
\hspace{16}\bf{(1)\;\;}$ Total Integer ordered pair,s of $\bf{(x,y)}$ in $\bf{x^2y! = 2001}$\\\\\\ $\bf{(2)\;\;}$ Total Integer ordered pair,s of $\bf{(x,y)}$ in $\bf{x^27y! = 2011}$\\\\\\ $\bf{(3)\;\;}$ Total Integer orde ...

\hspace{16}\bf{(1)\;\;}$ The sum of $\bf{5}$ digit no. that can be formed using the digits $\bf{0,0,1,2,3,4}$\\\\\\ $\bf{(2)\;\;}$ The sum of $\bf{5}$ digit no. that can be formed using the digits $\bf{0,0,1,1,2,3}$ ...

When any three points are selected from a circle, what is the probability that they will form an obtuseangled triangle? ...

\hspace{18}$All positive Integer ordered pairs $\bf{(x,y)}$ for which $\bf{\binom{x}{y} = 120}$ ...

\hspace{18}$Integer values of $\bf{x}$ for which $\bf{x^4+x^3+x^2+x+1}$ is a perfect square. ...

\hspace{18}$(1) The number of four digits having only two consecutive digits identical is\\\\\\ (2) The number of four digits having only three consecutive digits are\\\\ identical is ...

\hspace{16}$If $\bf{34! = 295232799039604140847618609643520000000}$.Then $\bf{(a,b,c,d)}$\\\\ ...

\hspace{16}$Solution for $\bf{a\;,b\;,c}$ in \\\\ $\bf{a[a]+c\{c\}b\{b\}=0.16}$\\\\ $\bf{b+a\{a\}c\{c\} = 0.25}$\\\\ $\bf{c[c]+b\{b\}a\{a\} = 0.49}$\\\\ Where $\bf{[x] = }$ Integer part of $\bf{x}$\\\\ and $\bf{\{x\} = }$ ...

What is the remainder 709! is divided by 719? ...

If you flip a fair coin ten times, what is the probability there will be at least one sequence of three consecutive heads or three consecutive tails? ...

There are two drawers in each of three boxes that are identical in appearance. The first box contains a gold coin in each drawer, the second contains a silver in each drawer, but the third contains a gold in one drawer and a ...

\hspace{16}$Determine all pairs $\bf{(a, b)}$ of natural numbers, for which the number\\\\ of $ \bf{a ^ 3 + 6ab + 1} $ and $ \bf{b ^ 3 + 6ab + 1}$ are cubes of natural numbers. ...

\hspace{16}$Calculation of real values of $\bf{(a,b,c)}$ such that $\bf{x^3ax^2+bxc =0}$\\\\ has a roots $\bf{a\;,b}$ and $\bf{c.}$ ...

\hspace{16}$factors of $\bf{a(bc)^3+b(ca)^3+c(ab)^3}$ ...

It is given that a1=1 and an=n(an1+1). Define a sequence pn as pn=(1+ 1/a1 )(1+ 1/a2 )...(1+ 1/an ). Find lim(nâ†’âˆž)pn. ...

Given a polynomial of n degree such that f(x)+f(1/x)=f(x)*f(1/x) Find the polynomial ...

\hspace{16}$Solution for real $\bf{\left(a\;,b\;,c\right)}$ in \\\\ $\bf{[a]+c\{c\}b\{b\}=0.16}$\\\\ $\bf{b+a\{a\}c\{c\} = 0.25}$\\\\ $\bf{c[c]+b\{b\}a\{a\} = 0.49}$\\\\ Where $\bf{[x] =}$ Integer part of $\bf{x}$\\\\ and ...

If p(x) is an 11th degree polynomial such that p(x) = 1/1+x for x = 1, 2, 3,...11, then find p(12). ...

Find n so that ( an+1 + bn+1 ) / (an +bn ) may be the harmonic Mean between a & b . ...

\hspace{16} $ Minimum value of $\bf{\leftz1i \right + \left z+23i \right + \left z+3+2i \right}$\\\\\\ where $\bf{z = x+iy}$ and $\bf{i = \sqrt{1}}$ ...

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Using the following no.s make a total of 24 by using + ,  , / , * and parantheses only . 8 8 3 3 ...

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Find remainder when 2013C101 is divided by 101 ...

If Î± and Î² be the roots of equation ax2+bx+c=0,aâ‰ 0 and (Î±+Î²)(Î±2+Î²2)(Î±3+Î²3)are in GP,Î” be the discriminant,then a) Î”â‰ 0 b) bÎ”â‰ 0 c) cÎ”=0 d) bcâ‰ 0 ...

\hspace{16}$Total Real solution of the equations in Diff. cases\\\\\\ (i) $\bf{2^x = 1+x^2}$\\\\\\ (ii) $\bf{e^x = x^2}$ ...

Reduce to lowest terms, (a2b2) / ab  (abb2) / (aba2). ...

In a triangle ABC, angleA is greater than angleB and A,B,C are the roots of the equation 3sinx4sin3xÎ»=0.Find the angleC.(0<Î»<1) Please show the workout ...

One corner of a long rectangular sheet of paper of width 1 foot is folded over so as to reach the opposite edge of length of the crease.What will be the minimum length of the crease. (Please show the workout) ...

Find the greatest integer k for which 1991^k divides 1990^1991^1992 + 1992^1991^1990 ...