Let \[{{v}_{1}}\] be the frequency of the series limit of the Lyman series, \[{{v}_{2}}\] be the frequency of the first line of the Lyman series, and \[{{v}_{3}}\] be the frequency of the series limit of the Balmer series, then
When an isolated gaseous cation \[{{X}^{+}}(g)\] is converted into \[{{X}^{-}}(g)\] anion, the amount of energy released is 16.8eV. Calculate the electro negativity value of the atom X on Pauling's scale.
Unknown sample [A] on heating swells up first and aqueous solution of [A] gives white ppt. with NaOH which becomes soluble with excess of NaOH addition
At 675K, \[{{\text{H}}_{\text{2}}}\] (g) and \[\text{C}{{\text{O}}_{\text{2}}}\] (g) react to form CO(g) and \[{{\text{H}}_{\text{2}}}\text{O}\](g), \[{{\text{K}}_{\text{p}}}\] for the reaction is 0.16. If a mixture of 0.25 mole of \[{{\text{H}}_{\text{2}}}\] (g) and 0.25 mol of \[\text{C}{{\text{O}}_{\text{2}}}\] is heated at 675K, mole % of CO (g) in equilibrium mixture is
What would be the reduction potential of an electrode at 298 K, which originally contained \[\text{1M}{{\text{K}}_{\text{2}}}\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{7}}}\] solution in acidic buffer solution of pH = 1.0 and which was treated with 50% of the Sn necessary to reduce all \[\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{7}}}^{2-}\] to \[\text{C}{{\text{r}}^{3+}}\]. Assume pH of solution remains constant. Given: \[\text{E}_{\text{C}{{\text{r}}_{\text{2}}}\text{O}\frac{\text{2-}}{\text{7}}\text{/C}{{\text{r}}^{\text{3+}}}\text{,}{{\text{H}}^{\text{+}}}}^{\text{0}}\]\[=1.33V,\log 2=0.3,\] \[\frac{2.303RT}{F}=0.06\]
The following statement(s) is (are) correct: (i) A plot of log \[{{\text{K}}_{\text{p}}}\] versus 1/T is linear (ii) A plot of log [X] versus time is linear for a first order reaction, \[X\to P\] (iii) A plot of log p versus 1/T is linear at constant volume (iv) A plot of p versus 1/V is linear at constant temperature
The conductivity of a saturated solution of \[A{{g}_{3}}P{{O}_{4}}\] is \[9\times {{10}^{-6}}S{{m}^{-1}}\]and its equivalent conductivity is \[1.50\times {{10}^{-4}}\,S{{m}^{2}}\] equivalent\[^{-1}\]. The \[{{K}_{sp}}\] of\[A{{g}_{3}}P{{O}_{4}}\] is
1 mole of gas X is present in a closed adiabatic vessel fitted with a movable frictionless piston. The initial temperature of gas X is 300 K. The vessel is maintained at constant pressure of 1 amt. Keeping the pressure constant at 1 atm the reaction \[(3X(g)\to 2Y(g);\]\[\Delta H=-30\,\text{kJ}\,\text{/mol)}\] is started with the help of negligible amount of electric energy. If finally 75 mole % of X undergone reaction at constant pressure of 1 atm, find the final temperature (in K) of reaction vessel. Given: \[{{C}_{p,m(X)}}=40\text{J/K}\,\text{mole,}\]\[{{\text{C}}_{\text{p,m(Y)}}}\text{=30J/K}\,\text{mole,}\]
Calculate the millimoles of \[Se{{O}_{3}}^{2-}\]in solution on the basis of following data: 70 ml of \[\frac{M}{60}\]solution of \[KBr{{O}_{3}}\] was added to \[Se{{O}_{3}}^{2-}\]solution. The bromine evolved was removed by boiling and excess of \[KBr{{O}_{3}}\] was back titrated with 12.5 mL of \[\frac{M}{25}\]solution of \[NaAs{{O}_{2}}.\] The reactions are given below. [a] \[\text{SeO}_{\text{3}}^{\text{2-}}\text{+BrO}_{\text{3}}^{\text{-}}\text{+}{{\text{H}}^{\text{+}}}\to \text{SeO}_{\text{4}}^{\text{2-}}\text{+B}{{\text{r}}_{\text{2}}}\text{+}{{\text{H}}_{\text{2}}}\text{O}\] [b] \[\text{BrO}_{\text{3}}^{\text{-}}\text{+AsO}_{\text{2}}^{\text{-}}\text{+}{{\text{H}}_{\text{2}}}\text{O}\to \text{B}{{\text{r}}^{\text{-}}}\text{+AsO}_{\text{4}}^{\text{3-}}\text{+}{{\text{H}}^{\text{+}}}\]
pH of a saturated solution of silver salt of monobasic acid HA is found to be 9. Find the \[{{\text{K}}_{\text{sp}}}\] of sparingly soluble salt Ag A(s). Given \[{{\text{K}}_{a}}(HA)={{10}^{-10}}\]
For the reaction takes place at certain temperature \[N{{H}_{4}}HSN{{H}_{3}}\,(g)+{{H}_{2}}S(g),\] if equilibrium pressure is X bar, then \[\Delta {{G}^{o}}\]would be
Aqueous solution of \[\text{(M)+(N}{{\text{H}}_{\text{4}}}{{\text{)}}_{\text{2}}}\text{S}\to \] yellow ppt \[\xrightarrow[{}]{{{\text{(N}{{\text{H}}_{\text{4}}}\text{)}}_{\text{2}}}{{\text{S}}_{\text{2}}}}\] insoluble. The cation present in (M) is
How many pairs of enantiomers are possible for following complex compound. \[{{[M(AB)(CD)\text{ef}]}^{n\pm }}\] (where AB, CD- Unsymmetrical bidentate ligand, e, f-Monodentate ligands)
For the reaction\[A(g)+2B(g)C(g)+\]\[D(g);\]\[{{K}_{C}}={{10}^{12}}\]. If the initial moles of A, B, C and D are 0.5, 1, 0.5 and 3.5 moles respectively in a one litre vessel. What is the equilibrium concentration of B?
Precautions to be taken in the study of reaction rate for the reaction between potassium iodate \[(KI{{O}_{3}})\] and sodium sulphite \[(N{{a}_{2}}S{{O}_{3}})\] using starch solution as indicator at different concentrations and temperature
A)
The concentration of sodium thiosulphate solution should always be less than the concentration of the potassium iodide solution.
doneclear
B)
Freshly prepared starch solution should be used
doneclear
C)
Experiments should be performed with the fresh solutions of \[{{H}_{2}}{{O}_{2}}\] and KI.
A substance 'A' decomposes in solution following first order kinetics. Flask I contains 1 L of a 1M solution of A and flask II contains 100 ml of a 0.6 M solution. After 8 hours the concentration of A in flask I has become 0.25. What will be the time taken for concentration of A in flask II to become 0.3M?
A)
0.4
doneclear
B)
2.4 h
doneclear
C)
4.0 h
doneclear
D)
Can't be calculated since rate constant is not given
A fixed resistor is in parallel with a variable resistor, both are connected to a real battery (internal resistance is not negligible). Originally the fixed and variable resistors have the same resistance. As the resistance of the variable resistor is decreased, the current through the fixed resistor
A glass prism is immersed in a hypothetical liquid. The curves showing the refractive index n as a function of wavelength X for glass and liquid are as shown in the figure. A ray of white light is incident on the prism parallel to the base. Choose the incorrect statement
A point particle of mass 0.1 kg is executing SHM of amplitude of 0.1m. When the particle passes through the mean position, its kinetic energy is \[18\times {{10}^{-3}}\text{J}\text{.}\]The equation of motion of this particle when the initial phase of oscillation is \[45{}^\circ \] can be given by
A man throws a ball making an angle of \[60{}^\circ \] with the horizontal. He runs on a level ground and catches the ball. If he had thrown the ball with speed v, then his average velocity must be
The mass of block is \[{{m}_{1}}\]and that of liquid with the vessel is \[{{m}_{2}}\]. The block is suspended by a string (tension T) partially in the liquid. Choose the incorrect statement:
A)
The reading of the weighing machine placed below the vessel can be \[({{m}_{1}}+{{m}_{2}})g\]
doneclear
B)
The reading of the weighing machine placed below the vessel can be greater than \[({{m}_{1}}+{{m}_{2}})g\]
doneclear
C)
The reading of the weighing machine placed below the vessel can be \[({{m}_{1}}g+{{m}_{2}}g-T)\]
doneclear
D)
The reading of the weighing machine placed below the vessel can be less than \[({{m}_{1}}+{{m}_{2}})g\]
Modem telescope uses mirrors, rather than lenses, to form images. One advantage of mirrors over lenses is that the images formed by mirrors are not affected by
A particle falls freely near the surface of the earth Consider a fixed point O (not vertically below the particle) on the ground. Then pickup the incorrect alternative or alternatives.
A)
The magnitude of angular momentum of the particle about O is increasing
doneclear
B)
The magnitude of torque of the gravitational force on the particle about O is decreasing
doneclear
C)
The moment of inertia of the particle about O is decreasing
doneclear
D)
The magnitude of angular velocity of the particle about O is increasing
The fundamental frequency of a sonometer wire of length \[\ell \]is \[{{n}_{0}}\]. A bridge is now introduced at a distance of \[\Delta \ell (<<\ell )\] from the centre of the wire. The lengths of wire on the two sides of the bridge are now vibrated in their fundamental modes. Then, the beat frequency nearly is
Two masses A and B are connected with two inextensible string to write constraint relation between \[{{\text{v}}_{\text{A}}}\] and \[{{\text{v}}_{\text{B}}}\]. Student A: \[{{\text{v}}_{\text{A}}}\text{cos}\,\text{ }\!\!\theta\!\!\text{ }\,\text{=}\,{{\text{v}}_{\text{B}}}\] Student B : \[{{\text{v}}_{\text{B}}}\text{cos}\,\text{ }\!\!\theta\!\!\text{ }\,\text{=}\,{{\text{v}}_{\text{A}}}\]
In an X-ray tube, if the accelerating potential difference is increased then
A)
the frequency of characteristic X-rays of a material will get changed
doneclear
B)
Number of electron reaching the anode will change
doneclear
C)
number of characteristics X-ray lines must decrease
doneclear
D)
the difference between\[{{\lambda }_{0}}\] (minimum wavelength) and \[{{\lambda }_{K\alpha }}\] (wavelength of \[{{K}_{\alpha }}\]X-ray) will get changed.
A rectangular loop of wire with dimensions shown is coplanar with a long wire carrying current I. The distance between the wire and the left side of the loop is r. The loop is pulled to the right as indicated. What are the directions of the induced current in the loop and the magnetic forces on the left and right sides of the loop as the loop is pulled?
Two plates of same mass 2 kg each are attached rigidly to the two ends of a spring (k = 100 N/m). One of the plates rests on a fixed horizontal surface and the other results some compression of the spring when it is in equilibrium state. The further minimum compression required, so that when the force causing compression is removed the lower plate is lifted off the surface will be (Take g = 10 m/s2)
A uniform solid sphere of mass m is lying at rest between a vertical wall and a fixed inclined plane as shown. There is no friction between sphere and the vertical wall but coefficient of friction between the sphere and the fixed inclined plane is \[\text{ }\!\!\mu\!\!\text{ =1/2}\]. Then the magnitude of frictional force exerted by fixed inclined plane on sphere is (g is acceleration due to gravity)
At very high temperatures vibrational degrees also becomes active. At such temperatures an ideal diatomic gas has a molar specific heat at constant pressure, \[{{C}_{p}}=\]
Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire 2 has cross-sectional area 3A. If the length of wire 1 increases by \[\Delta x\] on applying force F, how much force is needed to stretch wire 2 by the same amount?
A white light ray is incident on a glass prism, and it creates four refracted rays I, II, III, IV. Choose the possible correct option for refracted rays with the colours given (a & IV are rays due to total internal reflection).
An initially stationary box on a frictionless floor explodes into two pieces, piece A with mass \[{{\text{m}}_{\text{A}}}\], and piece B with mass \[{{\text{m}}_{\text{B}}}\]. Two pieces then move across the floor along x- axis. Graph of position versus time for the two pieces are given. Which graphs pertain to physically possible explosions
A positively charged disk is rotated clockwise as shown in the figure. What is the direction of the magnetic field at point A in the plane of the disk.
A radioactive material decays by simultaneous emission of two particles with respective half-lives 1620 and 810 years. The time, in years, after which one-fourth of the material remains is
In given figure, a wire loop has been bent so that it has three segments: segment ab (a quarter circle), be (a square comer), and a ca (straight). Here are three choices for a magnetic field through the loop
where \[\vec{B}\] is in milliteslas and t is in seconds. If the induced current in the loop due to \[{{\vec{B}}_{1}},{{\vec{B}}_{2}}\] and \[{{\vec{B}}_{3}}\] are \[{{i}_{1}},{{i}_{2}}\] and \[{{i}_{3}}\] respectively, then
Statement-1: Two stones are projected with different velocities from ground from same point and at same instant of time. Then these stones cannot collide in midair. (Neglect air friction)
Statement 2: If relative acceleration of two particles initially at same position is always zero, then the distance between the particles either remains constant or increases continuously with time.
A)
Statement-1 is false, Statement-2 is true.
doneclear
B)
Statement-1 is true, statement-2 is true and statement- is correct explanation for statement-1
doneclear
C)
Statement-1 is true, Statement-2 is true and statement- is NOT correct explanation for statement-1
Statement 1: When two conducting wires of different resistivity having same cross sectional area are joined in series, the electric field in them would be equal when they carry current.
Statement 2: When wires are in series they carry equal current.
A)
Statement-1 is false, Statement-2 is true.
doneclear
B)
Statement-1 is true, Statement-2 is true and statement- is correct explanation for statement-1
doneclear
C)
Statement-1 is true, Statement-2 is true and statement- is NOT correct explanation for statement-1
Let \[{{L}_{1}}\] be a straight line passing through the origin and \[{{L}_{2}}\] be the straight line x + y = 1. If the intercepts made by the circle \[{{x}^{2}}+{{y}^{2}}-x+3y=0\] on \[{{L}_{1}}\] and \[{{L}_{2}}\]are equal, then which of the following equation can represent\[{{L}_{1}}\]?
Let \[{{a}_{n}}=\int\limits_{0}^{\pi /2}{{{(1-\sin t)}^{n}}\sin 2tdt}\]then \[\underset{x\to \infty }{\mathop{\lim }}\,\sum\limits_{1}^{n}{\frac{{{a}_{n}}}{n}}\] is equal to
The trace \[{{\text{T}}_{\text{r}}}\] of a \[3\times 3\] matrix A = \[\text{(}{{\text{a}}_{\text{ij}}}\text{)}\] is defined by the relation \[{{\text{T}}_{\text{r}}}\] \[\text{=}{{\text{a}}_{\text{11}}}\text{+}{{\text{a}}_{\text{22}}}\text{+}{{\text{a}}_{\text{33}}}\] (i.e. \[{{\text{T}}_{\text{r}}}\] is sum of the main diagonal elements). Which of the following statements cannot hold?
A)
\[{{\text{T}}_{\text{r}}}\text{(kA)=k}{{\text{T}}_{\text{r}}}\text{(A)}\](k is a scalar)
Number of permutation of 1, 2, 3, 4, 5, 6, 7, 8 and 9 taken all at a time are such that the digit 1 appearing somewhere to the left of 2, 3 appearing to the left of 4 and 5 somewhere to the left of 6, is (e.g. 815723946 would be one such permutation)
If the function f: [0,16] \[\to \]R is differentiable. If \[0<\alpha <1\]and \[1<\text{ }\!\!\beta\!\!\text{ }<2,\], then \[\int\limits_{0}^{16}{f}\] (t) dt is equal to
The value of the expression\[\left( 1+\frac{1}{\omega } \right)\left( 1+\frac{1}{{{\omega }^{2}}} \right)+\left( 2+\frac{1}{\omega } \right)\left( 2+\frac{1}{{{\omega }^{2}}} \right)\]\[+\left( 3+\frac{1}{\omega } \right)\left( 3+\frac{1}{{{\omega }^{2}}} \right)+.....+\left( n+\frac{1}{\omega } \right)\left( n+\frac{1}{{{\omega }^{2}}} \right)\]where \[\omega \] is an imaginary cube root of unity, is
Let 'a' denote the roots of equation \[\cos ({{\cos }^{-1}}x)+{{\sin }^{-1}}\sin \left( \frac{1+{{x}^{2}}}{2} \right)=2{{\sec }^{-1}}(\sec x)\]then possible values of \[[|10a|]\] where [.] denotes the greatest integer function will be
Ifs, s' are the length of the perpendicular on a tangent from the foci, a, a' are those from the vertices is that from the centre and e is the eccentricity of the ellipse, \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]then \[\frac{ss'-{{c}^{2}}}{aa'-{{c}^{2}}}=\]
Given \[\vec{A}=2\hat{i}+3\hat{j}+6\hat{k},\]\[\vec{B}=\hat{i}+\hat{j}-2\vec{k}\]and \[\vec{C}=\hat{i}+2\hat{j}+\hat{k}\]Compute the value of \[|\vec{A}\times [\vec{A}\times (\vec{A}\times \vec{B})].\vec{C}|.\]
One percent of the population suffers from a certain disease. There is blood test for this disease, and it is 99% accurate, in other words, the probability that it gives the correct answer is 0.99, regardless of whether the person is sick or healthy. A person takes the blood test, and the result says that he has the disease. The probability that he actually has the disease, is
Two circle of radii a and b touch each other externally and are inscribed in the area bounded by \[y=\sqrt{1-{{x}^{2}}}\] and the x-axis Statement-1: If \[b=\frac{1}{2}\] then \[a=\frac{1}{2}\] Statement-2: Distance between the centre of two circles = a + b
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.
Set of values of m for which two points P and Q lie on the line y = mx + 8 so that \[\angle APB=\angle AQB=\frac{\pi }{2}\]where \[A\equiv (-4,0),\] \[B\equiv (4,0)\]is
The straight line joining any point P on the parabola \[{{y}^{2}}=4ax\]to the vertex and perpendicular from the focus to the tangent at P, intersect at R, then the equation of the locus of R is
A box contains 6 red, 5 blue and 4 white marbles. Four marbles are chosen at random without replacement. The probability that there is at least one marble of each colour among the four chosen, is
Consider the word \[D=F\,\text{ }R\,\text{ }E\,\text{ }E\text{ }\,W\text{ }\,H\text{ }\,E\text{ }\,E\,\text{ }L\]. Numbers of ways in which the letters of the word D can be arranged if vowels and consonants both are in alphabetical is
Statement-1: If \[{{x}^{2}}+x+1=0\] then the value of \[{{\left( x+\frac{1}{x} \right)}^{2}}+{{\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)}^{2}}+....+{{\left( {{x}^{27}}+\frac{1}{{{x}^{27}}} \right)}^{2}}\]is 54.
Statement-2: \[\omega ,{{\omega }^{2}}\] are the roots of equation\[{{x}^{2}}+x+1=0\]
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.
Statement 1: If a, b, c are non-real complex and \[\alpha ,\beta \] are the roots of the equation ax2 + bx + c = 0 then \[\operatorname{Im}(\alpha \beta )\ne 0.\]
Statement 2: A quadratic equation with non real complex coefficient do not have root which are conjugate of each other.
A)
Statement-1 is false, Statement-2 is true.
doneclear
B)
Statement-1 is true, statement-2 is true and statement- 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
Let C be a circle with centre \[O\] and \[HK\] is the chord of contact of pair of the tangents from points A. OA intersects the circle \[C\] at \[P\] and \[Q\] and \[B\] is the midpoint of\[HK\], then
Statement 1: AB is the harmonic mean of AP and AQ.
Statement 2: AK is the Geometric mean of AB and AO, OA is the arithmetic mean of AP and AQ.
A)
Statement-1 is false, Statement-2 is true.
doneclear
B)
Statement-1 is true.statement-2 is true and statement- 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