
\hspace{16}$Calculate total no. of real solution in each case\\\\\\ $\bf{(1)\;\;2^x = 1+x^2}$\\\\\\ $\bf{(2)\;\; 2^x+3^x+4^x = x^2}$\\\\\\ $\bf{(3)\;\; 3^x+4^x+5^x = 1+x^2}$ ...

Lim X→0 exe sinx/ xsinx Don't use L'Hospital ...

\text{Here is an awesome probability question that I solved recently.}\\\text{I know this is quite a popular question so don't just copypaste it directly from some other site.}\\\text{Try it yourself.It's a really good quest ...

6x+5y=7x+3y+1=2(x+6y1) AND x+y8/2 = x+2y14/3 = 3x+y12/11 ...

find the eqn. of those tangents to the circle x2 + y2  2x  4y  4 = 0 which are parallel to the line 3x  4y  1 = 0 ...

\hspace{16}$Calculate total no. of real solution in $\bf{e ^x = x^n}$\\\\ where $\bf{n\in \mathbb{N}}$ ...

x1, x2, x3 are in GP and y1, y2,y3 are also in GP with same common ratio. then (x1,y1), (x2,y2)&(x3,y3) these are a]vertices of a triangle b]situated on a circle c]collinear d]situated on an ellipse ...

\hspace{16}\bf{(1)\;\;}$ In how many ways can the letters of the word $"\bf{PERMUTATIONS}"$\\\\ be arranged so that there is always exactly $\bf{4}$ letters between $\bf{P}$ and $\bf{S}$, is\\\\\\ $\bf{(2)\;\;}$ Calculate To ...

\hspace{16}$ Prove that there exists a power of the number $\bf{2}$ such that the last\\\\ $\bf{1000}$ digits in its decimal representation are all $\bf{1}$ and $\bf{2}$ ...

\hspace{16}$Calculate total no. of real solution in each case\\\\\\ $\bf{(1)\;\;2^x = 1+x^2}$\\\\\\ $\bf{(2)\;\; 2^x+3^x+4^x = x^2}$\\\\\\ $\bf{(3)\;\; 3^x+4^x+5^x = 1+x^2}$ ...

√x^12x^9+x^4x+1 ...

How to find the circumference of an ellipse? ...

Ram and Sam are playing a ludo tiebreaker game where the first one who throws a six wins the game.Find the probability of Ram winning the game if : (a) Ram starts the game (b) Sam starts the game ...

6/5 alog9x+1=22log2x+3 value of X=? ...

s2 = Σ(yi  a  bxi)2 = ƒ(a,b) (i= 1,2....n) Given: ∂s2/∂a = 0 ∂s2/∂b = 0 Then solve for a and b ...

if, 2x=3y=6z,then what is the value of 1/x + 1/y + 1/z ..........????? plz do reply fast........ ...

A line is drawn through a fixed point P (m,n) to the circle x2 + y2 = r2 at A and B. Find PA x PB. ...

there is a isosceles triangle inside a parabola y2=x, with one vertex (0,0), than find the length of the sides of triangle ...

\hspace{16}$(1): The no. of Integer ordered pairs $\bf{(x,y)}$ in $\bf{x^2+y^2 = 2013}$\\\\\\ $(2):$ The no. of Integer ordered pairs $\bf{(x,y,z)}$ in $\bf{\begin{Vmatrix} \bf{x=yz} \\ \bf{y=zx} \\ \bf{z=xy} \end{Vmatrix}}$ ...

How do I PROVE the theorem. Remember not verify, I want to prove it Mathematically. ...

A circle along with one of its diameter AB are given.There lies a point P in the plane.Construct the perpendicular to AB through P using only a ruler.(A ruler can only connect 2 points). ...

\hspace{16}$Solution of following System of equations is\\\\\\ (1) $\bf{y^36x^2+12x8 = 0}$\\\\ $\bf{z^36y^2+12y8 = 0}$\\\\ $\bf{x^36z^2+12z8 = 0}$\\\\\\ (2) $\bf{2y^3+2x^2+3x+3 = 0}$\\\\ $\bf{2z^3+2y^2+3y+3 = 0}$\\\\ $ ...

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For n >=4 points in a plane , such that distance between any 2 points is an integer, prove that there are at least 1/6 distances , which are divisible by 3 ...

in an election contested by two candidates 5% of the voters did not cast their votes. the successful candidate won by 5100votes securing 48 4/7 % of the total votes. how many voters were there? how many votes were cast for ea ...

how can we prove gcd(n,n+1)=1 ...

\hspace{16}\bf{(1)\; \int\frac{1}{x^4.(x^6+1)}dx}$\\\\\\ $\bf{(2)\;\; \int\frac{2+\sqrt{x}}{(1+x+\sqrt{x})^2}dx}$\\\\\\ $\bf{(3)\;\; \int \left\{1+\tan x.\tan (x+\theta)\right\}dx}$\\\\\\ $\bf{(4)\;\; \int \frac{\sec x.\tan ...

logab=3/2 logcd=5/4 ac=9 find bd ...

Find [x]+\sum_{r=1}^{2000} \frac {\{x+r\}}{2000} , where [x] = GIF and {x} = FP. ...

What is the derivative of f(x)=x x ? ...