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Let ' c ' be a fixed real number. Show that a root of the equation (below) can have a multiplicity atmost 2 and Determine the number of such values of ' c '. x(x+1)(x+2).....(x+2009) = c Source: ISI (B.Math Admission Test 200 ...

Dehydration of 2,2,3,4,4-pentamethyl-3-pentanol gave two alkenes A & B. the ozonolysis products of A & B are : *Image* xplain it plz.. ...

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\hspace{-16}$Calculate $\mathbf{\int_{1}^{\infty}\left(\frac{\ln x}{x}\right)^{2011}dx=}$ ...

If the graph of xy = 1 is reflected in the graph of y =2x to give the graph of 12x^2+rxy+sy^2+t=0 , where r,s,t are some constant. Determine them. ...

\hspace{-16}$If\; $\mathbf{\frac{\alpha+\beta}{2\alpha+\gamma}=\frac{\beta+\gamma}{2\beta+\alpha}=\frac{\gamma+\alpha}{2\gamma+\beta}}$\\\\\\ Then $\mathbf{\frac{2\alpha+3\beta+5\gamma}{7\alpha+11\beta+13\gamma}=}$ ...

\hspace{-16}$Calculate value of $2$ Trignometric expression\\\\\\ $\mathbf{(1)\; \cos \left(\frac{\pi}{7} \right)-\cos \left(\frac{2\pi}{7}\right)+\cos\left(\frac{3\pi}{7}\right)=}$\\\\\\ $\mathbf{(2)\; \sin \left(\frac{\pi}{ ...

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Q1) *Image* Please explain whether (c) is true/false *Image* *Image* *Image* Answers Q67) 9 Q70) 4 Please explain your answers briefly. ...

\hspace{-16}$Show that the equation\\\\ $\mathbf{e^{1-\tan^{-1}x}+\tan^{-1}(e^x-1)=2}$\\\\ has no solution for $x\in\mathbb{R}$ ...

\hspace{-16}$Find all Real Value of $\mathbf{m}$ for Which the Given Equation\\\\ $x^2-\mid x \mid+m=0 $ has Real solution ...

\hspace{-16}$Find value of $\mathbf{m}$ in \\\\ $\mathbf{\begin{Vmatrix} 50\sin^2 t+5m\sin t+(4m-41)=0 \\\\ 50\cos^2 t+5m\cos t+(4m-41)=0 & \end{Vmatrix}}$\\\\\\ and $\mathbf{\tan t\neq o}.$ Then value of $\mathbf{m}$ is ...

Help please! \sum_{1\leq i\leq j\leq n}^{}{}\sum{\frac{9}{(2-\alpha _{i})(2-\alpha_{j})}} Where αi , αj are the roots of unity. ...

*Image* Please give brief explanation also ...

Hi I am getting 84+ percentile in Bmat (Brilliant Tutorials) Part tests for IITJEE 2012. Is it bad? Please comment!! ...

What is the probability that if a fair coin is tossed n times we will get at least two heads? ...

Q. Find largest possible integer ' n ' such that the following holds : n\left\{\frac{abc}{ab+bc+ca} \right\}\leq (a+b)^{2}+(a+b+4c)^{2} , a,b,c\in R ...

The coefficient of the term independent of x in the expansion of ( x+1/x 2/3 - x 1/3 +1 - x-1/x- x 1/2 )10 remember 10 is in the power..... ...

ABC is a triangle. The tangent to the circumcircle at A meets the line BC at D. The perpendicular to BC at B meets the perpendicular bisector of AB at E, and the perpendicular to BC at C meets the perpendicular bisector of AC ...

ABC is an equilateral triangle. P is any point in it satisfying PA=3, PB=4 & PC=5 units. Find area of the triangle. ...

*Image* is equal to (A) 3pi/10 (B) 7pi/10 (C) 4pi/5 (D) 3pi/5 (B) is the right answer as per my package but i feel its (A) ...

$\textbf{If $\mathbf{5x^2+y^2+1=4xy+2x}$.\;Then Calculate $\mathbf{x+y=}$} ...

*Image* The no. of compounds that are soluble in aq. NaOH is ans. 4 why isn't the 3rd compound also counted??? ...

The hybridization of Ni(CO)4 and Cr(H2O)62+, respectively are: Solution: It is sp3 and sp3d2, but none of the option matches. I have verified this from many sources. ...

let f(x)= sin x g(x)=2x h(x)= cosx if φ(x)= [g o (fh)]x, then find φ||( pi/4 ) A) 4 B) 0 C) -4 D) 1/4 E) none ...

New formula for IIT exam OUR SPECIAL CORRESPONDENT New Delhi, Oct. 19: When IIT aspirants sit for the joint entrance test next year, they will have the freedom to concentrate on questions of their choice and not worry about s ...

\int_{-1}^{2}{x^2} dx whats the need to integrate ?????jsut fill in values.. (2)^2-(-1)^2 =4-1 =3 [3][3] ...

A polynomial f(x) has integer coefficients such that f(0) and f(1) are both odd numbers. Prove that f(x) = 0 has no integer solutions. ...

if b is a real number satisfying b^4 + (1/b)^4 = 6 find the value of (b+ i/b )^16 where i is iota or √(-1). ...

1) If m is a root of the eqn. 4x2 + 2x - 1 = 0, then its other root is given by (a) 4m3 - 3m (b) 4m3 + 3m (c) m - (1/2) (d) -m-(1/2) 2) if a,b,c,p,q,r are six complex numbers, such that p/a + q/b + r/c = 1 + i and a/p + b/q + ...