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Match List I with List II
| List I | List II |
|---|---|
| A. Torque | I. kg m$$^{-1}$$ s$$^{-2}$$ |
| B. Energy density | II. kg m s$$^{-1}$$ |
| C. Pressure gradient | III. kg m$$^{-2}$$ s$$^{-2}$$ |
| D. Impulse | IV. kg m$$^2$$ s$$^{-2}$$ |
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A vehicle travels $$4$$ km with speed of $$3$$ km h$$^{-1}$$ and another $$4$$ km with speed of $$5$$ km h$$^{-1}$$, then its average speed is:
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An object is allowed to fall from a height $$R$$ above the earth, where $$R$$ is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be:
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A block of $$\sqrt{3}$$ kg is attached to a string whose other end is attached to the wall. An unknown force $$F$$ is applied so that the string makes an angle of $$30°$$ with the wall. The tension $$T$$ is: (Given $$g = 10$$ m s$$^{-2}$$)
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A machine gun of mass $$10$$ kg fires $$20$$ g bullets at the rate of $$180$$ bullets per minute with a speed of $$100$$ m s$$^{-1}$$ each. The recoil velocity of the gun is:
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A force is applied to a steel wire $$A$$, rigidly clamped at one end. As a result elongation in the wire is $$0.2$$ mm. If same force is applied to another steel wire $$B$$ of double the length and a diameter $$2.4$$ times that of the wire $$A$$, the elongation in the wire $$B$$ will be (wires having uniform circular cross sections)
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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Efficiency of a reversible heat engine will be highest at $$-273°$$C temperature of cold reservoir.
Reason R: The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as $$\eta = \left(1 - \frac{T_2}{T_1}\right)$$
In the light of the above statements, choose the correct answer from the options given below:
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A flask contains hydrogen and oxygen in the ratio of $$2 : 1$$ by mass at temperature $$27°$$C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:
For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is $$1$$ kg, the angular frequency is $$\omega_1$$. When the mass block is $$2$$ kg the angular frequency is $$\omega_2$$. The ratio $$\frac{\omega_2}{\omega_1}$$ is:
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As shown in the figure, a point charge $$Q$$ is placed at the centre of conducting spherical shell of inner radius $$a$$ and outer radius $$b$$. The electric field due to charge $$Q$$ in three different regions I, II and III is given by:
(I: $$r < a$$, II: $$a < r < b$$, III: $$r > b$$)
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As shown in the figure, a current of $$2$$ A flowing in an equilateral triangle of side $$4\sqrt{3}$$ cm. The magnetic field at the centroid $$O$$ of the triangle is:
(Neglect the effect of earth's magnetic field)
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A current carrying rectangular loop $$PQRS$$ is made of a uniform wire. The length $$PR = QS = 5$$ cm and $$PQ = RS = 100$$ cm. If the ammeter current reading changes from $$I$$ to $$2I$$, then the ratio of the magnetic forces per unit length on the wire $$PQ$$ due to the wire $$RS$$ in the two cases respectively $$(f^I_{PQ} : f^{2I}_{PQ})$$ is:
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In the given circuit, the rms value of current $$(I_{rms})$$ through the resistor $$R$$ is:
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A thin prism $$P_1$$ with an angle $$6°$$ and made of glass of refractive index $$1.54$$ is combined with another prism $$P_2$$ made from glass of refractive index $$1.72$$ to produce dispersion without average deviation. The angle of prism $$P_2$$ is:
A point source of $$100$$ W emits light with $$5\%$$ efficiency. At a distance of $$5$$ m from the source, the intensity produced by the electric field component is:
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An electron accelerated through a potential difference $$V_1$$ has a de-Broglie wavelength of $$\lambda$$. When the potential is changed to $$V_2$$, its de-Broglie wavelength increases by $$50\%$$. The value of $$\left(\frac{V_1}{V_2}\right)$$ is equal to:
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The nuclear density of nuclides $$^{10}_5$$B, $$^{6}_3$$Li, $$^{56}_{26}$$Fe, $$^{20}_{10}$$Ne and $$^{209}_{83}$$Bi can be arranged as
$$\rho^N_{Bi} > \rho^N_{Fe} > \rho^N_{Ne} > \rho^N_{B} > \rho^N_{Li}$$
Reason R: The radius $$R$$ of nucleus is related to its mass number $$A$$ as $$R = R_0 A^{\frac{1}{3}}$$, where $$R_0$$ is a constant.
In the light of the above statement, choose the correct answer from the options given below:
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The output $$Y$$ for the inputs $$A$$ and $$B$$ of circuit is given by
Truth table of the shown circuit is:
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Match List I with List II
| List I | List II |
|---|---|
| A. Attenuation | I. Combination of a receiver and transmitter |
| B. Transducer | II. Process of retrieval of information from the carrier wave at receiver |
| C. Demodulation | III. Converts one form of energy into another |
| D. Repeater | IV. Loss of strength of a signal while propagating through a medium |
A stone tied to $$180$$ cm long string at its end is making $$28$$ revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is $$\frac{1936}{x}$$ m s$$^{-2}$$. The value of $$x$$ ______. [Take $$\pi = \frac{22}{7}$$]
A body of mass $$2$$ kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power $$P$$. Its displacement in $$4$$ s is $$\frac{1}{3}\alpha^2\sqrt{P}$$ m. The value of $$\alpha$$ will be ______.
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A uniform disc of mass $$0.5$$ kg and radius $$r$$ is projected with a velocity $$18$$ m s$$^{-1}$$ at $$t = 0$$ s on a rough horizontal surface. It starts off with a purely sliding motion at $$t = 0$$ s. After $$2$$ s it acquires a purely rolling motion. The total kinetic energy of the disc after $$2$$ s will be ______ J.
(given, coefficient of friction is $$0.3$$ and $$g = 10$$ m s$$^{-2}$$).
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A faulty thermometer reads $$5°$$C in melting ice and $$95°$$C in steam. The correct temperature on absolute scale will be ______ K when the faulty thermometer reads $$41°$$C.
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The velocity of a particle executing SHM varies with displacement $$(x)$$ as $$4v^2 = 50 - x^2$$. The time period of oscillations is $$\frac{x}{7}$$ s. The value of $$x$$ is ______. [Take $$\pi = \frac{22}{7}$$]
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As shown in figure, a cuboid lies in a region with electric field $$E = 2x^2\hat{i} - 4y\hat{j} + 6\hat{k}$$ N C$$^{-1}$$. The magnitude of charge within the cuboid is $$n\varepsilon_0$$ C. The value of $$n$$ is ______ (if dimension of cuboid is $$1 \times 2 \times 3$$ m$$^3$$)
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The equivalent resistance between $$A$$ and $$B$$ is ______ $$\Omega$$.
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If the potential difference between $$B$$ and $$D$$ is zero, the value of $$x$$ is $$\frac{1}{n}$$ $$\Omega$$. The value of $$n$$ is ______.
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In an ac generator, a rectangular coil of $$100$$ turns each having area $$14 \times 10^{-2}$$ m$$^2$$ is rotated at $$360$$ rev min$$^{-1}$$ about an axis perpendicular to a uniform magnetic field of magnitude $$3.0$$ T. The maximum value of the emf produced will be ______ V. [Take $$\pi = \frac{22}{7}$$]
In a Young's double slit experiment, the intensities at two points, for the path difference $$\frac{\lambda}{4}$$ and $$\frac{\lambda}{3}$$ ($$\lambda$$ being the wavelength of light used) are $$I_1$$ and $$I_2$$ respectively. If $$I_0$$ denotes the intensity produced by each one of the individual slits, then $$\frac{I_1+I_2}{I_0} =$$ ______.
A radioactive nucleus decays by two different process. The half life of the first process is $$5$$ minutes and that of the second process is $$30$$ s. The effective half-life of the nucleus is calculated to be $$\frac{\alpha}{11}$$ s. The value of $$\alpha$$ is ______.
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