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Recent questions tagged jeemain

Let $ABC$ be a triangle such that $\angle ACB=\large\frac{\pi}{6}$.Let $a,b$ and $c$ denote the lengths of the sides opposite to $A,B$ and $C$ respectively.The value of $x$ for which $a=x^2+x+1,b=x^2-1$ and $c=2x+1$ is

asked Nov 18, 2013 by sreemathi.v

1 answer

Two sides of a $\Delta$le are given by the roots of the equation $x^2-2\sqrt 3x+2=0$,The angle between the sides is $\large\frac{\pi}{3}$.The perimeter of the triangle is

asked Nov 18, 2013 by sreemathi.v

1 answer

Find the maximum and minimum value of $\sin^6x+\cos^6x$

asked Nov 18, 2013 by sreemathi.v

1 answer

The value of $x$ where $d>0$ and $\tan[\sec^{-1}\big(\large\frac{1}{x}\big)]=$$\sin(\tan^{-1}2)$ is

asked Nov 18, 2013 by sreemathi.v

1 answer

If $\cot^{-1}(\sqrt{\cos\alpha})-\tan^{-1}(\sqrt{\cos\alpha})=x$ then $\sin x$ is equal to

asked Nov 18, 2013 by sreemathi.v

1 answer

$ABC$ is a triangle with $\angle A=30^{\large\circ}$ $BC=10$cm.The area of the circumcircle of the $\Delta$le is?

asked Nov 18, 2013 by sreemathi.v

1 answer

The circumradius of the $\Delta$le whose sides are $13,12\; and\; 5 \;is$?

asked Nov 18, 2013 by sreemathi.v

1 answer

Two sides of $\Delta$le are $\sqrt 2-1$ and $\sqrt 2+1$ unit and their included angle is $60^{\large\circ}$.Then the third side of the $\Delta$le is

asked Nov 18, 2013 by sreemathi.v

1 answer

The number of values of $x$ in $[0,2\pi]$ satisfying the equation $3\cos 2x-10\cos x+7=0$ is?

asked Nov 18, 2013 by sreemathi.v

1 answer

The solution of the equation $4\sin^4x+\cos^4x=1$ is

asked Nov 18, 2013 by sreemathi.v

1 answer

The number of values of $x$ in the interval $[0,3\pi]$ .Satisfying the equation $2\sin^2x+5\sin x-3=0$ is

asked Nov 18, 2013 by sreemathi.v

1 answer

Four charges of magnitude - 'Q' are placed at the four corners of a square and a charge 'q' is at its centre. If the system is in equilibrium the value of 'q' is :

asked Nov 17, 2013 by thanvigandhi_1

1 answer

The plates in a parallel plate capacitor are seperated by a distance 'd' with air as a medium between the plates. In order to increase the capacity by 66%, a dielectric slab of dielectric constant '5' is introduced between the plates. What is the thickness of the dielectric slab ?

asked Nov 17, 2013 by thanvigandhi_1

1 answer

A short bar magnet is arranged with its North pole pointing geographical North. It is found that the horizontal component of Earth's magnetic induction ($B_H$) is balanced by the magnetic induction of the magnet at a point which is at a distance of 20 cm from its center . The magnetic moment of the magnet is : $( If \: B_H = 4 \times 10^{-5}\: Wb\: m^{-2})$:

asked Nov 17, 2013 by thanvigandhi_1

1 answer

A short magnet oscillating in vibration magnetometer with a frequency 10 Hz . A downward current of 15 A is established in a long vertical wire placed 20 cm to the west of the magnet. The new frequency of the short magnet is : ( The horizontal component of earth's magnetic field is 12 $ \mu$ T)

asked Nov 17, 2013 by thanvigandhi_1

1 answer

If the ratio of maximum and minimum intensities of an interference pattern is 36 : 1, then the ratio of amplitudes of the two interfering waves will be :

asked Nov 17, 2013 by thanvigandhi_1

1 answer

A thin prism of angle $ 6^{\circ}$ made up of glass of refractive index 1.5 is combined with another prism made up of glass of refractive index 1.75 to produce dispersion without deviation. The angle of second prism is :

asked Nov 17, 2013 by thanvigandhi_1

1 answer

The magnification produced by an astronomical telescope for normal adjustment is 10 and the length of the telescope is 1.1 m. The magnification, when the image is formed at least distance of distinct vision is :

asked Nov 17, 2013 by thanvigandhi_1

1 answer

A ray of light travels from an optically denser medium towards rarer medium. The critical angle for the two media is 'C'. The maximum possible angle of deviation of the ray is :

asked Nov 17, 2013 by thanvigandhi_1

1 answer

A sound wave travels with a velocity of $ 300\: ms^{-1}$ through a gas. 9 beats are produced in 3 sec when two waves pass through it simultaneously. If one of the waves has 2 m wavelength, the wavelength of the other wave is :

asked Nov 17, 2013 by thanvigandhi_1

1 answer

A source of sound producing wavelength of 50 cm is moving away from stationary observer with $ \large\frac{1}{5}th $ speed of sound. Then, what is the wavelength of sound heard by observer ?

asked Nov 17, 2013 by thanvigandhi_1

1 answer

A cylinder of radius 'R' made of material of coefficient of thermal conductivity $'k_1'$ is surrounded by a cylindrical shell of inner radius 'R' and outer radius 2 R made of a material of coefficient of thermal conductivity $'k_2'$ . The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in the steady state. The effective coefficient of thermal conductivity of the system is :

asked Nov 17, 2013 by thanvigandhi_1

1 answer

A lead bullet of unknown mass is fired with a speed of $ 180 \: ms^{-1}$ into a tree in which it stops. Assuming that in this process two third of heat produced goes into the bullet and one third into wood. The temperature of the bullet raises by : ( Specific heat of lead $= 0.120 \: Jg^{-1\circ}C^{-1}$)

asked Nov 17, 2013 by thanvigandhi_1

1 answer

One mole of an ideal gas ( y = 1.4 ) is adiabatically compressed so that its temperature rises from $ 27^{\circ} C \: to \: 35^{\circ}C$. The change in the internal energy of the gas is $(R=8.3\: J \: mol^{-1}K^{-1}$) :

asked Nov 17, 2013 by thanvigandhi_1

1 answer

The pressure P for a gas is plotted against its absolute temperature T for two different volumes $V_1\: and \: V_2$ where $ V_1 > V_2$ . If P is plotted on $y$ - axis and T on $x$ - axis then :

asked Nov 17, 2013 by thanvigandhi_1

1 answer

An ideal gas is initially at temperature T and volume V. Its volume is increased by $ \Delta V$ due to an increase in temperature $ \Delta T$ , pressure remaining constant. The physical quantity $ \delta = \large\frac{\Delta V}{V \Delta T}$ varies with temperature as :

asked Nov 17, 2013 by thanvigandhi_1

1 answer

A tank of height 5 m is full of water. There is a hole of cross sectional area $1\: cm^2$ in its bottom. The value of water that will come out from this hole per second is ($ g = 10 m/s^2$)

asked Nov 16, 2013 by thanvigandhi_1

1 answer

A spherical liquid drop of diameter D breaks up to n identical spherical drops. If the surface tension of the liquid is $' \sigma'$ is , the change in energy in this process is :

asked Nov 16, 2013 by thanvigandhi_1

1 answer

A 4.0 m long copper wire of cross sectional area $ 1.2 \: cm^2$ is stretched by a force of $ 4.8 \times 10^3N$ If Young's modulus for copper is $ Y = 1.2 \times 10^{11}\: N/m^2$ , the increase in length of wire and strain energy stored per unit volume are :

asked Nov 16, 2013 by thanvigandhi_1

1 answer

A mass M is suspended from a light spring. An additional mass m is added, displaces the spring further by a distnce 'x'. Now the combined mass will oscillate with a period :

asked Nov 16, 2013 by thanvigandhi_1

1 answer

The period of revolution of Jupiter around the sun is 12 times the period of revolution of the earth around the sun. The distance between the Jupiter and sun is n times the distance between the earth and sun. Then the value of n is :

asked Nov 16, 2013 by thanvigandhi_1

1 answer

The radius of gyration of a solid sphere of radius R about a certain axes is also equal to R. If r is the distance between the axes and the centre of a sphere , then r is equal to

asked Nov 16, 2013 by thanvigandhi_1

1 answer

PQR is a right angled triangular plate of uniform thickness as shown in the figure. If $ I_1, I_2 \: and \: I_3$ are moments of Inertia about PQ, QR and PR axes respectively, then :

asked Nov 16, 2013 by thanvigandhi_1

1 answer

A car is travelling along a curved road of radius r. If the coefficient of friction between the tyres and the road is $ /mu$ , the car will skid if its speed exceeds :

asked Nov 16, 2013 by thanvigandhi_1

1 answer

Two particles A and B initially at rest move towards each other under a mutual force of attraction. At the instant when the velocity of A is V and that of B is 2 V , the velocity of centre of mass of the system is :

asked Nov 16, 2013 by thanvigandhi_1

1 answer

A sphere of mass m moving with constant velocity hits another stationary sphere of the same mass. If 'e' is the coefficient of restitution, then the ratio of velocities of the two spheres after the collision will be :

asked Nov 16, 2013 by thanvigandhi_1

1 answer

The kinetic energy energy K of a particle of mass 'm' moving along a circle of radius 'R' depends on distance covered 'S' as $K =AS^2$. Then the acceleration of particle is given by :

asked Nov 16, 2013 by thanvigandhi_1

1 answer

Given $NaSO_4.10H_2O (s) \rightleftharpoons NaSO_4 (s) + 10H_2O (g) ; K_p =4.08 \times 10^{-25} $ and vapour pressure of water at $0^\circ$C = 4.58 Torr. At what relative humidity will $Na_2SO_4$ be deliquescent when exposed to the air at $0^\circ$C ?

asked Nov 15, 2013 by mosymeow_1

1 answer

For the equilibrium $2SO_2 + O_2 \rightleftharpoons 2SO_3$ we start with 2 moles of $SO_2$ and 1 mole of $O_2$ at 3 atm. When equilibrium is attained, pressure changes to 2.5 atm. Hence, $K_p$ is:

asked Nov 15, 2013 by mosymeow_1

1 answer

For a very small extent of dissociation of $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$ is a gaseous phase reaction then degree of dissociation, x:

asked Nov 15, 2013 by mosymeow_1

1 answer

$PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2 (g)$ In the dissociation of $PCl_5, x $ varies with $\frac{D}{d}$ according to:

asked Nov 15, 2013 by mosymeow_1

1 answer

If $\overrightarrow a=2\hat i+3\hat j-\hat k\:\:and\:\:\overrightarrow b=\hat i-2\hat j+3\hat k$, then the value of $\lambda$ for which $\overrightarrow c=\lambda\hat i+\hat j+(2\lambda+1)\hat k$ is parallel to the plane containing $\overrightarrow a\:\:and\:\:\overrightarrow b$ is

asked Nov 15, 2013 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b\:\overrightarrow c$ are three vectors of equal magnitude and angle between $\overrightarrow a\:and\:\overrightarrow b$ is $\alpha$, that between $\overrightarrow b\:\overrightarrow c$ is $\beta$, and that between $\overrightarrow a\:and\:\overrightarrow c$ is $\gamma$ then the minimum value of $cos\alpha+cos\beta+cos\gamma$ is ?

asked Nov 15, 2013 by rvidyagovindarajan_1

1 answer

For the reversible reaction equilibrium is $ N_2(g) + O_2(g) \overset{\overset{k_r}{\rightleftharpoons}}{_{k_f}} 2NO(g), $ $C_0 = Ce^{-2.1 \times 10^{-3} t} $ for the forward reaction and $C'_0 = C'e^{-4.2 \times 10^{-4}} t$ for the backward reaction, hence, if both forward and backward reactions are first order reactions then $K_c$ for the above equilibrium is:

asked Nov 15, 2013 by mosymeow_1

1 answer

$ Solute + H_2O \rightleftharpoons solution; \Delta H=\pm x $ For the given equation, Solubility(S) of a solute in the solvent (say $H_2O$) is given by $S = A e^{-\frac{\Delta H}{RT}}$ For a given solution, variation of log S with temperature is shown graphically. Hence, Solute is:

asked Nov 15, 2013 by mosymeow_1

1 answer

$A + B \rightleftharpoons C + D$ One mole each of A and B and 3 moles each of C and D are placed in 1L flask, if equilibrium constant is 2.25. Equilibrium concentrations of A and C will be in the ratio:

asked Nov 15, 2013 by mosymeow_1

1 answer

Volume of the flask in which species are transferred is double of the earlier flask. In which of the following reversible reactions, equilibrium will be shifted in the forward direction?

asked Nov 15, 2013 by mosymeow_1

1 answer

$ I_2 + I^- \rightleftharpoons I^-_3 $ This reaction is set-up in aqueous medium. Initially we have 1 mole of $I_2$ and 0.5 mole of $I^-$ in 1 L flask. After equilibrium is reached, excess of $AgNO_3$ gave 0.25 mole of yellow ppt. Equilibrium constant is

asked Nov 15, 2013 by mosymeow_1

1 answer

We know that equilibrium constant, K changes with temperature. At 300K, equilibrium constant is 25 and at 400K it is 10. Hence, backward reaction will have energy of activation:

asked Nov 15, 2013 by mosymeow_1

1 answer

Given a reaction $ A + B \rightleftharpoons C + D $ taking place in a 1L vessel. If we start with 1 mole each of A and B, equilibrium concentration of [C] = [D] = 0.5 M. Percentage of A converted into C if we start with 2 moles of A and 1 mole of B, is

asked Nov 15, 2013 by mosymeow_1

1 answer

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