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A metal wire PQ slides on parallel metallic rails having separation 0.25 m, each having negligible resistance. There is a 2Ω resistor and 10V battery as shown in figure. There is a uniform magnetic field directed into the plane of the paper of magnitude 0.5 T. A force of 0.5N to the left is required to keep the wire PQ moving with constant speed to the right. With what speed is the wire PQ moving? (Neglect selfinductance of the loop)
In the given figure a ring of mass m is kept on a horizontal surface while a body of equal mass 'm' attached through a string, which is wounded on the ring. When the system is released the ring rolls without slipping. Consider the following statements and choose the correct option.
(i) acceleration of the centre of mass of ring is g/3
(ii) acceleration of the hanging particle is 2g/3
(iii) frictional force (on the ring) acts along forward direction
(iv) frictional force (on the ring) acts along backward direction
A concave mirror gives a real image magnified 6 times when the object is moved 6 cm the magnification of the real image is 4 times. What will be the focal length of the mirror?
A spring mass system with unequal masses is placed at rest on a smooth horizontal surface. The spring is initially kept compressed with a thread. When the spring is cut, the mass m moves so as to enter in a vertical circular loop of radius r. The minimum compression x in the spring so that the mass m may negotiate the vertical loop is
A plane electromagnetic wave of angular frequency ω propagates in a poorly conducting medium of conductivity σ and relative permittivity ε. Find the ratio of conduction current density and displacement current density in the medium.
A uniform electric field of magnitude 245 V/m is directed in the negative y direction as shown in figure. The coordinates of point P and Q are ( 0.5m,  0.8m) and (0.3m, 0.7m) respectively. Calculate the potential difference V_{Q}  V_{P} along the path shown in the figure,
A cylinder of radius r = 1 m and height 3 m filled with a liquid upto 2 m high and is rotated about its vertical axis as shown in the Figure.
The speed of rotation of the cylinder when the point at the centre of the base is just exposed is
A charge particle q of mass m_{0} is projected along the yaxis at t = 0 from origin with a velocity V_{0}. If a uniform electric field E_{0} also exists along the xaxis, then the time at which the deBroglie wavelength of the particle becomes half of the initial value is:
The beat frequency produced when the following two waves x_{1} = 12 sin (484πt − 7πx) and x_{2} = 12 sin (480πt − 7πx) are sounded together is
An 80 kg man standing on ice throws a 4 kg body horizontally at 6 ms^{−1}. The frictional coefficient between the ice and his feet is 0.02. The distance through which the man slips is (g = 10 ms^{−2})
Liquid cools from 50ºC to 45 ºC in 5 minutes and from 45ºC to 41.5ºC in the next 5 minutes. The temperature of the surrounding is : [Assume newton's law of cooling is applicable]
A long solenoid of selfinductance L and area of cross section A not carrying any current is placed in a uniform magnetic field of strength B with its axis parallel to the field direction. The total magnetic flux linked with the solenoid is φ. The energy of the magnetic field stored in the solenoid is
All wires have same resistance and equivalent resistance between A and B is R. Now keys are closed, then the equivalent resistance will become:
Steam at 100°C is passed into 1.4 kg of water kept in a calorimeter of water equivalent 0.03 kg at 20 °C till the temperature of the calorimeter and contents reach 80°C. Latent heat of steam is 2.26 × 10^{6} J kg ^{− 1} and sp.heat capacity of water is 4200 J /kg/°C. The mass of steam condensed in kilogram is nearly equal to
A satellite orbiting around the earth of radius R is shifted to an orbit of radius 2R. The time taken for one revolution will increase nearly by
Screw gauge shown in Figure has 50 divisions and in one complete rotation of circular scale the main scale moves 0.5 mm.
The given graph shows the extension (Δl) of a wire of length 1.0 m suspended from the top of a roof at one end and loaded at the other end. If the cross sectional area of the wire is 10^{− 6}m^{2}, the Young’s modulus Y of the material of the wire is
In Young’s double slit experiment, a monochromatic light of wavelength 5500 Å is used. The slits are 2 mm apart. The fringes are formed on a screen placed 20 cm away from the slits. It is found that the interference pattern shifts by 16 mm when a transparent plate of thickness 0.4 mm is introduced in the path of one of the slits. The refractive index of the transparent plate is
The average degree of freedom per molecule of a gas is 6. The gas performs 25 J work, while expanding at constant pressure. The heat absorbed by the gas is:
The radioactive sources A and B have half lives of 2hr and 4hr respectively, initially contain the same number of radioactive atoms. At the end of 2 hours, their rates of distintegration are in the ratio:
A Young's double slit apparatus is immersed in a liquid of refractive index 1.33. It has slit separation of 1 mm and interference pattern is observed on the screen at a distance 1.33 m from plane of slits. The wavelength of light used in air is 6300A°. When one of the slit is covered by a glass sheet of thickness and refractive index 1.53, the position of maxima and minima get interchanged. Find the maximum possible value of n.
An oscillator of frequency 425 Hz drives two speakers. The speaker are fixed on a vertical pole at a distance 2.4m from each other. A person whose height (of ears) is same as that of lower speaker runs horizontally away from the two speakers. Find the maximum distance (in m) of person from the pole where he hears no sound, (velocity of sound in air 340 m/s)
A particle of mass m = 1 kg and having charge Q = 2C is projected on a rough horizontal xy plane from (4, 0, 0) m with velocity and in the region there exist a uniform electric field and a uniform magnetic field The coefficient of friction between the particle and the horizontal surface is μ = 1/3 and the particle comes to rest by moving a distance 1000/n metres. Find n.
A wedge of inclination 45° is moved towards right with a constant acceleration of 2√6 m/s^{2} as shown in figure. Find magnitude of acceleration of the ball placed between an inclined wall and the wedge.
In the situation shown in figure, a particle having charge q = 2C and mass = 1 kg is projected from bottom of an inclined plane of inclination 45° at an angle 45° with horizontal, so that the particle strike the inclined plane normally due to a uniform horizontal electric field E. Find the value of E (in NC^{1})
Ratio of Boyle temperature and critical temperature of gas is:
Which of the following complex square having planner complex can exhibit geometrical isomerism?
An element has a bcc structure with a cell edge of 288 pm. The density of the element is 7.2 g cm^{–3}. Number of atoms present in 208 g of the element ?
The most acidic oxyacid of halogen among the given option is
The Clark cell ZnZn^{2+}// Hg_{2}SO_{4}Hg is often employed as a standard cell since its emf is known exactly as a function of temperature. The cell emf is 1.423 V at 298 K and its temperature coefficient of voltage is 1.2 × 10^{4} V K^{1}. What is ΔS_{cell} at 298 K?
In which of the following, colour can be explained due to ‘Ligand to Metal Charge Transfer’?
Observe the following reaction
Which of the following statement is true regarding solvent of the above reaction
The hydride ion H^{} has the same electron configuration as helium but is much less stable. Which of the following option explains the given statement
XeF_{2} when dissolved in water produces three compound A, B, C. A is inert. Compound B forms strongest Hbond with its anion and exists as D. Compound C is used in combustion. Which of the following is correct?
Which of the marked position is most susceptible to nucleophilic attack
Ester and amide are found in equilibrium which of the following is true regarding the equilibrium of following. K_{1} and K_{2} are equilibrium constants
Arrhenius relation is described as K= A e^{Ea/RT} which of the following statement is correct regarding activation energy
Which of the following is correct about acidic nature of boric acid?
The difference in the oxidation state of chromium in 'B' and 'C' is
For the reaction NO_{2 }+ CO → CO_{2}_{ }+ NO. The experimental rate expression is Find the number of molecules of CO involved in the slowest step.
What is the total score for the correct statement(s) from the following?
Give the answer of the following questions for the reaction product [X].
(P) In how many M–O bonds, the bond lengths are equal.
(Q) The oxidation state of the central metal ion.
(R) The magnetic moment of the central metal ion.
(S) The number of peroxide linkage in the product formed by the reaction of [X] with H_{2}O_{2} in acidic medium.
On moving across a period, the basic character of the oxides gradually changes first into amphoteric and finally into acidic character. The acidic character of oxides increases with increase in the oxidation states of the element that is combined with oxygen. Arrange the following oxides in order of increasing acidic character.
(1) SO_{3} (2) Cl_{2}O_{7} (3) N_{2}O_{5} (4) CO_{2}
Fill in the boxes provided below with suitable number. Least acidic oxide will come in first box and the strongest acidic oxide in the last box.
The area bounded by the curves x + 2y = 1 and x = 0 is:
The length of the common chord of the circles x^{2} + y^{2} + 2x + 3y + 1 = 0 and x^{2} + y^{2} + 4x + 2 = 0 is
In a triangle ABC, the angle B is greater than angle A. If the values of the angle A and B satisfy the equation 3 sin x  4 sin^{3} x  k = 0, 0 < k < 1, then value of C is
Suppose a, b, c are in AP and a^{2}, b^{2}, c^{2} are in GP. If a < b < c & a + b + c = 3/2, then the value of a is
If log_{2}(4^{x+1 }+ 4)log_{2}(4^{x} + 1) = log_{2} 8, then x equals
If ‘M’ and σ^{2} are mean and variance of random variable X, whose distribution is given by –
Then
If a,b,c are three unit vectors such that and b is not parallel to c, then the angle between a and c is:
The equation represents the equation of a circle with ω, ω^{2} as extremities of a diameter, then λ is , (where ω, ω^{2} are cube roots of unity)
If sin^{–1}x + sin^{–1}y + sin^{–1}z = π/2 then x^{2} + y^{2} + z^{2} + 2xyz is equal to 
If b^{2} > 4ac for the equation 4x^{4} + bx^{2} + c = 0, then all the roots of the equation will be real if:
The value of the definite integral for 0 < α < π, equal to
Coordinates of the orthocentre of the triangle whose sides are x = 3, y = 4 and 3x + 4y = 6 will be:
An equilateral triangle is inscribed in the parabola y^{2 }= 4ax whose vertex is at the vertex of the parabola. The length of its side is
The projection of the line joining the points (3,4,5) and (4,6,3) on the line joining the points (1,2,,4) and (1,0,5) is
Consider the following statements regarding the events E, A, B and C .
(i) Event E can take place due to the occurrence of any of the events A, B, C.
(ii) Events A, B and C are equiprobable, mutually exclusive and exhaustive.
(iii) Probability of occurrence of event E is 5/12.
Considering above data the value of P(E/C) is:
The equation of the hyperbola whose foci are (6, 5), ( 4, 5) and eccentricity 5/4 is
One mapping is selected at random from all mappings of the set S = {1, 2, 3,..., n} into itself. If the probability that the mapping is one  one is 3/32 then the value of n is
Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. Find the number of ways in which we can place the balls in the boxes so that no box remains empty.
Find the coefficient of x^{2009} in the expansion of (1 x)^{2008} (1 +x + x^{2})^{2007}
357 docs148 tests

357 docs148 tests
