
\hspace{16}\bf{\sum_{n=1}^{\infty}\;\sum_{m=1}^{\infty}\;\frac{1}{m.n.(m+n+1)}}$ ...

1. \text{If} \; \sum_{x=\pi^{10}C_7}^{x= \pi + ^{10}C_r} \; \sin(x^o) = 0 , then value of r is ? 2. Side lengths of the triangle are 3 consecutive integers, and one of the angles in twice that of other, then no. of such tria ...

Q) let a,b,c be distinct complex nos. such that a=b=c>0 . if a+bc , b+ac , c+ab are real numbers then abc = __ Ans. 1 a method or a solution would be appreciated. ...

Let z and w be two complex numbers such that z=w=1 and z+iw=ziw=2. then z= ...

1) If the curves ax2 + 4xy + 2y2 + x + y + 5 = 0 and ax2 + 6xy + 5y2 + 2x + 3y + 8 = 0 intersect at four concyclic points, then the value of a is... 2) For 0 < x < pi/2 the solution of \sum_{m=1}^{6}{} cosec {x + (m  ...

1. *Image* 2. Let Points P,Q correspond to the complex numbers a,b in the complex plane. If a = 4 and 4a22ab+b2 = 0 , then the area of the triangle OPQ, (O = Origin) is : ...

Let z=a(cos Ï€/5 + isin Ï€/5), aâˆˆr,  a  â‰¤1. Then z2010 +z2011............. equals? a) z2010/1a b) a2010/1a c) za2010/1z d) a2010/1z ...

The sum of roots of the equation x + 1  2 log2 (2x + 3) + 2 log4 (10  2x) = 0 is a) log211 b) log212 c) log213 d) log214 ...

plz give some short method for the following type quest. . Q1  find the sum of all the numbers greater then 10000 formed with digits 0,2,4,6,8. no digit being repeated. Q 2 whats the ans for this : how many numbers are divi ...

1. The no. of tangents to the curve y = cos(x+y) , x â‰¤ 2Î , that are parallel to the line x+2y=0 is ? 2. If 2008Î¸=Î , and 2 .\sum_{r=1}^{r=n} \sin(r\theta)\cos(r^2\theta) is an INTEGER , then find the least integral n ? ...

Find solution set of logx2 . log2x2 =log4x2 ...

'a' and 'b' are integers. Solve 2(a2b)=b2a ...

Let f(x)=x ( x Ï€) (2 + cos2x), xâˆˆR. Then the function f: Râ†’R is A) one  one but not onto B) onto but not one one C) both oneone and onto D) neither one one nor onto ...

A problem of statistics is given to 3 students A,B & C whose chances of solving it are 1/2,1/3 & 1/4 respectively.what is the probability that the problem is solved? The answer is given 3/4 ...

f:\bf{R}\to\bf{R} \;\;, f(x) is a function satisfying f(x)+f(x^2)=2 \;\; \forall x \in \bf{R} , then f(x) is : a) into b) many one c) constant d) periodic Morethan one! ...

If ax2bx+c=0 has two distinct roots lying in the interval (0,1), a,b,c(belong to) N, then log5abc= A)1 B)2 C)3 D)4 ...

can a cubic eqn. have three complex roots...!! I mean if there's 1 so there will be 2 can it be 3? if it can be... then look at this question, if b2 < 2ac, then prove that ax3 + bx2 + cx + d = 0 has exactly one real root. ...

\int_{0}^{2\pi} e^{\cos x} \cos({\sin x}) \; \mathrm{d}x ...

If sin(a+b)sin(ab)=sin c (2sin b+sin c) , 0 <a,b,c < Pi, then the family of lines xsin a+y sin b+ sin c = 0, passes through the fixed point? ...

\hspace{16}$If $\mathbf{a,b\in \mathbb{R}}$ and $\mathbf{a\neq b}$. Then Locus of all Complex no. $\mathbf{z}$ which\\\\ Satisfy the equation. $\mathbf{\mid za \mid^2\mid zb \mid^2=1}$ ...

*Image* I want to know how to solve these too if you cant see the Problems Copy and Paste the following link into the address bar http://imgur.com/EQ4vW *Image* ...

\textbf{Let}\; a \; \textbf{and} \; b \; \textbf{be the Real Parameters. One Root of the equation} \\\;x^{12}abx+a^2=0 \; \textbf{is greater than} \;\;2,\textbf{then find minimum value of }\; b ...

\hspace{16}$Let $\mathbf{x^n+a_{1}.x^{n1}+a_{2}.x^{n2}+a_{3}.x^{n3}+.......+a_{n}=2011}$\\\\ Where $\mathbf{a_{i}\in \mathbb{Z}\;\forall \;i\in \left\{1,2,3,....,n\right\}}$ has $\mathbf{4}$ Integrals Roots.\;\\\\ Then th ...

p(x) = x5 + x2 +1 have roots x1 , x2,x3,x4,x5. g(x) = x22. then the value of g(x1).g(x2).g(x3).g(x4).g(x5)  30g(x1.x2.x3.x4.x5) is ? ...

\hspace{16}$Find all Complex no. $\mathbf{z}$ that satisfy the equations\\\\ $\mathbf{\  z+3+z3=10}$ and $\mathbf{\ 2z+3i=\sqrt{109}}$. ...

\hspace{16}$The Least value of $\mathbf{S=\mid z23i\mid+\mid z4+3i\mid+\mid z1i\mid}$\\\\ Where $\mathbf{z\in \mathbb{C}}$ ...

how many 4digit numbers are there whose sum of the digits is odd? ...

Q: Functions f(x) and g(x) are defined in [a,b] such that f(x) is monotonically increasing while g(x) is monotonically decreasing. If it is given that range of f(X) and g(x) are subsets of the domain, then find the domain and ...

Let [x] denote the greatest integer less than or equal to x and {x} = x[x] (commonly known as fractional part of x). Find all continuous functions f such that {f(x+y)} ={f(x)}+{f(y)} ...

\hspace{16}$The Value of $\mathbf{m}$ for Which the equations\\\\ $\mathbf{(5mm^2)^2.\sin^2 x10.\sin x.(5mm^2)+24=0}$\\\\ Has exactly $\mathbf{\underline{\bold{Three}}}$ Solution in $\mathbf{[0,2\pi].}$ ...