Algebra
Quadratic Equation and Inequalities
Fill in the BlanksNumericalMCQ (Single Correct Answer)MCQ (Multiple Correct Answer)SubjectiveTrue of FalseSequences and Series
Fill in the BlanksNumericalMCQ (Single Correct Answer)MCQ (Multiple Correct Answer)SubjectiveMathematical Induction and Binomial Theorem
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Trigonometric Functions & Equations
Fill in the BlanksNumericalMCQ (Single Correct Answer)MCQ (Multiple Correct Answer)SubjectiveTrue of FalseInverse Trigonometric Functions
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Straight Lines and Pair of Straight Lines
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Limits, Continuity and Differentiability
NumericalMCQ (Single Correct Answer)MCQ (Multiple Correct Answer)Differentiation
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NumericalMCQ (Single Correct Answer)MCQ (Multiple Correct Answer)Subjective1
IIT-JEE 2010 Paper 1 Offline
Numerical
+4
-0
Let $$f$$ be a real-valued differentiable function on $$R$$ (the set of all real numbers) such that $$f(1)=1$$. If the $$y$$-intercept of the tangent at any point $$P(x,y)$$ on the curve $$y=f(x)$$ is equal to the cube of the abscissa of $$P$$, then find the value of $$f(-3)$$
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2
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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3
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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4
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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