Recent questions tagged 2016

Draw a ray diagram showing the geometry of formation of image of a point object situated on the principal axis and on the convex side of a spherical surface of radius of curvature R. Taking the rays as incident from a rarer medium of refractive index $n_1$ to a denser medium of refractive index $n_2$ derive the relation. $\large\frac{n_@}{v} -\frac{n_1}{u} = \frac{n_2-n_1}{R}$, Where symbols have their usual meaning ? (ii) Explain briefly how the focal length of a convex lens changes with increase in wave length of incident light . (iii) What happens to the focal length of convex lens when it is immersed in water ? Refractive index of the material of lens is greater than water .

asked Jun 9, 2016 by meena.p

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When a parallel beam of monochromatic source of light of wave length incident on a single slit of width, show how the diffraction pattern is formed at the screen by the interference of the wavelets from the slit.

asked Jun 9, 2016 by meena.p

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(a) Consider a beam of charged particles moving with varying speeds.Show how crossed electric and magnetic fields can be used to select charged particles of a particular velocity ? (b) Name another device / machine do and what are the functions of magnetic and electric fields in this machine ? Where do these exists in this machine ? Write about their natures .

asked Jun 9, 2016 by meena.p

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Express Biot-savart law in the vector form. (ii) Use it to obtain the expression for the magnetic field at an axial point, distance d from the center , of a circular coil of radius R carrying current I. (iii) Also , find the ratio of the magnitudes of the magnetic field of this coil at the center at an axial point for which $x= R\sqrt 3$

asked Jun 9, 2016 by meena.p

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During a thunderstorm the 'live' wire of the transmission line fell down on the ground from the poles in the street. A group of boys, who passed through,noticed it and some of them wanted to place the wire by the side. As they were approaching the wire and trying to lift the cable, Anuj noticed it and immediately pushed them away, thus preventing them from touching the live wire. During pushing some of them got hurt. Anuj took them to a doctor to get them medical aid. Based on the above paragraph, answer the following questions : (a) Write the two values which Anuj displayed during the incident. (b) Why is it that a bird can sit on a suspended 'live' wire without any harm whereas touching it on the ground can give a fatal shock ? (c) The electric power from a power plant is set up to a very high voltage before transmitting it to distant consumers. Explain, why.

asked Jun 9, 2016 by meena.p

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Derive an expression for the electric field intensity at a point on the equatorial line of an electric dipole moment $\overrightarrow{P}$ and length 2a. What is the direction of this field ?

asked Jun 9, 2016 by meena.p

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(i) Name the phenomenon on which the working of an optical fiber is based ? (ii) What are the necessary condition for this phenomenon to occur ?

asked Jun 9, 2016 by meena.p

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(i) For a glass prism $(\mu = \sqrt 3 )$ the angle of minimum deviation is equal to the angle of the prism. Calculate the angle of the prism . (ii) Draw ray diagram when incident ray falls normally on one of the two equal sides of a right angled isosceles prism having refractive index $\mu = \sqrt 3$

asked Jun 8, 2016 by meena.p

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(a)Define the term "intensity of radiation " in photon picture. (b) . plot a graph showing the variation of photo current vs collector potential for three different intensities $I_1 > I_2 > I_3$, two of which $(I_1$ and $I_2)$ have the same frequency v and the third has frequency $v_1 > v$ (c) Explain the nature of the curves on the basis of Einstein's equation .

asked Jun 8, 2016 by meena.p

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Draw a circuit diagram of a common emitter amplifier using n-p-n transistor . Derive an expression for the current gain $\beta _{ac}$

asked Jun 8, 2016 by meena.p

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Plot a graph showing the variation of binding energy per nucleon as a function of mass number. Which property of nuclear force explains the approximate constancy of binding energy in the range $30 < A < 170$ ? How does one explain the release of energy in both the processes of nuclear fission from the graph ?

asked Jun 8, 2016 by meena.p

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Plot a graph showing the variation of binding energy per nucleon as a function of mass number. Which property of nuclear force explains the approximate constancy of binding energy in the range $30 < A < 170$ ? How does one explain the release of energy in both the processes of nuclear fission from the graph ?

asked Jun 8, 2016 by meena.p

1 answer

Derive an expression for the axial magnetic field of a finite solenoid of length 2l and radius r carrying current I. Under what condition does the field become equivalent to that produced by a bar magnet ?

asked Jun 8, 2016 by meena.p

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(i) Mention two properties of soft iron due to which is preferred for making an electromagnet ? (ii) State Gauss's law in magnetism. How is it different from Gauss's law in electrostatics and why ?

asked Jun 8, 2016 by meena.p

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Three identical capacitors each of capacitance $3 \mu F$ are connected in term in series and in parallel combination to the common source of V volt . find out the ratio of the energies stored in two configurations.

asked Jun 7, 2016 by meena.p

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A parallel plate capacitor $(C_1)$ having charge Q is connected to an identical uncharged capacitor $C_2$ in series. What would be the charge accumulated on the capacitor $C_2$?

asked Jun 7, 2016 by meena.p

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Mention any three applications of the internet. explain one of these in detail .

asked Jun 7, 2016 by meena.p

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A capacitor of unknown capacitance,a resistor of $100 \Omega$ and an inductor of self inductance $L= (4/\pi ^2)$ hentry are connected in series to an ac source of 200 V and 50 Hz. Calculate the value of the capacitance and impedance of the circuit When the current is in phase with the voltage. Calculate the power dispersal in the circuit .

asked Jun 7, 2016 by meena.p

1 answer

(i) Explain briefly the process of emanation of light by light emitting Diode (LED). (ii) Which semiconductor are provided to make LED and why ? (iii) Give two advantages of using LED over conventional incandescent lamps

asked May 30, 2016 by meena.p

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Two harmonic waves of monochromatic light : $y_1$ = n const and $y_2 =a \cos (wt + \phi)$ are superimposed on each other. Show that maximum intensity in interference pattern is four times the intensity due to each slit. Hence write the condition for constructive and destructive interference in terms of the phase angle $\phi $

asked May 30, 2016 by meena.p

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What is electrostatic shielding ? . How is this properly used in actual practice ? Is the potential in the cavity of a charged conductor zero ?

asked May 30, 2016 by meena.p

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Write briefly the underlying principle used in Davison - germer experiment to verify wave nature of electron experimentally. What is the de- Broglie wavelength of an electron with kinetic energy (K.E) 120 eV?

asked May 30, 2016 by meena.p

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State two properties of electromagnetic waves.How can we show that em waves carry momentum ?

asked May 30, 2016 by meena.p

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Write the functions of a (i) transducer and (ii) repeater in a communication system.

asked May 30, 2016 by meena.p

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The energy levels of a hypothetical atom are shown below. Which of the shown transitions will result in the emission of photon wave length.

asked May 30, 2016 by meena.p

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In the ground state of hydrogen atom, its Bohr radius is given as $5.3 \times 10^{-11}\;m$ . The atom is excited such that the radius becomes $21.2 \times 10^{-11}\;m$ . Find (i) the value of the principal quantum number and (ii) the total energy of the atom in this excited state.

asked May 30, 2016 by meena.p

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The power factor of an a.c circuit is 0.5 . What is the phase difference between voltage and current in the circuit ?

asked May 30, 2016 by meena.p

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In which situation is there a displacement current but no conduction current ?

asked May 30, 2016 by meena.p

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Define the term relaxation time in a conductor .

asked May 30, 2016 by meena.p

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Two wires one of copper and other of manganin have same resistance and equal length. Which wire is thicker and why ?

asked May 30, 2016 by meena.p

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Name of the logic gates marked P and Q in the given circuit

asked May 30, 2016 by meena.p

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Three numbers are selected at random (with out replacement ) from first six positive integers. If X denotes the smallest of the three numbers obtained , find the probability distribution of X.Also find the mean and variance of the distribution .

asked May 30, 2016 by meena.p

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A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods $ F_1 \: and F_2$ are available . Food $ F_1 $ costs Rs. 4 perunit and $ F_2$ costs Rs. 6 per unit. One unit of food $ F_1 $ contains 3 units of vitamin A and 4 units of minerals. One unit of food $ F_2 $ contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem and find graphically the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

asked May 30, 2016 by meena.p

1 answer

Find the equation of the plane containg two parallel lines $ \large\frac{x-1}{2} = \frac{y+1}{-1} = \frac{z}{3} $ and $\large\frac{x}{4} = \frac{y-2}{-2} =\frac{z+1}{6}$ . Also find the plane thus obtained contains the line $ \large\frac{x-2}{3} =\frac{y-1}{1} =\frac{z-2}{5}$ or not .

asked May 30, 2016 by meena.p

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Using integration find the area of the region $f(x,y): y^2 \leq 6ax$ and $ x^2+y^2 \leq 16a^2$

asked May 30, 2016 by meena.p

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Find the maximum and minimum values of $f(x)=\sec x + \log \cos ^2x, 0 < x < 2 \pi$

asked May 30, 2016 by meena.p

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Determine the intervals in which the function $f(x)=x^4 -8x^3+22x^2-24 x +21$ is strictly increasing or strictly decreasing.

asked May 30, 2016 by meena.p

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Using of elementary row operations, find the inverse of the following matrix : $\begin{bmatrix} 2 & -1 & 3\\ -5 & 3 & 1\\-3 & 2 & 3\end{bmatrix}$

asked May 30, 2016 by meena.p

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Using properties of determinant prove that : $\begin{bmatrix}(b+c)^2 & a^2 & bc \\ (c+a)^2 & b^2 & ca \\ (a+b)^2 & c^2 & ab \end{bmatrix}$ $=(a-b)(b-c)(c-a) (a+b+c)(a^2+b^2+c^2)$

asked May 30, 2016 by meena.p

1 answer

Find the coordinates of the point where the line $ \overrightarrow {r} =(-\hat {i} - 2 \hat {j} - 3 \hat {k} )+ \lambda ( 3\hat i + 4 \hat j +3 \hat k )$ meets the plane which is perpendicular to the vector $ \overrightarrow n= \hat i + \hat j + 3 \hat k$ and at a distance of $\large\frac{4}{\sqrt {11}}$ from origin .

asked May 30, 2016 by meena.p

1 answer

Find the equation of plane passing through the point $A(3,2,1,) B(4,2,-1)$ and $C(6,5,-1)$ and $D(\lambda,5,5)$ are co planar

asked May 30, 2016 by meena.p

1 answer

Given that vectors $ \overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ from a triangle such that $\overrightarrow{a} = \overrightarrow{b}+ \overrightarrow{c}$. Find p,q,r,s such that area of triangle is $ 5 \sqrt 6$ where $\overrightarrow{a} = p \hat i +q \hat j +r \hat k$ ,$\overrightarrow{b} = s \hat i +3 \hat j +4 \hat k$ and $\overrightarrow{c} = 3 \hat i + \hat j -2 \hat k$

asked May 30, 2016 by meena.p

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There are two bags A and B . Bag A contains 3 white and 4 red balls whereas bag B contains 4 white and 3 red balls . Three balls are drawn at random ( with out replacement ) from one of the bags and are found to be two white and one red. Find the probability that these were drqwn from bag B.

asked May 30, 2016 by meena.p

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Solve the equation for $x: \cos ( \tan ^{-1} x ) = \sin \bigg( \cot ^{-1} \large\frac{3}{4}\bigg)$

asked May 27, 2016 by meena.p

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Prove that $ 2\sin ^{-1} \bigg( \large\frac{3}{5} \bigg) - \tan ^{-1} \bigg(\large\frac{17}{31} \bigg) = \large\frac{\pi}{4}$

asked May 27, 2016 by meena.p

1 answer

Ishan wants to donate a rectangular plot of land for a land for a school in his village . When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same. but if length is decreased by 10 m and breadth is decreased by 20 m. then its area will decrease by $5300\;m^2$ . Using matrices , find the dimension of the plot. Also give reasons why he wants to denote the plot for a school.

asked May 27, 2016 by meena.p

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Solve the differential equation : $ 2ye^{x/y} dx+ (y -2x e^{x/y})dy=0$

asked May 27, 2016 by meena.p

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Solve the differential equation : $(x+1)\large\frac{dy}{dx}$$-y =e^{3x}(x+1)^3$

asked May 27, 2016 by meena.p

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Evaluate : $\int \limits_0^1 \cot ^{-1} (1-x+x^2)dx$

asked May 27, 2016 by meena.p

1 answer

Evaluate: $ \int \limits_0^{\large\frac{\pi}{2}} \large\frac{sin ^2 x}{\sin x + \cos x}$$dx$

asked May 27, 2016 by meena.p

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