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Suppose that f (x) is a polynomial with integer coefficients such that f (2) = 3 and f (7) = −5. Show that f (x) has no integer roots. ...

A parabola passes through the points A and B. The ends of a diameter of a given circle of radius ' a '. A tangent to the concentric circle of radius ' b ' is the directrix of parabola. Q. If AB and the perpendicular diameter ...

\hspace{-16}$Find all Complex no. $\mathbf{z_{1}\;,z_{2}\;,z_{3}\in\mathbf{C}}$ in \\\\\\ $\mathbf{\begin{Vmatrix} \bold{\hspace{-70}z^3_{1}+z^3_{2}+z^3_{3}=24} \\\\ \bold{\left(z_{1}+z_{2}\right).(z_{2}+z_{3}).(z_{3}+z_{1})= ...

\hspace{-16}$If $\mathbf{a\;,b\;c\in\mathbb{R}}$ and $\mathbf{a+b+c=0\;,a^2+b^2+c^2=1}$\\\\ Then $\mathbf{a^4+b^4+c^4=}$ ...

\hspace{-16}$If $\mathbf{a\;,b\;c\geq 2\;,}$ Then find Min. value of \\\\ $\mathbf{\log_{b+c}a+\log_{c+a}b+\log_{a+b}c}$ ...

\hspace{-16}$\If $\mathbf{x=\left(8+3\sqrt{7}\right)^n\;,n\in\mathbb{N}}\;,$Then $\mathbf{x-x^2+x\left[x\right]=}$\\\\ Where $\mathbf{\left[x\right]=}$Greatest Integer Function ...

\ \boxed{\lim_{n\to\infty}\prod_{p=1}^{n}\left(1+\frac{p}{n^{2}}\right) = \sqrt{e}} ...

The equation of the straight line which bisects the intercepts made by the axes on the lines x+y=2 and 2x+3y=6 is : I'm getting answer:4x+5y=10. Answer is y=1. Please explain how you solved it! ...

1) What is the smallest distance between the point(-2,-2) and a point on the circumference of the circle given by (x - 1)2 + (y - 2)2 = 4? A) 3 B) 4 C) 5 D) 6 E) 7 2)Find a negative value of k so that the graph of y = x2 - 2x ...

\hspace{-16}$Find all Integer solution $\mathbf{(x,y)}$ in $\mathbf{x^3+y^3+6xy=8}$ ...

\hspace{-16}\mathbf{(1)\;\; \int\frac{1}{1+\sqrt{x^2+2x+2}}dx}\\\\\\ \mathbf{(2)\int_{1}^2\frac{x^2-1}{(x^2-x+1).(x^2-3x+1)}dx}$ ...

find the number of solutions of |[x]-2x| = 4 here [.] denotes the floor function... and |.| denotes modulus.. ...

\hspace{-16}$Show that $\mathbf{\begin{vmatrix} a^2+b^2+c^2 &bc+ca+ab &bc+ca+ab \\\\ bc+ca+ab &a^2+b^2+c^2 &bc+ca+ab \\\\ bc+ca+ab &bc+ca+ab & a^2+b^2+c^2 \end{vmatrix}}$\\\\\\ is always Positive \;, Where $\mathbf{a\;,b\;,c} ...

*Image* ...

A stone is projected from the ground so as to hit a bird on the top of a vertical pole of height h and then attain a maximum height 2h above the ground.if at the instant of projection the bird flies away horizontally with a u ...

In the evaluation of NSEP, is the total of Part A and Part B considered or only the score in Part B considered ? ...

can anybody throw some light as to how the online form filling would be beneficial?(for JEE 2012) i mean by registering online i guess there's no chance of mistake in admit card and someone says that forms by online are rarel ...

∫ dx/(sinx+cosx+tanx+secx+cosecx+cotx) ...

*Image* ...

\hspace{-16}$Prove that::\\\\\\ $\mathbf{\binom{n}{0}\binom{n}{k}+\binom{n}{1}\binom{n-1}{k-1}+...........+\binom{n}{k}\binom{n-k}{0}=2^k.\binom{n}{k}}$\\\\\\ Where $\mathbf{n\;,k\in\mathbb{N}\;,0\leq k\leq n}$ ...

how do we integrate this one- √2∫sinx/sin(x-pi/4)dx ...

\hspace{-16}$Calculate value of $\mathbf{x}$ in $\mathbf{\log_{3}(1+2x)=3^x-x-1}$\\\\ ...

the maximum value of the expression *Image* is,whee a and x are reals ...

Find all functions p:\mathbb{Z}\Rightarrow\mathbb{Z} such that p(x^2+1)=p(x)^2+1 . ...

Find the remainder when 599 is divided by 13? ...

In Arihant, it says that stability of carbocations is in the order: benzylic>allylic>3°>2°>1°>-CH3 While in Morrison Boyd, Solomons and BT, it is given 3°>benzylic,allylic,2°>1°>-CH3 which one is ...

\lfloor\dfrac{r+19}{100}\rfloor+\lfloor\dfrac{r+20}{100}\rfloor+....+\lfloor\dfrac{r+91}{100}\rfloor=546 Find \lfloor r \rfloor ...

\int_{0}^{\propto }{\frac{sinx}{x}} ...

A natural number is called "nice" if it is the product of its distinct proper divisors. Find the sum of first 10 nice numbers. ...

Find the value of i + -i ? ...