Water from a tap at a very large distance maintained at a potential of V is allowed to fall by drops of radius r through a small hole into a hollow conducting sphere of radius R standing on an insulating stand until it fills the entire sphere. Then the potential of the hollow conductor is
Two parallel conducting plates each of area A, are placed 3d apart and are both earthed. A third plate, identical with the first two, is placed at a distance d from one of the earthed plates and is given a charge of Q coulomb. The potential of the central plate is
The capacitor C is initially without charge. X is now joined to Y. for a long time, during which\[{{H}_{1}}\] heat is produced in the resistance R. X is now joined to Z for a long time, during which \[{{H}_{2}}\]heat is produced in R. Then
In the circuit shown, the cell is ideal. The coil has an inductance of 4H and zero resistance. F is a fuse of zero resistance and will blow when the current through it reaches 5 A. The switch is closed at t = 0. The fuse will blow
Two conducting rings of radii \[r\] and 2\[r\] move in opposite directions with velocities 2\[v\] and \[v\] respectively on a conducting surface S. There is a uniform magnetic field of magnitude B perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is
A body of mass m is released from a height h to a scale pan hung from a spring as shown in figure. The spring constant of the spring is k, the mass of the scale pan is negligible and the body does not bounce relative to the pan, then the amplitude of vibration is
A block of mass m is suspended from the ceiling of a stationary elevator through a spring of spring constant k. Suddenly, the cable breaks and the elevator starts falling freely. The block now executes a simple harmonic motion. The amplitude of S.H.M. is
Two identical organ pipes are producing fundamental notes of frequencies 200 Hz at \[15{}^\circ C\]. If the temperature of one pipe is raised to \[27{}^\circ C\], the number of beats produced will be
In diagrams (i) to (iv) of figure, variation of volume by changing pressure is shown. A gas is taken along the path ABCD. The change in internal energy of the gas will be
A)
positive in all the cases (i) to (iv)
doneclear
B)
positive in cases (i), (ii) and (iii) but zero m case (iv)
doneclear
C)
negative in cases (i), (ii) and (iii) but zero in case (iv)
A body cools from\[60{}^\circ C\]to\[50{}^\circ C\]in 10 minutes. If the room temperature is \[25{}^\circ C\] and assuming Newton's laws of cooling to hold good, the temperature of the body at the end of the next 10 minutes will be
A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity of the material of A is twice that of B. Under thermal equilibrium, the temperature difference across the layer A, if the temperature across the free surfaces is \[36{}^\circ C\], is
A plane mirror is placed at the bottom of a tank containing a liquid of refractive index\[\mu \]. P is a small object at a height h above the mirror. An observer O, vertically above P, outside the liquid sees P and its image in the mirror. The apparent distance between these two will be
A particle executes S.H.M. of amplitude 1 mm along the principal axis of a convex lens of focal length 12 cm. The mean position of oscillation is at 20 cm from the lens. The amplitude of oscillation of the image of the particle is
A person sets up Young's experiment using a sodium lamp and placing two slits 1 meter away from a screen. The person is not sure of slit separation and he varies the separation and finds that the interference fringes disappear if the slits are too far apart. The angular resolution of his eye is (1/60). How far apart are the slits when he just cannot see the interference pattern? \[[\lambda =5890\,\overset{\text{o}}{\mathop{\text{A}}}\,]\]
The radioactivity of a sample is \[{{R}_{1}}\] at a time \[{{T}_{1}}\]and \[{{R}_{2}}\] at a time \[{{T}_{2}}\]. If the half-life of the specimen is \[T,\] the number of atoms that have disintegrated in the time \[({{T}_{2}}-{{T}_{1}})\] is proportional to
A homogenous rod of length \[2l\] floating partly immersed in water is supported by a string at one of its ends. If the specific gravity of rod is 3/4, what is the fraction of the length of the rod that extends out of water?
A small ball rests at the bottom of a watch glass of radius\[R\]. It is displaced through a small distance \[x\] from this position and released, then the total distance covered before it comes to the bottom and rests there is [Coefficient of friction between watch glass surface and the ball is\[\mu ,\]\[x<<R\]] is
A sealed tank containing a liquid of density\[\rho \] moves with a horizontal acceleration a, as shown in the figure. The difference in pressure between the point B and A is
A uniform sphere of mass m and radius \[r\] rolls without sliding over a horizontal plane, rotating about horizontal axis OA. In the process, centre of sphere moves with velocity \[v\] along a circle of radius\[r\]. Total kinetic energy of the sphere is
A uniform rod of length \[l\], hinged at the lower end is free to rotate in a vertical plane. Initially, the rod is held vertically and then released. The angular acceleration of the rod when it makes an angle of\[45{}^\circ \]with the vertical is
A sound source is situated at the origin and is continuously emitting sound waves of frequency 660 Hz. The velocity of sound in air is 330 m/s. An observer is moving along the X = 335 m line with a constant velocity of 26 m/s. When the observer is at positions where y = -140 m, y = 0 m and y = 140 m, the frequencies of the sound observed by him will be
A semiconductor X is made by doping a germanium crystal with arsenic (Z = 33). A second semiconductor Y is made by doping germanium with indium (Z = 49). The two are joined end to end and connected to a battery as shown. Which of the following statements is correct?
A)
X is P-type, Y is N-type and the junction is forward biased
doneclear
B)
X is N-type, Y is P-type and the junction is forward biased
doneclear
C)
X is P-type, Y is N-type and the junction is reverse biased
doneclear
D)
X is N-type, Y is P-type and the junction is reverse biased
Two discs of moment of inertia \[{{I}_{1}}\] and \[{{I}_{2}}\] and angular speeds \[{{\omega }_{1}}\] and \[{{\omega }_{2}}\] are rotating along collinear axes passing through their centre of mass and perpendicular to their plane. If the two are made to rotate together along the same axis, the rotational KE of system will be
A convex lens of focal length\[f\]is placed somewhere in between an object and a screen. The distance between the object and the screen is\[x\]. If the magnification produced by the lens is\[m,\]the focal length of the lens is
In an astronomical telescope in normal adjustment, a straight black line of length L is drawn on the objective lens. The eyepiece forms a real image of this line. The length of this image is\[l\]. The magnification of the telescope is
The wavelength of radiation emitted is \[{{\lambda }_{0}}\]when an electron jumps from the third to the second orbit of hydrogen atom. For the electron jumps from the fourth to the second orbit of the hydrogen atom, the wavelength of radiation emitted will be
An infinite number of identical capacitors each of capacitance 1\[\mu F\] are connected as shown in adjoining figure. The equivalent capacitance between A and B is
Consider the following perhalate ions in acidic medium. \[Cl{{O}_{4}}^{-}(I),\,Br{{O}_{4}}^{-}(II),\,I{{O}_{4}}^{-}(III)\] Arrange these in the decreasing order of oxidizing power.
The quantity of electricity needed to electrolyse completely 1 M solution of \[CuS{{O}_{4}},\,B{{i}_{2}}{{(S{{O}_{4}})}_{3}},\] \[AlC{{l}_{3}}\] and \[AgN{{O}_{3}}\] each will be
Suppose 5 gm of\[C{{H}_{3}}COOH\]is dissolved in one litre of ethanol. Assume that no reaction between them takes place. Calculate molality of resulting solution if density of ethanol is 0.789 gm/ml.
The\[p{{K}_{a}}\]of acetylsalicylic acid (aspirin) is 3.5. The pH of gastric juice in human stomach is about 2-3 and pH in the small intestine is about 8. Aspirin will be
A)
unionized in the small intestine and in the stomach.
doneclear
B)
completely ionized in the stomach and almost unionized in the small intestine.
doneclear
C)
ionized in the stomach and almost unionized in the small intestine.
doneclear
D)
ionised in the small intestine and almost unionised in the stomach.
Three moles of a gas are present in a vessel at a temperature of\[27{}^\circ C\]. Calculate the value of gas constant (R) in terms of kinetic energy of the molecules of gas.
\[2A{{B}_{2}}\rightleftharpoons 2AB+{{B}_{2}}\]. Degree of dissociation of\[A{{B}_{2}}\]is\[x\]. What will be equation for\[x\]in terms of\[{{K}_{p}}\]and equilibrium pressure P?
The minimum energy required to overcome the attractive forces electron and surface of Ag metal is \[7.52\times {{10}^{-19}}J\]. What will be the maximum K.E. of electron ejected out from Ag which is being exposed to U.V. light of\[\lambda =360\overset{\text{o}}{\mathop{\text{A}}}\,\]?
12 g of gas occupy a volume of\[4\times {{10}^{3}}c{{m}^{3}}\]at a temperature of\[27{}^\circ C\]. After the gas is heated at constant pressure, its density becomes equal to\[6\times {{10}^{-4}}g\,c{{m}^{-3}}\]. What is the temperature to which gas is heated?
Calculate the rate constant of first order reaction\[C{{H}_{3}}CHO(g)\xrightarrow{Heat}C{{H}_{4}}(g)+CO(g);\] if the initial pressure of \[C{{H}_{3}}CHO\] is 80 mm Hg and the total pressure at the end of 20 minutes is 120 mm Hg.
Assertion: \[N_{3}^{-}\]is a weaker base than\[NH_{2}^{-}\].
Reason: The lone pair of electrons on atom in\[N_{3}^{-}\] is in the \[s{{p}^{2}}\text{-}\]orbital while in \[NH_{2}^{-}\] it is in\[s{{p}^{3}}\text{-}\]orbital.
A)
Both assertion and reason are correct and the reason is correct explanation to assertion.
doneclear
B)
Both assertion and reason are correct but reason is not the correct explanation of assertion.
The absolute value of parameter\[t\]for which the area of the triangle whose vertices are \[A\,(-1,\,1,\,\,2);\] \[B\,(1,2,3)\] and \[C\,(t,1,1)\] is minimum is
Let \[{{P}_{1}}=\vec{r},\,\,{{\vec{r}}_{1}}={{d}_{1}},\]\[{{P}_{2}}=\vec{r}.\,{{\vec{r}}_{2}}={{d}_{2}},\]\[{{P}_{3}}=\vec{r}.\,{{\vec{r}}_{3}}={{d}_{3}}\]be three planes where \[\vec{r},\,\,{{\vec{r}}_{2}}\] and \[{{\vec{r}}_{3}}\] are three non-coplanar vectors. Then the lines \[{{P}_{1}}=0={{P}_{2}};\]\[{{P}_{2}}=0={{P}_{3}};\] and\[{{P}_{3}}=0={{P}_{1}}\]are
If in an isosceles triangle with base \[a,\] vertical angle of \[20{}^\circ \] and lateral side each of length \[b\] are given then value of\[{{a}^{3}}+{{b}^{3}}\]equals
Given\[\frac{x}{a}+\frac{y}{b}=1\]and\[ax+by=1\]are two variable lines, \['a'\] and \['b'\] being the parameters connected by the relation\[{{a}^{2}}+{{b}^{2}}=ab\]. The locus of the point of intersection has the equation
If locus of a point, whose chord of contact with respect to the circle\[{{x}^{2}}+{{y}^{2}}=4\]is a tangent to the hyperbola\[xy=1\]is\[xy={{c}^{2}}\], then value of\[{{c}^{2}}\] is
The curve\[y=a{{x}^{2}}+bx+c\]passes through the point (1, 2) and its tangent at origin is the line\[y=x\]. The area bounded by the curve, the ordinate of the curve at minima and the tangent line is
If a variable tangent to the curve \[{{x}^{2}}y={{c}^{3}}\]makes intercepts \[a\] and \[b\] on \[x\] and \[y\] axis, respectively, then the value of\[{{a}^{2}}b\]is
\[{{\Delta }_{1}}={{\Delta }_{1}}=\left| \begin{matrix} x & b & b \\ a & x & b \\ a & a & x \\ \end{matrix} \right|\] and \[{{\Delta }_{2}}=\left| \begin{matrix} x & b \\ a & x \\ \end{matrix} \right|\] are the given determinants, then
Let \[{{a}_{n}}\] be the \[{{n}^{th}}\] term of an A.P. If \[\sum\limits_{r=1}^{{{10}^{99}}}{{{a}_{2r}}}={{10}^{100}}\] and \[\sum\limits_{r=\,1}^{{{10}^{99}}}{{{a}_{2r-1}}}={{10}^{99}},\] then the common difference of the A.P. is
Three vertices are chosen randomly from the seven vertices of a regular 7-sided polygon. The probability that they form the vertices of an isosceles triangle is
A question paper on mathematics consists of twelve questions divided into three parts A, B and C, each containing four questions. In how many ways can an candidate answer five questions, selecting at least one from each part?
If the complex number\[z\]lies on a circle with centre at the origin and radius\[\frac{1}{3},\]then the complex number \[-1+6z\] lies on a circle with radius
If\[\left[ \begin{matrix} \alpha & \beta \\ \gamma & -\,\alpha \\ \end{matrix} \right]\]is to be the square root of two-rowed unit matrix, then \[\alpha ,\]\[\beta \] and \[\gamma \] should satisfy the relation
Statement 1: If \[({{a}_{1}}x+{{b}_{1}}y+{{c}_{1}})+({{a}_{2}}x+{{b}_{2}}y+{{c}_{2}})\]\[+\,({{a}_{3}}x+{{b}_{3}}y+{{c}_{3}})=0\]then lines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0,\]\[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]and \[{{a}_{3}}x+{{b}_{3}}y+{{c}_{3}}=0\]cannot be parallel.
Statement 2: If sum of three straight lines equations is identically zero then they are either concurrent or parallel.
A)
Statement 1 is true, statement 2 is true and statement 2 is correct explanation for statement 1.
doneclear
B)
Statement 1 is true, statement 2 is true and statement 2 is NOT the correct explanation for statement.