A truck moving on a smooth horizontal surface with a uniform speed u is carrying dust. If a mass \[\Delta m\] of the dust leaks from the truck in vertical downward direction in time \[\Delta t,\] the force needed to keep the truck moving at its constant speed is
A wooden block of mass m & density p is tied to a string. The other end of the string is fixed to the bottom of the tank. The tank is filled with a liquid of density \[\sigma .\] For this situation mark the INCORRECT statement(s)
A)
lf\[\sigma <\rho \] the string will slack and block sinks
doneclear
B)
If \[\sigma <\rho \] the string is taut
doneclear
C)
if \[\sigma >\rho \] the string is taut
doneclear
D)
If \[\sigma >\rho \]the string is taut and tension in string is\[\frac{\sigma -\rho }{\rho }\times mg\]
Two different metal rods of equal lengths & equal cross section area have their ends kept at the same temperatures \[{{\theta }_{1}}\And {{\theta }_{2}}.\]If \[{{K}_{1}}\And {{K}_{2}}\] be the thermal conductivities of rod, \[{{\rho }_{1}}\And {{\rho }_{2}}\] are their densities and \[{{s}_{1}},{{s}_{2}}\] are their specific heats, then the rate of flow of heat in the two rods will be same if
A student in a hot air balloon ascends vertically at constant speed. Consider the following four forces that arise in this situation \[{{F}_{1}}:\] The weight of the hot air balloon \[{{F}_{2}}:\]The weight of the student \[{{F}_{3}}:\]The force of the student pulling on the earth \[{{F}_{4}}:\]The force of the hot air balloon pulling on the student Which of the following relationships concerning the forces or their magnitudes is true?
A thin uniform rod of mass m & length \[\ell \] is free to rotate about its upper end. When it is at rest, it receives an impulse J at its lowest point, normal to its length. Immediately after the impact, mark the correct statement (s)
A)
the angular velocity of the rod is \[\frac{3J}{m\ell }\]
A conducting rod of length L and mass m is moving down a smooth inclined plane of inclination 0 with constant speed v. A current I is flowing in the conductor perpendicular to plane of paper (inwards). A vertically upward uniform magnetic field B exists in space there. The magnitude of magnetic field is
The fossil bone \[^{14}C{{:}^{12}}C\]ratio is \[\frac{1}{16}th\] of that in living animal bone. If the half-life of \[^{14}C\] is 5730 years, then the age of the fossil bone is
Steam at \[1atm\And 100{}^\circ C\] enters a radiator & leaves as water at \[1atm\And 80{}^\circ C,\] take \[{{L}_{y}}=540\text{ }cal/cm\And {{s}_{water}}\]\[=11\text{ }cal/gm/{}^\circ C.\] If the total energy given off as heat, the % age arises from the cooling of water is
In YDSE how many maxima can be obtained on a screen (including central maxima) on both sides of the central maxima if \[d=\frac{5\lambda }{2}\]where\[\lambda \] is the wavelength of light.
Two concentric spheres of radii \[{{r}_{1}}\And {{r}_{2}}\]carry charges \[{{q}_{1}}\And {{q}_{2}}\]respectively. If the surface charge density \[(\sigma )\] is the same for both spheres, the electric potential at the common center will be
A person standing on the floor of an elevator drop a coin. The coin reaches the floor of the elevator in time t, if elevator is moving uniformly & in time \[t{{ & }_{2}}\] if is accelerating up, then
The ratio of de-Broglei wavelength of molecules of hydrogen & helium which are at temperatures \[27{}^\circ C\text{ }\And \text{ }127{}^\circ C\] respectively
. Find the real angle of dipole if a magnet is suspended at an angle of \[30{}^\circ \] to the magnetic meridian & the dip needle makes an angle of \[45{}^\circ \] with horizontal
The rate of steady volume flux of water through a capillary tube of radius r under a pressure difference P is V. What is the rate of steady flow through a series combination of this tube with another tube of the same length and half the radius if the same pressure difference P is maintained across the combination?
How much energy would be spent to pull the satellite out of the earth's gravitational field if the earth shrank suddenly to half its present size (Assume satellite is orbiting in an orbit of radius R + h where R is radius of earth & h is height of satellite, from earth's surface).
Two coherent mono-chromatic light beams of intensities \[l\] and \[\text{4}l\] are superposed. The maximum and minimum possible intensities in the resulting beam are
In an a.c. circuit the voltage applied is \[E={{E}_{0}}\sin \omega t.\] The resulting current in the circuit is \[l={{l}_{0}}\sin \left( \omega t-\frac{\pi }{2} \right).\]The power consumption in the circuit is given by
In the figure given below there are two convex lens\[{{L}_{1}}\] and \[{{L}_{2}}\] having focal length \[{{F}_{1}}\] and \[{{F}_{2}}\] respectively. The distance between \[{{L}_{1}}\] and \[{{L}_{2}}\] will be
Two concentric coplanar circular loops of radii \[{{R}_{1}}\] and \[{{R}_{2}}\] carry currents \[{{l}_{1}}\] and \[{{l}_{2}}\] respectively in opposite directions. The magnetic field at the center of the loops is half that due to\[{{l}_{1}}\] at the center. Lf \[{{R}_{2}}=2{{R}_{1}},\]the value of \[{{I}_{2}}/{{I}_{1}}\] is
A student is given a sealed box containing an electrical circuit. After taking a series of current and voltage readings, he plots the current - voltage characteristic as shown below Which of the following circuits is most likely to be enclosed within the box
Two resistances of\[10\Omega \]and \[20\Omega \]and an ideal inductor of inductance 5H are connected to a battery of 2V through a key K as shown. At t = 0, K is closed, then which of the following is not correct.
A)
initial current through the battery is \[\frac{1}{15}A\]
doneclear
B)
initial potential difference across the inductor is \[\frac{2}{3}\]volt
doneclear
C)
final current through \[10\Omega \]resistor is zero
doneclear
D)
final current through \[20\Omega \] resistor is ?A
The density of copper is \[8.94g\ m{{L}^{-1}}.\]Find the charge needed to plate an area of \[10\times 10c{{m}^{2}}\] to a thickness of \[{{10}^{-2}}cm\]using a \[CuS{{O}_{4}}\] solution as electrolyte (atomic weight of \[Cu=63.6\])
Consider the following statements, (I) \[[Mn{{({{H}_{2}}O)}_{4}}]S{{O}_{4}}\]is paramagnetic and square planar. (II) crystal field splitting energy \[(i.e.{{\Delta }_{0}})\] in \[{{[Cr{{({{H}_{2}}O)}_{6}}]}^{+3}}\] is higher than in \[{{[Cr{{({{H}_{2}}O)}_{6}}]}^{+2}}\] (III) Wilkinson catalyst, a red - violet complex \[[RhCl{{(P{{H}_{3}}P)}_{3}}]\] is diamagnetic and square planar (IV)\[Hg[Co{{(SCN)}_{4}}]\] a deep blue complex is paramagnetic and tetrahedral and of these select the correct one from the given codes.
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
Vapour pressure of a solution of 5 g of non - electrolyte in 100 g of water at a particular temperature is \[2985\text{ }N/{{m}^{2}}.\] The vapour pressure of pure water is \[3000\text{ }N/{{m}^{2}},\]the molecular weight of the solute is
\[RN{{H}_{2}}\]reacts with \[{{C}_{6}}{{H}_{5}}S{{O}_{2}}Cl\] in aqueous KOH to give a clear solution. On acidification, a precipitate is obtained which is due to the formation of
A)
\[R-\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\overset{\begin{smallmatrix} H \\ | \end{smallmatrix}}{\mathop{{{N}^{+}}}}}\,-S{{O}_{2}}{{C}_{6}}{{H}_{5}}O{{H}^{-}}\]
Sewage containing organic waste should not be disposed in water bodies because it causes major water pollution. Fishes in such a polluted water die because of
A)
large number of mosquitoes
doneclear
B)
increase in the amount of dissolved oxygen
doneclear
C)
decrease in the amount of dissolved oxygen in water
Passage (Q. - 62) If z satisfies \[|z-(2-\sqrt{3}+i)|+|z-(2+\sqrt{3}+i)|=4.\]If a & b are two complex numbers which satisfies above equations which corresponds to maximum & minimum value of arg (z) respectively. If there exist a complex number 'c' which satisfy the equation, such that area of triangle formed by a, b, c is maximum. Then The ordered pair (a, b) is
Passage (Q. - 63) If z satisfies \[|z-(2-\sqrt{3}+i)|+|z-(2+\sqrt{3}+i)|=4.\]If a and b are two complex numbers which satisfies above equations which corresponds to maximum & minimum value of arg (z) respectively. If there exist a complex number 'c' which satisfy the equation, such that area of triangle formed by a, b, c is maximum. Then Complex number C is given by
An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are \[60{}^\circ \] and \[45{}^\circ \] respectively. Then the height of the lower plane from the ground is
If a & b are randomly choosen from {1,2,3,....,9} with replacement, then the probability that function\[f(x)=\frac{{{x}^{3}}}{3}+\frac{a{{x}^{2}}}{2}+bx+c(C\in R)\]is strictly increasing is
Passage (Q. - 68) Consider the rectangular hyperbola \[xy=15!,\] the number of points \[(\alpha ,\beta )\] lying the curve is \[\alpha ,\beta \in l\]is (where l is integer)
Passage (Q. - 69) Consider the rectangular hyperbola \[xy=15!,\] the number of points \[(\alpha ,\beta )\] lying the curve is \[\alpha ,\beta \in {{l}^{+}}\And HCF(\alpha ,\beta )=1\]is
The equations \[{{L}_{1}}\] and \[{{L}_{2}}\] are y = mx and y = nx respectively. Suppose \[{{L}_{1}}\] makes twice as large of an angle with the horizontal (measured counter clock wise from the +ve x-axis) as does \[{{L}_{2}}\] and \[{{L}_{1}}\] has 4 times the slope of \[{{L}_{2}}\]. If \[{{L}_{1}}\] is not horizontal then the value of the product (mn) equals
Let\[\vec{r}=(\vec{a}\times \vec{b})sinx+(\vec{b}\times \vec{c})cosy+2(\vec{c}\times \vec{a})\]where\[\vec{a},\vec{b},\vec{c}\]are three non-coplanar vectors. If r is perpendicular to \[\vec{a}+\vec{b}+\vec{c},\] then minimum value of \[{{x}^{2}}+{{y}^{2}}\] is
If x, y and z are positive real numbers, then the minimum value of the expression \[{{x}^{\ln \frac{y}{z}}}+{{y}^{\ln \frac{x}{y}}}+{{z}^{\ln \frac{x}{y}}}\]is equal to
If area of the region bounded by the curves \[y=|1+\{|x|\}|\]and\[3y=|-2{{x}^{2}}+5x+3|\]for \[-\frac{1}{2}<x\le 1,\](where {.} denotes fractional part of x) is A, then \[\frac{72}{17}A\]equals
If \[{{\text{p}}_{\text{n}}}\]denotes the product of all the coefficients in the expansion of \[{{(1+x)}^{n}}\]and \[9!{{P}_{n+1}}={{10}^{9}}.{{P}_{n}},\]then n =
An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent is
The ends A and B of a rod of length \[\sqrt{5}\] are sliding along the curve \[y=2{{x}^{2}}.\] Let \[{{x}_{A}}\] and \[{{x}_{B}}\] be the x-coordinates of the ends. At the moment when A is at (0,0) and B is at (1,2), the derivative \[\frac{d{{x}_{B}}}{d{{x}_{A}}}\] has the value equal to
The figure below shows a right triangle with its hypotenuse OB along the y-axis and its vertex A on the parabola \[y={{x}^{2}}.\] Let h represents the length of the hypotenuse which depends on the x-coordinate of the point A. The value of \[\underset{x\to 0}{\mathop{\lim }}\,(h)\] equals
Let \[f(x)=\int\limits_{-1}^{x}{{{e}^{{{t}^{2}}}}}dt\]and \[h(x)=f(1+g(x)),\] where g(x) is defined for ail x, g'(x) exist for all x, and \[g(x)\le 0\] for x > 0. If h'(1) = 1, then the possible value which g(l) can take is
Passage (Q. - 88) Let \[{{S}_{1}}\] be the set of all those solutions of the equation\[(1+a)cos\theta cos(2\theta -b)=\]\[(1+acos2\theta )cos(\theta -b)\]which are independent of a and b and \[{{S}_{2}}\] be the set of all such solutions which are dependent on a and b. Then The set \[{{S}_{1}}\] and \[{{S}_{2}}\] are
Passage (Q. - 89) Let \[{{S}_{1}}\] be the set of all those solutions of the equation\[(1+a)cos\theta cos(2\theta -b)=\]\[(1+acos2\theta )cos(\theta -b)\]which are independent of a and b and \[{{S}_{2}}\] be the set of all such solutions which are dependent on a and b. Then Conditions that should be imposed on a and b such that \[{{S}_{2}}\] is non-empty.
Passage (Q. - 90) Let \[{{S}_{1}}\] be the set of all those solutions of the equation\[(1+a)cos\theta cos(2\theta -b)=\]\[(1+acos2\theta )cos(\theta -b)\]which are independent of a and b and \[{{S}_{2}}\] be the set of all such solutions which are dependent on a and b. Then All the permissible values of b if a = 0 and \[{{S}_{2}}\] is a subset\[(0,\pi )\]: