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Maximum slope of the curve y = x^{3} + 3x^{2} + 9x − 27 is
The area bounded by the parabola x = 4 − y^{2} and the yaxis, in square units is
The area bounded by the curve y=xsinx and xaxis between x=0 and x=2π is
If x dy = y(dx + y dy), y > 0 and y (1) = 1, then y (3) is equal to
The solution of the equation (1+x^{2})(1+y)dy+(1+x)(1+y^{2})dx=0 is
The solution of the differential equation 2xy(dy/dx) = x^{2}+3y^{2} is (where c is a constant)
If y = sin^{1} [(1  x^{2})/(1 + x^{2})], then (dy/dx) =
f : R → R is a function defined by f(x) = 10 x − 7. If g = f ^{1} then g(x) =
The determinant of skewsymmetric matrix of odd order is always zero
Therefore the inverse of skewsymmetric matrix does not exist
How many numbers between 3000 and 4000 divisible by 5 can be formed from the digits 3,4,5,6,7,8 if repetition of any digit is not allowed?
A card is drawn at random from a well shuffled pack of 52 cards. The probability of getting a heart or diamond is
Each coefficients in the equation ax^{2}+bx+c=0 is determined by throwing an ordinary die. The probability that the equation will have equal roots is
Two persons A and B takes turn in throwing a pair of dice. The first person to through 9 from both dice will be avoided the prize. If A throws first, then the probability that B wins the game is
If the side of a triangle are 13, 14, 15, then the radius of the incircle is
The number of terms of the A.P. 3, 7, 11, 15,...to be taken so that the sum is 406 is
The Quartile Deviation of the daily wages (in Rs) of 7 persons given below :
12, 7, 15, 10, 17, 19, 25 is
If the roots of 5x^{2} + 13x + k = 0 are reciprocal of each other, then the value of k is____
The standard deviation of 25 numbers is 40. If each of the numbers is increased by 5, then the new standard deviation will be
If each item of a data is increased (or decreased) by the same quantity, the standard deviation (and the variance) is not changed.
If α,β are the roots of the equation x^{2 } 2x + 4 = 0 then α^{5 }+ β^{5}=
If a line makes angles α,β,γ with the +ve direction of x,y and z axis respectively, then cos^{2}α + cos^{2}β + cos^{2}γ
The line (x  2)/3 = (y  3)/4 = (z  4)/5 is parallel to the plane
The pair of lines represented by 3ax^{2}+ 5xy + (a^{2}  2) y^{2 }= 0 and at right angles to each other for
A force acts at a point A whose position vector is . If point of application of F^{ →} moves from A to the point B with position vector , then work done by F is
If P is any point on the hyperbola [(x  1)^{2}/9  (y + 1)^{2}/16] = 1 and S_{1}, S_{2} are its foci, then s_{1} P  S_{2} P 
If a = i + 2 j + 3k, b =  i + 2 j + k and c = 3 i + j and a + tb is perpendicular to c, the value of t is
If two atoms have their atomic numbers as z_{1} and z_{2} , the ratio of the wavelengths λ_{1} and λ_{2} corresponding to their K_{α } lines is
The deBroglie wavelength of a particle moving with a velocity 2.25 x 10^{8} m s^{1} is equal to the wavelength of a photon. The ratio of kinetic energy of the particle to the energy of the photon is [ velocity of light = 3 x 10^{8} m s^{1}]
From Compton effect
λ = h/p = c/v [From deBroglie wavelength]
c p = h v
An electron having charge e and mass m is moving in a uniform electric field E. Its acceleration will be
A rectangular, a square, a circular and an elliptical loop, all in the (x  y) plane, are moving out of a uniform magnetic field with a constant velocity, V^{→} = vî . The magnetic field is directed along the negative z axis direction. The induced emf, during the passage of these loops, out of the field region, will not remain constant for:
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 Xaxis is approximately proportional to
Two point charges each equal to 2μC are 0.5 m apart. If both of them exist inside vaccum, then electrostatic force between them is
The size of the nucleus varies as  power of the atomic number
If the two slits in Young's experiment have width ratio 1:4, the ratio of intensity at maxima and minima in the interference pattern in
When ethanol is refluxed with conc. sulphuric acid at 160^{o} it gives
Which of the following gives iodoform on heating with a solution of l_{2} containing Na_{2}CO_{3} ?
How many monochlorobutanes will be obtained on chlorination of nbutane?
Which of the following reactions can be used for the synthesis of an alkene
Molarity of liquid HCl with density equal to 1.17 g/cc is
Which one of the following proteins transports oxygen in the blood stream?
In a reaction involving ring substitution of C_{6}H_{5}Y, the major product is meta isomer. The group Y can be
Electron withdrawing groups favour meta substitution
 COOH group is metadirecting group
The equilibrium constant in a reversible chemical reaction at a given temperature
C + O_{2} → CO_{2} , Δ H = − 94 K cals ,
CO + 1/2O_{2} → CO_{2} , Δ H = − 67.7 K . cal.
On the basis of above data, the heat of formation of CO is
For the melting of a solid at 25^{0}C, the fusion process requires energy equivalent to 2906 Joules to be added to system considering the process to be reversible at fusion point, the entropy change of the process is
Heat of combustion of carbon is 96k cal mol^{1}. When some quantity of carbon is burnt in oxygen, 48 k cal of heat is liberated. What is the volume (in lit) of oxygen at STP reacted with this carbon?
∵ 96 k cal heat is produced by 1 mol of carbon.
∴ 48 k cal heat is produced by 0.5 mol of carbon.
As 1 mol carbon reacts with 1 mol of oxygen, which has 22.4 litre volume at NTP.
∴ The volume of O_{2} at NTP reacts with 0.5 mol carbon = 22.4/2 = 11.2 litre.
The rate, at which a substance reacts at constant temperature, depends upon its
Which one of the following is an example of octahedral complex?
Which one of the following will not show geometrical isomerism?
Out of Cu, Ag, Fe and Zn, the metal which can displace all others from their salt solutions is
The electrode potentials of halfcell reactions are: Zn → Zn^{2+} + 2e⁻ ; E = 0.76 V and Fe → Fe^{2+} + 2e⁻ ; E=0.41 V. The e.m.f. of the cell Fe^{2+} + Zn → Zn^{2+} + Fe is
Molten CuCl_{2} is electrolysed using platinum electrodes. The reaction occuring at anode is .......
Absolute ethyl alcohol can be converted to diethyl ether by heating it to 410 K in the presence of
The most electropositive metals are isolated from their ores by
50 mL of hydrogen diffuses out through a small hole of a vessel, in 20 minutes. The time taken by 40 mL of oxygen to diffuse out is
A crystal lattice with alternate positive and negative ions has radius ratio 0.524. Its coordination number is
Radius ratio of the given crystal lattice is in the range of 0.414  0.732. So the coordination number is 6.
A colloidal system in which gas bubbles are dispersed in liquid is known as
Fill in the blank with appropriate word.
I am given to.......that you are going abroad.
Choose the alternative which best expresses the meaning of the idiom/phrase.
Bring forth
Improve the sentence by choosing best alternative for capitalised part of the sentence.
ANY ABLE BODIED MAN eligible for the job.
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