR circuit, different physical quantities vary with frequency v. Which of the following curves represent correct frequency variation of the corresponding quantity?
The wavelengths and frequencies of photons in transitions 1, 2, and 3 for hydrogen like atom are \[{{\lambda }_{1}},{{\lambda }_{2}},{{\lambda }_{3}};{{\upsilon }_{1}},{{\upsilon }_{2}}\] and \[{{\upsilon }_{3}}\] respectively. Then
A lift is tied with thick iron wire and its mass is 1000 kg. The minimum diameter of the wire if the maximum acceleration of the lift is \[1.2m{{s}^{-2}}\]and the maximum safe stress is \[1.4\times {{10}^{8}}N\text{ }{{m}^{-}}^{2}\], is (Take \[g=9.8\text{ }m\text{ }{{s}^{-}}^{2}\])
2 kg of ice at \[-20{}^\circ C\] is mixed with 5 kg of water at \[20{}^\circ C\] in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. (Given : Specific heat capacities of water and ice are \[1\,\,ca\operatorname{l}\,{{g}^{-1}}{}^\circ {{C}^{-1}}\]and \[0.5\text{ }cal\text{ }{{g}^{-}}^{1}{}^\circ {{C}^{-}}^{1}\] respectively. Latent heat of fusion of ice \[=80\,cal\,{{g}^{-1}})\]
The escape velocity for a planet is \[{{v}_{e}}\]. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be
In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of \[2\times {{10}^{10}}\] Hz and amplitude 54 V \[{{\text{m}}^{-1}}\].
A)
The amplitude of oscillating magnetic field will be \[18\times {{10}^{-7}}\text{Wb}\,{{\text{m}}^{-2}}\].
doneclear
B)
The amplitude of oscillating magnetic field will be \[18\times {{10}^{-8}}\text{Wb}\,{{\text{m}}^{-2}}\].
A uniform rod of mass m and length \[{{l}_{0}}\]is pivoted at one end and is hanging in the vertical direction. The period of small angular oscillations of the rod (if displaced slightly from its position) is
Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0, number of P species are \[4{{N}_{0}}\]and that of Q are \[{{N}_{0}}\]. Half-life of P (for conversion to R) is 1 minute where as that of Q is 2 minutes. Initially no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be
A particle is projected from a horizontal plane with velocity of \[5\sqrt{2}\,m{{s}^{-1}}\]at an angle. If at highest point its velocity is found to be \[5\,m\,{{s}^{-1}}\]. Then its range ______ m. (Take\[g=10\,m\,{{s}^{-2}}\])
For a certain organ pipe, three successive resonance frequencies are observed at 425, 595 and 765 Hz respectively. Taking the speed of sound in air to be \[340\,m\,{{s}^{-1}}\], the length of the pipe will be ___ m.
A fish at a depth of 12 cm in water is viewed by an observer on the bank of a lake. The image of fish is raised by height ___ cm. (Refractive index of lake water \[=\frac{4}{3}\])
The number of isomers for the complexes X and Y are, respectively, \[X={{[Pt(N{{H}_{3}})(N{{H}_{2}}OH)(N{{O}_{2}})(py)]}^{\oplus }}\] \[Y=\left[ Cr \right[\left( N{{H}_{3}} \right){{\left( OH \right)}_{2}}C{{l}_{3}}]\]
Number of water molecules coordinated to the central metal ion to form complexes in (I) Blue vitriol, (II) White vitriol and (III) Green vitriol are, respectively,
The quantum number of the last electron of an element are given below. Predict the atomic number and name of the element from the following quantum numbers \[n=3,l=2,m=0,s=-\frac{1}{2}\]
From the given following sol, how many can coagulate the haemoglobin sol? \[Fe{{\left( OH \right)}_{3}},Ca{{\left( OH \right)}_{2}},\text{ }Al{{\left( OH \right)}_{3}},\text{ }starch,\text{ }clay,\]\[A{{s}_{2}}{{S}_{3}},CdS,\text{ }basic\text{ }dye\]
Compound \[(A)({{C}_{4}}{{H}_{8}}{{O}_{3}})\] reacts with \[NaHC{{O}_{3}}\]and evolves \[C{{O}_{2}}\left( g \right)\]. (A) reacts with LAH to give a compound (B) which is a chiral. The structure of (A) is
Consider the following reactions: Arrange the above reactions in the decreasing order of greater proportion of inverted product and select the correct answer.
The freezing point of the solution of compound \[(X)Co{{(N{{H}_{3}})}_{4}}C{{l}_{3}}\], containing 23.35 of solute per kg water is Given \[{{K}_{f}}=1.86{}^\circ \text{ }K\text{ }kg\text{ }mo{{l}^{-1}}\] Mwt of \[X=233.5\text{ }g\,\,mo{{l}^{-1}}\]
If \[\tan \,\,{{q}_{1}}\]\[\tan \,\,{{q}_{2}}=-\frac{{{a}^{2}}}{{{b}^{2}}},\] then the chord joining two points \[(a\,\,\cos \,\,{{q}_{1}},\,\,b\,\,\sin \,\,{{q}_{1}}),\] and \[(a\,\,\cos \,\,{{q}_{2}},\,\,b\,\,\sin \,\,{{q}_{2}})\] on the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] will subtend a right angle at
If \[S*(p,q,r)\] is the dual of the compound statement \[S(p,q,r)\]and \[S(p,q,r)=\,\sim p\wedge [\sim (q\vee r)]\] then \[S*(\sim p,\sim q,\sim r)\] is equivalent to-
The angles of elevation of the top of a tower from the top and bottom at a building of height a are \[30{}^\circ \] and \[45{}^\circ \] respectively. If the tower and the building stand at the same level, then the height of the tower is
Let r be the range and \[{{S}^{2}}=\frac{1}{n-1}\sum\limits_{i=1}^{n}{{{\left( {{x}_{i}}-\bar{x} \right)}^{2}}}\]be the S.D. of a set of observations \[{{x}_{1}},{{x}_{2}},.....{{x}_{n}},\] then
If at least one value of the complex number \[z=x+iy\] satisfy the condition \[|z+\sqrt{2}|={{a}^{2}}-3a+2\] and the inequality \[|z+i\sqrt{2}|<{{a}^{2}},\] then
A letter is known to have come either from LONDON or CLIFTON; on the postmark only the two consecutive letters ON are legible. The probability that it came from LONDON is
If \[\int{f(x)}\,\sin x\,\,\cos x\,dx=\frac{1}{2({{b}^{2}}-{{a}^{2}})}{{\log }_{e}}\,\left( f(x) \right)+A\], \[b\ne \pm a,\] then \[{{\left\{ f(x) \right\}}^{-1}}\] is equal to
If \[f(x)\] is differentiable and strictly increasing function, then the value of \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{f({{x}^{2}})-f(x)}{f(x)-f(0)}\] is
Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:
The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices \[(0,0),\] \[(0,21)\] (0,21) and \[(21,0),\] is
If a and b are the roots of the equation \[{{x}^{2}}-4x+1=0\] \[(a>b)\]then the value of \[f(\alpha ,\beta )=\frac{{{\beta }^{3}}}{2}\text{cose}{{\text{c}}^{2}}\left( \frac{1}{2}{{\tan }^{-1}}\frac{\beta }{\alpha } \right)+\frac{{{\alpha }^{3}}}{2}{{\sec }^{2}}\left( \frac{1}{2}{{\tan }^{-1}}\frac{\alpha }{\beta } \right)\]is