Two circular coils P and Q lie in the same plane co-axially. The coil P has 10 turns and radius 4 cm and carries current of 1 A. The coil Q has 40 turns of radius 4 cm and current in it is such that resultant magnetic field at the common centre becomes zero. When coil P is rotated such that planes of coils become perpendicular to each other, then magnetic field at the common centre becomes
A long straight wire is carrying a current of \[I=2A\]. A bar magnet of magnetic dipole moment M is placed as shown in figure, gently. Then, the bar magnet
A)
Experiences a net force only.
doneclear
B)
Experiences a torque only.
doneclear
C)
May undergo translatory motion as well as rotational motion.
A non-conducting V-shaped rod of length \[2\ell \] has linear charge density \[\lambda \] as shown in figure. The rod is rotated about point \[O\] with an angular velocity \[\omega \] in the horizontal plane. The magnetic moment of system will be
A charged particle of \[q=6\,\mu C\] is projected in a uniform magnetic field \[\vec{B}=\left( 10\sqrt{3}\,\hat{i}+10\hat{j} \right)Wb/{{m}^{2}}\] with velocity with velocity\[\vec{V}=(2\hat{i}+3\sqrt{3}\hat{j})m/s\]. The pitch of helix becomes [Assume mass of particle, \[m=10\sqrt{3}\times {{10}^{-6}}kg\]]
For an ideal toroid, an observer starts travelling from centre of toroid along radial direction. Which of the following diagram best describes the magnetic field variation observed by him?
A straight wire of length f. carrying a current i, is bent into following shapes as shown in figure, keeping length and current constant. The magnetic field at point 0 is maximum for
A coil of inductance \[\frac{32}{9}mH\] having negligible resistance is connected to a source of \[emf\] \[e=\left( 2{{t}^{2}}-4t \right)V\]. The energy stored in inductor during the time interval when \[emf\] reverses its polarity first time, will be
An inductor of inductance 2 H is connected across two conducting parallel rails of negligible resistances. A conducting rod of length 20 cm and mass of 320 gm is given a speed of 4 m/s along the rails. If a magnetic field of strength 10T is switched on perpendicular to the plane of rails, then maximum current that develops in the inductor will be (neglect friction and gravity)
An ideal solenoid stores 32 J of magnetic field energy and when a current of 4 Amp is passed through it, the rate of energy dissipation becomes 320 watt in the form of heat. The time constant of the circuit is (assume ideal battery connected)
A long straight wire carrying a current of 10 A is placed parallel to one of the side of square as shown in figure. If the resistance of the square loop is \[2\,\Omega \] and loop is rotated by \[180{}^\circ \] about side AB, then total charge flowing during this interval becomes
A force of 10 N is required to move a conducting loop through a non-uniform magnetic field at a speed 2 m/s. The rate of production of electrical energy in the loop will be
The equation of an AC voltage is\[V=220\sin \left( \omega t+\frac{\pi }{6} \right)\] and the equation of the current in the circuit is \[l=22\sin \left( \omega t-\frac{\pi }{6} \right)\]. Which of the following is a correct statement?
A)
The impedance of circuit is \[10\,\Omega \]
doneclear
B)
The reactance in circuit is \[5\sqrt{3}\,\Omega \]
The potential difference across A and B points of circuit is (assume above circuit is a part of some network and left over for long time in connection)
In the LCR series, circuit reading of voltmeters are shown in the figure. When same devices are connected in parallel across the same sources, the current drawn from source will be
The alternating current in a circuit varies as \[I=(t-2)\,Amp\]. The ratio of mean current to that of \[rms\] current in the interval \[t=0\] to \[t=4\,s\] will
Two particles move parallel to x-axis about the origin with the same amplitude and frequency. At a certain instant they are found at distance A/3 from the origin on opposite sides but their velocities are found to be in the same direction. The phase difference between the two particles is
Observe the following set of oscillations of spring system and identify the quantity that remains same in all the conditions. (Assume a smooth surface and same force applied on each)
A uniform square lamina of side 2a is hung up by one comer and it oscillates in its own plane which is vertical. The length of the equivalent simple pendulum is
A block of mass m is hanging freely from a spring of stiffness k. A particle of mass m falls on the block with a velocity v and gets stuck to it. The amplitude and angular frequency of oscillations during subsequent motion are respectively.
An air bubble of radius ?a? initially rests on the bottom of vessel filled with a liquid of constant density \['\rho '\] as shown in figure. When the air bubble starts rising vertically, then which of the following graph represents he variation of radius of bubble with depth of liquid? (Neglect atmospheric pressure).
A container is filled with a liquid whose density varies as \[\rho =(10-2y)\,kg/{{m}^{3}}\] with height. If the area of bottom surface of container is \[200\,\text{c}{{\text{m}}^{2}}\] and height of liquid is 2 m, then the force exerted by container on the liquid is (Take \[g=10\,m/{{s}^{2}},\] neglect atmospheric pressure)
A disc of radius a and mass m with small thickness, is suspended through a thread in air with the disc in horizontal plane. When the same set-up is placed above a liquid such that the plane of disc just makes contact with liquid surface, then the tension in thread is doubled. The surface tension of liquid is
A spherical ball of density p and radius R is floating in completely submerged condition in a liquid of density \[\rho \] and surface tension T. When a cavity of radius \[\frac{5R}{6}\] is created within the ball, the ball now floats half submerged in liquid. Then value of \[\frac{T}{{{R}^{2}}}\] is given by \[(\rho =1\,kg/{{m}^{3}})\]:
A wooden block is floating in a liquid in partially submerged condition. If the same set-up is taken at Mount Everest peak, then one should observe that the piece of wood will float with
Two close containers P and Q are filled with Helium gas and water respectively at same temperature. A ball is released from top in the containers and temperatures of both containers are kept constant. The diagram which best represents the motion of ball in containers is
Six waves of equal frequency 50 Hz and having amplitudes 8 cm, 12 cm, 6 cm, 3 cm, 17 cm and 12 cm reach at point O with successive phase difference of \[\pi /3\]. Amplitude of the resultant wave after superposition is
A tuning fork, when sounded with a column of air at temperature \[{{T}_{1}}\] gives 4 beats per second. When the temperature of air column is increased to \[{{T}_{2}}\] it gives 6 beats per second. If the original frequency of tuning fork is 4 Hz, then ratio of \[{{T}_{2}}/{{T}_{1}}\] becomes
Two transverse waves having amplitude 3 cm, frequency 50 Hz and wavelength \[\lambda ,\] moving in opposite directions are superimposed on fixed end of a steel rod of 5 cm whose other end is free. A stationary wave is setup in the rod with 3 node and 3 antinode points, then which of the following is correct statement?
A)
The wavelength of wave is 4 cm.
doneclear
B)
The maximum displacement of free end of rod about mean position is 3 cm.
A boy and a girl start running with speed of 4 m/s and 3 m/s respectively around a circular track in a park from same point and in same direction. The radius of track is \[\left( \frac{4}{\pi } \right)m\]. If boy blows whistle at t = 4 s and t = 6 s with frequency of 160 Hz, then difference of apparent frequency heard by girl at these moments will be (assume speed of sound in air = 330 m/s)
In a saturated solution of sparingly soluble strong electrolyte \[AgI{{O}_{3}}\] (Molecular mass = 283), the equilibrium which sets in is\[AgI{{O}_{3}}(s)\,A{{g}^{+}}(aq.)+lO_{3}^{-}(aq.)\]. If the solubility product constant \[{{k}_{sp}}\] of \[AgI{{O}_{3}}\] at a given temperature is \[1.0\times {{10}^{-8}},\] what is the mass of \[AgI{{O}_{3}}\] contained in 100 ml of its saturated solution?
Which will be the major product if \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-CH=C{{H}_{2}}\] reacts with \[HBr\]?
The number of moles of iron metal produced by passage of 4.00 A of current for 1.00 hour through \[FeS{{O}_{4}}\] solution is (Assume current efficiency to be 60%)
A solution is obtained by mixing two solutions of same electrolyte with \[pH=5\] and \[pH=3\]respectively. The resulting solution has pH (Given \[\log \,0.5=-0.3\]
In which of the following compounds, enol form will be maximum?
A)
\[C{{H}_{3}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\]
doneclear
B)
\[C{{H}_{3}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-{{C}_{2}}{{H}_{5}}\]
doneclear
C)
\[C{{H}_{3}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\]
doneclear
D)
\[C{{H}_{3}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}\]
Consider the following reaction: \[C{{H}_{3}}C{{H}_{2}}\xrightarrow{B{{r}_{2}}/hv}(A)\xrightarrow{alc.\,KOH}(B)\] \[\xrightarrow{NBS}(C)\xrightarrow{+{{(C{{H}_{3}})}_{2}}CHONa}(D)\] in this sequence will be
If the chord \[y=mx+1\] of the circle \[{{x}^{2}}+{{y}^{2}}=1\] subtends an angle \[45{}^\circ \] at the major segment of the circle, then value of m is
The range of values of 'a' such that the angle \[\alpha \] between the tangents drawn from (a, 0) to the circle \[{{x}^{2}}+{{y}^{2}}=4\] which lies in \[\left( \frac{\pi }{3},\,\frac{\pi }{2} \right)\] are (where a is the angle in which circle lies)
If the vertices of a triangle are (12,5), \[(13\,\sin \,\theta ,\,-13\cos \theta )\] and \[\left( -13\cos \theta ,\,13\sin \theta \right),\] where \[\theta \] is arbitrary, then locus of its orthocentre is
Water is dropped at the rate of \[2\,{{m}^{3}}\] per second into a cone with semi-vertical angle \[45{}^\circ \]. The rate at which circumference of water (in contact with air) changes when height of the water in the cone is 2 m, is
Tangent to curve \[y=f(x)\] intersects the y-axis at P. A line through P and perpendicular to this tangent passes through (1, 0). The differential equation of curve is
The equation of curve passing through (0, 0), if midpoint of segment of its normal from any point on the curve to the y-axis lying on the parabola \[{{x}^{2}}=\frac{y}{2}\] is
If the square ABCD where A(0,0), B(2,0), C(2,2) and D(0, 2) undergoes the following three transformations in that order, for all the four vertices (i) \[(x,\,y)\to \,(y,\,x)\] (ii) \[(x,\,y)\to (x+3y,\,y)\] (iii) \[(x,y)\to \,\left( \frac{x-y}{2},\,\frac{x+y}{2} \right)\] then the final figure is:
If the points \[(-2,\,0),\,\left( -1,\,\frac{1}{\sqrt{3}} \right)\] and \[(\cos \theta ,\,\sin \theta )\] are collinear, then the number of values of \[\theta \in \,[0,\,2\pi ]\] are:
\[f(x)=\left\{ \begin{matrix} \{x\}, & [x]\,\text{is}\,\text{odd} \\ 1-\{x\}, & [x]\,\text{is}\,\text{even} \\ \end{matrix} \right.\] [.] denotes greatest integer function and {.} denotes fractional part function, then area bounded by \[y=f(x),\,x\in [0,\,5]\] and \[x\]-axis is
Directions: Read the fallowing questions and choose: Statement 1: No line can be drawn through the point (-4, 5) such that its distance from (2, -3) will be equal to 8. Statement 2: The distance between the two points is 10.
A)
Both statements are True, Statement-2 explains Statement-1.
doneclear
B)
Both statements are True, Statement-2 does not explain Statement-1.
Directions: Read the fallowing questions and choose: Statement 1: The differential equation \[\frac{dy}{dx}=\frac{\sqrt{1-{{y}^{2}}}}{y}\] determines a family of circles. Statement 2: \[{{x}^{2}}+{{y}^{2}}+2kx+{{k}^{2}}-1=0\] represents a family of circles with fixed radius 1 and variable centres lying along x-axis.
A)
Both statements are True, Statement-2 explains Statement-1.
doneclear
B)
Both statements are True, Statement-2 does not explain Statement-1.
Directions: Read the fallowing questions and choose: Statement 1: \[{{x}^{3}}+3{{x}^{2}}+9x+\sin x=0\] has exactly one real root in R. Statement 2: \[{{x}^{3}}+3{{x}^{2}}+9x+\sin x=0\] does not satisfy Rolle?s Theorem in any closed interval [a, b].
A)
Both statements are True, Statement-2 explains Statement-1.
doneclear
B)
Both statements are True, Statement-2 does not explain Statement-1.
Directions: Read the fallowing questions and choose: Statement 1: Condition of orthogonality of two circles \[{{x}^{2}}+{{y}^{2}}+2{{g}_{1}}x+2{{f}_{1}}y+{{c}_{1}}=0\] and \[{{x}^{2}}+{{y}^{2}}+2{{g}_{2}}x+2{{f}_{2}}y+{{c}_{2}}=0\] is \[2{{g}_{1}}{{g}_{2}}+2{{f}_{1}}{{f}_{2}}={{c}_{1}}+{{c}_{2}}\]. Statement 2: Angle between the two circles whose distance between the centres is d and radii \[{{r}_{1}},\,{{r}_{2}}\] given by \[\tan \theta =\frac{{{d}^{2}}-r_{1}^{2}-r_{2}^{2}}{2{{r}_{1}}{{r}_{2}}}\]
A)
Both statements are True, Statement-2 explains Statement-1.
doneclear
B)
Both statements are True, Statement-2 does not explain Statement-1.