1

JEE Advanced 2020 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

Consider the rectangles lying the region

$$\left\{ {(x,y) \in R \times R:0\, \le \,x\, \le \,{\pi \over 2}} \right.$$ and $$\left. {0\, \le \,y\, \le \,2\sin (2x)} \right\}$$

and having one side on the X-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is

$$\left\{ {(x,y) \in R \times R:0\, \le \,x\, \le \,{\pi \over 2}} \right.$$ and $$\left. {0\, \le \,y\, \le \,2\sin (2x)} \right\}$$

and having one side on the X-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is

2

JEE Advanced 2017 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

By approximately matching the information given in the three columns of the following table.

Let f(x) = x + log

Column 1 contains information about zeroes of f(x), f'(x) and f"(x).

Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.

Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).

Let f(x) = x + log

_{e}x $$-$$ x log_{e}x, x$$ \in $$(0, $$\infty $$)Column 1 contains information about zeroes of f(x), f'(x) and f"(x).

Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.

Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).

Column - 1 | Column - 2 | Column - 3 | |
---|---|---|---|

(i) | f(x) = 0 for some $$x \in (1,{e^2})$$ | (i) $$\mathop {\lim }\limits_{x \to \infty } \,f(x) = 0$$ | f is increasing in (0, 1) |

(ii) | f'(x) = 0 for some $$x \in (1,e)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f(x) = - \infty $$ | f is decreasing in (e, $${e^2}$$) |

(iii) | f'(x) = 0 for some $$x \in (0,1)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = - \infty $$ | f' is increasing in (0, 1) |

(iv) | f'(x) = 0 for some $$x \in (1,e)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = 0$$ | f' is decreasing in (e, $${e^2}$$) |

Which of the following options is the only INCORRECT combination?

3

JEE Advanced 2017 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

By approximately matching the information given in the three columns of the following table.

Let f(x) = x + log

Column 1 contains information about zeroes of f(x), f'(x) and f"(x).

Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.

Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).

Let f(x) = x + log

_{e}x $$-$$ x log_{e}x, x$$ \in $$(0, $$\infty $$)Column 1 contains information about zeroes of f(x), f'(x) and f"(x).

Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.

Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).

Column - 1 | Column - 2 | Column - 3 | |
---|---|---|---|

(i) | f(x) = 0 for some $$x \in (1,{e^2})$$ | (i) $$\mathop {\lim }\limits_{x \to \infty } \,f(x) = 0$$ | f is increasing in (0, 1) |

(ii) | f'(x) = 0 for some $$x \in (1,e)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f(x) = - \infty $$ | f is decreasing in (e, $${e^2}$$) |

(iii) | f'(x) = 0 for some $$x \in (0,1)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = - \infty $$ | f' is increasing in (0, 1) |

(iv) | f'(x) = 0 for some $$x \in (1,e)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = 0$$ | f' is decreasing in (e, $${e^2}$$) |

Which of the following options is the only CORRECT combination?

4

JEE Advanced 2017 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

By approximately matching the information given in the three columns of the following table.

Let f(x) = x + log

Column 1 contains information about zeroes of f(x), f'(x) and f"(x).

Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.

Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).

Let f(x) = x + log

_{e}x $$-$$ x log_{e}x, x$$ \in $$(0, $$\infty $$)Column 1 contains information about zeroes of f(x), f'(x) and f"(x).

Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.

Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).

Column - 1 | Column - 2 | Column - 3 | |
---|---|---|---|

(i) | f(x) = 0 for some $$x \in (1,{e^2})$$ | (i) $$\mathop {\lim }\limits_{x \to \infty } \,f(x) = 0$$ | f is increasing in (0, 1) |

(ii) | f'(x) = 0 for some $$x \in (1,e)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f(x) = - \infty $$ | f is decreasing in (e, $${e^2}$$) |

(iii) | f'(x) = 0 for some $$x \in (0,1)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = - \infty $$ | f' is increasing in (0, 1) |

(iv) | f'(x) = 0 for some $$x \in (1,e)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = 0$$ | f' is decreasing in (e, $${e^2}$$) |

Which of the following options is the only CORRECT combination?

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)
JEE Advanced 2020 Paper 1 Offline (1)
JEE Advanced 2017 Paper 1 Offline (3)
JEE Advanced 2016 Paper 1 Offline (1)
JEE Advanced 2013 Paper 2 Offline (2)
IIT-JEE 2012 Paper 2 Offline (2)
IIT-JEE 2008 Paper 1 Offline (1)
IIT-JEE 2007 (4)
IIT-JEE 2005 Screening (1)
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IIT-JEE 2000 Screening (5)
IIT-JEE 1999 (1)
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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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