At \[t=0,\] a particle at \[(1,0,0)\] moves towards point \[(3,4,12)\] with a constant velocity of magnitude\[65\text{ }m/s\]. The position of the particle is measured in metres and time in seconds. Assuming constant velocity, the position of the particle at \[t=2\text{ }sec\]is
Blocks A and C start from rest and move to the right with acceleration \[{{a}_{A}}=12t\,\,m/{{s}^{2}}\] and\[{{a}_{C}}=3\,\,m/{{s}^{2}}\]. Here t is in seconds. The time when block B again comes to rest is
The maximum value of mass of block C so that neither A nor B moves is (Given that mass of .4 is 100 kg and that of B is 140 kg. Pulleys are smooth and friction coefficient between A and B, and between B and horizontal surface is \[\mu =0.3;\] \[g=10\,m/{{s}^{2}}\])
A smooth sphere is moving on a horizontal surface with velocity vector \[2\hat{i}+2\hat{j}\] immediately before it hits a vertical wall. The wall is parallel to \[\hat{j}\] vector and the coefficient of restitution between the sphere and the wall is\[e=\frac{1}{2}\]. The velocity vector of the sphere after it hits the wall is
A uniform circular ring of radius R is fixed in plane. A particle is placed on the axis of the ring at a distance much greater than R and allowed to fall towards the ring under the influence of the Ting's gravity. The particle achieves a maximum speed v. The ring is replaced with another ring of the same (linear) mass density but radius 2R, and the experiment is repeated. What is the new maximum speed of the particle?
A cubical block is placed on a thin liquid layer of thickness\[0.2\text{ }mm\]. The load moves downward with a constant speed of \[2\text{ }cm/sec\]after the system is released. If coefficient of viscosity of liquid is \[\frac{x}{1000}Pa-\sec ,\] then x is (Take\[g=10m/{{s}^{2}}\]) '
A hot body placed in air is cooled according to Newton's law of cooling, the rate of decrease of temperature being k times the temperature difference from the surroundings. Starting from \[t=0,\]find the time in which the body will lose half the maximum heat it can lose.
An ideal gas is initially at a temperature T and volume K Its volume is increased by \[\Delta V\]due to an increase in temperature \[\Delta T,\]pressure remains constant. The quantity \[\delta =\frac{\Delta V}{V\Delta T}\] varies with temperature as
A sound wave of wavelength 'k travels towards the right horizontally with a velocity V. It strikes and reflects from a vertical plane surface, traveling at a speed v towards the left. The number of crests striking in a time interval of three seconds on the wall is
Two small balls each carrying a charge q and mass m are attached to the ends of a light rod of length d which is suspended from the ceiling by a thin tension free fiber as shown in the figure. There is a uniform magnetic B pointing straight down, in the cylindrical region of radius R around the fiber. The system is initially at rest. If the magnetic field is turned off, which of the following describes what happens to the system immediately?
A)
It rotates with angular momentum \[qB{{R}^{2}}\]
doneclear
B)
It rotates with angular momentum \[\frac{qB{{d}^{2}}}{4}\]
doneclear
C)
It rotates with angular velocity \[\frac{qB{{R}^{2}}}{m{{d}^{2}}}\]
doneclear
D)
It rotates with angular velocity \[\frac{qB}{2m}\]
In a Vernier Calliper, the zero of Vernier scale is slightly left to the zero of main scale when both jaws are closely joined to each other. Total number of divisions on Vernier scale is 80 which is equal to \[2.32\text{ }cm.\] 70th division of Vernier is exactly coinciding with 2nd division of main scale when jaws are closely joined to each other. Now diameter of cylinder is measured, it is found that zero of Vernier lies between \[6.2\text{ }cm\]to \[6.23\text{ }cm\]on the main scale and 50th division of Vernier exactly coincides with a main scale. Then choose the correct option.
A)
Vernier callipers has negative zero error of\[1.97\text{ }cm\].
doneclear
B)
Vernier callipers has positive zero error of\[1.97\text{ }cm\].
doneclear
C)
Vernier callipers has negative zero error of\[0.01\text{ }cm\].
doneclear
D)
Vernier callipers has positive zero error of\[0.01\text{ }cm\].
In the figure shown XX represents a vertical plane perpendicular to the plane of the figure. To the right of this plane there is a uniform horizontal magnetic field B directed into the plane of the figure. A uniform electric field E exists horizontally perpendicular to the magnetic field in entire space. A charge particle having charge q and mass m is projected vertically upward from point 0. It crosses the plane XX after time T. Find the speed of projection of the particle if it was observed to move uniformly after time T. It is given that\[qE=mg\].
A square loop of side length L carries a current which produces a magnetic field \[{{B}_{0}}\] at the centre \[(O)\] of the loop. Now the. Square loop is folded into two parts with one half being perpendicular to the other (see figure). Calculate the magnitude of magnetic field at the centre O.
A capacitor of capacitance C is having a charge\[{{Q}_{0}}\]. It is connected to a pure inductor of inductance L. The inductor is a solenoid having N turns. Find the magnitude of magnetic flux through each of the N turns in the coil at the instant charge on the capacitor becomes\[\frac{{{Q}_{0}}}{2}\].
A large transparent cube (refractive index\[=1.5\]) has a small air bubble inside it. When a coin (diameter\[2\text{ }cm\]) is placed symmetrically above the bubble on the top surface of the cube, the bubble cannot be seen by looking down into the cube at any angle. However, when a smaller coin (diameter\[1.5cm\]) is placed directly over it, the bubble can be seen by looking down into the cube. What is the range of the possible depths d of the air bubble beneath the top surface?
Four point charges q, q, q and \[-q\]are placed at the vertices of a square of side length a. The configuration is changed and the charge are positioned at the vertices of a rhombus of side length a with \[-q\] charge at the vertex where angle is\[120{}^\circ \]. Find the work done by the external agent in changing the configuration.
Seven identical plates, each of area A, are placed as shown. Any two adjacent plates are at separation d. Conducting wires have been used to connect the plates and a cell of emf V volt as shown in the figure. How much charge does the cell supply?
In Young's double-slit experiment, the separation between two slits is \[d=0.32\text{ }mm\]and the wavelength of light used is\[\lambda =5000\text{ }\overset{o}{\mathop{A}}\,\]. Find the number of maxima in the angular range\[-{{\sin }^{-1}}(0.6)\le \theta \le {{\sin }^{-1}}(0.6)\].
The speed of a projectile when it is at its greatest height is \[\sqrt{2/5}\] times its speed at half the maximum height. What is the angle of projection in (Degree)?
A particle is moving in a circle of radius \[\frac{2}{3}m\] and mass of the particle is 2 kg. The kinetic energy of the particle depends on distance 'S" travelled by the particle as K.E. is\[4{{S}^{4}}\]. The angle made by net acceleration with the radial acceleration when the particle rotate by \[60{}^\circ \] is \[\tan \left( \frac{K}{\pi } \right).\] . Find the value of K.
The resistance between P and S in shown circuit is of \[300\,\Omega ,\] which is tapped at Q and R such that\[PQ=QR=RS\]. If the potential difference between A and B is \[320\text{ }V,\] the potential difference between R and S is \[2\times {{10}^{N}}V.\] Find the value of N.
Convex surface of thin concavo-convex lens of refractive index \[1.5\] is silvered as shown. A small object is kept in air at 30 cm left of the lens on its principal axis. What is the distance (in cm) of the final image from mirror?
In the circuit shown in figure AB is a uniform wire of length\[L=5\text{ }m\]. It has a resistance of\[2\Omega /m\]. When \[AC=2.0\text{ }m,\]it was found that the galvanometer shows zero reading when switch S is placed in either of the two positions 1 or 2. Find the emf \[{{E}_{1}}\](in V)
The correct order of equivalent conductance at infinite dilution in water at room temperature for \[{{H}^{+}},\] \[{{K}^{+}},\]\[C{{H}_{3}}CO{{O}^{-}}\]and \[H{{O}^{-}}\] ions is
Which of the following structures correspond to the product expected, when excess of \[{{C}_{6}}{{H}_{6}}\] reacts with \[C{{H}_{2}}C{{l}_{2}}\]in presence of anhydrous\[AlC{{l}_{3}}\]?
[A] In the Aluminothermite process, aluminium acts as reducing agent.
[B] The process of extraction of gold involves the formation of \[{{[Au{{(CN)}_{2}}]}^{-}}\] and \[{{[Zn{{(CN)}_{4}}]}^{2-}}\].
[C] In the extractive metallurgy of zinc, partial fusion of \[ZnO\]with coke is called sintering and reduction of ore to the molten metal is called smelting.
[D] Extractive metallurgy of silver from its ore argentite involves complex formation and displacement by more electropositive metal.
What will be the final product in the following reaction sequence - \[C{{H}_{3}}C{{H}_{2}}CN\xrightarrow{{{H}^{+}}/{{H}_{2}}O}A\xrightarrow{N{{H}_{3}}}B\xrightarrow{NaOBr}C\]
For the reaction system: \[2NO(g)+{{O}_{2}}(g)\to 2N{{O}_{2}}(g)\]volume is suddenly reduced to half its value by increasing the pressure on it. If the reaction is of first order with respect to \[{{O}_{2}}\] and second order with respect to NO, the rate of reaction will
\[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-Cl\xrightarrow[KOH]{alc.}B\xrightarrow[{}]{HBr}C\xrightarrow[ether]{Na}D\]In the above sequence of reactions, the product D is -
Two moles of \[PC{{l}_{5}}\] were heated in a closed vessel of 2 L. At equilibrium 40% of \[PC{{l}_{5}}\] is dissociated into \[PC{{l}_{3}}\] and \[C{{l}_{2}}\]. Calculate the value of equilibrium constant.
If tangent to the curve \[{{y}^{2}}={{x}^{3}}\] at its point \[\left( {{m}^{2}},{{m}^{3}} \right)\] is also normal to the curve at \[\left( {{M}^{2}},{{M}^{3}} \right),\] then what is the value of mM ?
If the \[{{(r+1)}^{th}}\]term in the expansion of\[{{\left( \sqrt[3]{\frac{a}{\sqrt{b}}}+\sqrt[{}]{\frac{b}{\sqrt[3]{a}}} \right)}^{21}}\]has the same power of a and b, then the value of r is
In an experiment with 15 observations on x, the following results were available. \[\Sigma {{x}^{2}}=2830,\Sigma x=170\] One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is
If the lines \[\frac{1-x}{3}=\frac{y-2}{2\alpha }=\frac{z-3}{2}\]and \[\frac{x-1}{3\alpha }=y-1=\frac{6-z}{5}\]are perpendicular, then the value of \[\alpha \] is
The sum of the terms of an infinitely decreasing G.P. is equal to the greatest value of the function \[f(x)={{x}^{3}}+3x-9\] on the interval [-4, 3] and the difference between the first and second terms is \[f'(0)\]. Then the value of 3 r (where r is common ratio) is_________.