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If you draw the figure the question becomes clear.
The locus is outside the circle with centre (0,0) and radius=5-3=2 and inside the circle with centre (0,0) and radius= 5+3=8.
Locus is :
(5-3)2 <= x2 + y2 <= (5+3)2
4 <= x2 + y2 <= 64
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kiran is right.
follow the link :
http://cmm.cit.nih.gov/modeling/guide_documents/quantum_mechanics_document.html
its explained nicely there.
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kghedriu is correct.
cosC = (a2 + b2 - c2)/2ab = (b2 - 12)/4b
1/4 = (b2 - 12)/4b
b2 - b - 12 = 0
taking +ve value of b we get b = 4
then sides would be (2,4,4) which is a possible triplet.
Hence 1 triangle is possible.
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If the grignard reagent is used in limited quantity then ketone formation would take place with a little amount of tertiary alcohol.
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Aman is right. S.N. Sanyal is a good book and everything is clearly explained in it.
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You may also refer to the link :
http://www.hamline.edu/~rmajerle/Chem3460/pdf/May0306.pdf
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|z - 4/z| = 2
Applying |z| - |4/z| <= |z - 4/z|
|z| - |4/z| <= 2
|z|2 - 2|z| - 4 <= 0
|z|  [1 -  5 , 1 +  5]
Hence |z|max = 1 + 5
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No such marks are allocated to any particular topic.It varies every year.
If its a mixed question from physical and inorganic then how it would be counted.
Fluctuations are there but chemical kinetics is an important topic and you should grasp it potentially.
Best Wishes
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2N2+O2  2N2O
Initially concentration of N2 = 0.482/10 = 0.0482 = c1(let)
and that of O2 = 0.933/10 = 0.0993 = c2(let)
At equilibrium let the concentration of N2O = c'
then that of N2 will be c1 - c' and of O2 will be c2 - (c'/2)
Kc = [N2O]2/([N2]2.[O2]) = (c')2/[(c1 - c')2.(c2 - (c'/2))]
1) Kc = 2x10-37 << 1 indicates that concentration of product is less.
Hence c' in denominator can be neglected and c' comes out to be
c' = c1Kc.c2
2) When Kc = 4 , product concentration cannot be neglected and you have to solve the quadratic equation for c'.
hope its clear now
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Two squares have same side if they are in the same row or same column and thay are adjacent.
7 such pairs are possible along a row and there are 8 such rows gives 8*7=56 pairs.
Similarly 56 pairs are possible for 8 columns.
Hence total no. of possible pairs = 56 + 56 = 112
2 squares can be choosen in 64C2 ways.
Hence required probability = 112/64C2 = 1/18
Best Wishes
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Equation of chord of hyperbola with mid-point (x1,y1) is : T = S1
where T = xx1/a2 - yy1/b2 - 1
S1 = x12 /a2 - y12 /b2 - 1
Now make the equation of hyperbola homogenous :
x2/a2 - y2/b2 = 1 = (T/S1)2
since the chord subtends right angle at the centre
therefore coeffcient of x2 + coeffcient of y2 = 0
Applying this you will get the required locus.
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Since k (0, ) hence k is positive.
expression is : x4 + kx2 + k = 0
now x4 >= 0 kx2 >= 0 k > 0
Hence LHS > 0
Hence no real values of k are possible.
Please post your other query on a new page.
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Since it is a perfect square, its discriminant should be 0.
Quadratic equn. : (16+9k) x2 + (12-2k) x + 39 + 11k = 0
Discriminant = (12-2k)2 - 4(16+9k) (39+11k) = 0
98k2 + 539k + 588 = 0
gives k = -4 , -3/2
only one integral value k = -4 is possible but its not positive integral solution.
please put ur question again if u have mistyped.
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First of all mug up all the formulas and apply it to some of the easy problems.
As you practice more and more your mind will set for trigo problems.
After practcing a lot u will find that now u can crack those problems which you were not able to solve before.
The main advice behind all this is practice.Go ahead step by step.
Best Wishes
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You may also refer to the link :
http://www.school-for-champions.com/science/frictionrolling.htm
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Let the equation of SHM be y = Asinwt
Let the time intervals of displacements X,Y,Z be t'-1 , t' , t'+1 respectively.
X = Asinw(t'-1) and Z = Asinw(t'+1)
adding X + Z = A[sinw(t'-1) + sinw(t'+1)] = 2A(sinwt')(cosw)
and Y = Asinwt'
eliminating sinwt' (by dividing) we get
(X+Z)/Y = 2cosw
w = cos-1[(X+Z)/2Y]
Hence time period = 2 /w = 2/cos-1[(X+Z)/2Y]
Best Wishes
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The ionization potential, or ionization energy, of an atom or molecule is the energy required to strip it of an electron. More generally, the nth ionization energy is the energy required to strip it of an nth electron after the first n ? 1 have already been removed. It is centrally significant in physical chemistry as a measure of the reluctance of an atom or of a molecule to surrender an electron, or the strength by which the electron is bound
The electron affinity of an atom or molecule is the energy required to detach an electron from a singly charged negative ion.An equivalent definition is the energy released (Einitial ? Efinal) when an electron is attached to a neutral atom or molecule.
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rik_mad has done a great job.
If we multiply any number by 6 then at most its last three digits are altered.
Hence 6[(abc)103 + def] = [(def)103 + abc]
=> 857(abc) = 142(def)
Hence abc = 142 and def = 857
Hence the orignal no. = 142857
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A short cut method could be consider it as an equilateral triangle.
Then A=B=C=600
cosA/(sinB.sinC) = (1/2)/(3/4) = 2/3
Hence summation cosA/(sinB.sinC) = 3.(2/3) = 2
Best Wishes
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Kiran has explained it in a nice way.
Aromatic compound should be planar.
Since it is non-planar, so it is not aromatic.
Best Wishes
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