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The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is
A particle is moving in a circular path of radius a under the action of an attractive potential
U = – K /2R^{2}
It’s total energy is :
In a collinear collision, a particle with an initial speed V_{o} strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is:
Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m2 to stop the motion is:
If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest?
A mass m attached to spring of natural length l_{0} and spring constant k. One end of string is attached to centre of disc in horizontal plane which is being rotated by constant angular speed Ï‰. Find extension per unit length in spring (given k >> mÏ‰^{2} ) :
A string of mass per unit length Âµ = 6 Ã— 10â€“3 kg/m is fixed at both ends under the tension 540 N. If the string is in resonance with consecutive frequencies 420 Hz and 490 Hz. Then find the length of the string?
A particle is projected from the ground with speed u at angle 60Â° from horizontal. It collides with a second particle of same mass moving with horizontal speed u in same direction at highest point of its trajectory. If collision is perfectly inelastic then find horizontal distance travelled by them after collision when they reached at ground
Hlike atom with ionization energy of 9R. Find the wavelength of light emitted (in nm) when electron jumps from second excited state to ground state. (R is Rydberg constant)
Two gases Ar (40) and Xe (131) at same temperature have same number density. Their diameters are 0.07 nm and 0.10 nm respectively. Find the ratio of their mean free time
A litre of dry air at STP expands adiabatically to a volume of 3 litres. If Î³ = 1.40, the work done
by air is (3^{1.4}= 4.6555) [Take air to be an ideal gas]
A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations.The density of granite is 2.7Ã—10^{3} kg/m^{3} and its Young’s modulus is 9.27 Ã— 10^{10} Pa. What will be the fundamental frequency of the longitudinal vibrations ?
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is :
A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz ?
A parallel plate capacitor of capacitance 90pF is connected to a battery of emf 20 V. If a dielectric material of dielectric K = 5/3 is inserted between the plates, the magnitude of the induced charge will be :
A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20Â°C is : [Given that R = 8.31 J mol^{1} K^{1}]
In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line.
A message signal of frequency 100 MHz and peak voltage 100 V is used to execute amplitude modulation on a carrier wave of frequency 300GHz and peak voltage 400 V. The modulation index and difference between the two side band frequencies are :
A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a linepassing through the source detect sound to be of frequencies 480 Hz and 530 Hz. Their respective speeds area, in ms^{1}, (Given speed of sound = 300 m/s)
The value of acceleration due to gravity at Earth’s surface is 9.8 ms^{2}. The altitude above its surface at which the accelerate due to gravity decreases to 4.9 ms^{2}, is close to : (Radius of earth= 6.4Ã—10^{6} m)
The angular width of the central maximum in a single slit diffraction pattern is 60Â°. The width of the slit is 1 Âµm. The slit is illuminated by monochromatic plane waves. if another slit of same width is made near it, Young’s fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance ? (i.e., distance between the centres of each slit)
Tip : Only write the magnitude of the physical quantity)
The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to 135Â° and 0Â°, respectively, It is observed that mercury gets depressed by an amount h in a capillary tube or radius r_{1}, while water rises by the same amount h in a capillary tube of radius r_{2}. The ratio, (r1/r2), is then close to :
A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of :
Speed of a transverse wave on a straight wire (mass 6.0 g. length 60 cm and area of crosssection 1.0 mm2) is 90 msâ€“1 . If the Young’s modulus of wire is 16Ã—1011 Nm^{â€“2} , the extension of wire over its natural length is :
Tip : Write your answer with appropriate units
A Carnot engine having an efficiency of 1/10 is being used as a refrigerator. If the work done on the refrigerator is 10 J, the amount of heat absorbed from the reservoir at lower temperature is:
Tip : Write your answer with appropriate units
Amongst the following statements, that which was not proposed by Dalton was
The theory that can completely/properly explain the nature of bonding in [Ni(Co)4] is :
Oxidation number of potassium in K_{2}O. K_{2}O_{2}and KO_{2} respectively is
Which of the following statement is not true of glucose ?
The third ionization enthalpy is minimum for
A flask contains a mixture of isohexane and 3methylpentane. One of the liquids boils at 63Â°C
while the others boils at 60Â°C. What is the best way to separate the two liquids and which one will
be distilled out first.
The number of bonds between sulphur and oxygen atoms in S_{2}O_{8}^{2â€“} and the number of bonds between sulphur and sulphur atoms in rhombic sulphur, respectively, are :
Arrange the following compounds in increasing order of Câ€“OH bond length :
methanol, phenol, pethoxyphenol
Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams) of the
salt required to achieve 10ppm of iron in 100 kg of wheat is ___________.
Atomic weight : Fe = 55.85; S 32.00; O ; 16.00
Tip: Write your answer along with the appropriate measurement units
The number of chiral centres in penicillin is _______.
The number of orbitals associated with quantum number n = 5, ms= + 1/2 is :
During the nuclear explosion, one of the products is 90Sr with half life of 6.93 years. If 1 Î¼g of ^{90}Sr
was absorbed in the bones of newly born baby in placed of Ca, how much time, in years, is required
to reduce much time, in year, is required to reduce it by 90% if it not lost metabolically.
Chlorine reacts with hot and concentrated NaOH and produces compounds (X) and (Y). Compound (X) gives white precipitate with silver nitrate solution. The average bound between CI and O atoms in (Y) is.
The number of sp^{2} hybrid orbitals in a molecule of benzene is:
In the figure shown below reactant A (represented by square) is in equilibrium with product B(represented by circle). The equilibrium constant is :
Among the following, the form of water with the lowest ionic conductance at 298 K is :
Which of the following has the shortest C – Cl bond ?
The first and second ionisation enthalpies of a metal are 496 and 4560 Kj mol1 respectively. How many moles of HCl and H_{2}SO_{4}, respectively, will be needed to react completely with 1 mole of the metal hydroxide ?
The correct order of the spin only magnetic moments of the following complexes is:
(I) [Cr(H_{2}O)_{6}]Br
(II) Na_{4}[Fe(CN)_{6}]
(III) Na_{3}[Fe(C_{2}O_{4})_{3}](Î”_{0}> P)
(IV) (Et_{4}N)_{2}[CoCl_{4}]
Preparation of Bakelite proceeds via reactions :
A metal (A) on heating in nitrogen gas gives compound B. B on treatment with H_{2}O gives a colorless gas which when passed through CuSO_{4} solution gives a dark blueviolet coloured solution. A and B respectively, are :
Hydrogen has three isotopes (A), (B) and (C). If the number of neutron(s) in (A), (B) and (C) respectively, are (x), (y) and (z), the sum of (x), (y) and (z) is :
While phosphorus on reaction with concentrated NaOH solution in an inert atmosphere of CO_{2} gives phosphine and compound (X). (X) on acidification with HCl gives compound (Y). The basicity of compound (Y) is :
Which of the following compounds is likely to show both Frenkel and Schottky defects in its crystallline form ?
The equation of the circle, which is the mirror image of the circle, x^{2}+ y^{2} â€“ 2x = 0, in the line, y = 3 â€“ x is :
If the line, y = mx, bisects the area of the region {(x, y) : 0 â‰¤ x â‰¤ 32, 0 â‰¤ y â‰¤ 1 + 4x â€“ x^{2}}, then m equals
Water is running into an underground right circular conical reservoir, which is 10m deep and radius of its base is 5m. If the rate of change in the volume of water in reservoir is 3/2 Ï€m^{3}/min., then the rate (in m/min) at which water rises in it, when the water level is 4m, is
The sum of the abscissae of the points where the curves, y = kx^{2}+ (5k + 3) x + 6 k + 5, (kÎµR),touch the xaxis, is equal to
Total number of 6digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is:
Five numbers are in A.P. whose sum is 25 and product is 2520. If one of these five numbers is 1/2, then the greatest number amongst them is:
If y = mx + 4 is a tangent to both the parabolas, y^{2} = 4x and x2= 2by, then b is equal to:
If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is:
The area of the region, enclosed by the circle x^{2}+ y^{2}= 2 which is not common to the region bounded by the parabola y^{2} = x and the straight line y = x, is:
If g(x) = x^{2} + x – 1 and (goÆ’) (x) = 4x^{2} – 10x + 5, then Æ’ (5/4) is equal to:
Let P be a plane passing through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R be any point
(2, 1, 6). Then the image of R in the plane P is:
If the system of linear equations
2x + 2ay + az = 0
2x + 3by + bz = 0
2x + 4cy + cz = 0,
where a, b, c Îµ R are nonzero distinct; has a nonzero solution, then:
The logical statement (p â‡’ q) ^ ( q â‡’ ~p) is equivalent to:
Let S be the set of points where the function, ƒ(x) = 2x3, x ∈ R is not differentiable. Then ∑_{ x∈ S} ƒ(ƒ(x)) is equal to_____.
Let the normal at a point P on the curve y^{2} – 3x^{2 }+ y + 10 = 0 intersect the y – axis at (0, 3/2 . If m is the slope of the tangent at P to the curve, then m is equal to …..
The number of all 3 × 3 matrices A, with enteries from the set {–1,0,1} such that the sum of the diagonal elements of AA^{T} is 3, is ………….
An urn contains 5 red, 4 black and 3 white marbles. Then the number of ways in which 4 marbles
can be drawn from it so that at most 3 of them are red, is :
For which of the following ordered pairs (μ, Δ), the system of linear equations
x + 2y + 3z = 1
3x + 4y + 5z = μ
4x + 4y + 4z = Δ
is inconsistent ?
A line y = mx + 1 intersects the circle (x â€“ 3)^{2} + (y + 2)^{2}= 25 at the points P and Q. If the midpoint of the line segment PQ has x coordinate – 3/5, then which one of the following
The least positive value of 'a' for which the equation, 2x^{2} + (a – 10)x + 33 2 = 2a has real roots is ………..
Let two points be A(1,–1) and B(0,2). If a point P(x',y') be such that the area of ΔPAB = 5 sq. units and it lies on the line, 3x + y – 4λ = 0, then a value of λ is :
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