1

IIT-JEE 2001 Screening

MCQ (Single Correct Answer)

+2

-0.5

The triangle formed by the tangent to the curve $$f\left( x \right) = {x^2} + bx - b$$ at the point $$(1, 1)$$ and the coordinate axex, lies in the first quadrant. If its area is $$2$$, then the value of $$b$$ is

2

IIT-JEE 2001 Screening

MCQ (Single Correct Answer)

+2

-0.5

Let $$f\left( x \right) = \left( {1 + {b^2}} \right){x^2} + 2bx + 1$$ and let $$m(b)$$ be the minimum value of $$f(x)$$. As $$b$$ varies, the range of $$m(b)$$ is

3

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)

+2

-0.5

Consider the following statements in $$S$$ and $$R$$

$$S:$$ $$\,\,\,$$$ Both $$\sin \,\,x$$ and $$\cos \,\,x$$ are decreasing functions in the interval $$\left( {{\pi \over 2},\pi } \right)$$

$$R:$$$$\,\,\,$$ If a differentiable function decreases in an interval $$(a, b)$$, then its derivative also decreases in $$(a, b)$$.

Which of the following is true ?

$$S:$$ $$\,\,\,$$$ Both $$\sin \,\,x$$ and $$\cos \,\,x$$ are decreasing functions in the interval $$\left( {{\pi \over 2},\pi } \right)$$

$$R:$$$$\,\,\,$$ If a differentiable function decreases in an interval $$(a, b)$$, then its derivative also decreases in $$(a, b)$$.

Which of the following is true ?

4

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)

+2

-0.5

Let $$f\left( x \right) = \int {{e^x}\left( {x - 1} \right)\left( {x - 2} \right)dx.} $$ Then $$f$$ decreases in the interval

Questions Asked from Application of Derivatives (MCQ (Single Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced 2023 Paper 1 Online (1)
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IIT-JEE 2008 Paper 1 Offline (1)
IIT-JEE 2007 (4)
IIT-JEE 2005 Screening (1)
IIT-JEE 2004 Screening (2)
IIT-JEE 2003 Screening (2)
IIT-JEE 2002 Screening (2)
IIT-JEE 2001 Screening (3)
IIT-JEE 2000 Screening (5)
IIT-JEE 1999 (1)
IIT-JEE 1998 (2)
IIT-JEE 1997 (1)
IIT-JEE 1995 Screening (3)
IIT-JEE 1994 (2)
IIT-JEE 1987 (2)
IIT-JEE 1986 (1)
IIT-JEE 1983 (4)

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