The density of water at the surface of ocean is p. If the bulk modulus of water is B, what is the density of ocean water at a depth where the pressure is \[n{{P}_{0}},\] where \[{{P}_{0}}\] is the atmospheric pressure?
A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is \[{{L}_{A}}\] when it is at A and \[{{L}_{B}}\] when it is at B, then
A)
\[{{L}_{A}}={{L}_{B}}\]
doneclear
B)
\[{{L}_{A}}>{{L}_{B}}\]
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C)
\[{{L}_{A}}<{{L}_{B}}\]
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D)
The relationship between \[{{L}_{A}}\]and \[{{L}_{B}}\] depends upon the slope of the line AB
The ratio \[\frac{g}{gh},\] where g and \[{{g}_{h}}\] are the accelerations due to gravity at the surface of the earth and at a height h above the earth's surface respectively, is
If n drop, each of capacitance C, coalesce to form a single big drop, then the ratio of the energy stored in the big drop to that in each small drop will be
Two resistances of \[400\Omega \]and \[800\Omega \] are connected in series with 6 volt battery of negligible internal resistance. A voltmeter of resistance \[10,000\Omega \] is used to measure the potential difference across\[400\Omega \]. The error in the measurement of potential difference in volt approximately is
The co-ordinates of a moving particle at any time ?t? are given by \[x=\alpha {{t}^{3}}\] and \[y=\beta {{t}^{3}}\] . The speed of the particle at time 't? is given by
The input signal given to a CE amplifier having a voltage gain of 150 is \[{{V}_{i}}=2\cos \left( 15+\frac{\pi }{3} \right)\].The corresponding output signal will be:
The anode voltage of a photocell is kept fixed. The wavelength \[\lambda \] of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows
Suppose an electron is attracted towards the origin by a force \[\frac{k}{r}\] where 'k' is a constant and 'r' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be \['{{r}_{n}}'\] and the kinetic energy of the electron to be \['{{T}_{n}}'\]. Then which of the following is true?
Ideal gas undergoes an adiabatic change in its state from \[({{P}_{1}},{{V}_{1}},{{T}_{1}})\] to\[({{P}_{2}},{{V}_{2}},{{T}_{2}})\]. The work done (W) in the process is (\[\mu \]= number of moles, \[{{C}_{P}}\] and \[{{C}_{V}}\] are molar specific heats of gas)
An isotropic point source S of sound emits constant power. Two points A and B separated by a distance r are situated near the source as shown in figure. The difference of the intensity level of sound at the points A & B is about
An ideal gas has a specific heat at constant pressure\[{{C}_{P}}=\frac{5R}{2}\]. The gas is kept in a closed vessel of volume \[0.0083\text{ }{{m}^{3}},\] at a temperature of \[300\text{ }K\]and a pressure of\[1.6\times {{10}^{6}}N/{{m}^{2}}\]. An amount of \[2.49\times {{10}^{4}}\] Joules of heat energy is supplied to the gas. Calculate the final pressure of the gas
In Young's double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If \[{{I}_{m}}\]be the maximum intensity, the resultant intensity I when they interfere at phase difference \[\phi \] is given by
Which of the following figure correctly depicts the Lenz's law. The arrows show the movement of the labelled pole of a bar magnet into a closed circular loop and the arrows on the circle show the direction of the induced current
A point source of electromagnetic radiation has an average power output of 800 W. The maximum value of electric field at a distance 4.0 m from the source is
A current of 4A flows in a coil when connected to a \[12\,V\] dc source. If the same coil is connected to a \[12\,V\], \[50\text{ }rad/s\text{ }a.c.\]source, a current of \[2.4A\] flows in the circuit. Determine the inductance of the coil.
A heater coil is rated\[100\,W,\]\[200V\]. It is cut into two identical parts. Both parts are connected together in parallel, to the same source of\[200V\]. Calculate the energy liberated (in watt) in the new combination.
Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done (in joule) on the particle during its displacement of 12 m is
The focal length of lens of refractive index \[1.5\] in air is 30 cm. When it is immersed in water of refractive index \[4/3,\]then find its focal length (in cm).
Steam at \[100{}^\circ C\] is passed into \[1.1\text{ }kg\]of water contained in a calorimeter of water equivalent \[0.02\text{ }kg\]at \[15{}^\circ C\]till the temp. of the calorimeter and its contents rises to \[80{}^\circ C\]. What is the mass (in kg) of steam condensed? Latent heat of steam\[=536\,ca\,Vg\].
Assume that a neutron breaks into a proton and an electron. The energy released during this process is: (mass of neutron \[=1.6725\times {{10}^{-27}}kg,\] mass of proton \[=1.6725\times {{10}^{-27}}kg,\]mass of electron\[=9\times {{10}^{-31}}kg\]).
We have three aqueous solutions of NaCI labelled as 'A', '5' and 'C' with concentrations M, 0.01 M and 0.001 M, respectively. The value of vant Hoff factor for these solutions will be in the order
\[C{{H}_{3}}{{(C{{H}_{2}})}_{4}}C{{H}_{3}}\xrightarrow[773K,10-20atm]{Cr{{O}_{3}}/A{{l}_{2}}{{O}_{3}}}A\xrightarrow[{}]{B{{r}_{2}}/Fe}B\] \[\xrightarrow[ether]{Mg}C\xrightarrow[{}]{{{H}_{2}}O}D\] What is D?
A white solid (X) on heating evolves \[C{{O}_{2}}\]and gives a white residue (Y) which is soluble in water. (Y) also gives\[C{{O}_{2}}\]when treated with dilute acid. (X) and (Y) are respectively
Which of the following statements is correct for the periodic classification of elements?
A)
Atomic size gradually increases from left to right in a period of representative elements.
doneclear
B)
Across a transition series, atomic size gradually but somewhat irregularly decreases and then increases at the end of the series.
doneclear
C)
Electron gain enthalpies of third period elements, sulphur and chlorine are less negative than those of oxygen and fluorine of second period in respective groups.
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D)
lonisation potential gradually but irregularly decreases across a period in representative elements.
The number of ethers in the given list which cannot be prepared by Williamsons synthesis is___. \[C{{H}_{3}}OC{{H}_{2}}C{{H}_{3}},{{C}_{6}}{{H}_{5}}OC{{H}_{3}},\] \[{{C}_{6}}{{H}_{5}}OC{{H}_{2}}C{{H}_{3}},{{({{C}_{6}}{{H}_{5}})}_{2}}O,{{(C{{H}_{3}})}_{3}}COC{{H}_{3}}\], \[{{(C{{H}_{3}})}_{3}}COC{{H}_{2}}C{{H}_{3}},{{(C{{H}_{3}})}_{3}}COC{{(C{{H}_{3}})}_{3}},\] \[{{({{C}_{2}}{{H}_{5}})}_{2}}O,{{C}_{6}}{{H}_{5}}C{{H}_{2}}O{{C}_{6}}{{H}_{5}}\]
At 400 K, the root mean square speed of a gas X (molecular weight == 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of Y is____.
At a certain temperature and total pressure of \[{{10}^{5}}Pa\], iodine vapour contains 40% by volume of I atoms, \[{{I}_{2(g)}}2{{I}_{(g)}}\]. The \[{{K}_{p}}\]for the equilibrium is \[x\times {{10}^{4}}\]. The value of x is____.
To stop the flow of photoelectrons produced by electromagnetic radiation incident on a certain metal, a negative potential of 300 V is required. If the photoelectric threshold of metal is \[1500\overset{\text{o}}{\mathop{\text{A}}}\,\], the frequency of the incident radiation is \[x\times {{10}^{16}}\] Hz. the value of x is_____.
In \[\Delta ABC,\] the median divides \[\angle BAC\] such that \[\angle BAD:\angle CAD=2:1.\] Then the value of \[\cos \left( \frac{A}{3} \right)\]equals
If a, b and c are the first three non-zero terms of a geometric progression such that \[a-2,\]2b and 12c form another geometric progression with common ratio 5, then the sum of the series \[a+b+c+......\infty \] is
The slope of the tangent to the curve represented parametrically by the equations \[x={{t}^{2}}-3t+1\]and \[y=2{{t}^{2}}+3t-4\] at the point \[M(-1,10)\] is
A curve satisfies the differential equation \[\sqrt{{{x}^{4}}-{{x}^{2}}}\,\,dy-\sqrt{{{y}^{4}}-{{y}^{2}}}\,\,dx=0.\]If \[y(0)=0,\]then curve also passes through the point
If \[[\vec{a}\,\,\vec{b}\,\,\vec{c}]=1,\]then the value of is \[[\vec{a}\times (\vec{b}+\vec{c})\,\,\,\vec{b}\times (\vec{c}-2\vec{a})\,\,\vec{c}\times (\vec{a}+3\vec{b})]\]
A tangent to the hyperbola \[{{x}^{2}}-2{{y}^{2}}=4\]meets x-axis at P and y-axis at Q. Lines PR and QR are drawn such that OPRQ is a rectangle (where 0 is origin). The locus of R is
We have 19 identical gems available with us which are needed to be distributed among A, B and C such that A always gets an even number of gems and a minimum of 2 gems. The number of ways this can be done is
The equation of line of shortest distance between the lines \[\frac{x+4}{4}=\frac{y-2}{-2}=\frac{z-3}{0}\] and \[\frac{x-5}{5}=\frac{y-3}{3}=\frac{z}{0}\] is
A biased coin has \[\frac{2}{3}\] as probability of landing heads. If the coin is tossed 50 times, then the probability that the number of heads is zero or even is
A man standing on a level plane observes the elevation of the top of a pole to be \[\theta \]. He then walks a distance equal to double the height of the pole and then finds that the elevation is now \[2\theta \]. Then \[\cot \theta \]is equal to
The correct order towards electrophilic substitution reaction is 
