
\hspace{16}\mathbb{F}$ ind value of $\bf{p}$ for which the eqn. $\bf{(x^22x)^2(p+3)(x^22x)+(p2)=0}$\\\\\\ $\bf{(i)}\;$ has $\bf{4}$ real solutions\\\\ $\bf{(ii)}\;$has $\bf{3}$ real solutions only \\\\ $\bf{(iii)}\;$has ...

\hspace{16}$If $\bf{r_{1}\;,r_{2}\;,r_{3}\;,r_{4}}$ are the roots of the equation $\bf{4x^4ax^3+bx^2cx+5=0}$\\\\\\ Where $\bf{r_{1}\;,r_{2}\;,r_{3}\;,r_{4}>0}$ and satisfy $\bf{\frac{r_1}{2} + \frac{r_2}{4} + \frac{r_3} ...

\hspace{16}$If $\bf{x=\frac{\sqrt{10+\sqrt{1}}+\sqrt{10+\sqrt{2}}+\sqrt{10+\sqrt{3}}+.......+\sqrt{10+\sqrt{99}}}{\sqrt{10\sqrt{1}}+\sqrt{10\sqrt{2}}+\sqrt{10\sqrt{3}}+.......+\sqrt{10\sqrt{99}}}}$\\\\\\ Then value of $\ ...

If the roots of the equation : x48x3+bx2 + cx +16= 0 are positive then the root of the equation 2bx +c =0 is ???? ...

\hspace{16}$If $\bf{f(x,y)=\frac{\sin(x)\sin (y)}{xy},}$ Where $\bf{x\neq y}$\\\\\\ Then $\bf{\lfloor f(x,y)\rfloor =}$\\\\\\ Where $\bf{\lfloor x \rfloor = }$ Floor function ...

\hspace{16}$find value of $\bf{x}$ in \\\\\\ $\bf{\left\left\left\left\leftx^2x1\right2\right3\right4\right5\right=x^2+x30} ...

log x x  1 > 0 , x E R ...

\hspace{16}$If $\bf{a,b,c\in\mathbb{R}}$ and $\bf{f(x)}$ is a Quadratic Polynomial such that\\\\ $\bf{\begin{Bmatrix} \bf{f(a)=bc} \\\\ \bf{f(b)=ca} \\\\ \bf{f(c)=ab} \end{Bmatrix}}$\\\\\\ Then $\bf{f(a+b+c)=}$ I am Getting ...

1) 2 players A and B play a series of 2n games. Each game can result in either a win or a loss for A. Find the total no. of ways in which A can win the series of these games. (All the games are to be played) Ans: 22n1  1/2. ...

\hspace{16}$Find all ordered pairs $\bf{(x,y)}$ in $\bf{x^2y!=2001}$\\\\ Where $\bf{x,y\in \mathbb{N}}$ ...

\hspace{16}$Determine all Real $\bf{2\times 2}$ matrix $\bf{A=\begin{pmatrix} \bf{a} & \bf{b}\\ \bf{c} & \bf{d} \end{pmatrix}}$ that satisfying \\\\ The equation $\bf{A^2+A+I=O}$ ...

*Image* ...

Let f(x) be a function such that on putting any value of x we get the equation of a hyperbola which is conjugate of the hyperbola having x as eccentricity. then find, f(f(f(f(x))) ...

*Image* ...

this is a gud one... find the last two digits of 32012 or find 32012 mod 100? ...

In an examination hall there are four rows of chairs. Each row has 8 chairs one behind the other.There are two classes sitting for the examination with 16 students in each class.It is desired that in each row,all students bel ...

Find nc0 + nc3 + nc6 + nc9.....................nterms ...

GIVEN: The Largest number of ways in which 6 persons each throwing a single dice once make a sum of 17 is n. Then find [n/1000] where [.] is the Greatest integer function.. ...

What is the distance x between two cities A and B in integral number of kilometres? I. x satisfies the equation log2 x = √x II. x≤10 km Plz ans in detail. ...

\hspace{16}$Find value of $\bf{x}$ in $\bf{\lfloor 2^x \rfloor+\lfloor 3^x \rfloor=\lfloor 6^x \rfloor}$\\\\ Where $\bf{\lfloor . \rfloor}$ = floor function. ...

Prove that 33! is divisible by 215. What is the largest integer n such that 33! is divisible by 2n? Plz give detailed ans. ...

*Image* ...

1) 2 nos. x and y are chosen at random(without replacement) from amongst 1,2,3,...3n.Find the probability that x3+y3 is divisible by 3. ...

1) 7 digits from the nos.1,2,3,...9. are written in a random order. Find the probability that this 7 digit no. is divisible by 9. ...

Checkout this book to drastically improve your mental calculation abilities: http://tinyurl.com/bcummathgenius ...

Suppose p(x) is a polynomial and that p(x)  p'(x) = x^2 + 2x +1. Compute p(5). ...

if z = 2, then find the locus of complex number (a + bz), where a,b E R ...

given, y = x + x  1 + x  3 + x  6 + .................. + x  5151 let m = no. of terms in the expression y and, n = no. of integers for which y has min. value then find the value of m + n  18/10 ...

Eva.uate : \int_{2n}^{2n+\frac 12}{\sin(\pi x)\left\{\frac x2 \right\}} \;\; \mathrm{d}x ...

1) Find the remainder when (103+93)752 is divided by (12)3. ...