The root mean square speed of gas molecules at 25K & \[1.5\times {{10}^{5}}N{{m}^{-2}}\] is \[100.5\,m{{s}^{-1}}\]. If the temperature is raised to 100 K & pressure to \[6.0\times {{10}^{5}}N{{m}^{-2}},\] the root mean square speed becomes.
Reduction with aluminium isopropoxide in excess of isopropyl alcohol is called Meer we in Ponndorff-Verley reduction (MPV). What will be the final product when cyclohex-2-enone is selectively reduced in MPV reaction?
The wave number of first line of Balmer series of hydrogen is \[15200\text{ }c{{m}^{-1}}\] .The wave number of first Balmer line of \[L{{i}^{2+}}\]ion is
'a' gm of element A reacts with 'b' gm of element B. Also 'b' gm of element B combines with 2c gm of C. If one gm equivalent of B weighs 'b' gm. Then the mass ratio in which A and C combine is
The uncertainty in the position of an electron (mass \[9.1\times {{10}^{-28}}g\]) moving with a velocity of \[3.0\times {{10}^{4}}\,cm\,{{s}^{-1}}\]accurate up to \[0.011\text{ }%\] will be
If \[{{s}_{0}},{{s}_{1}},{{s}_{2}}\] and \[{{s}_{3}}\]. are the solubility's of \[AgCl\] in water, \[0.01M\,CaC{{l}_{2}},\,\,0.01\,M\,\,NaCl\] and \[0.05\,M\,\,AgN{{O}_{3}}\] solutions, respectively, then
An organic compound is treated with \[NaN{{O}_{2}}\] and dil. \[HCl\]at \[{{0}^{o}}C\]. The resulting solution is added to an alkaline solution of \[\beta \] -naphthol where by a brilliant red dye is produced. It shows the presence of
The vapour pressure of benzene at a certain temperature \[640\text{ }mm\] of Hg. A non-volatile and non-electrolyte solid weighing \[2.175\text{ }g\] is added to \[39.08\text{ }g\] of benzene. If the vapour pressure of the solution is \[600mm\] of Hg, what is the molecular weight of solid substance?
If a \[0.1\text{ }M\] solution of glucose (Mol. wt 180) and \[0.1\]molar solution of urea (Mol. wt. 60) are placed on two sided semipermeable membrane to equal heights, then it will be correct to say that
A)
there will be no net movement across the membrane
doneclear
B)
glucose will flow across the membrane into urea solution
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C)
urea will flow across the membrane into glucose solution
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D)
water will flow from urea solution to glucose solution
When \[C{{O}_{2}}\] dissolves in water, the following equilibrium is established \[C{{O}_{2}}+2{{H}_{2}}O{{H}_{3}}{{O}^{+}}+HC{{O}_{3}}^{-};\]for which the equilibrium constant is \[3.8\times {{10}^{-6}}\] and \[pH=6.0\] What would be the ratio of concentration of bicarbonate ion to carbon dioxide?
The e.m.f of a Daniell cell, \[Zn\left| \underset{(0.01M)}{\mathop{ZnS{{O}_{4}}}}\, \right|\left| \underset{(1.0M)}{\mathop{CuS{{O}_{4}}}}\, \right|Cu,\], at \[298\text{ }K\] is \[{{E}_{1}}\]. When the concentration of ZnS04 is 1.0 M and that of \[CuS{{O}_{4}}\] is \[0.01\text{ }M,\] the e.m.f. changed to \[{{E}_{2}}\]. What is the relationship between \[{{E}_{1}}\] and \[{{E}_{2}}\]?
A bus is moving with a velocity of \[10\text{ }m/s\] on a straight road. A scooters wishes to overtake the bus in 100 seconds. If the bus is at a distance of 1 km from the scooters, at what velocity should the scooters chase the bus?
The masses of the blocks A and B are 0.5 kg and 1 kg respectively. These are arranged as shown in the figure and are connected by a massless string. The coefficient of friction between all contact surfaces is \[0.4\]. The force, necessary to move the block B with constant velocity, will be \[(g=10\,m/{{s}^{2}})\]
A rod of length L is placed on x - axis between \[x=0\] and \[x=L\]. The linear density i.e., mass per unit length denoted by p, of this rod, varies as, \[p=a+bx\]. What should be the dimensions of b?
A body is thrown vertically upwards from the surface of earth in such a way that it reaches upto a height equal to \[10{{R}_{e}}\]. The velocity imparted to the body will be
.A wheel is rolling on a plane road. The linear velocity of centre of mass is v. Then velocities of the points A and B on circumference of wheel relative to road will be
Two points of a rod move with velocities 3v and v perpendicular to the rod and in the same direction, separated by a distance r. Then the angular velocity of the rod is
A non-conducting partition divides a container into two equal compartments. One is filled with helium gas at 200 K and the other is filled with oxygen gas at 400 K. The number of molecules in each gas is the same. If the partition is removed to allow the gases to mix, the final temperature will be
A bucket full of hot water is kept in a room and it cools from \[{{75}^{o}}C\] to \[{{70}^{o}}C\] in \[{{T}_{1}}\] minutes, from \[{{70}^{o}}C\] to \[{{65}^{o}}C\] in \[{{T}_{2}}\] minutes and from \[{{65}^{o}}C\] to \[{{60}^{o}}C\] in \[{{T}_{3}}\] minutes. Then
sThe current I vs voltage V graphs for a given metallic wire at two different temperatures \[{{T}_{1}}\] and \[{{T}_{2}}\] are shown in the figure. It is concluded that
A straight section \[PO\] of a circuit lies along the x-axis from \[x=-a/2\]to \[x=+a/2,\]and carries a steady current 'T'. The magnitude of magnetic field due to the section PO at a point to \[y=+a\] will be
A transformer is used to light a \[140\text{ }W,\text{ }24\text{ }V\] bulb from a \[240\text{ }V\] a.c. mains. The current in the main cable is \[0.7\] A. The efficiency of the transformer is
Two circular coils X and Y, having equal number of turns, carry equal currents in the same sense and subtend same solid angle at point O. If the smaller coil X is midway between O and Y, then if we represent the magnetic induction due to bigger coil Y at O as By and due to smaller coil X at O as \[{{B}_{X}}\] then
A flat plate P of mass 'M? executes SHM in a horizontal plane by sliding over a frictionless surface with a frequency V. A block 'B' of mass 'm' rests on the plate as shown in figure. Coefficient of friction between the surface of B and P , is a. What is the maximum amplitude of oscillation that the plate block system can have if the block B is not to slip on the plate:
A glass slab has the left half of refractive index \[{{n}_{1}},\] and the right half of\[{{n}_{2}}=3{{n}_{1}}\]. The effective refractive index of the whole slab is
What is the ratio of the circumference of the first Bohr orbit for the electron in the hydrogen atom to the de Broglie wavelength of electrons having the same velocity as the electron in the first Bohr orbit of the hydrogen atom?
The radioactivity of a sample is \[{{R}_{1}}\] at a time \[{{T}_{1}}\] and \[{{R}_{2}}\]at a time\[{{T}_{2}}\]. If the half-life of the specimen is T, the number of atoms that have disintegrated in the time \[({{T}_{2}}-{{T}_{1}})\] is proportional to
Two identical thin rings, each of radius R metres, are coaxially placed at a distance R metres apart. If \[{{Q}_{1}}\] coulomb and \[{{Q}_{2}}\]coulomb are respectively, the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of the other is
If \[a,\,\,\,b,\,\,\,c,\,\,\,d\] and \[p\] are distinct non zero real numbers such that \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}}){{p}^{2}}\]\[-2(ab+bc+cd)p+({{b}^{2}}+{{c}^{2}}+{{d}^{2}})\le 0\] then\[a,\,\,\,b,\,\,\,c,\,\,\,d\]are in
The value of\[\cos {{36}^{o}}\cos {{42}^{o}}\cos {{78}^{o}}\]is\[\left[ Given:\sin 18\frac{\sqrt{5}-1}{4}\,\,and\,\,\cos 36=\frac{\sqrt{5}+1}{4} \right]\]
If \[0<\alpha ,\,\,\beta ,\,\,\gamma <\pi /2\] such that \[\alpha +\beta +\gamma =\frac{\pi }{2}\]and\[\cot \alpha ,\,\,\cot \beta ,\,\,\cot \gamma \] are in arithmetic progression, then the value of \[\cot \alpha \cot \gamma \] is
If \[{{\theta }_{1}},\,\,{{\theta }_{2}}\] are the solutions of the equation\[2{{\tan }^{2}}\theta -4\tan \theta +1=0\], then \[\tan ({{\theta }_{1}}+{{\theta }_{2}})\]is equal to
The order of the differential equation\[{{\left[ 1+5{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{3/2}}=11{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{5}}\]is
The function \[f(x)={{(x-3)}^{2}}\] satisfies all the conditions of mean value theorem in \[\{3,\,\,4\}\]. A point on \[y={{(x-3)}^{2}}\], where the tangent is parallel to the chord joining \[(3,\,\,0)\] and \[(4,\,\,1)\] is
In\[\Delta \,\,ABC\], if\[\left| \begin{matrix} 1 & a & b \\ 1 & c & a \\ 1 & b & c \\ \end{matrix} \right|=0\], then\[{{\sin }^{2}}A+{{\sin }^{2}}B+{{\sin }^{2}}C=\]