A metre stick of length 1m is held vertically with one end in contact of the floor and is then allowed to fall. If the end touching the floor is now allowed to slip, the other end will hit the ground with a velocity of \[\left( g = 9.8 m/{{s}^{2}} \right)\]
Two soap bubbles of radii \[{{r}_{1}}\,\,and\,\,{{r}_{2}}\] equal to 4 cm and 5 cm are touching each other over a common surface \[{{S}_{1}}{{S}_{2}}\] (show in figure). Its radius will be
A thin rectangular magnet suspended freely has a period of oscillation equal to T. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is 'T', the ratio \[\frac{T'}{T}\] is
An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is true?
A)
They will never come out of the magnetic field region.
doneclear
B)
They will come out travelling along perpendicular paths.
The resistance of a wire at \[20{}^\circ \,C\] is \[20\,\Omega \] and at \[500{}^\circ \,C\] is 60 ohm. At which temperature its resistance will be 25 ohm?
Three blocks are placed as shown in figure below. The mass of A, B and C are \[{{m}_{1}},{{m}_{2}}\,\,and\,\,{{m}_{3}}\], respectively. The force exerted by block C on B is
A physical quantity P is given by \[P=\frac{{{A}^{3}}{{B}^{\frac{1}{2}}}}{{{C}^{-\,4}}{{D}^{\frac{3}{2}}}}\]. The quantity which brings in the maximum percentage error in P is
A transistor connected in common emitter configuration has input resistance \[{{\operatorname{R}}_{B}}= 2 k\Omega \] and load resistance of \[5 k\Omega \]. If \[\beta = 60\] and an input signal 12 mV is applied, calculate the voltage gain, the power gain and the value of output voltage
The coefficient of thermal conductivity of copper is nine times that of steel in the composite cylindrical bar shown in the figure. What will be the temperature at the junction of copper and steel
The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is \[{{t}_{0}}\] in air. Neglecting frictional force of water and given that the density of the bob is \[\left( 4 / 3 \right) \times 1000 kg/{{m}^{3}}\]. What relationship between t and \[{{t}_{0}}\] is true
The figure shows the \[\operatorname{P} - V\] plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semi-circle and CDA is half of an ellipse. Then,
A)
the process during the path \[\operatorname{A}\,\to B\] is isothermal
doneclear
B)
heat flows out of the gas during the path \[\operatorname{B}\,\to C\,\to D\]
doneclear
C)
work done during the path \[\operatorname{A} \to B\to C\] is zero
doneclear
D)
negative work is done by the gas in the cycle ABCDA
Two waves originating from source \[{{\operatorname{S}}_{1}}\,and\,\,{{S}_{2}}\] having zero phase difference and common wavelength X will show completely destructive interference at a point P if \[\left( {{S}_{1}}P-{{S}_{2}}P \right)\] is
The xy plane is the boundary between two transparent media. Medium 1 with \[\operatorname{z}\,\,\ge 0\] has a refractive index of \[\sqrt{2}\] and medium 2 with \[\,\operatorname{z}\,\,\le 0\] has refractive index of\[\sqrt{3}\] . A ray of light in medium 1 given by the vector \[6\sqrt{3}\,\hat{i}+8\sqrt{3}\hat{j}-10\hat{k}\] is incident of the plance of separation. Find the angle of refraction in medium 2 vector in the direction of the refracted ray in medium 2
In an a.c. circuit the voltage applied is\[\operatorname{E}={{E}_{0}}\sin \,\,\omega t\]. The resulting current in the circuit is \[I={{I}_{0}}\sin \left( \omega t-\frac{\pi }{2} \right)\]. The power consumption in the circuit is given by
A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be
In an electromagnetic wave, the amplitude of electric field is 1 V/m. The frequency of wave is \[5 \times 1{{0}^{14}}Hz\]. The wave is propagating along z-axis. What will be the average energy density of electric field, in\[joule/{{m}^{3}}\]?
A parallel-plate capacitor is formed by two plates, each of area \[100\text{ }c{{m}^{2}}\], separated by a distance of 1 mm. Adielectric of dielectric constant 5.0 and dielectric strength \[1.9 \times 1{{0}^{7}}V/m\] is filled between the plates. Find the maximum charge (in coulomb) that can be stored on the capacitor without causing any dielectric breakdown.
The width of one of the two slits in a Young's double slits experiment is double of the other slit. Assuming that the amplitude of the light coming from a slit is proportion to slit- width. Find the ratio of the maximum to the minimum intensity in the interference pattern.
A motor cycle starts from rest and accelerates along a straight path at \[2 m/{{s}^{2}}\]. At the starting point of the motor cycle there is a stationary electric siren. How far (in metre) has the motor cycle gone when the driver hears the frequency of the siren at \[94\,%\] of its value when the motor cycle was at rest? \[\left( Speed of sound = 330 m{{s}^{-}}^{1} \right)\]
For what kinetic energy (in joule) of a neutron will the associated de-Broglie wavelength be\[1.40 \times {{10}^{-\,10}}m\]? Mass of neutron is\[1.675 \times 1{{0}^{-}}^{27}\,kg\] \[\left( h = 6.6 \times 1{{0}^{-}}^{34}J-s \right)\].
In the reaction,\[BrO_{3(aq)}^{-}+5Br_{(aq)}^{-}+6H_{(aq)}^{+}\xrightarrow[{}]{{}}\] \[3Br_{2(aq)}^{{}}+3{{H}_{2}}{{O}_{(l)}}\] the expression of rate of appearance of bromine \[[B{{r}_{2}}]\] to rate of disappearance of bromide ion \[[B{{r}^{-}}]\] is \[3Br_{2(aq)}^{{}}+3{{H}_{2}}{{O}_{(l)}}\]
In the reaction : \[S+3/2{{O}_{2}}\to S{{O}_{3}}+2x\]kcal and \[S{{O}_{2}}+1/2{{O}_{2}}\to S{{O}_{3}}+y\]kcal, heat of formation of \[S{{O}_{2}}\]is \[3Br_{2(aq)}^{{}}+3{{H}_{2}}{{O}_{(l)}}\]
In the complexes \[{{[Fe{{({{H}_{2}}O)}_{6}}]}^{3+}},{{[Fe{{(CN)}_{6}}]}^{3-}}\],\[{{[Fe{{({{C}_{2}}{{O}_{4}})}_{3}}]}^{3-}}\]and\[{{[FeC{{l}_{6}}]}^{3-}}\], more stability is shown by
A dihaloalkane 'X' having formula \[{{C}_{3}}{{H}_{6}}C{{l}_{2}},\]on hydrolysis gives a compound that can reduce Tollens' reagent. The compound 'X' is
At constant temperature, the equilibrium constant \[({{K}_{p}})\]for the decomposition reaction,\[{{N}_{2}}{{O}_{4}}2N{{O}_{2}}\]is expressed by \[{{K}_{p}}=4{{x}^{2}}P/(1-{{x}^{2}})\], where P = pressure and x = extent of decomposition. Which of the following statements is true?
A)
\[{{K}_{p}}\]increases with increase in P.
doneclear
B)
\[{{K}_{p}}\]increases with increase in x.
doneclear
C)
\[{{K}_{p}}\]increases with decrease in x.
doneclear
D)
\[{{K}_{p}}\]remains constant with change in P and x.
On passing I ampere of current for time t sec through 1 litre of \[2M\,CuS{{O}_{4}}\]solution (atomic weight of Cu = 63.5), the amount m of Cu (in g) deposited on cathode will be
AB crystallises in a rock salt structure with A : B = 1 : 1. The shortest distance between A and B is \[{{Y}^{1/3}}\]nm. The formula mass of AB is 6.023 Y a.m.u. where Y is an arbitrary constant. The density (in \[\text{kg}\,{{\text{m}}^{-3}}\]) is __.
In 1 L saturated solution of \[AgCl[{{K}_{sp}}(AgCl)=1.6\times {{10}^{-10}}]\],1 mol of CuCl\[[{{K}_{sp}}(CuCl)=1.0\times {{10}^{-6}}]\] is added. The resultant concentration of \[A{{g}^{+}}\]in the solution is \[1.6\times {{10}^{-x}}\]. The value of x is__.
If the chords of contact of tangents from two points \[(-4,2)\] and \[(2,1)\] to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] are at right angle, then the eccentricity of the hyperbola is
The value of \[\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{k=1}^{n}{\frac{1}{n+k}}\left( {{\log }_{e}}(n+k)-{{\log }_{e}}n \right)\] is equal to
A ray of light passing through the point \[A(2,3)\] is reflected at a point B on line \[x+y=0\]and then it passes through the point \[(5,3)\]. Then the coordinates of B are
Let\[P(x)={{x}^{2}}-2({{a}^{2}}+a+1)x+{{a}^{2}}+5a+2\]. If the minimum value of \[P(x)\] for \[x\le 0\] is 8, then the sum of the squares of all possible values of a is
The first term of an arithmetic progression is 1 and the sum of the first nine terms is 369. The first and the ninth terms of a geometric progression coincide with the first and the ninth terms, respectively, of the arithmetic progression. The seventh term of the geometric progression is
20 soldiers are standing in a row. The captain wants to make a team of 7 out of them for a mission. In how many ways can the captain select them such that at least one soldier finds the soldier next to him also selected.
Two players A and B play a match which consists of a series of games (independent). Whoever first wins two games, not necessarily consecutive, wins the match. The probabilities of A's winning, drawing and losing a game against B are \[\frac{1}{2},\frac{1}{3}\] and \[\frac{1}{6},\] respectively. It is known that A won the match at the end of 11th game, then the probability that B wins only one game is
Let \[\Delta ABC\] be an equilateral triangle with side length a. For any point P inside \[\Delta ABC\], let S' denote the sum of the distances of P from each of the sides of \[\Delta ABC\]. The difference between the maximum and minimum values of S is
A circle S touches the line \[x+y=2\] at \[(1,1)\] and cuts the circle \[{{x}^{2}}+{{y}^{2}}+4x+5y-6=0\]P and Q, respectively. Then PQ always passes through the point
If area of triangle formed by tangent (with positive slope) and normal to a curve at any point in first quadrant with x-axis is cube of its ordinate, then differential equation of such a family of curves is
X in the above reaction is 
\[(c\ne 0)\] is differentiable at \[x=0,\]then locus of the point \[(b+c,a)\] is 
