At certain temperature (T) if conductivity of pure water is \[5.5\times {{10}^{-7}}S\text{ }c{{m}^{-1}},\]then calculate pOH of pure water at temperature T. Given \[\lambda _{{{H}^{+}}}^{\infty }=350\,S\,c{{m}^{2}}e{{q}^{-1}},\,\,\lambda _{O{{H}^{-}}}^{\infty }=200\,\,c{{m}^{2}}\,e{{q}^{-1}}\]
What volume of \[0.2\text{ }M\text{ }RN{{H}_{3}}Cl\]solution should be added to 100 ml. of \[0.1\text{ }M\text{ }RN{{H}_{2}}\]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\[{{N}_{2}}{{O}_{5}}(g)\rightleftharpoons {{N}_{2}}{{O}_{3}}(g)+{{O}_{2}}(g),\]\[{{K}_{c}}=2.5.\]At the same time \[{{N}_{2}}{{O}_{3}}\]decomposes as \[{{N}_{2}}{{O}_{3}}(g)\rightleftharpoons {{N}_{2}}O(g)+{{O}_{2}}(g).\] 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 -
How many times solubility of \[Ca{{F}_{2}}\]is decreased in \[4\times {{10}^{-3}}M\text{ }KF\](aq). solution as compare to pure water at \[25{}^\circ C\]. Given\[{{K}_{sp}}(Ca{{F}_{2}})=3.2\times {{10}^{-11}}.\]
A sample of \[{{U}^{238}}({{t}_{1/2}}=4.5\times {{10}^{9}}yrs)\]is found to contain \[11.9gm\text{ }{{U}^{238}}\]and \[20.6gm\text{ }P{{b}^{206}}.\]The age of sample is - (Given In\[2=0.693,\ln 3=1.1\]]
96.5gm. of oxidized as \[A\to {{A}^{3+}}+3e{{~}^{-}},\]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 \[Ag|A{{g}^{+}}(aq\,0.1\,M)|\,\,|{{H}^{+}}(aq,\,0.1M),\]\[{{H}_{2}}(g,\,0.1\,\,bar)|Pt\] Given: \[E_{Ag/A{{g}^{+}}}^{0}=-0.8\,V\]
\[\xrightarrow{B{{r}_{2/hv}}}\] Major (X) \[\xrightarrow[KOH/\Delta ]{Alcoholic}\] Major (Y)\[\xrightarrow[Peroxide]{H-Br}\]Major (Z) Major final product (Z) is -
Light of wavelength \[\lambda \]strikes a metal surface with intensity ?x? and the metal emits ?y? electrons per second of maximum energy ?z?. What will happen to y and ?z? if ?x? is halved?
\[A\xrightarrow[(ii)\,{{H}^{\oplus }}]{(i)\,NaOl}B\xrightarrow{SOC{{l}_{2}}}C\xrightarrow[NaOH]{{{C}_{6}}{{H}_{5}}N{{H}_{2}}}\]\[D\xrightarrow[\begin{smallmatrix} Conc.\,\,{{H}_{2}}S{{O}_{4}} \\ (1\,\,equivalent) \end{smallmatrix}]{Conc.\,\,HN{{O}_{3}}}E\](Major) E can be -
The in \[{{\Delta }_{f}}H{}^\circ ({{N}_{2}}{{O}_{5}},g)\] kJ/mol on the basis of the following data is - \[2NO(g)+{{O}_{2}}(g)\to 2N{{O}_{2}}(g);\,\,{{\Delta }_{r}}H{}^\circ =-114\,kJ/mol\]\[4N{{O}_{2}}(g)+{{O}_{2}}(g)\to 2{{N}_{2}}{{O}_{5}}(g);\,\,{{\Delta }_{r}}H{}^\circ =-102.6\,kJ/mol\]\[{{\Delta }_{f}}H{}^\circ (NO,g)=90.2kJ/mol\]
This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the One that best describes the two statements.
Statement 1: Anhydrous copper (II) chloride is a covalent while anhydrous copper (II) fluoride is ionic in nature.
Statement 2: In halides of transition metals, the ionic character decreases with increase in atomic mass of the halogen.
A)
Statement-1 is false, Statement-2 is true.
doneclear
B)
Statement-1 is true, statement-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
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 \[P_{B}^{0}?\]
The standard redox potentials \[E{}^\circ \] of the following systems are: System \[E{}^\circ \](volts) (i) \[MnO_{4}^{-}+8{{H}^{+}}+5e\to M{{n}^{2+}}+4{{H}_{2}}O\] 1.51 (ii) \[S{{n}^{4+}}+2e\to S{{n}^{2+}}\] 0.15 (iii)\[C{{r}_{2}}{{O}_{7}}^{2-}+14{{H}^{+}}+6e\to 2C{{r}^{3+}}+7{{H}_{2}}O\] 1.33 (iv) \[C{{e}^{4+}}+e\to C{{e}^{3+}}\] 1.61 The oxidizing power of the various species decreases in the order-
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.
Consider the following statements \[{{S}_{1}}\]: Non zero work has to be done on a moving particle to change its momentum. \[{{S}_{2}}\]: To change momentum of a particle a non zero net force should act on it. \[{{S}_{3}}\]: 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. \[{{S}_{4}}\]: 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 \[{{S}_{1}}\text{, }{{S}_{2}},\text{ }{{S}_{3}},\text{ }{{S}_{4}}\]are true or false.
A particle moves along x-axis with initial position \[x=0.\] Its velocity varies with x-coordinate as shown in graph. The acceleration 'a' of this particle varies with x as
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 Held as indicated (not to scale) in the diagram. The Held is into the page on the diagram. The electron travels ............ around the ............ circle and the proton travels........... around ...............circle.
DIRECTION (Qs. 47): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (Only one option is correct) from the following - This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement 1: When an electrical heater is switched on, the colour of the filament gradually changes from red to yellow to almost white.
Statement 2: Wien's displacement law states that \[{{\lambda }_{m}}T=b\] (constant) where symbols have their usual meaning.
A)
Statement -1 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
DIRECTION (Qs. 48): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (Only one option is correct) from the following ? This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Gas in cylinder with light piston is slowly heated till all the mercury spils over. (\[{{P}_{atm}}=76cm\]of Hg column)
Statement 1: The temperature of gas continuously increases.
Statement 2: According to first law of thermodynamics \[dQ=dU+dW\]where symbols have their usual meaning.
A)
Statement -1 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
DIRECTION (Qs. 49): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (Only one option is correct) from the following ?
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 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
A dipole consisting of two charges +q and -q joined by a massless rod of length \[\ell ,\] is seen oscillating with a small amplitude in a uniform electric field of magnitude E. The period of oscillation
A)
is proportional to E
doneclear
B)
is proportional to 1/E
doneclear
C)
is \[\pi \sqrt{\frac{m\ell }{3qE}}\]
doneclear
D)
is proportional to \[\frac{1}{\sqrt{E}}\]but \[\ne \pi \sqrt{\frac{m\ell }{3qE}}\]
DIRECTION (Qs. 52) Read the following passage and answer the questions that follows: A sinusoidal wave is propagating in negative x-direction in a string stretched along x-axis. A particle of string at \[x=2m\]is found at its mean position and it is moving in positive y-direction at \[t=1\text{ }\sec .\]The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1 meter, \[\pi /2\]meter and In \[2\pi \,rad/\sec \]respectively. The equation of the wave is
DIRECTION (Qs. 54) Read the following passage and answer the questions that follows: The instantaneous power transfer through \[x=2m\]and \[t=1.25\text{ }\sec ,\]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 unstretched 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?
In a photoelectric experiment, with light of wavelength \[\lambda ,\]the fastest electron has speed v. If the exciting wavelength is changed to \[3\lambda /4,\] the speed of the fastest emitted electron will become -
Three moles of an ideal monoatomic gas perform a cycle shown in figure. The gas temperatures in different states are\[{{T}_{1}}=200K,{{T}_{2}}=400K,{{T}_{3}}=1600K\]and \[{{T}_{4}}=800K.\]The work done by the gas during the cycle is (Take\[R=25/3\text{ }J/mol\text{-}K\])
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
A thin convex lens of focal length 10 cm 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?
Given \[f(x)=\left\{ \begin{matrix} \,\,\sqrt{10-{{x}^{2}}}\,\,if\,\,-3<x<3 \\ 2-{{e}^{x-3}}\,\,if\,\,x\ge 3\,\,\,\,\,\,\,\,\,\,\,\,\, \\ \end{matrix} \right.\]. The graph off (x) is-
If \[x\ne 2,\,y\ne 2,\,z\ne 2\]and\[\left| \begin{matrix} 2 & y & z \\ x & 2 & z \\ x & y & 2 \\ \end{matrix} \right|=0,\]then the value of \[\frac{2}{2-x}+\frac{y}{2-y}+\frac{z}{2-z}=\]
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, \[\int\limits_{{{\theta }_{1}}}^{{{\theta }^{2}}}{\frac{d\theta }{1+\tan \theta }}=\frac{50\,1\pi }{K}\]were \[{{\theta }_{2}}=\frac{1003\pi }{2008}\]and \[{{\theta }_{1}}=\frac{\pi }{2008}.\]The value of K equals
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\[^{n}{{C}_{k}}:{{\,}^{n}}{{C}_{k+1}}:{{\,}^{n}}{{C}_{k+2}}.\]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
. The function \[f:[2,\infty )\to (0,\infty )\]denned by\[f(x)={{x}^{2}}-4x-+\text{ }a,\]then the set of values of 'a' tor which \[f(x)\]becomes onto is
If \[\alpha \]and \[\beta \] are the real roots of the equation \[{{x}^{2}}-(k-2)x+({{k}^{2}}+3k+5)=0(k\in R).\] Find the maximum and minimum values of \[({{\alpha }^{2}}+{{\beta }^{2}}).\]
The sum of the coefficient of all the terms in the expansion of \[{{(2x-y+z)}^{20}}\] in which y do not appear at all while x appears in even powers and z appears in odd powers is -
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
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
DIRECTION (Qs. 80): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct the answer (Only one option is correct) from the following-
Statement-1: If \[|{{z}_{1}}|=30,|{{z}_{2}}-(12+5i)|=6,\] 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, \[{{z}_{1}}\]are \[{{z}_{2}}\]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, Statement-2 is true, and 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.
DIRECTION (Qs. 81): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct the answer (Only one option is correct) from the following- Consider the family of straight lines \[2x{{\sin }^{2}}\theta +y{{\cos }^{2}}\theta =2\cos 2\theta \]
Statement-1: All the lines of the given family pass through the point (3, 2).
Statement-2: All the lines of the given family pass through a fixed point.
A)
Statement-1 is false, Statement-2 is true
doneclear
B)
Statement-1 is true, Statement-2 is true, and 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.
DIRECTION (Qs. 82): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct the answer (Only one option is correct) from the following- Consider \[I=\int\limits_{\pi /4}^{\pi /4}{\frac{dx}{1-\sin x}}\]
Statement-1: \[1=0\] because
Statement-2: \[\int\limits_{a}^{a}{f(x)dx=0.}\]wherever f (x) is an odd function.
A)
Statement-1 is false, Statement-2 is true
doneclear
B)
Statement-1 is true, Statement-2 is true, and 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.
DIRECTION (Qs. 83): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct the answer (Only one option is correct) from the following-
Statement-1: Let \[f:R\to R\]be a function such that \[f(x)={{x}^{3}}+{{x}^{2}}+3x+\sin x.\]Then f is one-one.
Statement-2: f(x) neither increasing nor decreasing function.
A)
Statement-1 is false, Statement-2 is true
doneclear
B)
Statement-1 is true, Statement-2 is true, and 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.
DIRECTION (Qs. 84): Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct the answer (Only one option is correct) from the following-
Statement-1: If the lengths of sub tangent and subnormal at point (x, y) on \[y=f(x)\] are respectively 9 and 4. Then \[x=\pm 6\]
Statement-2: Product of sub tangent and sub normal is square of the ordinate of the point.
A)
Statement-1 is false, Statement-2 is true
doneclear
B)
Statement-1 is true, Statement-2 is true, and 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.
Consider the following statements: \[{{S}_{1}}\]: Number of integrals values of 'a' for which the roots of the equation \[{{x}^{2}}+ax+7=0\]are imaginary with positive real parts is 5. \[{{S}_{2}}\]: Let \[\alpha ,\,\beta \]are roots \[{{x}^{2}}-(a+3)x+5=0\]and \[\alpha ,\]a, \[\beta \]are in A. P. then roots are 2 and 5/2 \[{{S}_{3}}\]: Solution set of \[{{\log }_{x}}(2+x)\le {{\log }_{x}}(6-x)\]is (1, 2] State, in order, whether \[{{S}_{1}},{{S}_{2}},{{S}_{3}}\]are true or false.
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
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 \[{{f}_{3}}(x){{f}_{2}}(x)f(x)\]\[-25{{f}_{2}}(x)f(x)+175f(x)=375.\]Which also satisfy equation \[f(x)=-\text{ }x\]will be
A triangle ABC satisfies the relation \[2\sec 4C\]\[+{{\sin }^{2}}\text{ }2A+\sqrt{\sin B}=0\] 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 circumcentre and orthocentre of A \[\Delta ABC.\]If \[PQ:QR:RP=1:\alpha :\beta ,\]then the value of \[{{\alpha }^{2}}+{{\beta }^{2}}.\]
If a is real and \[\sqrt{2}ax+\sin \text{ }By+\cos \text{ }Bz=0,\] \[x+\cos \text{ }By+\sin \text{ }Bz=0,-x+\sin \text{ }By-\cos \]\[Bz=0,\]then the set of all values of a for which the system of linear equations has a non-trivial solution, is -