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The area bounded by the curve y = x^{3}, xaxis and two ordinates x = 1 to x = 2 is equal to
If x is so small that x^{3} and higher power of x may be neglected, then [(1+x)^{3/2}  [1+(1/2)x]^{3}] / [(1x)^{1/2}] may be approximated as
If f x and if f is continuous at x = 1 then f(1) =
Area of the triangle in the Argand diagram formed by the complex numbers z, iz and z + iz is
The solution of differential equation (dy/dx)=[((1+x)y)/((y1)x)] is
The solution of the equation (1x^{2})dy+xydx=xy^{2}dx is
The eccentricity of the ellipse 9x^{2} + 5y^{2}  30y = 0 is
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): is discontinuous for integral values of x.
Reason(R): f(x) is not defined for integral values of x.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): The function f (x) ≡ x^{5} − 5x^{3} − 20x + 7 attains its maximum at x = − 1 .
Reason(R) : f ′ (−1) = 0
In the following question, a Statement1 is given followed by a corresponding Statement2 just below it. Read the statements carefully and mark the correct answer
Tangents are drawn from the point (17,7) to the circle x^{2}+y^{2}=169.
Statement1:
The tangents are mutually perpendicular.
Statement2:
The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^{2}+y^{2}=338.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): If the 21st and 22nd terms in the expansion of (1+x)^{44} are equal, then the value of x is 7/8.
Reason(R): In the expansion of (x+y)^{n}, (r+1)th term , T_{r+1} = ^{n}C_{r+1}x^{nr+1} y^{r+1}.
The number of solutions of 2x + y = 4, x  2 y = 2, 3x + 5y = 6 is
The focus of the parabola (y2)^{2}=20(x+3) is
The value of cos 20ºcos40ºcos60ºcos80º is equal to
If a+b=ab, then the angle between a and b is
The compound obtained by the reaction of ethene with diborane followed by hydrolysis with alkaline hydrogen peroxide is
Which of the following forms a hydroxide highly soluble in water?
Number of electrons in Li^{2+} is one similar to the hydrogen atom. One electron system shows similar king of spectra. Many electron system spectra is complex due to interelectronic repulsions
Which bond angle θ would result in the maximum dipole moment for triatomic molecule XY_{2} as shown below?
The dipole moment of two dipoles inclined at an angle θ is given by equation
cos 90 = 0. Since the angle increase from 98180, the value of cos θ becomes more and more negative and hence resultant decreases. Thus, dipole moment is maximum when θ = 90º.
Which of the following involve sp^{2} hybridisation?
Only SO_{2} has sp^{2} hybridisation while all the remaining molecules i.e., CO_{2}, N_{2}O and CO has sphybridisation.
The geometric form of crystals is the result of orderly arrangement of
The heat required to raise the temperature of a body by 1K is called
The equilibrium constant for the following reaction will be 3 A + 2 B → C
The correct answer is k= [C]/[A]^{3}.[B]^{2}
A chemical reaction is catalysed by X. Hence X
Work done during the compression of a gas from a volume of 6dm^{3} to 4 dm^{3} against a constant external pressure of 3 atm is (1atmlitre=101.32J)
Gallium and Germanium were unknown at the time when Mendeleev's periodic table was formulated. But Mendeleev's predicted the properties of these elements and named them ekaaluminium and ekasilicon. Later when these elements were discovered, their properties were found to be similar to those of aluminium and silicon.
In a closed insulated container a liquid is stirred with a paddle to increase the temperature. Which of the following is true
Which of the following is not isoelectronic?
Isoelectronic species: a group of ions, atoms, or molecules that have the same number of electrons.
Number of electrons in Na^{+} = 10
Number of electrons in Mg^{2+} = 10
Number of electrons in O^{2 − } = 10
Number of electrons in Cl^{ − } = 18
Which of the complexes is expected to have lowest Δ_{0} value?
The magnitude of Δ_{0} varies from stronger to weaker ligands. According to spectrochemical series F^{−} is weaker while NH_{3} is a stronger ligand. Stronger ligand gives a larger value of Δ_{0}
Which of the following belongs to the actinide series?
Which of the following is the use of electrolysis?
The property of hydrogen which distinguishes it from other alkali metals is
A sample of gas has a volume of 0.2 lit. measured at 1 atm. pressure and 0ºC . At the same pressure but at 273ºC its volume will become
Which of the following reacts with chloroform and base to form phenyl isocyanide?
Which one of the following compounds is a Lewis acid ?
Maximum number of active hydrogens are present in
The standard reduction potential at 298 K for the following half cell reaction are given below
Which one is the strongest reducing agent?
Ethynic hydrogen is released most easily in :
Among the following, the optically inactive compound is
Which of th following transitions in a hydrogen atom emits the photon of highest frequency?
A nucleus with Z = 92 emits the following in a sequence: α,β⁻,β⁻,α,α,α,α,α,β⁻,β⁻,α,β⁺,β⁺,α. The atomic no. of the resulting nuclues is
Uniform wire 16 Ω resistance is made in the form of a square. Two opposite corners of the square are connected by a wire of resistance of 16 Ω . The effective resistance between the other two opposite corners is
Three similar cells, each of e.m.f. 2V and internal resistance r Ω send the same current through an external resistance of 2 Ω, when connected in series or in parallel. The strength of the current flowing through the external resistance is
Uncertainty in position of the electron is of the order of deBroglie wavelength. Making use of Heisenberg's uncertainty principle, it will be found that uncertainty in velocity ν is of the order of
If momentum of a particle is doubled, then its deBroglie's wavelength will
Radio wave diffract around building although light waves do not. The reason is that radio waves:
Five equal capacitors connected in series have a resultant capacitance of 4 μF. The total energy stored in these, when these are connected in parallel and charged to 400V is
A 20F capacitor is charged to 5V and isolated. It is then connected in parallel with an uncharged 30F capacitor. The decrease in the energy of the system will be
Taking that earth revolves round the sun in a circular orbit of radius 15 x 10^{10} m, with a time period of 1 year, the time taken by another planet, which is a distance of 540 x 10^{10} m, to revolve round the sun in circular orbit once, will be
The periodic time of a communication satellite is
The energy spectrum of a black body exhibits a maximum around a wavelength λ₀. The temperature of a black body is now changed such that the energy is maximum around a wavelength 0.75 λ₀. The power radiated by the black body will now increase by a factor of
A liquid cools down from 70ºC to 60ºC in 5 minutes. The time taken to cool it from 60ºC to 50ºC will be
If a particle covers half the circle of radius R with constant speed, then
A wire of length L metre, carrying a current I ampere is bent in the form of a circle. its magnitude of magnetic moment will be
A particle is moving eastwards with a velocity of 5 m − s⁻^{1}. In 10 s, the velocity changes to 5 m − s⁻1 northwards. The average acceleration in this time is
A particle is viberating in a simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position, is its energy half potential and kinetic ?
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): Due to opposition offered by selfinductance, work is done by external agent in establishing current in circuit. This work done is stored as potential energy.
Reason(R): Selfinductance of a coil depends on the geometry of coils and medium.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): Both heat energy and charge are carried by the free electrons in pure metals.
Reason(R) : For pure metals, the electrical conductivity σ is directly related to the thermal conductivity K.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): Costly wrist watches and other instruments are enclosed in a softiron case to protect it from external field.
Reason(R): Ironcase is used as magnetic screening or shielding.
If 'S' is stress and 'Y' is Young's modulus of material of a wire, then the energy stored in the wire per unit volume is
The density of ice is 9.0 g/c.c. and that of sea water is 1.1 g/c.c. An ice berg of volume V is floating in sea water. The fraction of ice berg above water level is
A light ray passed through an equilateral prism. If the angles of incidence and emergence are 45°45° and 55°55°respectively, the angle of deviation is
A constant torque of 314 Nm is exerted on a pivoted wheel. If angular acceleration of wheel is 4π rads⁻², then the moment of inertia of the wheel is
Two bodies M and N of equal masses are suspended from two separate massless springsof force constants K₁ and K₂ respectively. If the two bodies oscillate vertically such that their maximum velocities are eqaul, the ratio of the amplitude of M to that of N is
A stretched string is in unison with a tuning fork of frequency 392 Hz. If the length of the string is decreased by 2%, the number of beats heard per second is
During the adiabatic process, the pressure of gas is found to be proportional to the cube of its absolute temperature. The ratio CP/CV for gas is
A given system undergoes a change, in which work done by a system equal to decrease in its internal energy. The system must have undergone an
Which of the following is not a unit of energy
For the constructive interference the path difference between the two interfering waves must be equal to
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