What will be the a vs x graph for the following graph?

The driver of a car travelling with speed $$30 \mathrm{~ms}^{-1}$$ towards a hill sounds a horn of frequency $$600 \mathrm{~Hz}$$. If the velocity of sound in air is $$330 \mathrm{~ms}^{-1}$$, the frequency of reflected sound as heard by driver is :

An interference pattern is observed by Young’s double slit experiment. If now the separation between coherent source is halved and the distance of screen from coherent sources

Two capacitors $$C$$ and $$\frac{C}{2}$$ are connected to a battery of $$V$$ volts, as shown below

The work done in charging both the capacitors fully is

A series R-C circuit is connected to AC voltage source. Consider two cases; (A) When C is without a dielectric medium and (B) When C is filled with dielectric of constant 4. The current I$$_R$$ through the resistor and voltage V$$_C$$ across the capacitor are compared in two cases.

A space ship is launched into a circular orbit close to earth’s surface. What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull?

(Radius of earth = 6400 km, g = 9.8 m/s$$^2$$)

A force $$\mathbf{F}=-k(y \hat{\mathbf{i}}+x \hat{\mathbf{j}})$$ where $$k$$ is a positive constant, acts on a particle moving in the $$x y$$ plane. Starting from the origin, the particle is taken along the positive $$x$$-axis to the point $$(a, 0)$$ and then parallel to the $$y$$-axis to the point $$(a, a)$$. The total work done by the force on the particle is

With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is $$2 / 3$$ of the weight?

Four blocks of same mass connected by strings are pulled by a force $$F$$ on a smooth horizontal surface as shown in figure. The tension $$T_1, T_2$$ and $$T_3$$ will be

What is the maximum height attained by a body projected with a velocity equal to one-third of the escape velocity from the surface of the earth? (Radius of the earth $$=R$$ )

A block is dragged on a smooth plane with the help of a rope which moves with a velocity v as shown in the figure. The horizontal velocity of

A tube of sugar solution $$20 \mathrm{~cm}$$ long is placed between crossed nicols and illuminated with light of wavelength $$6 \times 10^{-5} \mathrm{~cm}$$. If the optical rotation produced is $$13^{\circ}$$ and the specific rotation is $$65^{\circ}$$, determine the strength of the solution.

A long wire having a semicircular loop of radius r carries a current i as shown in figure. The magnetic induction at the centre O due to entire

Two satellites $$S_1$$ and $$S_2$$ are revolving round a planet in coplanar circular orbits of radii $$r_1$$ and $$r_2$$ in the same direction, respectively. Their respective periods of revolution are $$1 \mathrm{~h}$$ and $$8 \mathrm{~h}$$. The radius of orbit of satellite $$S_1$$ is equal to $$10^4 \mathrm{~km}$$. What will be their relative speed (in $$\mathrm{km} / \mathrm{h}$$) when they are closest?

A body of mass $$4 \mathrm{~kg}$$ moving with velocity $$12 \mathrm{~m} / \mathrm{s}$$ collides with another body of mass $$6 \mathrm{~kg}$$ at rest. If two bodies stick together after collision, then the loss of kinetic energy of system is

The coefficient of cubical expansion of mercury is $$0.00018 /{ }^{\circ} \mathrm{C}$$ and that of brass $$0.00006 /{ }^{\circ} \mathrm{C}$$. If a barometer having a brass scale were to read $$74.5 \mathrm{~cm}$$ at $$30^{\circ} \mathrm{C}$$, find the true barometric height at $$0^{\circ} \mathrm{C}$$. The scale is supposed to be correct at $$15^{\circ} \mathrm{C}$$.

The particle of mass $$m$$ is moving in a circular path of constant radius $$r$$ such that its centripetal acceleration $$a_c$$ is varying with time $$t$$ as $$a_c=k^2 r t^2$$, where $$k$$ is a constant. The power delivered to particle by the forces acting on it is

A body of mass $$5 \times 10^{-3} \mathrm{~kg}$$ is launched upon a rough inclined plane making an angle of $$30^{\circ}$$ with the horizontal. Obtain the coefficient of friction between the body and the plane if the time of ascent is half of the time of descent.

A boy is pushing a ring of mass $$3 \mathrm{~kg}$$ and radius $$0.6 \mathrm{~m}$$ with a stick as shown in figure. The stick applies a force of $$3 \mathrm{~N}$$ on the ring and rolls it without slipping with an acceleration of 0.4 m/s$$^2$$. The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is $$\frac{F}{10}$$. The value of $$F$$ is

A load of mass $m$ falls from a height $$h$$ on the scale pan hung from a spring as shown. If the spring constant is $$k$$ and mass of the scale pan is zero and the mass $$m$$ does not bounce relative to the pan, then the amplitude of vibration is

In an experiment to measure the height of a bridge by dropping stone into water underneath. If the error in measurement of time is $$0.2 \mathrm{~s}$$ at the end of $$4 \mathrm{~s}$$, then the error in estimation of height of bridge will be (neglect the water resistance, i.e. thrust)

A conductor lies along the z-axis at $$-1.5 \leq Z \leq 1.5 \mathrm{~m}$$ and carries a fixed current of 10.0 $$\mathrm{A}$$ in $$-a_z$$ direction as shown in figure for a field $$B=3 \times 10^{-4} e^{-0.2 x} a_y \mathrm{~T}$$, the total power required to move the conductor at constant speed to $$x=2.0 \mathrm{~m}, y=0 \mathrm{~m}$$ in $$5 \times 10^{-3} \mathrm{~s}$$ is (Assume parallel motion along the $$x$$-axis)

A lens of refractive index $$\mu$$ is put in a liquid of refractive index $$\mu^{\prime}$$. If the focal length of lens in air is $$f$$, then its focal length in liquid will be

A parallel plate capacitor has an electric field of $$10^5 \mathrm{~Vm}^{-1}$$ between the plates. If the charge on the capacitor plates is $$1 \mu \mathrm{C}$$, the force on each capacitor plate is

In the given figure, the angle of reflection is

A person of weight $$70 \mathrm{~kg}$$ wants to loose $$7 \mathrm{~kg}$$ by going up and down $$12 \mathrm{~m}$$ high stairs. Assume he burns twice as much fat while going up than going down. If $$1 \mathrm{~kg}$$ of fat is burnt on expending 9000 k-cal. How many times must he go up and down to reduce his $$7 \mathrm{~kg}$$ weight?

(Take $$g=10 \mathrm{~ms}^{-2}$$)

The current gain of a transistor in common emitter mode is 49. The change in collector current and emitter current corresponding to change in base current by $$5.0 \mu \mathrm{A}$$, will be

A cylindrical conductor AB of non-uniform area of cross-section carries a current of 5A. The radius of the conductor at one end A is 0.5 cm. The current density at the other end of the conductor is half of the value at A. The radius of the conductor at the end B is nearly

One mole of an ideal diatomic gas undergoes transition from A to B along a path AB as shown below.

The change in internal energy of the gas during the transition is

A nuclear explosive is designed to deliver $$1 \mathrm{~MW}$$ power in the form of heat energy. If the explosion is designed with nuclear fuel consisting of $$U^{235}$$ to run a reactor at this power level for one year, then the amount of fuel needed is (Given energy per fission is $$200 \mathrm{~MeV}$$)

A thin prism $$P_1$$ of angle $$4^{\circ}$$ and refractive index 1.54 is combined with another prism $$P_2$$ of refractive index 1.72 produce dispersion without deviation, the angle of $$P_2$$ is

The effective resistance between p and q in given figure is

Charges $$+q$$ and $$-q$$ are placed at points $$A$$ and $$B$$ respectively which are a distance $$2 L$$ apart, $$C$$ is the mid-point between $$A$$ and $$B$$. The work done in moving a charge $$+Q$$ along the semicircle $$C R D$$ is

In the given figure, $$C$$ is middle point of line $$S_1 S_2$$. A monochromatic light of wavelength $$\lambda$$ is incident on slits. The ratio of intensities of $$S_3$$ and $$S_4$$ is

A simple telescope, consisting of an objective of focal length $$60 \mathrm{~cm}$$ and a single eye lens of focal length $$5 \mathrm{~cm}$$ is focused on a distant object in such a way that parallel rays emerge from the eye lens. If the object subtends an angle of $$2^{\circ}$$ at the objective, the angular width of the image is

A specimen of silicon is to be made $$P$$-type semiconductor for this one atom of indium, on an average, is doped in $$5 \times 10^7$$ silicon atoms. If the number density of silicon is $$5 \times 10^{22}$$ atom/$$\mathrm{m}^3$$ then the number of acceptor atoms per $$\mathrm{cm}^3$$ will be

The angle of dip, if dip needle oscillating in vertical plane makes 40 oscillations per min in a magnetic meridian and 30 oscillations per minute in vertical plane at right angle to the magnetic meridian is

Two batteries, one of emf $$18 \mathrm{~V}$$ and internal resistance $$2 \Omega$$ and the other of emf $$12 \mathrm{~V}$$ and internal resistance $$1 \Omega$$ are connected as shown. The voltmeter $$V$$ will record a reading of

The Young's double slit experiment is performed with blue and green light of wavelengths 4360 Å and 5460 Å respectively. If $$x$$ is the distance of 4th maxima from the central one, then

A proper combination of $$3 \mathrm{NOT}$$ and 1 NAND gates is shown. If $$A=0, B=1, C=1$$, then the output of this combination is

Assertion : For looping a vertical loop of radius, $$r$$ the minimum velocity at lowest point should be $$\sqrt{5 g r}$$.

Reason : In this event the velocity at the highest point will be zero.

Assertion : A beam of charged particles is employed in the treatment of cancer.

Reason : Charged particles on passing through a material medium lose their energy by causing ionization of the atoms along their path.

Assertion : A spring of force constant $k$ is cut into two pieces having lengths in the ratio 1 : 2. The force constant of series combination of the two parts is $$\frac{3 k}{2}$$.

Reason : The spring connected in series are represented by $$k=k_1+k_2$$

Assertion : The total kinetic energy of a rolling solid sphere is the sum of translational and rotational kinetic energies.

Reason : For all solid bodies, total kinetic energy is always twice of translational kinetic energy.

Assertion : In He-Ne laser, population inversion takes place between energy levels of neon atoms.

Reason : Helium atoms have a metastable energy level.

Assertion : It is hotter over the top of a fire than at the same distance on the sides.

Reason : In the upward direction, the heat propagate through convection.

Assertion : The average value of alternating emf is $$63.39 \%$$ of the peak value.

Reason : The rms value of alternating emf is $$70.72 \%$$ of peak value.

Assertion : Photoelectric effect can take place only with an electron bound in the atom.

Reason : Electron is a fermion whereas proton is a boson.

Assertion : When $$\theta=45^{\circ}$$ or $$135^{\circ}$$, the value of $$R$$ remains the same, only the sign changes.

Reason : $$R=\frac{u^2 \sin 2 \theta}{g}$$

Assertion : In adiabatic expansion the product of $$p$$ and $$V$$ always decreases.

Reason : In adiabatic expansion process, work is done by the gas at the cost of internal energy of gas.

Assertion : Cyclotron does not accelerate electron.

Reason : Mass of the electron is very small.

Assertion : The electric field due to a dipole on its axis line at a distance $$r$$ is $$E$$. Then, electric field due to the same dipole on the equatorial line and at the same distance will be $$E / 2$$.

Reason : Electric field due to dipole varies inversely as the square of the distance.

Assertion : A potentiometer is preferred over that of a voltmeter for measurement of emf of a cell.

Reason : Potentiometer does not draw any current from the cell.

Assertion : The magnetism of magnet is due to the spin motion of electrons.

Reason : Dipole moment of electron is smaller than that due to orbit motion around nucleus.

Assertion : The mirror used in search lights are parabolic and not concave spherical.

Reason : In concave spherical mirror, the image formed is always virtual.

Assertion : The molecules of a monoatomic gas has three degrees of freedom.

Reason : The molecules of diatomic gas has five degrees of freedom.

Assertion : Corpuscular theory fails in explaining the velocities of light in air and water.

Reason : According to corpuscular theory is that light should travel faster in denser media than rarer media.

Assertion : In $$\alpha$$-decay atomic number of daughter nucleus reduces by 2 units from the parent nucleus.

Reason : An $$\alpha$$-particle carries four units of mass.

Assertion : Angle of deviation depends on the angle of prism.

Reason : For thin prism $$\delta=(\mu-1) A$$

Where $$\delta=$$ angle of deviation, $$\mu=$$ refractive index, $$A=$$ angle of prism

Assertion : Molar heat capacity cannot be defined for isothermal process.

Reason : In isothermal process $$p$$-$$V$$ versus $$T$$ graph is a dot.