JEE Main 2016 (Offline) | Application of Derivatives Question 99 | Mathematics

JEE Main 2016 (Offline)

MCQ (Single Correct Answer)

-1

A wire of length $$2$$ units is cut into two parts which are bent respectively to form a square of side $$=x$$ units and a circle of radius $$=r$$ units. If the sum of the areas of the square and the circle so formed is minimum, then:

$$x=2r$$

$$2x=r$$

$$2x = \left( {\pi + 4} \right)r$$

$$\left( {4 - \pi } \right)x = \pi \,\, r$$

JEE Main 2016 (Offline)

MCQ (Single Correct Answer)

-1

Consider :
f $$\left( x \right) = {\tan ^{ - 1}}\left( {\sqrt {{{1 + \sin x} \over {1 - \sin x}}} } \right),x \in \left( {0,{\pi \over 2}} \right).$$

A normal to $$y = $$ f$$\left( x \right)$$ at $$x = {\pi \over 6}$$ also passes through the point:

$$\left( {{\pi \over 6},0} \right)$$

$$\left( {{\pi \over 4},0} \right)$$

$$(0,0)$$

$$\left( {0,{{2\pi } \over 3}} \right)$$

JEE Main 2015 (Offline)

MCQ (Single Correct Answer)

-1

Let $$f(x)$$ be a polynomial of degree four having extreme values
at $$x=1$$ and $$x=2$$. If $$\mathop {\lim }\limits_{x \to 0} \left[ {1 + {{f\left( x \right)} \over {{x^2}}}} \right] = 3$$, then f$$(2)$$ is equal to :

$$0$$

$$4$$

$$-8$$

$$-4$$

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)

-1

If $$f$$ and $$g$$ are differentiable functions in $$\left[ {0,1} \right]$$ satisfying
$$f\left( 0 \right) = 2 = g\left( 1 \right),g\left( 0 \right) = 0$$ and $$f\left( 1 \right) = 6,$$ then for some $$c \in \left] {0,1} \right[$$

$$f'\left( c \right) = g'\left( c \right)$$

$$f'\left( c \right) = 2g'\left( c \right)$$

$$2f'\left( c \right) = g'\left( c \right)$$

$$2f'\left( c \right) = 3g'\left( c \right)$$

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