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With a given surface area, the volume of a right circular cylinder will be maximum if height is
The smaller area enclosed by the circle x2 + y2 = 9 and the line x = 1 is
The function f(x) = tan x/x for x ≠ 0 ; f (0) = 1 at x = 0 is
If 1 , ω , ω2 , … ωn-1 are the n, nth roots of unity and z1 and z2 are any two, complex numbers, then
The solution of the equation cosx cosy (dy/dx)=-sinx siny is
The differential equation of family of lines which passes (1,-1) is
If f : R → R is defined by f x = 2 x + | x | then f (3x) − f (-x) − 4 x =
If f(x) = e -1/x2 , x ≠ 0, and f(0) = 0 then f ′(0) is
y = A ex + B e2x + C e3x satisfies the diferential equation
∫logx dx =
= x log x − ∫ d x + c
= x log x − x + c
If A and B are two matrices such that AB = B and BA = A, then A2+ B2 =
In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs if the boys and girls alternate?
When two dice are thrown, the probability of getting the sum 10 or 11 is
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is
A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour is
In a Δ A B C , 2s = perimeter and R = circumradius. Then s/R is equal to
= sin A + sin B + sin C .
If m is a root of the equation (1 - ab) x2 - (a2 + b2)x - (1 + ab) = 0, and m harmonic means are inserted between a and b, then the difference between the last and the first of the means equals
The roots of the equation (q-r)x2 + (r-p)x + (p-q)=0 are
If α , β , γ are the roots of x3 − 2 x2 + 3x − 4 = 0, then the value of α 2β2 + β2γ2+ γ2α 2 is
The distance between the parallel planes x + 2y - 3z = 2 and 2x + 4y - 6z + 7 = 0 is
Lines OA, OB are drawn from 0 with directions cosines proportional to < 1, -2, -1 > ans < 3, -2, 3 > respectively. The direction ratios of the normal to the plane AOB are
If the straight lines x = 1 + s, y = -3 - λs, z = 1 + λs and x = t/2, y = 1 + t, z = 2 - t, with parameters s and t respectively, are co-planar, then λ equals
The equation of the parabola whose focus is (1,-1)and directrix is x + y + 7 = 0 is
A force of magnitude 5 units along the vector 2 î − 2j^ + k^ displaces the point of application from (1,2,3) to (5,3,7), then the work done is
The time constant of an LR circuit represents the time in which the current in the circuit
The work function of Potassium is 2.0 eV. When it is illuminated by light of wavelength 3300 A0 photoelectrons are emitted. The stopping potential of photoelectrons is
λ = 3300 A0 = 330 nm
hu = 1240 330 = 3.757
eV0 = hu - W = 3.757 - 2 = 1.757eV
⇒ V0 = 1.757 V
Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance and breakdown voltage of the combination will be:
The electrochemical equivalent of magnesium is 0.126 mg/C. A current of 5 A is passed in a suitable solution for one hour. The mass of the magnesium deposited will be
If the resistance of a conductor is 5 Ω at 50oC and 7 Ω at 100oC, then the mean temperature coefficient of resistance of the material is
The electric intensity E, current density j and specific resistance k are related to each other by the relation
In an experiment to measure the internal resistance of a cell, by a potentiometer, it is found that the balance point is at a length of 2 m, when the cell is shunted by a 5 Ω resistance and is at a length of 3m when the cell is shunted by a 10 Ω resistance. The internal resistance of the cell is
Two resistances R₁ and R₂ are made of different materials. The temperature coefficient of the material of R₁ is α and of the material of R₂ is −β. The resistance of the series combination of R₁ and R₂ will not change with temperature, if R₁/R₂ equals
Gases begin to conduct electricity at low pressure because
The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux φ linked with the primary coil is given by φ = φ 0 + 4t, where φ is in weber, t is time in second and φ 0 is a constant, the output voltage across the secondary coil is
No. of turns across primary Np = 50
Number of turns across secondary Ns = 1500
Magnetic flux linked with primary, Φ = Φ0 + 4t
∴ Voltage across the primary,
Vp = dΦ /dt = d/dt (Φ0 + 4t) = 4 volt
Aslo, Vs /Vp = Ns /Np
∴ Vs = ( 1500/50 ) x 4 = 120 V
At resonance, in a series LCR circuit, which relation does not hold
A solenoid of length 20 cm area of cross-section 4 cm2 and having 4000 turns is placed inside another solenoid of 2000 turns having a cross-section area 8 cm2 and length 10 cm. The mutual inductance of the system is
A charge is placed at the centre of a cube, the flux emitted through its one face is
A hollow metal sphere of radious 10 cm is charged such that the potential on its surface is 80V. The potential at the centre of the sphere is
Two equal charges, q each are placed at a distance of 2a, and a third charge -2q is placed at the mid point. The potential energy of the system is
The capacities of three capacitors are in ratio 1 : 2 : 3. Their equivalent capacity when connected in parallel is 60/11 μ F more than that when they are connected in series. The individual capacities of capacitors in μ F are
Two insulated matallic spheres of 3 μ F and 5 μ F are charged to 300V and 500V respectively. The energy loss when they are connected by a wires is...
A long copper pipe carries a current. Then the magnetic field is
In the following reaction the energy released is 4 1H1 → 2He4 + 2 +1e0 + energy
An infinite number of identical capacitors, each of capacitance 1 μ F, are connected as in the figure. The equivalent capacitance between 'A' and 'B' is
Rows contain capacitors 1, 1/2 , 1/4 , 1/8 ... μF
All in parallel. Therefore effective capacity
C = 1 + 1/2 + 1/4 + 1/16 + ...
It is a Geometrical progression with common ratio 1/2
So C = 1/(1 - 1/2 ) = 2 μF
When P1530 decays to become Si1430 the particle released is
When the light source is kept 20 cm away from a photocell, stopping potential is 0.6 V is obtained. When the source is kept 40 cm away, the stopping potential will be
The slope of frequency of incident light and stopping potential for a given surface will be
In a n-p-n transistor amplifier, the collector current is 9 mA. If 90% of the electron from the emitter reach the collector, then
The band gap in Germanium and silicon in eV respectively is
In the forward bias arrangement of a p-n junction diode
The penetration of light into the region of geometrical shadow is called
What is the effect on the interference fringes in a Young's double slit experiment, if the monochromatic source is replaced by another monochromatic source of shorter wavelength?
Which of the following property of light waves is not observed in sound waves?
2R ― OH + 2Na → 2RONa + H₂. In the above reaction the reactivity of different alcohols is
A compound A has molecular formula C₂Cl₃OH. It reduce Fehling's solution and on oxidation gives a monocarboxylic acid B. A is obtained by the action of Cl₂ on ethyl alcohol. A is
To which of the following four types does this reaction belong? B- + R - A → B - R + A-
A compound possesses 8% sulphur by mass. The least molecular mass is
Self condensation of two moles of ethyl acetate in presence of sodium ethoxide yields
The acid showing salt like character in aqueous solutions is
If a mixture containing 3 moles of hydrogen and 1 mole of nitrogen is converted completely into ammonia, the ratio of volumes of reactants and products at the same temperature and pressure would be
3H2 + N2 → 2NH3
∴ 3V 1V → 2V
Total initial volume = 3V + 1V = 4V
Final volume = 2V
Hence, ratio of initial and final volume will be 2 : 1
The equilibrium constant for the following reaction will be 3 A + 2 B → C
A system is said to be in thermodynamic equilibrium when it is in
The heats of dissociation (k.cals/mole) of methane and ethane are 360 and 620 respectively. From these, C - C bond energy (k.cals/mole) in ethane can be evaluated as
If the enthalpy of vaporisation of water is 186.5 J mol-1, the entropy of its vaporisation will be
Which of the following reagent can be used to convert benzene diazonium chloride into benzene ?
Aromatic nitriles (ArCN) are not prepared by
In Ar-X (Aryl halides) C-X bond has partial double bond character and hence is difficult to break.
Conductivity (Unit:siemen's S) is directly proportionally to the area of the vessel and the concentration of the solution in it and is inversely proportional to the length of vessel,then the unit of constant of proportionally is
When the densities of the ore particles and gangue particles are different, then the ore is concentrated by
A gas a diffuses 5 times faster than gas B. Density of A compared with B is
The pH of aqueous KCl solution is 7.0. This solution was electrolysed for a few seconds using Pt electrodes. Which of the following is correct?
Which of the following reacts rapidly with oxygen in air at ordinary temperature
In crystal structure of sodium chloride, the arrangement of Cl- ions is
Which one of the following is used in the industrial preparation of nitric acid by Ostwald's process ?
Fill in the blank with appropriate word.
The twins are so alike that I cannot.......one from the other.
Out of the given alternatives, choose the one which can be substituted for the given capitalised word.
The old man CUT TO THE QUICK when his rich son refused to recognise him.
Improve the sentence by choosing best alternative for capitalised part of the sentence.
After a few minutes the unconscious boxer began to come OUT.