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 electronegativity value of the atom X on Pauling's scale.
Unknown sample on heating swells up first and aqueous solution of gives white ppt. with \[NaOH\] which becomes soluble with excess of \[NaOH\] addition -
At \[675\,K,\]\[{{H}_{2}}(g)\] and \[C{{O}_{2}}(g)\] react to form \[CO(g)\] and \[{{H}_{2}}O(g),\]\[{{K}_{p}}\] for the reaction is 0.16. If a mixture of \[0.25\] mole of \[{{H}_{2}}(g)\]and \[0.25\text{ }mol\] of \[C{{O}_{2}}\] is heated at \[675\,\,K,\] mole % of \[CO\,(g)\] in equilibrium mixture is -
For the extraction of Pb when impurity content is very high, then during roasting of galena, the formation of which compound (s) is/are prevented by lime -
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 \[1.50\times {{10}^{-4}}S{{m}^{2}}\]\[equivalen{{t}^{-1}}\]. The \[{{K}_{sp}}\] of \[A{{g}_{3}}P{{O}_{4}}\] is -
\[pH\] of a saturated solution of silver salt of monobasic acid HA is found to be 9. Find the \[{{K}_{sp}}\]of sparingly soluble salt \[Ag\] \[A\,(s)\]. Given \[{{K}_{a}}(HA)={{10}^{-10}}\].
For the reaction takes place at certain temperature \[N{{H}_{4}}HS\rightleftharpoons N{{H}_{3}}(g)+{{H}_{2}}S(g),\]if equilibrium pressure is X bar, then \[\Delta {{G}^{o}}\] would be
Aqueous solution of \[(M)+{{(N{{H}_{4}})}_{2}}S\to \] yellow \[ppt\,(B)\xrightarrow{{{(N{{H}_{4}})}_{2}}{{S}_{2}}}\] insoluble. The cation present in (M) is -
How many pairs of enantiomers are possible for following complex compound. \[{{[M(AB)\,(CD)ef]}^{n\pm }}\](where AB, CD-Unsymmetrical bidentate ligand, e, f-Monodentate ligands)
For the reaction \[A(g)+2B(g)\rightleftharpoons C(g)+D(g);\] \[{{K}_{C}}={{10}^{12}}\]If the initial moles of A, B, C and D are \[0.5,\text{ }1,\text{ }0.5\]and \[3.5\]moles respectively in a one litre vessel. What is the equilibrium concentration of B?
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: \[{{[HeH]}^{+}}\] is more stable as compared to \[{{H}_{2}}^{+}\].
Statement 2: Both the above species are having equal bond order.
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
The variation of concentration of A with time in two experiments starting with two different initial concentration of A is given in the following graph. The reaction is represented as \[A(aq)\to B(aq)\]. What is the rate of reaction (M/min) when concentration of A in aqueous solution was \[1.8M\]?
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 \[KI\].
Calculate the mill moles of \[Se{{O}_{3}}^{2-}\] in solution on the basis of following data: \[70\text{ }ml\] 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 \[12.5mL\] of \[\frac{M}{25}\] solution of \[NaAs{{O}_{2}}\] The reactions are given below
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 aim. Keeping the pressure constant at 1 atm the reaction \[(3X\,(g)\to 2Y(g);\,\Delta H=-30kJ/mol)\]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: \[{{C}_{p,m(X)}}=40J/K\,mole,\]\[{{C}_{p,m(Y)}}=30J/K\,mole,\]
What would be the reduction potential of an electrode at \[298\text{ }K,\]which originally contained \[1M\,\,{{K}_{2}}C{{r}_{2}}{{O}_{7}}\] solution in acidic buffer solution of \[pH=1.0\]and which was treated with 50% of the \[Sn\] necessary to reduce all \[C{{r}_{2}}{{O}_{7}}^{2-}\] to \[C{{r}^{3+}}\] Assume pH of solution remains constant. Given: \[E_{C{{r}_{2}}O_{7}^{2-}/C{{r}^{3+}},{{H}^{+}}}^{0}=1.33V,\,\log 2\,=0.3,\] \[\frac{2.303\,RT}{F}=0.06\]
A glass prism is immersed in a hypothetical liquid. The curves showing the refractive index n as a functions of wavelength \[\lambda \]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-
The speed of sound is measured by a resonance tube at the room temperature once by filling the tube with water and then with glycerine as \[{{v}_{1}}\] and \[{{v}_{2}}\]. Which of the following relation relations is/are true in this context?
A)
\[{{v}_{1}}=2{{v}_{2}}\]
doneclear
B)
\[{{v}_{1}}>{{v}_{2}}\]
doneclear
C)
\[{{v}_{1}}<{{v}_{2}}\]
doneclear
D)
\[{{v}_{1}}\] and \[{{v}_{2}}\] does not depend on the nature of the liquid taken in the tube.
Two potentiometers A and B having 4 wires and 10 wires, each having \[100\text{ }cm\] in length are used to compare e.m.f. of 2 cells. Which one will give a larger balancing length?
A)
Balancing length doesn't depend on the total length of the wire.
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 \[({{m}_{1}}+{{m}_{2}})g\]
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
Two masses A and B are connected with two inextensible string to write constraint relation between \[{{v}_{A}}\] and \[{{v}_{B}}\]. Student A: \[{{v}_{A}}\,\cos \theta ={{v}_{B}}.\] Student B: \[{{v}_{B}}\,\cos \theta ={{v}_{A}}.\]
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 m^ and piece B with mass \[{{m}_{B}}\]. Two pieces then move across the floor along x-axis. Graph of position versus time for the two pieces are-given.
(I)
(II)
(III)
(IV)
(V)
(VI)
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.
DIRECTIONS: 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: 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 particle 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; 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
DIRECTIONS: 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 m four choices given after the statements, choose the one that It best describes the two statements.
The electrostatic potential on the surface of a charged solid conducting sphere is 100 volts. Two statements are made in this regard.
Statement 1: At any point inside the sphere, electrostatic potential is 100 volt.
Statement 2: At any point inside the sphere, electric field is zero.
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 correct explanation for Statement -1
DIRECTIONS: 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: 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; Statement -2 is a correct explanation for Statement -1
doneclear
C)
Statement - 1 is true, Statement -2 is true; Statement -2 is not correct explanation for Statement -1
An ideal ammeter (zero resistance) and an ideal voltmeter (infinite resistance) are connected as shown. The ammeter and voltmeter reading for \[{{R}_{1}}=5\Omega ,\,{{R}_{2}}=15\,\Omega ,{{R}_{3}}=1.25\Omega \]and \[E=20V\] are given as
Consider an optical communication system operating at \[1\tilde{\ }800mm.\]Suppose, only 1% of the optical source frequency is the available channel bandwidth for optical communication. How many channels can be accommodated for transmitting audio signals requiring a bandwidth of 8 kHz?
DIRECTIONS: Read the following passage and answer the questions that follows:
A monoatomic ideal gas is filled in a no conducting container. The gas can be compressed by a movable no conducting piston. The gas is compressed slowly to 12.5% of its initial volume.
Find final temperature of the gas if it is \[{{T}_{0}}\]initially-
DIRECTIONS: Read the following passage and answer the questions that follows:
A monoatomic ideal gas is filled in a no conducting container. The gas can be compressed by a movable no conducting piston. The gas is compressed slowly to 12.5% of its initial volume.
The initial adiabatic bulk modulus of the gas is \[{{B}_{i}}\] and the final value of the adiabatic bulk modulus of the gas is \[{{B}_{f}}\].then
DIRECTIONS: Read the following passage and answer the questions that follows:
A monoatomic ideal gas is filled in a no conducting container. The gas can be compressed by a movable no conducting piston. The gas is compressed slowly to 12.5% of its initial volume.
The summation of work done by the gas and the change in the internal energy of the gas is
A point particle of mass \[0.1\text{ }kg\] is executing SHM of amplitude of \[0.1m\]. When the particle passes through the mean position, its kinetic energy is \[18\times {{10}^{-3}}J\] The equation of motion of this particle when the initial phase of oscillation is \[{{45}^{o}}\] can be given by -
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 -
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?
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 \[\mu =1/2\]. Then the magnitude of frictional force exerted by fixed inclined plane on sphere is -(g is acceleration due to gravity)
The circuit shown has been operating for a long time. The instant after the switch in the circuit labeled S is opened, what is the voltage across the inductor \[{{V}_{L}}\] and which labeled point (A or B) of the inductor is at a higher potential? Take, \[{{R}_{1}}=4.0\Omega ,{{R}_{2}}=8.0\Omega \] and \[L=2.5H\].
A)
\[{{V}_{L}}=12V,\] point A is at the higher potential
doneclear
B)
\[{{V}_{L}}=12V,\] point B is at the higher potential
doneclear
C)
\[{{V}_{L}}=6V,\] point A is at the higher potential
doneclear
D)
\[{{V}_{L}}=12V,\] point B is at the higher potential
A point charge \[+Q\] is positioned at the center of the base of a square pyramid as shown. The flux through one of the four identical upper faces of the pyramid is -
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\[{{L}_{1}}\]?
Number of permutations\[1,\,\,2,\,\,3,\,\,4,\,\,5,\,\,6,\,\,7,\,\,8\]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)
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
Vertices of a parallelogram taken in order are \[A(2,\,\,-1,\,\,4),\]\[B(1,\,\,0,\,\,-1),\]\[C(1,\,\,2,\,\,3)\] and \[D\]. Distance of the point \[P(8,\,\,2,\,\,-12)\] from the plane of the parallelogram is-
Given\[\overrightarrow{A}=2\widehat{i}+3\widehat{j}+6\widehat{k},\,\,\overrightarrow{B}=\widehat{i}+\widehat{j}-2\widehat{k}\]and\[\overrightarrow{C}=\widehat{i}+2\widehat{j}+\widehat{k}\]. Compute the value of\[|\overrightarrow{A}\times [\overrightarrow{A}\times (\overrightarrow{A}\times \overrightarrow{B}).\overrightarrow{C}]\].
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 atleast one marble of each colour among the four chosen, is -
DIRECTION: 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: If\[a,\,\,b,\,\,c\]are noncomplex and\[\alpha ,\,\,\beta \] are the roots of the equation\[a{{x}^{2}}+bx+c=0\] 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 other.
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.
DIRECTION: 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: The line\[\frac{x}{a}+\frac{y}{b}=1\]touches the curve\[y=b{{e}^{-x/a}}\]at some point\[x={{x}_{0}}\] because
DIRECTION: 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-
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 \[A\] because
Statement-2: \[AK\] is the Geometric mean of \[AB\] and\[AO,\,\,\,OA\] is the arithmetic mean of \[AP\] and \[A\]
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.
DIRECTION: 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-
DIRECTION: 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-
Statements-1: Period of \[f(x)=\sin 4\pi \{x\}\]\[+\tan \pi [x]\], where,\[[x]\And \{x\}\] denote the \[G.I.F.\] & fractional part respectively is \[1\].
Statements-2: A function is said to be periodic if there exist a positive number \[T\] independent of \[x\] such that \[f(T+x)=f(x)\]. The smallest such positive value of \[T\] is called the period or fundamental period.
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.
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
If \[s\], \[s'\] 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\[\frac{ss'-{{c}^{2}}}{aa'-{{c}^{2}}}=\]
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-
Set of values of \[m\] for which two points \[P\] and \[Q\] lie on the line\[y=mx+8\]so that\[\angle APB=\angle AQB=\frac{\pi }{2}\]\[A\equiv (-4,\,\,0),\,\,\,B\equiv (4,\,\,0)\]is-
The trace \[{{T}_{r}}(A)\] of a \[3\times 3\] matrix \[A=({{a}_{ij}})\] is defined by the\[{{T}_{r}}(A)={{a}_{11}}+{{a}_{22}}+{{a}_{33}}(i.e.,\,\,{{T}_{r}}(A)\]diagonal elements). Which of the following statements cannot hold?