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The coefficient of linear expansion for a certain metal varies with absolute temperature as α = aT. If L_{o} = 1 m is the initial length of the metal and the temperature of metal is changed from 27^{o}C to 127^{o}C, then final length is (where a = 2 × 10^{5} K^{−2})
A billiard player hits a billiard ball of mass m and radius r lying at rest on the billiard table. When the cue hits the ball horizontally with force F at a height (r + h) from the table top the ball rolls without slipping. h is given as
A conducting rod is rotated by means of strings in a uniform magnetic field with constant angular velocity as shown in the figure. Potential of points A, B and C are V_{A}, V_{B} and V_{C} respectively. Then
In the circuit shown (R = 1 Ω) current in branch CD is
A Π s haped wire frame with a light, smooth, sliding wire connected to its open end (width of open end is l) is dipped in a soap solution and then raised, such that a soap film forms between the slider and the closed end of the wire frame. If the wire frame is now placed in a vertical plane and a block of mass m is hung from the slider then for mass m to remain in equilibrium the surface tension of the soap film is
An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the Earth. Suddenly due to internal explosion the satellite breaks into two parts of equal masses. One part of the satellite stops just after the explosion and then falls to the surface of the Earth. The increase in the mechanical energy of the system (satellite + Earth) due to explosion will be (take acceleration due to gravity on the surface of Earth as g)
In position A kinetic energy of a particle is 60 J and potential energy is −20 J. In position B, kinetic energy is 100 J and potential energy is 40 J. Then in moving the particle from A to B
A metal rod is fixed in horizontal position and a force of magnitude F is applied as shown. If R_{A} = force by wall A and R_{B} = force by wall B, then
Two waves travelling in opposite directions produce a standing wave. The individual wave functions are given by y_{1} = 4 sin (3x – 2t) cm and y_{2} = 4 sin (3x + 2t) cm, where x and y are in centimeter. Now, select the correct statement(s) from the following.
A point source S is placed anywhere in between two converging mirrors having focal lengths f and 2f, respectively as shown. The value of d for which only single image may be formed is /are
In the circuit shown, initially keys K_{1}, K_{2} and K_{3} are all open. Now certain events as described below are performed successively on the circuit which involve closing and opening of the keys K_{1}, K_{2} and K_{3}.
Event 1: Keys K_{1} and K_{2} are closed and K_{3} is left open.
Event 2: After a long time K_{2} is opened and K_{3} is closed.
Event 3: After a long time K_{1} is opened and K_{2} is closed.
Q.
The time constants for charging of capacitor (completion of Event 1) and rise of current through the inductor (completion of Event 2) respectively are
In the circuit shown, initially keys K_{1}, K_{2} and K_{3} are all open. Now certain events as described below are performed successively on the circuit which involve closing and opening of the keys K_{1}, K_{2} and K_{3}.
Event 1: Keys K_{1} and K_{2} are closed and K_{3} is left open.
Event 2: After a long time K_{2} is opened and K_{3} is closed.
Event 3: After a long time K_{1} is opened and K_{2} is closed.
Q.
Find the maximum charge that can come on the capacitor after the completion of all the three events
In the circuit shown, initially keys K_{1}, K_{2} and K_{3} are all open. Now certain events as described below are performed successively on the circuit which involve closing and opening of the keys K_{1}, K_{2} and K_{3}.
Event 1: Keys K_{1} and K_{2} are closed and K_{3} is left open.
Event 2: After a long time K_{2} is opened and K_{3} is closed.
Event 3: After a long time K_{1} is opened and K_{2} is closed.
Q.
Find the maximum current that can pass through the inductor after the completion of all the three events
A liquid flowing from a vertical pipe has a very definite shape as it flows from the pipe. To get the equation for this shape assume that the liquid is in free fall once it leaves the pipe. Just as it leaves the pipe, the liquid has speed v_{o} and the radius of the cross section of the liquid stream is r_{o}.
Q.
An equation for the speed v of the liquid as a function of the distance y it has fallen, is
A liquid flowing from a vertical pipe has a very definite shape as it flows from the pipe. To get the equation for this shape assume that the liquid is in free fall once it leaves the pipe. Just as it leaves the pipe, the liquid has speed v_{o} and the radius of the cross section of the liquid stream is r_{o}.
Q.
The expression for the radius of the crosssection of the liquid stream at a distance ‘y’ below the pipe is
The correct order of acidic strength of the compounds, 1 – 3 is
The mechanism involved in the following conversion is
The correct order of bond angle of the following compound is
The rate law for one of the mechanism of the pyrolysis of CH_{3}CHO at 520^{o}C and 0.2 bar is
The overall activation energy Ea in terms of rate law is:
The stopping potential (V_{0}) of photosensitive surface varies with the frequency of incident radiation as shown in the following figure.
The work function of photosensitive surface.
5.6 litre of an unknown gas at NTP requires 12.5 calorie to raise its temperature by 10^{o}C at constant volume.
The value of (PV_{m})_{P→0} of a real gas is independent of the nature of gas because
Which of the following oxide cannot be reduced by carbon reduction?
Which of the following can show both optical and geometrical isomeris?
Which of the following is (are) correct statement (s)?
Which of the following gives Cannizzaro’s reaction?
A reversible process is performed in such a way that the system passes from state 1 to state 2 by pathI and then from state 2 to state one by pathII as shown in figure 5. For the above process
That the quantity is not depends on the path of the reaction, but depends on initial and final state of the system.
Q.
The quantity in the above process is called
A reversible process is performed in such a way that the system passes from state 1 to state 2 by pathI and then from state 2 to state one by pathII as shown in figure 5. For the above process
That the quantity is not depends on the path of the reaction, but depends on initial and final state of the system.
Q.
In thermodynamics, a process is called reversible when:
A reversible process is performed in such a way that the system passes from state 1 to state 2 by pathI and then from state 2 to state one by pathII as shown in figure 5. For the above process
That the quantity is not depends on the path of the reaction, but depends on initial and final state of the system.
Q.
Observe the given curve for a substance and identify the correct statement.
There are some deposits of nitrates and phosphates in the earth’s crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions.
Q.
Select the correct statement among the following:
There are some deposits of nitrates and phosphates in the earth’s crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions.
Nitrates are mainly produced for use as fertilizers in agriculture because of their
The degree of unsaturation in the product of following reaction is
Which chlorine in the following compound is most reactive towards nucleophilic (weak base) substitution reaction?
Range of the function,
, (where sgn (⋅) denotes the signum function and [⋅] greatest integer function, {.} is a fractional function)
Let the circles S_{1} ≡ x^{2} + y^{2} – 4x – 8y + 4 = 0 and S_{2} be its image in the line y = x, the equation of the circle touching y = x at (1, 1) and orthogonal to S_{2} is
Let the line x + y = meets the lines y = xtanθ; θ = 0, at A, B, C and D respectively. If AB, BC and CD are in A.P., then α =
Three parallel chords of a circle have lengths 2, 3, 4 and subtend angles α, β, α + β at the centre respectively (given α + β < π), then cos α is equal to
If α, β , γ are the roots of the equation x^{3} = x^{2} + 1, then the equation whose roots are α^{2} + β^{3} + γ^{4}, β^{2} + γ^{3} + α^{4}, γ^{2} + α^{3} + β^{4} is
be a point and be a line. If PQ is the distance of plane from point P measured along a line inclined at an angle of 60^{o} with the L and is minimum, then PQ is equal to
If polynomials f(x), g(x) and h(x), are such that
Q.
f(x) =
If polynomials f(x), g(x) and h(x), are such that
Q.
g(0) =
If polynomials f(x), g(x) and h(x), are such that
Q.
h' (0) =
P, Q are two points on the rectangular hyperbola (x – 1)(y – 2) = c^{2}, O is the centre of hyperbola, also tangent at P is perpendicular to OQ and meets OQ at N such that (OQ)(ON) = 4
Q.
One of the equation of directrix of the hyperbola is
P, Q are two points on the rectangular hyperbola (x – 1)(y – 2) = c^{2}, O is the centre of hyperbola, also tangent at P is perpendicular to OQ and meets OQ at N such that (OQ)(ON)=4
Q.
An ellipse confocal with the hyperbola and with eccentricity equal to is intersected by the line x + y – 7 = 0 at A and B, then intersection point of tangents at A and B will lie on
‘A’ tosses a coin. If it shows a tail, ‘A’ is asked to roll a fair die and A’s score is the number that die shows. If the coin shows a head, ‘A’ is asked to toss five more coins and A’s score is that total number of heads shown including the first coin. If A tells you only that his score is 3, and if ‘P’ is the probability that ‘A’ rolled a die, then [1/P] is equal to (where [ ] is the greatest integer function)
The number of solution of the curve sin x = cos y and the circle x^{2} + y^{2} = 1 is/are
366 docs219 tests

366 docs219 tests
