Recent questions in Model Papers

Using the properties of determinants prove the following : $\begin{vmatrix}3a & -a+b & -a+c \\ a-b & 3b & c-b \\ a-c & b-c & 3c \end{vmatrix}$$=3( a+b+c)(ab+bc+ca)$

asked Feb 9, 2015 by meena.p

0 answers

Find the differential equation of the family of curves given by $y^2-2ky +x^2=k^2$

asked Feb 9, 2015 by meena.p

1 answer

Evaluate $\int \limits ^{\pi/4} _{-\pi/4} |\sin x |dx$

asked Feb 9, 2015 by meena.p

0 answers

Solve : $\int \large\frac{2 \sin x + 3 \cos x}{3 \sin x +4 \cos x }$$dx$

asked Feb 9, 2015 by meena.p

1 answer

Solve :$\int \large\frac{\sin \theta \cos \theta}{\cos ^2 \theta - \cos \theta -2}$$d \theta$

asked Feb 9, 2015 by meena.p

0 answers

A water tank has a shape of an inverted right circular cone with its axis vertical and vertex lower most. Its semi vertical angle is $\tan^{-1} (0.5)$.Water is poured into it at a constant rate of 5 cubic meter per hour. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is $4\; m$

asked Feb 9, 2015 by meena.p

2 answers

Verify Rolle's theorem for the function $f(x)= \sin x + \cos x , x \in [0,\pi/2]$

asked Feb 9, 2015 by meena.p

0 answers

A die is tossed thrice. getting an even number is considered as success . What is the variance of the binomial distribution ?

asked Feb 9, 2015 by meena.p

1 answer

Find the angle between the vectors $ \overrightarrow {a} = \hat i - \hat j$ and $\overrightarrow {b} = \hat j +\hat k$

asked Feb 9, 2015 by meena.p

1 answer

What is the integrating factor of $\large\frac{dy}{dx}$4+y \sec x =\tan x $ ?

asked Feb 9, 2015 by meena.p

1 answer

If the binary operation * on the set of integers Z, is defined by $a * b = a+3b^2$ then find the value of $8 * 3$

asked Feb 9, 2015 by meena.p

1 answer

Solve $2 \tan ^{-1} (\cos x)= \tan ^{-1} (2 cosec \;x)$

asked Feb 9, 2015 by meena.p

1 answer

Prove that $(A^{-1})'=(A')^{-1}$, where A is an invertible matrix .

asked Feb 9, 2015 by meena.p

0 answers

If $a=2$ and $b=3$ , then the value of $\bigg( \large\frac{1}{a} +\frac{1}{b}\bigg)^a $=_____

asked Jan 30, 2015 by meena.p

1 answer

State Guass’s theorem in electrostatics. Use it to obtain field strength ata distance x from an infinitely large flat charged sheet having surface charge density $\sigma$

asked Jan 30, 2015 by meena.p

0 answers

A) With the help of a labeled circuit diagram explain the rectification action of a full wave rectifier b)What are energy bands? How are these formed? Distinguish between a conductor, insulator, and a semiconductor on the basis of the energy band diagram.

asked Jan 30, 2015 by meena.p

0 answers

Sonia was watching a movie, in which he saw the automatic opening of a garage door. She was fascinated about this and asked her brother to explain about this. Even though her brother did not know much about this he decided to learn about this and explain it to Sonia. He came to know about the photoelectric effect in the automatic opening of the door. He explained about this in detail to Sonia. She thanked him for this. a) What are values of Sonia’s brother in enlightening her about the subject? b) How is photoelectric effect involved in the automatic opening of the garage door? c) Why alkali metals are most suitable for photoelectric emission?

asked Jan 30, 2015 by meena.p

0 answers

Sona was often surprised by the reproduction of sound in cinemas. She asked her uncle about this. Even though her uncle didn’t know much about this, he decided to give Sona a clear picture about the reproduction of sound in cinemas. He went to the operator of the projector of the cinema hall and learnt about this. Then he took Sona to the projector room and the operator explained about this very clearly. She thanked her uncle. A) What according to you are the values displayed by Sona’s uncle? B) What is the role of Photoelectric effect in the reproduction of sound in cinema film? C) State two different situation in which free electrons may be emitted from a surface.

asked Jan 30, 2015 by meena.p

0 answers

a) Why is Diamagnetism independent of temperature? b) State and prove tangent law in magnetism c) What happens if an iron bar is melted? Will it regain its magnetism?

asked Jan 30, 2015 by meena.p

0 answers

What are coherent sources of light? Deduce an expression for the intensity at any point on the screen in Young’s double slit experiment. What is a Polaroid? How is plane polarized light obtained with its help? How will you use it to distinguish between unpolarised light and plane polarized light.

asked Jan 30, 2015 by meena.p

0 answers

A) Calculate the equivalent resistance between the points M and N. B) Deduce Ohms’s law using the concept of drift velocity and relaxation time.

asked Jan 30, 2015 by meena.p

0 answers

A pure inductor is connected across an a.c. source. Show mathematically that the current in it lags behind the applied e.m.f by a phase angle of $\large\frac{\pi}{2}$ What is its inductive reactance? Draw a graph showing variation of inductive reactance with the frequency of the a.c. source.

asked Jan 30, 2015 by meena.p

1 answer

Explain the term FAX. Distinguish between FAX and E-Mail.

asked Jan 30, 2015 by meena.p

0 answers

The ground state energy of hydrogen atom is $-13.6\;eV$ 1.What are the potential and kinetic energy of an electron in the 3rd excited state? 2.If the electron jumps to the ground state from the third excited state, calculate the frequency of the photon emitted.

asked Jan 30, 2015 by meena.p

1 answer

a) Define ‘disintegration constant’ and ‘mean life’ of a radioactive substance. Give the unit for each. b)Obtain the amount of $^{60}Co_{27}$ necessary to provide a radioactive source of $8.0\;mCi$ strength. The half life of $^{60}Co_{27}$ is $5.3$ years.

asked Jan 30, 2015 by meena.p

0 answers

The potential difference across the collector of a transistor, used in common emitter mode is $1.5\;V,$ with the collector resistance of $3\;k \Omega.$ Find 1. The emitter and 2. The base current, if the d.c. gain of the transistor is $50$

asked Jan 30, 2015 by meena.p

1 answer

Draw a ray diagram of an astronomical telescope in the near point adjustment position, Write the expression for its magnifying power .

asked Jan 30, 2015 by meena.p

0 answers

Describe the principle construction and uses of a choke coil. A coil is represented as $z = (8+6j)\; ohm$. Calculate the inpedence of the coil.

asked Jan 30, 2015 by meena.p

0 answers

A storage battery of e.m.f of $12.0\; V$ and internal resistance $0.5 \omega$ is to be charged by a $120\;V$ d.c. supply of negligible resistance. What resistance is required in the circuit for the charging current to be $3\; A?$ What is the terminal voltage of the battery during the charging?

asked Jan 30, 2015 by meena.p

0 answers

A) Two point charges of values $q$ and $2q$ are kept at a distance d apart from each other in air. A third charge $Q$ has to be kept along the same line in such a way that the net force acting on q and $2q$ is zero. Calculate the position of charge $Q$ in terms of q and d. b)A capacitor of capacitance C is charged fully by connecting it to a battery of e.m.f ‘e’. It is then disconnected from the battery. If the separation from the plates of the capacitor is $b$ now doubled, what will be a) charge stored in the capacitor? b) potential difference across it c) field strength between the plates d) energy stored by the capacitor

asked Jan 30, 2015 by meena.p

0 answers

a) A bubble inside a glass slab appears to be at a depth of $3\;cm$ from one face and $2\;cm$ from opposite face. If $\mu= 1.5,$ what is the actual thickness of the slab? b) An astronomical telescope consists of two thin lenses set $36\;cm$ apart and has a magnifying power of $8$. Calculate the focal lengths of the lenses.

asked Jan 30, 2015 by meena.p

0 answers

(A) Draw a labeled diagram to show the formation of the image of a distant object through a reflecting telescope (B) A converging lens has a focal length of $20\; cm$ in air. It is made of refractive index $1.6$. If it is immersed in a liquid of refractive index $1.3,$ what will be its new focal length?

asked Jan 30, 2015 by meena.p

0 answers

A metal has a threshold wavelength of $6000 ^{\circ} A$. Calculate its 1) threshold frequency and 2) work function of the metal in eV.

asked Jan 29, 2015 by meena.p

1 answer

Prove that an ideal capacitor , in an a.c. circuit does not dissipate power.

asked Jan 29, 2015 by meena.p

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Define $\alpha$ and $\beta$ of a transistor. How are they related?

asked Jan 29, 2015 by meena.p

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A)Name any two modes of modulation used for pulsed waves. B) What is the order of energy gap in an insulator?

asked Jan 29, 2015 by meena.p

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The sequence of the stepwise decay of radio active nucleus is If the nucleon number and atomic number for $D_2$ are respectively 176 and 71, what are the corresponding values for D and $D_4$ nuclei? Justify your answer.

asked Jan 29, 2015 by meena.p

0 answers

Name two factors on which the resisitivity of a given material depends. A carbon resistor has a value of 62 KΩ with a tolerance of 5%. Give the color code of this resistor.

asked Jan 29, 2015 by meena.p

0 answers

A straight wire of length of $1.5\;m$ and mass $200\;g$ carries a current of $2A$. It is suspended in mid-air by a uniform horizontal magnetic field B. What is the magnitude of the magnetic field?

asked Jan 29, 2015 by meena.p

0 answers

State Lenz’s law. On which law of conservation is it based?

asked Jan 29, 2015 by meena.p

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What is the de-Broglie wavelength of an electron accelerated from rest through a potential difference of V volts?

asked Jan 29, 2015 by meena.p

0 answers

How does the electric field of an electric dipole vary with distance?

asked Jan 29, 2015 by meena.p

0 answers

What is the ratio of infra red rays to ultra violet rays in vaccum?

asked Jan 29, 2015 by meena.p

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Why are microwaves used in Radar?

asked Jan 29, 2015 by meena.p

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Why does the acceleration of a magnet falling through a long solenoid decrease?

asked Jan 29, 2015 by meena.p

0 answers

Draw a circuit diagram and explain the operations of a transistor as a switch .

asked Jan 28, 2015 by meena.p

0 answers

(a)Draw a circuit diagram of an n-p-n transmitter with its emitter base function forward biased and base collector junction reverse biased. Describe briefly its properties (b) Explain how a transistor in active state exhibits a low resistance at its emitter base junction and high resistance at its base collector junction .

asked Jan 28, 2015 by meena.p

1 answer

a) Explain the formation of depletion layer and barrier potential in a P-n junction . (b) With the help of a labelled circuit diagram explain the use of P-n junction diode as a full wave rectifier. Draw the input and out put waveform

asked Jan 28, 2015 by meena.p

0 answers

a)Draw a ray diagram for formation of images of a point object by a thin double convex lens having radii of curvatures $R_1$ and $R_2$ and hence derive lens makers formula. b) Define power of a lens and give its S.I units . If a convex lens of length 50 cm is placed in contact coaxially with a concave lens of focal length 20 cm , what is the power of the combination ?

asked Jan 28, 2015 by meena.p

0 answers

An angular magnification (managing power) of 30 X is descibed using an objective of focal length $1.25\;cm$ and an eyepiece of focal length $5\;cm$ . how will you set up the compound microscope.

asked Jan 28, 2015 by meena.p

0 answers

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