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\hspace{-16}$If $\bf{(x-8).(x-10)=2^y}$ where $\bf{x,y\in \mathbb{Z}}$. Then no. of ordered pairs of $\bf{\left(x,y\right)}$ ...

Given that a,b,c are the sides of ΔABC which is rt.angled at C.Then the min. value of (c/a + c/b)2 is ?? ...

\hspace{-16}$How many digits are used in total to write the natural numbers \\\\ from $\bf{1}$ to $\bf{100 ^ {1000}.}$ ...

A train goes around a circle, the first time with an average velocity of 100 km/h. How fast should the train be when going around the circle again a second time, so that the average velocity over the two loops is 200 km/h? ...

\hspace{-16}$The no. of positive integer value of $\bf{n}$ for which $\bf{n^2 - 19n + 99}$\\\\ is perfect square. ...

1.12 ml of a gas is produced at S.T.P. by the action of 4.12 mg of alcohol, ROH, with methyl magnesium iodide. find the molecular mass of alcohol. ...

solve: 2sinx=|x| +a find 'a' such that there is no real root! ...

\hspace{-16}$If $\bf{f(x)=\frac{x^2}{1+x^2}.}$ Then Determine value of the following expression\\\\\\ $\bf{f\left(\frac{1}{2000}\right)+f\left(\frac{2}{2000}\right)+...+f\left(\frac{1999}{2000}\right)+f\left(\frac{2000}{2000} ...

Remember the formula for the sum of cubes of 1st n naturals..... \frac{n^2(n+1)^2}{4} Remember the formula we learnt in progressions for deriving this? Now derive this using bionomial theorem..... ...

z has property that |z-5i|=1 & z1 is such that |z1-5|=1 find z1 with the property that |z-z1| is maximum ...

Differentiate this ( a+x - a-x )/( a+x + a-x ) ...

In how many ways can you put 9 coins of into 2 pockets? Consider the cases as (a) All 9 coins are different (b) all 9 coins are same ...

if a,b,c,d and p are different real numbers such that (a2+ b2+c2)p2 -2(ab+bc+cd) p +(b2+c2+d2) ≤ 0 then a,b,c and d are in geometric progression ...

prove tan 3a - tan 2a - tan a = tan a . tan 2a . tan 3a ...

\hspace{-16}$\bf{(A)} No. of ordered pairs $\bf{(n,r)}$ which satisfy $\bf{\binom{n}{r}=2013}$\\\\\\ (B) No. of ordered pairs $\bf{(n,r)}$ which satisfy $\bf{\binom{n}{r}=2014}$ ...

2 parallel st. lines are inclined to the horizontal at an angle α .A particle is projected from a point midway between them so as to graze one of the linesand strike the other at right angle .If θ be the nagle btwn directio ...

In the problem, I cannot do the marked ones. Please tell me how can I find the path difference in this problem for 2nd part. *Image* ...

Prove that n*(n+1)*(2n+1) is divisible by 6, for any n>0 ...

We all know that the c.o.m of a spherical ball having a small hole through which water leaks out at the bottom first goes down and then comes up..Ques is..->wat is the maximum depth till which the c.o.m. goes down..do the ...

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If a , b , c are a triangle angles, prove : csc(a/2)+csc(b/2)+csc(c/2)≥6 ...

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\hspace{-16}$In a $\bf{â–³ABC}$ If $\bf{P}$ be a point which is Inside the $\bf{â–³ABC}$ such that\\\\ Area of $\bf{â–³APB=}$ Area of $\bf{â–³BPC=}$ Area of $\bf{â–³CPA}$.\\\\ Then prove that the point $\bf{P}$ is the centroi ...

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