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The area in square units of the region bounded by the curves x^{2} = 4y, the line x = 2 and the xaxis is
The required area
The area bounded by two curves y^{2}=4ax and x^{2}=4ay is
Let [ ] denote the greatest integer function and f(x) = [tan^{2}x]. Then
The differential equation of the family of curves y^{2}=4a (x+a) is
The solution of the equation (1+x^{2})(1+y)dy+(1+x)(1+y^{2})dx=0 is
Let A = { x ∈ R : x ≠ 0, − 4 ≤ x ≤ 4 } and f : A → R is defined by f (x) =  x /x for x ∈ A . Then the range of f is
⇒ z  log(z + 1) = x + c ⇒ x + y + 1 = log(x + y + 2) + x + c ⇒ y = log(x + y + 2) + log c
⇒ e^{y} = (x + y + z)c ⇒ x + y + 2 = ce^{y}
if f(m) = 3, f^{'}(m) = 2, g(m) =  1 and g'(m) = 2 is
The number of ways in which a committee of 6 members can be formed from 8 gentlemen and 4 ladies so that the committee contains atleast 3 ladies is
A committee of 6 members is to formed from 8 gentlemen and 4 ladies by taking
(i) 3 lady out of 4 and 3 gentlemen out of 8
(ii) 4 lady out of 4 and 2 gentlemen out of 8
In case (i) the number of ways = ^{4}c_{3} x ^{8}c_{3}
= 4 x 56 = 224
In case (ii) the number of ways = ^{4}c_{4} x ^{8}c_{2}
= 1 x 28 = 28
Hence, the required number of ways = 224 + 28 = 252
If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3, is
If A and B are square matrices of the same order, then
If A and B are two events such that P(A) = p, P(B) = q, P (A ∩ B) = r , then the probability that A occurs but B does not occur, is
If A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36. The probabilities P(A) and P(B) are respectively
In Δ A B C , If a^{2} + b^{2} + c^{2} = 8 R^{2} , then the triangle is
If b + c, c + a, a + b are in H.P., then a^{2}, b^{2}, c^{2} will be in
The condition for the roots of the equation (c^{2}ab)x^{2}2(a^{2}bc)x+(b^{2}ac)=d are equal, is
If α,β are the roots of equation x+1=λx(1λx) and two values of λ can be determined from the equation (α/β)+(β/α)=π2, then (λ₁^{2}/λ₂^{2})+(λ₂^{2}/λ₁^{2})+2=
The angle between the line (x + 1)/3 = (y  1)/2 = (z  2)/4 and the plane 2x + y  3z + 4 = 0 is
The general value of θ which satisfies tanθ=1 and cosθ=(1/√2) the equations is
The slope of the tangent at the point (h, h) of the circle x^{2} + y^{2} = a^{2 }is
The distance of the point (2, 1, 1) from the plane x  2y + 4z = 9 is
In short wave communication waves of which of the following frequencies will be reflected back by the ionospheric layer having electron density 10^{11} per m^{3}?
N max = 10^{11} per m^{3}
A step up transformer operates on a 230 volt line and supplies 2 amp to a load. The ratio of primary and secondary windings is 1:25. Determine the primary current .
Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining centre to this point makes an angle θ with the axis of the dipole, then potential at the point P is given by
Two charges 'Q' and 'Q' are kept at a distance 'd' .The charge 'q' is kept at the midpoint of line joining the charges. The magnitude of 'q' to keep the system in equilibrium is
Pick out the incorrect statement regarding reverse saturation current in a p  n junction diode.
For the constructive interference the path difference between the two interfering waves must be equal to
In the propagation of light waves, the angle between the direction of vibration and plane of polarisation is
Final product formed on reduction of glycerol by hydriodic acid is
Two moles of an aldehyde react with concentrated solution of sodium hydroxide and produce one mole of acid and one mole of alcohol. The aldehyde is
Which of the following method is most appropriate for the manufacture of methane?
Propene is reacted with HBr in presence of peroxide, the product is
Which one of the following compounds is not a vitamin?
4.4 g of an unknown gas occupies 2.24 L of volume at standard temperature and pressure. The gas may be
The reagent which forms crystalline osazone derivative when reacted with glucose is
A cylinder filled with a movable piston contains liquid water in equilibrium with water vapour at 25^{0}C. Which one of the following operations results in a decreace in the equilibrium vapour pressure ?
The enthalpy of a solution of KNO_{3} is + 35.64 kJ. This denotes
The acid showing salt like character in aqueous solutions is
In the presence of acid, the hydrolysis of methyl cyanide gives
The delectron configurations of Cr^{2+}, Mn^{2+}, Fe^{2+} and Ni^{2+} are 3d^{4}, 3d^{5, 3d6} and 3d^{8} respectively. Which one of the following aqua complexes will exhibit the minimum paramagnetic behaviour?
(At No. Cr = 24, Mn = 25, Fe = 26, Ni = 28)
Which of the following reagent can be used to convert benzene diazonium chloride into benzene ?
At STP,1.12 litre of H₂ is obtained on flowing a current for 965 seconds in a solution.The value of current is
Which of the following reactions does not yield an alkyl halide?
On heating quick lime with coke in an electric furnace, we get
The single electrode reactions Cd(s) → Cd + 2(aq) + 2e^{} E^{0} = 0.403 V
Cu^{+2} (aq) + 2 e^{} → Cus E^{0} = 0.337 V can be combined to give the cell reaction
. Cd (s) → Cu^{+2} (aq) → Cd^{+2} (aq) + Cu s . The emf of such cell is
In which of the following solutions are ions present?
When the product of pressure and volume is plotted against pressure for a given amount of the gas, the line obtained is
Among the trihalides of nitrogen which one is most basic?
The intermetallic compound LiAg crystallizes in cubic lattice in which both lithium and silver have coordination number of eight. The crystal class is
A compound contains atoms of three elements : A,B and C. If the oxidation number of A is + 2, B is + 5 and that of C is 2, the possible formula of the compound is
The oxide which is the anhydride of orthophosphoric acid is
The bleeding on a wound is stopped by the application of ferric chloride due to
In the ground state, an element has 13 electrons in its "Mshell". The element is.......
Fill in the blank with appropriate word.
.........learning does not help the mental growth of a student.
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.
I waited for half an hour for my friend, but the train didn't TURN IN.
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