Two waves coming from two coherent sources, having different intensities interfere. Their ratio of maximum intensity to the minimum intensity is 25. The intensities of the sources are in the ratio
If the energy, \[E={{G}^{p}}{{h}^{q}}{{c}^{r}}\], where G is the universal gravitational constant, h is the Planck's constant and c is the speed of light, then the values of p, q and r are, respectively
A body floats in water with one-third of its volume above the surface of water. If it is placed in oil, it floats with half of its volume Max. Marks: 300 above the surface of the oil. The specific gravity of oil is
The third overtone of an open organ pipe is in resonance with the second overtone of a closed organ pipe. If the length of the open pipe is 8 cm, then the length of the closed pipe is
The current gain of a transistor in a common base arrangement is 0.98. Find the change in collector current corresponding to a change of 5.0 mA in emitter current. What would be the change in base current?
A particle is executing linear simple harmonic motion. The fraction of the total energy to its potential energy, when its displacement is\[\frac{1}{2}\]of its amplitude is
A convex lens of focal length 20 cm made of glass of refractive index 1.5 is immersed in water having refractive index 1.33. The change in the focal length of lens is
The plates of a parallel plate capacitor are charged up to 100 V. A 2 mm thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by mm. The dielectric constant of the plate is
A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the 5th second to that covered in 5 seconds is
The specific heat c of a solid at low temperature shows temperature dependence according to the relation\[c=D{{T}^{3}}\]where D is a constant and Tis the temperature in kelvin. A piece of this solid of mass m kg is taken and its temperature is raised from 20 K to 30 K. The amount of heat required in the process in energy units is
The instantaneous magnetic flux \[\phi \]in a circuit is \[\phi =4{{t}^{2}}-4t+1Wb\] The total resistance of the circuit is \[10\Omega \]. At \[t=\frac{1}{2}s,\]the induced current in the circuit is
The rms value of the electric field of the light coming from the sun is \[720N{{C}^{-1}}\]. The average total energy density of the electromagnetic wave is
A geostationary satellite is orbiting the earth at a height of 6R from the surface of the earth, where R is the radius of the earth. The time period of another satellite at a height of 2.5R from the surface of the earth is \[\sqrt{2}\times n\]hours. The value of n is _______.
A solid sphere of radius R has a charge Q distributed in its volume with a charge density \[\rho =\kappa {{r}^{a}}\],, where K and a are constants and r is the distance from its centre. If the electric field at r = R/2 is 1/8 times that at r = R, the value of a is ________.
An ideal monoatomic gas is compressed adiabatically to \[\left( \frac{1}{8} \right)th\] initial volume. If the initial temperature of the gas is \[{{T}_{i}}\](in Kelvin) and the final temperature is \[a{{T}_{i}}\]then the value of a will be _______.
Three blocks of masses \[{{m}_{1}},{{m}_{2}}\]and \[{{m}_{3}}\]are connected by massless string as shown in the figure on a frictionless table. They are pulled with a force \[F=60N\]. If \[{{m}_{1}}=10kg,{{m}_{2}}=20kg\]and \[{{m}_{3}}=30kg\], then the ratio \[\frac{{{T}_{2}}}{{{T}_{1}}}\] is ________.
A capacitor and a coil in series are connected to a 6 volt AC source. By varying the frequency of the source, maximum current of 600 mA is observed. If the same coil is now connected to a cell of emf 6 V and internal resistance of \[2\Omega ,\] then the current through it will be _______ A.
The number of isomers for the complexes (X) and (Y) are, respectively, \[(X)=[Pt\,{{(gly)}_{2}}],\] \[(Y)={{[Pt\{P{{({{C}_{2}}{{H}_{5}})}_{3}}\}C{{l}_{2}}]}_{2}}\]
The fraction of molecules having speeds in the range of u to \[u+du\] of a gas of molar mass, Mat temperature Tis the same as that of the gas of molar mass 2M at temperature\[T/2\].
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B)
The product of pressure and volume of a fixed mass of a gas is independent of temperature.
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C)
Rise in compressibility factor with increasing pressure is due to van der Waal's constant b.
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D)
All molecules in a gas are moving with the same speed.
\[100mL\] samples of distilled water and boiled water required, respectively, \[2mL,\] \[17mL,\] and\[7mL\] of soap solution to form permanent lather. The ratio of permanent to temporary hardness in the tap water is
A photon of frequency v causes photoelectric emission from a surface with threshold frequency \[{{v}_{0}}\]. The de Broglie wavelength \[(\lambda )\] of the photoelectron emitted is given by
Select the INCORRECT statement about the solubility of gases and Henry's constant.
A)
Partial pressure of a gas is related to number of moles of the dissolved gas and \[{{K}_{H}}\] (Henry's constant)
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B)
\[{{O}_{2}}(g)\] and \[{{N}_{2}}(g)\] are less soluble in \[{{H}_{2}}O\] and solubility of these gases decrease with increase of temperature. These gases have higher \[{{K}_{H}}\] value at a given pressure and \[{{K}_{H}}\] value increases with temperature.
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C)
\[S{{O}_{2}}(g)\]and \[N{{H}_{3}}(g)\] are more soluble in \[{{H}_{2}}O\] and solubility of these gases decrease with increase of temperature These gases have lower \[{{K}_{H}}\] value at a given pressure.
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D)
Helium \[(g)\] and Argon \[(g)\]are sparingly soluble in acetone and solubility of these gases increases increase slightly with increase of temperature. These gases have higher \[{{K}_{H}}\]value at a given pressure.
Enthalpy of combustion \[({{\Delta }_{C}}{{H}^{\bigcirc -}})\] for \[C{{H}_{4}},\] \[{{C}_{2}}{{H}_{6}}\] and \[{{C}_{3}}{{H}_{8}}\] are \[-200.0,-300.0\] and \[-400.0~kcal\text{ }mo{{l}^{-1}}\] respectively. \[{{\Delta }_{C}}{{H}^{\bigcirc -}}\]in Kcal for octane is
\[500\text{ }mL\] of 1N solution of \[CuC{{l}_{2}}\] was electrolysed with a current of 2 amperes for 1 hour. What is the normality of the remaining \[CuC{{l}_{2}}\] solution?
If one starts with 1 Curie\[(Ci)\] of radioactive substance \[({{t}_{1/2}}=15hr),\] the activity left after a period of two weeks will be about \[0.02x\,\mu Ci\]. Find the value of x.
Let A, B, and C are the angles of a plain triangle and \[\tan \frac{A}{2}=\frac{1}{3},\]\[\tan \frac{B}{2}=\frac{2}{3}.\] Then \[\tan \frac{C}{2}\] is equal to
A line \[4x+y=1\] passes through the point \[A(2,-7)\] meets the line 5C whose equation is \[3x-4y+1=0\] at the point5. The equation to the line AC so that \[AB=AC,\] is
If the circles \[{{x}^{2}}+{{y}^{2}}+2ax+cy+a=0\] and \[{{x}^{2}}+{{y}^{2}}-3ax+dy-1=0\] intersect in two distinct points P and Q then the line \[5x+by-a=0\] passes through P and Q for
The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse \[{{x}^{2}}+9{{y}^{2}}=9\] meets its auxiliary circle at the point M. Then the area of the triangle with vertices at A, M and the origin O is
A school has four sections of chemistry in class XII having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the four sections, the overall average of marks per students is
If the set of natural numbers is partitioned into subsets \[{{S}_{1}}=\{1\},{{S}_{2}}=\{2,3\},{{S}_{3}}=\{4,5,6\}\] and so on. Then the sum of the terms in \[{{S}_{50}}\] is
If \[\overrightarrow{a}=3\hat{i}-\hat{j}-4\hat{k},\] \[\overrightarrow{b}=-2\hat{i}+4\hat{j}-3\hat{k}\] and \[\overrightarrow{c}=\hat{i}+2\hat{j}-\hat{k}\] then \[|3\overrightarrow{a}-2\overrightarrow{b}+4\overrightarrow{c}|\] is \[\sqrt{k},\] then k is