At certain temperature (T) if conductivity of pure water is \[5.5\times {{10}^{-7}}S\,c{{m}^{-1}},\]then calculate pOH of pure water at temperature T. Given \[\lambda _{{{H}^{+}}}^{\infty }=350\,S\,c{{m}^{2}}e{{q}^{-1}},\] \[\lambda _{O{{H}^{-}}}^{\infty }=200\] \[\,S\,c{{m}^{2}}e{{q}^{-1}}\]
What volume of 0.2 M \[RN{{H}_{3}}Cl\]solution should be added to 100 ml. of 0.1 M \[RN{{H}_{2}}\] solution to produce a buffer solution of pH = 8.7? Given: \[p{{K}_{b}}\] of \[RN{{H}_{2}}=5,\], log 2 = 0.3
When \[{{N}_{2}}{{O}_{5}}\] is heated at temp. T, it dissociates as \[{{N}_{2}}{{O}_{5}}\]\[(g){{N}_{2}}{{O}_{3}}(g)\] \[+{{O}_{2}}(g),\] \[{{K}_{c}}=2.5\]. At the same time \[{{N}_{2}}{{O}_{3}}\] also decomposes as \[{{N}_{2}}{{O}_{3}}(g)\] \[{{N}_{2}}O(g)+{{O}_{2}}(g)\]. If initially 4.0 moles of \[{{N}_{2}}{{O}_{5}}\]are taken in 2.0 litre flask and allowed to attain equilibrium, concentration of \[{{O}_{2}}\] was formed to be 2.5M. Equilibrium concentration of \[{{N}_{2}}O\] is
The \[{{\Delta }_{f}}{{H}^{o}}({{N}_{2}}{{O}_{5}},g)\]in kJ/mol on the basis of the following data is - \[\text{2NO(g)+}{{\text{O}}_{\text{2}}}\text{(g)}\to \text{2N}{{\text{O}}_{\text{2}}}\text{(g);}{{\text{ }\!\!\Delta\!\!\text{ }}_{\text{r}}}{{\text{H}}^{\text{o}}}\text{=-114kJ/mol}\] \[\text{4N}{{\text{O}}_{\text{2}}}\text{(g)+}{{\text{O}}_{\text{2}}}\text{(g)}\to \text{2}{{\text{N}}_{\text{2}}}{{\text{O}}_{5}}\text{(g);}{{\text{ }\!\!\Delta\!\!\text{ }}_{\text{r}}}{{\text{H}}^{\text{o}}}\text{=-102}\text{.6kJ/mol}\] \[{{\text{ }\!\!\Delta\!\!\text{ }}_{f}}{{\text{H}}^{\text{o}}}\text{(NO,g)=90}\text{.2}\,\text{kJ/mol}\]
How many times solubility of \[Ca{{F}_{2}}\]is decreased in \[4\times {{10}^{-3}}M\]KF (aq). solution as compare to pure water at \[25{}^\circ C\]. Given \[{{K}_{sp}}(Ca{{F}_{2}})=3.2\times {{10}^{-11}}.\]
Number of electrons transfered in each case when \[KMn{{O}_{4}}\] acts as an oxidising agent to give \[Mn{{O}_{2}},M{{n}^{2+}},\] \[Mn{{\left( OH \right)}_{3}}\] and \[MnO_{4}^{2-}\] are respectively
96.5gm. of oxidized as \[A\to {{A}^{3+}}+3{{e}^{-}},\]when 2F charge is passed through solution with current efficiency of 90%. What is electrochemical equivalent of A?
What is the EMF of represented cell at 298 \[Ag|A{{g}^{+}}(aq.0.1M)||{{H}^{+}}(aq.0.1M),{{H}_{2}}\] \[(g,0.1\,\text{bar})\text{Pt}\] Given: \[E_{Ag/A{{g}^{+}}}^{0}=-0.8\text{V}\]
At 300K, the vapour pressure of an ideal solution containing 3 mole of A and 2 mole of B is 600 torr. At the same temperature, if 1.5 mole of A and 0.5 mole of C (non- volatile) are added to this solution the vapour pressure of solution increases by 30 torr. What is the value of\[P_{B}^{0}\] ?
If \[{{E}_{1}},{{E}_{2}},\] and \[{{E}_{3}}\]represent respectively the kinetic energies of an electron and an alpha particle and a proton each having same de-broglie wavelength then
Three charges Q, + q and +q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to
When an ideal monoatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is
N divisions on the main scale of a vernier callipers coincide with N + 1 divisions on the vernier scale. If each division on the main scale is of a units, determine the least count of the instrument.
A body is executing simple harmonic motion. At a displacement x from mean position, its potential energy is \[{{E}_{1}}=2J\]and at a displacement y from mean position, its potential energy is \[{{E}_{2}}=8J\]. The potential energy E at a displacement (x + y) from mean position is
In the figure (i) as extensible string is fixed at one end and the other end is pulled by a tension T. In figure (ii) another identical string is pulled by tension T at both the ends. The ratio of elongation in equilibrium of string in (i) to the elongation of string in (ii) is
A block of mass m is attached with massless spring of force constant k. The block is placed over a fixed rough inclined surface for which the coefficient of friction is \[\mu =3/4.\] The block of mass m is initially at rest. The block of mass M is released from rest with spring in un stretched state. The minimum value of M required to move the block up the plane is (neglect mass of string and pulley and friction in pulley.)
A charged particle of mass m and having a charge Q is placed in an electric field E which varies with time as \[E={{E}_{0}}\] \[\sin \omega t\]. What is the amplitude of the S.H.M. executed by the particle?
Consider the following statements \[{{\text{S}}_{\text{1}}}\]: Non zero work has to be done on a moving particle to change its momentum. \[{{\text{S}}_{2}}\]: To change momentum of a particle a non zero net force should act on it. \[{{\text{S}}_{3}}\]: Two particles undergo rectilinear motion along different straight lines. Then the centre of mass of system of given two particles also always moves along a straight line. \[{{\text{S}}_{4}}\]: If direction of net momentum of a system of particles (having nonzero net momentum) is fixed, the centre of mass of given system moves along a straight line. State, in order, whether \[{{\text{S}}_{\text{1}}}\text{,}{{\text{S}}_{\text{2}}}\text{,}{{\text{S}}_{\text{3}}}\text{,}{{\text{S}}_{\text{4}}}\] are true or false.
In a photoelectric experiment, with light of wavelength \[\lambda \] the fastest electron has speed v. If the exciting wavelength is changed to \[3\lambda \text{/4}\], the speed of the fastest emitted electron will become
A metal rod of length 1 m is rotated about one of its ends in plane at right angles to a field of inductance \[2.5\times {{10}^{-3}}\]\[Wb/{{m}^{2}}\]. If it makes 1800 revolutions/min, calculate induced e.m.f. between its ends.
A ring of mass M and radius R lies in x-y plane with its centre at origin as shown. The mass distribution of ring is nun-uniform such that at any point P on the ring, the mass per unit length is given by \[\lambda ={{\lambda }_{0}}\]\[{{\cos }^{2}}\theta \]where \[{{\lambda }_{0}}\] is a positive constant). Then the moment of inertia of the ring about z-axis is
An electron and a proton each travels with equal speed around circular orbits in the same uniform magnetic field as indicated (not to scale) in the diagram. The field is into the page on the diagram. The electron travels ............... around the ............ circle and the proton travels............... around the............... circle.
The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If \[{{\text{Y}}_{\text{A}}}\]and\[{{\text{Y}}_{\text{B}}}\] are the Young's modulii of the materials, then
A metal sheet 14 cm x 2 cm of uniform thickness is cut into two pieces of width two cm. The two pieces are joined and laid along XY plane as shown. The centre of mass has the coordinates
Three moles of an ideal monoatomic gas perform a cycle shown in figure. The gas temperatures in different states are \[{{\text{T}}_{\text{1}}}\] = 200K, \[{{\text{T}}_{2}}\] = 400K, \[{{\text{T}}_{3}}\] = 1600 K, and \[{{\text{T}}_{4}}\] = 800K. The work done by the gas during the cycle is (Take R= 25/3 J/mol-K)
The circuit shown in the figure contains two diodes each with a forward resistance of 50 ohms and with infinite backward resistance. If the battery voltage is 6V, the current through the 100 ohm resistance (in amperes) is
A ball of mass m is thrown vertically upwards. Air resistance is not negligible. Assume the force of air resistance has magnitude proportional to the velocity, and direction opposite to that of velocity. At the highest point, the ball's acceleration is
A particle of mass m = 1 kg moves in a circle of radius R = 2m with uniform speed \[v=3\pi \,\text{m/s}\]. m/s. The magnitude of impulse given by centripetal force to the particle in one second is
A thin convex lens of focal length 10cm and refractive index 1.5 is cut vertically into two equal pieces. They are placed as shown with a liquid of refractive index 3 between them. What is the focal length of the combination?
If g is the acceleration due to gravity on the earth's surface, the change in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is
Statement 1: In YDSE, as shown in figure, central bright fringe is formed at O. If a liquid is filled between plane of slits and screen, the central bright fringe is shifted in upward direction.
Statement 2: If path difference at 0 increases, y-coordinate of central bright fringe will change.
A)
Statement -1 is False, Statement -2 is True
doneclear
B)
Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement -1
doneclear
C)
Statement -1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement -1
Box contains 2 one rupee, 2 five rupee, 2 ten rupee and 2 twenty rupee coin. Two coins are drawn at random simultaneously. The probability that their sum is Rs. 20 or more, is
The value of the definite integral, \[\int\limits_{{{\theta }_{1}}}^{{{\theta }_{2}}}{\frac{d\theta }{1+\tan \theta }}=\frac{501\pi }{K}\]where \[{{\theta }_{2}}\frac{1003\pi }{2008}\]and \[{{\theta }_{1}}=\frac{\pi }{2008}.\]The value of K equals
If a is real and \[\sqrt{2ax}+\sin \]By\[+\cos Bz=0\],\[x+\cos \]By\[+\sin \]\[Bz=0,-x+\sin By-\]\[\cos Bz=0,\]then the set of all values of a for which the system of linear equations has a non-trivial solution, is
Consider the following statements : \[{{\text{S}}_{\text{1}}}\]: Number of integrals values of 'a' for which the roots of the equation x2 + ax + 7 = 0 are imaginary with positive real parts is 5. \[{{\text{S}}_{2}}\]: Let \[\alpha ,\beta \] are roots x2 - (a + 3) x + 5 = 0 and \[\alpha ,a,\beta \] pare in P. then roots are 2 and 5/2 \[{{\text{S}}_{\text{3}}}\]: Solution set of \[(2+x)\le {{\log }_{x}}(6-x)\]is (1, 2] State, in order, whether \[{{\text{S}}_{\text{1}}}\text{,}{{\text{S}}_{\text{2}}}\text{,}{{\text{S}}_{\text{3}}}\]are true or false.
The expansion of \[{{(1+x)}^{n}}\]has 3 consecutive terms with coefficients in the ratio 1 : 2 : 3 and can be written in the form\[^{\text{n}}{{\text{C}}_{\text{k}}}{{\text{:}}^{\text{n}}}{{\text{C}}_{\text{k+1}}}{{\text{:}}^{\text{n}}}{{\text{C}}_{\text{k+2}}}\text{.}\] The sum of all possible values of (n + k) is
The mean and standard deviation of 6 observations are 8 and 4 respectively. If each observation is multiplied by 3, find the new standard deviation of the resulting observations.
A triangle ABC satisfies the relation \[2\sec 4C+{{\sin }^{2}}2A+\sqrt{\sin B}=0\]and a point P is taken on the longest side of the triangle such that it divides the side in the ratio 1:3. Let Q and R be the circum centre and orthocenter of\[\Delta ABC\]. If PQ: QR; RP= 1 : \[\alpha :\beta ,\], then the value of \[{{\alpha }^{2}}+{{\beta }^{2}}.\]
All the five digit numbers in which each successive digit exceeds is predecessor are arranged in the increasing order. The (105)th number does not contain the digit
Let \[f:R\to R\] and\[{{f}_{n}}(x)=f\]\[({{f}_{n-1}}(x)\forall n\ge 2,\]\[n\in N,\]the roots of equation \[{{f}_{3}}(x){{f}_{2}}(x)f(x)\]\[-25{{f}_{2}}(x)+175f(x)\]= 375. Which also satisfy equation f(x) = x will be
Statement-1: If [.] denotes the greatest integer function then the integral \[\int\limits_{0}^{\pi /2}{\frac{{{e}^{\sin x-[\sin x]}}d({{\sin }^{2}}x-[{{\sin }^{2}}x])}{\sin x-[\sin x]}}\] is equal to 0
Statement-2: \[fog(x)\] is an odd function, if f and g both are odd functions
A)
Statement-1 and 2 are true and Statement-2 is correct explanation of Statement-1.
doneclear
B)
Statement-1 and 2 are true and Statement-2 is not correct explanation of Statement-1.
Consider the lines represented parametrically as : \[{{\text{L}}_{\text{1}}}\text{:}\,\text{x}\,\text{=1-2}\,\text{t}\,\text{;}\,\text{y}\,\text{=}\,\text{t}\,\text{;}\,\text{z}\,\text{=}\,\text{-1+}\,\text{t}\] \[{{\text{L}}_{2}}\text{:}\,\text{x}\,\text{=4-s}\,\,\text{;}\,\text{y}\,\text{=5+4s}\,\text{;}\,\text{z}\,\text{=}\,\text{-2-s}\]
If\[\vec{a},\vec{b},\vec{c}\]are non-coplanar unit vector such that \[\vec{a}\times (\vec{b}\times \vec{c})=\frac{1}{\sqrt{2}}(\vec{b}+\vec{c})\]then the angle between the vectors\[\vec{a},\vec{b}\]is
If the substitution \[x={{\tan }^{-1}}\] (t) transforms the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+xy\frac{dy}{dx}+{{\sec }^{2}}\] x = 0 into a differential equation \[(1+{{t}^{2}})\frac{{{d}^{2}}y}{d{{t}^{2}}}++(2t+y){{\tan }^{-1}}(t))\frac{dy}{dt}=k\] then k is equal to
Statement 1: If \[|{{z}_{1}}|=30,|{{z}_{2}}-(12+5i)=6,\] then maximum value of\[|{{z}_{1}}-{{z}_{2}}|\] is 49.
Statement 2: If \[{{z}_{1}},{{z}_{2}}\] are two complex numbers, then \[|{{z}_{1}}-{{z}_{2}}|\le |{{z}_{1}}|+|{{z}_{2}}|\]and equality holds when origin, \[{{z}_{1}}\]and \[{{z}_{2}}\] are collinear and \[{{z}_{1}},{{z}_{2}}\] are on the opposite side of the origin.
A)
Statement-1 is false, Statement-2 is true.
doneclear
B)
Statement-1 is true, statemerit-2 is true and Statement-2 is correct explanation for statement-1
doneclear
C)
Statement-1 is true, Statement-2 is true and Statement-2 is NOT correct explanation for statement-1