The potential energy of a particle of mass 1 kg in motion along the x-axis is given by: \[U=4\left( 1-cos\,2x \right)J\], where x is in metres. The period of small oscillations (in sec) is -
Two circular coils X and Y have equal number of turn and 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 that due to smaller coil X at\[O\text{ }{{B}_{X}}\], then:
A short magnet produces a deflection of \[30{}^\circ \] when placed at certain distance in \[tanA\]position of magnetometer. If another short magnet of double the length and thrice the pole strength is placed at the same distance in \[tanB\] position of the magnetometer, the deflection produced will be -
The loop ABCD is moving with velocity 'v' towards right. The magnetic field is 4T. The loop is connected to a resistance of 8 ohm. If steady current of 2 A flows in the loop then value of v if loop has a resistance of 4 ohm, (Given AB = 30cm, AD = 30 cm) is-
When a wave travels in a medium, the particle displacement is given by the equation \[y=a\,\,sin\,2\pi \left( bt-cx \right)\] where a, b and c are constant. The maximum particle velocity will be twice the wave velocity if-
A source of sound is travelling towards a stationary observer. The frequency of sound heard by the observer is of three times the original frequency. The velocity of sound is v m/sec. The speed of source will be-
A vessel is partitioned in two equal halves by a fixed diathermic separator. Two different ideal gases are filled in left (L) and right (R) halves. The rms speed of the molecules in L part is equal to the mean speed of molecules in the R part. Then the ratio of the mass of a molecule in L part to that of a molecule in R part is -
The minimum (threshold) KE of the proton to initiate the nuclear reaction \[p{{+}^{7}}Li{{\xrightarrow{{}}}^{7}}Be+n\] Given \[{{m}_{p}}=1.0073\text{ }amu;\text{ }{{m}_{Li}}=7.0144\text{ }amu,\] \[{{m}_{Be}}=7.0147\text{ }amu,\text{ }{{\text{m}}_{n}}=1.0087\text{ }amu.\]
What should be the velocity of a \[{{e}^{-}}\]so that its momentum becomes equal to that of a photon of wavelength\[\text{5200}\overset{\text{o}}{\mathop{\text{A}}}\,\]?
Two long straight wires are placed on a smooth horizontal table. Wires have equal but opposite charges. Magnitude of linear charge density on each wire is\[\lambda \]. For unit length of wires, the work required to increase the separation between the wires from a to 2a.
In the circuit shown in figure, the switch is shifted from position 1 to 2 at t = 0. The switch was initially in position 1 since a long time. The graph between charge on upper plate of capacitor versus time -
In figure, the resistance of galvanometer G is 50 ohm and the battery is ideal. Of the following alternatives, in which case, are the currents arranged strictly in the order of decreasing magnitudes with the larger coming earlier-
A person standing between two parallel hills fires a gun. He hears the first echo after 1.5 s & second after 2.5 s. If the speed of sound is 332 m/s calculate the distance (in m) between the hills.
A whistle sends out 256 waves in a second. If the whistle approaches the observer with velocity 1/3 of the velocity of sound in air. Find the number of waves per second the observer.
A flat plate with dimensions \[4\text{ }cm\times 6\text{ }cm\] is set with its plane at \[37{}^\circ \] to a uniform electric field\[\vec{E}=600\hat{j}\text{ }N/C\], as shown below. What is the flux (in \[N{{m}^{2}}C\]) through the plate?
Two metal plates form a parallel plate condenser. The distance between the plates is d. A metal plate of thickness d/2 and of the same area is inserted completely between the plates. The ratio of capacitances in the two cases (later to initial) is-
For driving a current of 3 ampere for 5 minutes in an electrical circuit, 900 joule of work is to be done. Find the emf of the source in the circuit, (in V)
The following species, (I) \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}},\] (II) \[{{I}_{3}}^{\Theta },\] (III) \[SnC{{l}_{6}}^{\Theta },\] (IV) \[IC{{l}_{4}}^{\Theta }\]and the d-orbitals involved in the hybridisation of central atom of the above species are given.
Consider the following statements and choose the INCORRECT one.
A)
Work in the reversible isothermal expansion of an ideal gas is less than for a van der Waals gas.
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B)
The Joule-Thomson coefficient for an ideal gas is zero.
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C)
Criterion of spontaneity reaction is: (i) \[{{(dS)}_{U,V}}\ge 0\] (ii) \[{{(dG)}_{T,P}}\le 0\] (iii) \[{{(dU)}_{S.V}}\le 0\] (iv) \[{{(dh)}_{S.P}}\le 0\] Where in equality (< or >) refers to an irreversible process (Spontaneous) while equality (=) refers to a reversible process at equilibrium.
doneclear
D)
Endergonic reaction is a reaction for which \[\Delta G=+ve\] and for exergonic reaction \[\Delta G=-ve\]
\[30\text{ }mL\]of a solution containing \[9.15g\,{{L}^{-1}}\] of an oxalate \[{{K}_{x}}{{H}_{y}}{{({{C}_{2}}{{O}_{4}})}_{z}}.n{{H}_{2}}O\]required for titration \[27\text{ }mL\]of \[0.12\text{ }N\text{ }NaOH\]and \[36\text{ }mL\]of \[0.12\text{ }N\]\[KMn{{O}_{4}}\] for oxidation. Find the ratio \[x:y:z\]and the value of n.
For pseudo alum, the ionic equivalent and ionic molar conductivities of their ions are given. \[\lambda {{{}^\circ }_{eq}}(S{{O}_{4}}^{2-})'\lambda {{{}^\circ }_{eq}}(F{{e}^{2+}})\] and \[\lambda {{{}^\circ }_{m}}(A{{l}^{3+}})\] are x, y and z respectively: \[\lambda {{{}^\circ }_{m}}(S{{O}_{4}}^{2-})'\lambda {{{}^\circ }_{eq}}(F{{e}^{2+}})\]and \[\lambda {{{}^\circ }_{m}}(A{{l}^{3+}})\]are \[{{x}^{1}},{{y}^{1}}\] and \[{{z}^{1}}\] respectively For pseudo alum, the correct relation between \[\wedge {{{}^\circ }_{eq}}\] and \[\wedge {{{}^\circ }_{m}}\] is
\[15\text{ }mL\]of gaseous hydrocarbon was required for complete combination. \[357\text{ }mL\]of air (\[21%\]oxygen by volume) and gaseous products occupied \[327\text{ }mL\](all volumes being measured at STP). The molecular formula of the hydrocarbon is
In the following reaction sequence: Product X and F are given as: and Select the INCORRECT statement.
A)
In Reaction-1 product (Y) is obtained
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B)
In Reaction-2 both products (X) and (Y) are obtained.
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C)
Cross aldol reaction using strong bulky base in non-protic solvent gives single cross aldol product via kinetic enolate. Thus it is regioselective and is called directed aldol.
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D)
Cross aldol reaction using a weak base in protic solvent produces a mixture via both kinetic and thermodynamic enolate and is called classical aldol
A cylinder filled with laughing gas had a small thin orifice through which laughing gas escaped into an evacuated space at the rate of \[5.61\] moles\[h{{r}^{-1}}\]. The time (hr) it take for 9 moles of weeping gas to leak through a similar orifice if the weeping gas is confined at the same pressure? (Take \[\sqrt{3.5}=1.87\])
The number of moles of ethanol must be added to 1.00 L of water so that solution will not freeze at \[-4{}^\circ F\]is \[({{K}_{f}}=1.86\,K\,{{m}^{-1}})\]
In an adsorption experiment, a graph between \[\log (x/m)\] versus log P was found to be linear with a slope of\[45{}^\circ \]. The intercept on the axis was found to be\[0.301\]. The amount of the gas adsorbed per gram of charcoal under a pressure of \[3.0\] atm is
The rate of a first order reaction increases by \[7%\] when its temperature is raised from \[300K\] to \[310\text{ }K,\] while its equilibrium constant increases by\[3%\]. The activation energy of the backward reaction \[(700+x)\] cal. Find the value of. x. (In \[1.07=0.0677\]and In\[1.03=0.02956\])
A straight line through origin bisect the line passing through the given points \[(a\,cos\,\alpha ,\,\,a\,sin\alpha )\] and \[(a\,\,\cos \beta ,a\sin \beta ),\]then the lines are
In a class of 30 pupils, 12 take needle work, 16takephysics and 18 take history. If all the 30 students take at least one subject and no one takes all three then the number of pupils taking 2 subjects is
Equation of plane passing through line \[\frac{(x-1)}{2}=\frac{(y+1)}{-1}=\frac{(z-3)}{4}\]and perpendicular to the plane \[x+2y+z=12\]is given by \[ax+by+cz+4=0,\]then
ABC is a triangular park with \[AB=AC=100\text{ }m.\]A TV tower stands at the mid-point of BC. The angles of elevation of the top of the tower at A, B, C are \[45{}^\circ ,\text{ }60{}^\circ ,\text{ }60{}^\circ \]respectively The height of the tower is
Odds 8 to 5 against a person who is 40 years old living till he is 70 years and 4 to 3 against another person now 50 years till he will be living 80 years. Probability that one of them will be alive next 30 years
If the second term in the expansion \[{{\left( \sqrt[13]{a}+\frac{a}{\sqrt{{{a}^{-1}}}} \right)}^{n}}\] is \[14{{a}^{5/2}},\]then \[\frac{^{n}{{C}_{3}}}{^{n}{{C}_{2}}}=\]
The values of A and B such that the function \[f(x)=\left\{ \begin{matrix} -2\sin x, \\ A\sin x+B, \\ \cos x, \\ \end{matrix} \right.\,\,\,\,\,\,\begin{matrix} x\le -\frac{\pi }{2} \\ -\frac{\pi }{2}<x<\frac{\pi }{2} \\ x\ge \frac{\pi }{2} \\ \end{matrix}\] is continuous everywhere are
If a, b, c are non-coplanar unit vectors such that \[\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})=\frac{(\overrightarrow{b}+\overrightarrow{c})}{\sqrt{2}},\] then the angle between \[\overrightarrow{a}\] and \[\overrightarrow{b}\] is
Let \[y'9x)+y(x)g'(x)=g(x)g'(x),\] \[y(0)=0,\] s\[x\in R\] where \[f'(x)\] denotes \[\frac{df\,(x)}{dx}\]and \[g(x)\] is a given non-constant differentiable function on R with \[g(0)=g(2)=0.\] Then the value of \[y(2)\] is
There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 the number of games that the men played with the women. The number of participants is
If the length of the tangent from any point on the circle \[{{(x-3)}^{2}}+{{(y+2)}^{2}}=5{{r}^{2}}\]to the circle \[{{(x-3)}^{2}}+{{(y+2)}^{2}}={{r}^{2}}\] 16 units, if the area between the two circles in sq. units is R, then \[\frac{R}{25\pi }=\]
Number of real roots of the equation \[\left| \begin{matrix} {{x}^{2}}-12 & -18 & -5 \\ 10 & {{x}^{2}}+2 & 1 \\ -2 & 12 & {{x}^{2}} \\ \end{matrix} \right|=0\] is
If the roots of the equation \[{{x}^{2}}-5x+16=0\]are \[\alpha ,\beta \] and the roots of equation \[{{x}^{2}}+px+q=0\] are \[{{\alpha }^{2}}+{{\beta }^{2}},\] \[\frac{\alpha \beta }{2},\]then \[|p+q|=\]