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The area, in square unit, bounded by the curves y = x3, y = x2 and the ordinates x = 1, x = 2 is
If z₁ and z₂ are two non-zero complex numbers such that |z₁ + z₂| = |z₁| + |z₂|, the value of arg(z₁) - arg(z₂) is
If n is any positive integer ,then the value of
[i(4n+1) - i(4n-1)] /2 equals
If the function f is defined by f(x) = x / 1 + | x | then at what points is f differentiable
The differential equation for the family of curves x2 + y2 - 2ay = 0, where a is an arbitrary constant is
The slope of the tangent at (x,y) to a curve passing thro' a point (2,1) is x2+y2/2xy, then the eqution of the curve is
If x(dy/dx) = y(log y - log x + 1), then the solution of the equation is
The solution of differential equation (x+2y3) dy/dx = y is
The interval in which y=x2ex is increasing with respect to x, is
Let f : R → R be defined by
Then the value of f(-1.75) + f(0.5) + f(1.5) is
If cot-1[(cos α)1/2] - tan-1[(cot α)1/2] = x, then sin x =
"If Deb and Sam go to the mall, then it is snowing."
Which statement below is logically equivalent?
A statement is logically equivalent to its contrapositive.
Number of numbers greater than 1000 but less than 4000 that can be formed by using the digits 0, 1, 2, 3, 4 when repetition is allowed is
Two dice are thrown simultaneously. The probability of getting a pair of 1 is
In a Binomial distribution, the probability of getting a success is 1/4 and standard deviation is 3. Then its mean is
A and B are two independent events. P( A and B) = 1/6 and the probability that neither of them occur is 1/3 . Find the probability occurrence of A?
Let P(A) = X and P(B) = Y;
So, P(A’) = 1 - X and P(B’) = 1 - Y
P(A and B) = P(A) x P(B) = XY = 1/6
Probability that neither of them occurs = P(A’) x P(B’) = (1 - X) x (1 - Y) = 1/3
Solving the resulting quadratic equation, we get X = 1/3 or 1/2 that is the probability of occurrence of A
The angles of a triangle are in the ratio 3:5:10. Then the ratio of the smallest side to the greatest side is
Given n = 10, ∑x = 4, ∑y = 3, ∑x2 = 8, ∑y2 = 9 and ∑xy = 3, then coefficient of correlation is
If each observation of a raw data, whose variance is σ2, is multiplied by λ, then the variance of new set is
Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is
The radius of the circle in which the sphere x2 + y2 + z2 + 2x - 2y - 4z - 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0, is
The normal to the curve x = a(1+cosθ), y = a sinθ at θ always passes through the fixed point
Eliminating θ we get (x – a)2 + y2 = a2
Hence normal always pass through (a, 0)
The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq.units. Then the equation of the cirlce is
The value of c for which the angle between the vectors cxi-6j+3k, xi+2j+2cxk is obtuse is
In a pure inductive circuit or in an A.C. circuit containing inductance only, the current
Light rays of wavelengths 6000 Å and of photon intensity 39.6 watts/m2 is incident on a metal surface. If only one percent of photons incident on the surface emit photo electrons, then the number of electrons emitted per second per unit area from the surface will be [ Planck constant = 6.64 x 10-34 J − s ; Velocity of light = 3 x 108 ms-1 ]
A capacitor of capacity C₁ is charged by connecting it across a battery of e.m.f. V₀. The battery is then removed and the capacitor is connected in parallel with an uncharged capacitor of capacity C₂. The potential difference across this combination is
In connection with chemical effect of current, Faraday constant is equal to
E ∝ z or E = Fz or F = E/z
Where E = chemical equivalent
z = electrochemical equivalent
Intensity of X - rays in coolidge tube is controlled by
A laser beam is used for carrying out surgery because it
As the laser beam is highly monochromatic, directional and coherent, it can be sharply focussed.
Therefore it is used for carrying out surgery
Resistance in the two gaps of a meter bridge are 10 ohm and 30 ohm respectively. If the resistances are interchanged the balance point shifts by
A resistance R is stretched to four times its length. Its new resistance will be
A wire of resistance 12 ohms per meter is bent to form a complete circle of radius 10 cm. The resistance between its two diametrically opposite points, A and B as shown in the Figure, is:
When a current flows through a conductor its temperature
In a noiseless transformer, an alternating current of 2 ampere is flowing in the primary coil. The no. of turns in the primary and secondary coils are 100 and 20 respectively. The value of the current in secondary coil is
In an A.C. circuit, maximum value of voltage is 423 volt. Its effective voltage is
Which of the following electromagnetic waves have the smallest wavelength?
A sphere S1 of radius r1 encloses a total charge Q. If there is another concentric sphere S1 of radius r 2 > r 1 and there be no additional charges between S1 and S2, the ratio of electric flux through S1 and S2 is
Two charges -10 C and + 10 C are placed 10cm apart. Potential at the centre of the line joining two charges is
Two equal print charges are fixed at x = -a and x = +a on the X axis. Another point charge Q is placed at the origin. The change in electrical potential energy of Q, when it is displaced by a small distance x along the X-axis is approximately proportional to
A 5 μ F capacitor is fully charged across a 12V battery. It is then disconnected from the battery and connected to an uncharged capacitor. If the voltage across the capacitor becomes 3V, the capacitance of the uncharged capacitor is
The electric potential V is given as a function of distance x (metre) by V = (5x2 + 10x - 9) volt. Value of electric field at x = 1m is
V = 5x2 + 10x - 9
E = - dv / dx
= - (10x + 10)
= -(10 x 1 + 10)
= - 20 V/m
A quatity X is given by ε0 L ΔV/Δt , where ε0 is the permittivity of free space, L is a length, ΔV is potential difference and Δt is the time interval. The dimensional formula for X is the same as that of
[ε0 L] = [capacitance] = [C]
∴ X = ε0L ( ΔV/Δt ) = CΔV/Δt = ΔQ/Δt = current
A charged particle moves through a magnetic field in a direction perpendicular to it. then the
The average binding energy of the nucleon is
The binding energy per nucleon of a nucleus is the binding energy divided by the total number of nucleons. Important features of the graph: Excluding the lighter nuclei, the average binding energy per nucleon is about 8 MeV.
A radio active nucleus with mass number 'A' splits into the nuclei whose mass numbers are in the ratio 3:2, the ratio of their radii is
Photons of energy of 6 eV are incident on a metal surface whose work function is 4 eV. The minimum kinetic energy of the emitted photoelectrons will be
Which of the following pairs have linear relationship between themselves when photoelectrons are emitted from a surface :
In the formation of a spectrum of white light by a prism, the deviation of violet colour is
The majority charge carriers in p - type semiconductor are
A p-n photodiode is fabricated from a semiconductor with band gap of 2.8 eV. Which of the following wavelengths it can detect?
The difference in the number of wavelengths, when yellow light propagates through air and vacuum columns of the same thickness, is one. The thickness of the air column is
(Refractive index of air μ a = 1.0003 ; Wavelength of yellow light in vacuum 6000 Å )
Let λa and λ be the wavelengths of yellow light in air and vacuum respectively and va and c be their respective speeds in air and vacuum.
Since the frequency of light is the same in both media, we have
Now, if t is the thickness of each columm, then the number of wavelengths in the two media are
A semi-conducting device is connected in a series circuit with a battery and a resistance. A current is found to pass through the circuit. If the polarity of the battery is reversed, the current drops to almost zero the device may be
Which of the following when added as an impurity into the silicon produces n-type semiconductor?
When two coherent monochromatic light beams of intensities I and 4I are superimposed, the ratio between maximum and minimum intensities in the resultant beam is
If Young's double slit experiment of light, interference is performed in water, which one of the following is correct?
If the ratio of intensities of two waves causing interference be 9:4, then the ratio of maximum and minimum intensities will be
3 moles of ethanol react with one mole of phosphorus tribromide to form 3 moles of bromoethane and one mole of X. Which of the following is X?
Which of the following compounds does not react with NaHSO₃?
In nucleophilic substitution reactions, the reactivity of carbonyl compounds follows the order
The authenticity of an observation, made from an instrument depends upon its
Ozonolysis of C₇H₁₄ gave 2-methyl-3-pentanone toluene. The alkene is
Assuming full decomposition, the volume of CO₂ released at STP on heating 9.85 g of BaCO₃ (At. mass Ba = 137) will be
The hormone which controls the process like burning of fats, proteins and carbohydrates to liberate energy in the body is
Thyroxine is a hormone secreted by thyroid gland.
This hormone controls various biochemical reactions involving burning of proteins carbohydrates, fats to release energy.
Which of the following compounds is responsible for the transmission of heredity characters?
Which of the following compounds is formed when benzamide is warmed with bromine and alkali?
Which of the following salt can be produced by the reaction of CO and caustic soda ?
A glass bulb is filled with NO₂ gas and immersed in an ice bath at 00C which becomes colourless after some time . This colourless gas will be
The rate, at which a substance reacts at constant temperature, depends upon its
One mole of an ideal gas at 300 K is expanded isothermally from an initial volume of 1 litre to 10 litres. The ΔE for this process is (R = 2 cal.K-1 mol-1)
For isothermal reversible expansion of an ideal gas
W = - 2.303n RT log V2/V1
= - 2.303 x 1 x 2 x 300 log 10/1 (log 10 = 1)
= - 2.303 x 2 x 300 = - 1381.8 Cal
[R = 2 Cal mol-1 K-1, T = 300 K]
As ΔE = q + W (1st law of thermodynamics)
For isothermal process q = - W
So ΔE = - W + W = 0
For an isothermal change ΔE = 0
(Since internal energy is a function of temp and in an isothermal process temp remains constant)
In which one the following reactions does the heat change represents the heat of formation of water
The arrangement of hydrogen atoms around carbon in the methane molecule is
Considering H₂O as a weak field ligand, the number of unpaired electrons in [Mn(H₂O)₆]2+ will be (At no.Mn=25)
In the presence of acid, the hydrolysis of methyl cyanide gives
The oxidation state of copper in the above complex is
O.N. of Cu in [Cu (NH3)4] SO4 is +2.
Which of the following shows maximum no. of oxidation states?
The specific conductance of a 0.1 N KCl solution at 230C is 0.012 ohm⁻1 cm⁻1. The resistance of cell containing the solution at the same temperature was found to be 55 ohm. The cell constant will be
Standard electrode potentials are Fe2+∕Fe (E0 = -0.44) Fe3+∕Fe2+(E0 = 0.77) Fe2+, Fe3+ and Fe blocks are kept together, then
The natural materials from which an element can be extracted economically are called
At constant temperature, in a given mass of an ideal gas
In nitrogen family, the H-M-H bond angle in the hydrides gradually becomes closer to 90o on going from N to Sb. This shows that gradually
SnCl₂ gives a precipitate with a solution of HgCl₂. In this process HgCl₂ is
Types of geometrical isomerism shown at the points x, y and z of the following compound are respectively:
Both acid and base may react with which of the following oxides?
Fill in the blank with appropriate word.
He is working under such........conditions that it is difficult to maintain his self-respect.
Improve the sentence by choosing best alternative for capitalised part of the sentence.
It was SHE NOT ME who put forth the attractive proposition.
Out of the given alternatives, choose the one which can be substituted for the given capitalised word.
The rebels HELD OUT for about a month.