1
IIT-JEE 2010 Paper 2 Offline
Numerical
+4
-0
Let $$f$$ be a function defined on $$R$$ (the set of all real numbers)
such that $$f'\left( x \right) = 2010\left( {x - 2009} \right){\left( {x - 2010} \right)^2}{\left( {x - 2011} \right)^3}{\left( {x - 2012} \right)^4}$$ for all $$x \in $$$$R$$
such that $$f'\left( x \right) = 2010\left( {x - 2009} \right){\left( {x - 2010} \right)^2}{\left( {x - 2011} \right)^3}{\left( {x - 2012} \right)^4}$$ for all $$x \in $$$$R$$
If $$g$$ is a function defined on $$R$$ with values in the interval $$\left( {0,\infty } \right)$$ such that
$$$f\left( x \right) = ln\,\left( {g\left( x \right)} \right),\,\,for\,\,all\,\,x \in R$$$
then the number of points in $$R$$ at which $$g$$ has a local maximum is ___________.
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2
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1
Let $$p(x)$$ be a polynomial of degree $$4$$ having extremum at
$$x = 1,2$$ and $$\mathop {\lim }\limits_{x \to 0} \left( {1 + {{p\left( x \right)} \over {{x^2}}}} \right) = 2$$.
$$x = 1,2$$ and $$\mathop {\lim }\limits_{x \to 0} \left( {1 + {{p\left( x \right)} \over {{x^2}}}} \right) = 2$$.
Then the value of $$p (2)$$ is
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3
IIT-JEE 2009 Paper 2 Offline
Numerical
+4
-0
The maximum value of the function $$f(x) = 2{x^3} - 15{x^2} + 36x - 48$$ on the set $$A = \{ x|{x^2} + 20 \le 9x|\} $$ is __________.
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4
IIT-JEE 2006
Numerical
+3
-0
If $f(x)$ is a twice differentiable function such that $f(A)=0, f(B)=2, f(C)=-1, f(D)=2$, $f(e)=0$, where $a < b < c < d < e$, then the minimum number of zeroes of $g(x)=\left(f^{\prime}(x)\right)^2 +f^{\prime \prime}(x) f(x)$ in the interval $[a, e]$ is :
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