The moon has a mass of \[\frac{1}{81}\] that of the earth and radius of \[\frac{1}{4}\] that of the earth. The escape speed from the surface of the earth is 11.2 km/s. The escape speed from the surface of the moon is -
The displacement of a particle executing SHM is given by \[y=5\,\sin \left( 4t+\frac{\pi }{3} \right)\] If T is the time period and the mass of the particle is 2 g, the kinetic energy of the particle when \[t=\frac{T}{4}\] is given by-
A wooden block of mass 8 kg is tied to a string attached to the bottom of a tank. The block is completely inside the water. Relative density of wood is 0.8. Taking\[g=10m/{{s}^{2}}\], what is the tension in the string?
Two long parallel wires carry currents \[{{i}_{1}}\] and \[{{i}_{2}}\] such that\[{{i}_{1}}>{{i}_{2}}\]. When the currents are in the same direction, the magnetic field at a point midway between the wires is\[6\times {{10}^{-6}}T\]. If the direction of ii is reversed, the field becomes\[3\times {{10}^{-5}}T\]. The ratio of \[{{i}_{1}}/{{i}_{2}}\] is -
A copper disc of radius 0.1 m is rotated about its centre with 20 revolution per second in a uniform magnetic field of 0.1 T with its plane perpendicular to the field. The emf induced across the radius of the disc is -
A bulb is rated at 100 V, 100 W, it can be treated as a resistor. Find out the inductance of an inductor (called choke coil) that should be connected in series with the bulb to operate the bulb at its rated power with the help of an ac source of 200V and 50 Hz.
Equal temperature difference exists between the ends of two metallic rods 1 and 2 of equal length. Their thermal conductivities are \[{{K}_{1}}\] and \[{{K}_{2}}\] and cross sectional areas are respectively \[{{A}_{1}}\] and\[{{A}_{2}}\]. The condition for equal rate of heat transfer will be-
Two wires of copper are given. Wire A: length \[\ell \] and radius r, wire B: length \[\ell \] and radius 2r. If Young's modulus for wire A is \[{{Y}_{A}}\] and for wire B is\[{{Y}_{B}}\]. Then -
What is the base resistance \[{{R}_{B}}\] in the circuit as shown in figure, if\[{{\beta }_{d.c.}}=90,\,\,{{V}_{BE}}=0.7\text{ }V\text{ };\]\[{{V}_{CE}}=4V\]?
Two waves \[{{y}_{1}}=A\,cos\left( 0.5\pi x-100\pi t \right)\] and \[{{y}_{2}}=A\,cos\left( 0.46\pi x-92\pi t \right)\] are travelling in a pipe along x-axis. (y and x are in metre). How many times in a second does a stationary any observer hear loud sound (maximum intensity)?
Two boys stand close to a long straight metal pipe and at some distance from each other. One boy fires a gun and the other hears two explosions, with a time interval of one second between them. If the velocity of sound in metal is \[3630\text{ }m\text{ }{{s}^{-1}}\] and in air is \[330\text{ }m\text{ }{{s}^{-1}}\] the distance between the two boys is
A gas mixture consists of molecules of type 1,2 and 3, with molar masses \[{{m}_{1}}>{{m}_{2}}>{{m}_{3}}.\text{ }{{V}_{rms}}\] and \[\overline{K}\] are the r.m.s. speed and average kinetic energy of the gases. Which of the following is true-
A He-atom is de-excited from an energy level "n" to ground state to emit two consecutive photons of wavelength \[1085\overset{\text{o}}{\mathop{\text{A}}}\,\] and\[3040\overset{o}{\mathop{\text{A}}}\,\]. Then n will be-
A radioactive decay chain starts from \[_{93}N{{p}^{237}}\] and produces \[_{90}T{{h}^{22}}^{9}\] by successive emissions. The emitted particles can be-
A)
Two \[\alpha \]-particles and one \[\beta \]-particles
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B)
Three \[{{\beta }^{+}}\] particles
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C)
One \[\alpha \]-particle and two \[{{\beta }^{+}}\] particles
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D)
One \[\alpha \]-particle and two \[{{\beta }^{-}}\] particles
A potential difference of \[{{10}^{3}}V\] is applied across an X-ray tube. The ratio of the de- Broglie wavelength of the incident electrons to the shortest wavelength of X-rays produced is -
A)
1/20
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B)
1/100
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C)
1
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D)
None of these (\[e/m=1.8\times {{10}^{14}}C/kg\] for an electron)
A charge q is placed at (1, 2, 1) and another charge -q is placed at (0, 1, 0), such that they form an electric dipole. There exists a uniform electric field\[\vec{E}=\left( 2\hat{i}+3\hat{j} \right)\]. The torque experienced by the dipole is-
Two identical square rods of metal are welded end to end as shown in figure , 20 calories of heat flows through it in 4 minutes. If the rods are welded as shown in figure . The same amount of heat will flow through the rods in (in min)
A 30 cm long cylinder floats vertically in mercury at \[0{}^\circ C\]. If the temperature rises to \[100{}^\circ C\], find the increase in length of the cylinder (in cm) under mercury. The density of mercury at \[0{}^\circ C=13.6/c{{m}^{3}}\] density of iron at\[0{}^\circ C=7.6/c{{m}^{3}}\], coefficient of volume expansion of mercury \[=1.82\times {{10}^{-4}}/{}^\circ C\] and coefficient of cubical expansion of iron \[=3.51\times {{10}^{-5}}/{}^\circ C\]
In Melde's experiment it was found that the string vibrates in 3 loops when 8 gm were placed in the pan. What mass (in gm) must be placed in the pan to make the string vibrate in 5 loops. (Neglect the mass of string)
Consider the reaction The equilibrium constant of the above reaction is \[{{K}_{p}}\]. If pure ammonia is left to dissociate, the partial pressure of ammonia at equilibrium is given by (Assume that \[{{P}_{N{{H}_{3}}}}<<{{P}_{total}}\] at equilibrium)
The standard emf of a cell, involving one electron change is found to be \[0.591\text{ }V\]at\[25{}^\circ C\]. The equilibrium constant of the reaction is \[(F=96500\,\,C\,\,mo{{l}^{-1}})\]
When a small quantity of \[FeC{{l}_{3}}\] solution is added to the fresh precipitate of \[Fe{{(OH)}_{3}}\] a colloidal sol is obtained. The process through which this sol is formed is known as
The molal elevation constant of water \[=0.52{}^\circ C\,\,kg\,\,mo{{l}^{-1}}\] . The boiling point of \[1.0\] molal aqueous \[KCl\] solution (assuming complete dissociation of \[KCl\]), therefore should be
Standard reduction potentials of the half reactions are given below : \[{{F}_{2}}(g)+2{{e}^{-}}\to 2{{F}^{-}}(aq);\] \[{{E}^{o}}=+2.85V\] \[C{{l}_{2}}(g)+2{{e}^{-}}\to 2C{{l}^{-}}(aq);\] \[{{E}^{o}}=+1.36V\] \[B{{r}_{2}}(l)+2{{e}^{-}}\to 2B{{r}^{-}}(aq);\] \[{{E}^{o}}=+1.06V\] \[{{I}_{2}}(s)+2{{e}^{-}}\to 2{{I}^{-}}(aq);\] \[{{E}^{o}}=+0.53V\] The strongest oxidising and reducing agents respectively are:
Cyclopropane rearranges to form propene This follows first order kinetics. The rate constant is \[2.714\times {{10}^{-3}}{{s}^{--1}}.\]The initial concentration of cyclopropane is\[0.29\text{ }M\]. What will be the concentration of cyclopropane after 100s?
At infinite dilution, the molar conductance of \[B{{a}^{2+}}\] and \[C{{l}^{-}}\]are 127 and\[76\text{ }S\text{ }c{{m}^{2}}\text{ }mo{{l}^{-1}}\]. What is the molar conductivity of \[BaC{{l}_{2}}\] at indefinite dilution?
The enthalpy of hydrogenation of cyclohexene is\[-\text{ }119.5\text{ }kJ\text{ }mo{{l}^{-1}}\]. If resonance energy of benzene is \[-150.4\text{ }kJ\text{ }mo{{l}^{-1}},\]calculate its enthalpy of hydrogenation in kJ.
The algebraic sum of distances of the line \[ax+by+2=0\] from \[(1,2),\]\[(2,1)\] and \[(3,5)\]is zero. If the lines \[bx-ay+4=0\]and \[3x+4y+5=0\] cut the coordinate axes at concyclic points, then
A)
\[a+b=-\frac{2}{7}\]
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B)
Area of the triangle formed by the line \[ax+by+2=0\]with coordinate axes is\[\frac{14}{5}\].
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C)
Line \[ax+by+3=0\]always passes through the point\[(-1,1)\].
The line \[y=mx\]intersects the circles \[{{x}^{2}}+{{y}^{2}}-2x-2y=0\]and \[{{x}^{2}}+{{y}^{2}}+6x-8y=0\]at points A and B, respectively, (points being other than origin). The range of m such that origin divides AB internally is
In \[\Delta ABC,\] I is the in centre. Areas of \[\Delta IBC,\] \[\Delta lAC\] and \[\Delta lAB\] are, respectively, \[{{\Delta }_{1}},{{\Delta }_{2}}\] and\[{{\Delta }_{3}}\]. If \[{{\Delta }_{1}},{{\Delta }_{2}}\]and \[{{\Delta }_{3}}\] are in A.R, then the altitudes of \[\Delta ABC\]are in
Number of common normals to hyperbolas \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=-1\] is
If \[1,\,{{\omega }_{1}},{{\omega }_{2}},....{{\omega }_{6}}\] are 7th roots of unity, then \[\operatorname{Im}\,({{\omega }_{1}}+{{\omega }_{2}}+{{\omega }_{4}})\] is equal to
A batch of 50 transistors was purchased from three different companies A, B and C. 18 of them were manufactured by A, 20 by B and the rest were manufactured by C. The companies A and C produce excellent quality transistors with probability equal to \[0.9,\] B produces the same with the probability equal to\[0.6\]. Then the probability of the event that an excellent quality transistor chosen at random is manufactured by the company B is
Let \[f(x),\,g(x)\] and \[h(x)\]be quadratic polynomials having positive leading coefficients as well as real and distinct roots. If each pair of them has a common root, then the roots of \[f(x)+g(x)+h(x)=0\] are
Let \[{{S}_{0}},{{S}_{1}},{{S}_{2}}.....\] be the areas bounded by the x-axis and half-wave of the curve \[y=\sin \pi \sqrt{x}.\] Then \[{{S}_{0}},{{S}_{1}},{{S}_{2}},....\] are in
The equation of motion of a particle is given by \[\frac{dx}{dt}=t(t+1),\] \[\frac{dy}{dt}=\frac{1}{t+1},\] where particle is at \[(x(t),y(t))\]at time t. If the particle is at the origin at \[t=0\]and passes through the point \[(d,2),\] then the value of d is
Consider a function \[f(n)=\frac{1}{1+{{n}^{2}}}.\]. Let \[{{\alpha }_{n}}=\frac{1}{n}\sum\limits_{r=1}^{n}{f\left( \frac{r}{n} \right)}\] and \[{{\beta }_{n}}=\frac{1}{n}\sum\limits_{r=0}^{n-1}{f\left( \frac{r}{n} \right)}\] for \[n=1,2,3,....\] Then which of the following inequalities is true?
The least integral value of m for which the angle between the two vectors \[{{\vec{V}}_{1}}={{x}^{2}}\hat{i}-4\hat{j}+(3m+1)\hat{k}\] and \[{{\vec{V}}_{2}}=m\hat{i}-x\,\hat{j}+\hat{k}\] is acute \[\forall \,x\in R\] is ____.
Suppose a population A has 100 observations 101, 102... 200, and another population B has 100 observations 151, 152, ..., 250. If \[{{V}_{A}}\] and \[{{V}_{B}}\] represent the variances of the two populations, respectively, then \[\frac{{{V}_{A}}}{{{V}_{B}}}\] is _____
The equilibrium constant of the above reaction is \[{{K}_{p}}\]. If pure ammonia is left to dissociate, the partial pressure of ammonia at equilibrium is given by (Assume that \[{{P}_{N{{H}_{3}}}}<<{{P}_{total}}\] at equilibrium) 
This follows first order kinetics. The rate constant is \[2.714\times {{10}^{-3}}{{s}^{--1}}.\]The initial concentration of cyclopropane is\[0.29\text{ }M\]. What will be the concentration of cyclopropane after 100s? 
