Aditya Prakash
  • Member for 3 years
  • Last seen more than a week ago
  • Jamshedpur, Jharkhand, India
How many strings are there of four decimal digits that:
3 votes

If I am not getting your question wrong then your answers are wrong. a)If a 4 digit number contains exactly four 9's , then $^9C_4$ is not your solution , there is only one way i.e 9999 , so answer ...

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If a,b,c are positive rational numbers such that a>b>c then tell which of the following statement are correct following quadratic equation
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1 votes

Building up on your work :- You have found that $$2b>a+c... (1)$$$$2a>b+c...(2)$$Note that $ax^2+2bx+c$ has all positive coefficients , there fore the parabola of this quadratic equation will ...

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Please, help to simplify set theory expression
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1 votes

I am not using the TeX codes , sorry . I hope you can understand this handwritten version.

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All answers of $abcd=a+b+c+d-3$ in natural numbers
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0 votes

There are obvious answers of the form $(n,1,1,1,)$ and its permutations as you have correctly pointed out.Let there be two numbers from $a,b,c,d$ greater than 1 , suppose a and b are greater than 1 ...

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can someone help me prove this
0 votes

I thought a diagram will be useful here.As you can see I have drawn sets A & B and X & Y.The symmetric difference of A and B i.e. $A\Delta B$ is coloured in buff color(light orange).You have ...

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Difficult inequality with 4 variables
0 votes

Tchebychef's inequality-If $a_1,a_2..a_n$ and $b_1,b_2..b_n$ are real numbers then $$\frac{a_1b_1+a_2b_2+ .. +a_nb_n}{n}\geq\left(\frac{a_1+a_1+...+a_n}{n}\right)\left(\frac{b_1+b_1+...+b_n}{n}\right)$...

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The lengths of the sides of a triangle are $\sin\alpha$, $\cos\alpha$ and $\sqrt{(1+\sin\alpha\cos\alpha)}$...
0 votes

Obviously $\sqrt{1+sin\alpha cos\alpha}$ will always be the longest side (always >1).Now we find $\alpha$ for which this will be maximum.$$\frac{d}{d\alpha}\sqrt{1+sin\alpha cos\alpha}=\frac{cos(2\...

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Should we consider number of ways of choosing the first channel?
0 votes

The answer is given as 12 probably because the question asks for the number of ways to return to original channel for a particular starting channel and not for all possible original channels , ...

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Find the moment of inertia of a homogenous solid right circular cylinder around a diameter of its base.
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You can approach in the following way :-Take an elementary disc of infinitesimal thickness at a distance $x$ from the center of the face which is having the diameter.Calculating the linear density(I ...

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