1
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
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:

A
$$\left( {{\pi \over 6},0} \right)$$
B
$$\left( {{\pi \over 4},0} \right)$$
C
$$(0,0)$$
D
$$\left( {0,{{2\pi } \over 3}} \right)$$
2
JEE Main 2015 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
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 :
A
$$0$$
B
$$4$$
C
$$-8$$
D
$$-4$$
3
JEE Main 2015 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The normal to the curve, $${x^2} + 2xy - 3{y^2} = 0$$, at $$(1,1)$$
A
meets the curve again in the third quadrant.
B
meets the curve again in the fourth quadrant.
C
does not meet the curve again.
D
meets the curve again in the second quadrant.
4
JEE Main 2014 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
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 $$c \in \left] {0,1} \right[$$
A
$$f'\left( c \right) = g'\left( c \right)$$
B
$$f'\left( c \right) = 2g'\left( c \right)$$
C
$$2f'\left( c \right) = g'\left( c \right)$$
D
$$2f'\left( c \right) = 3g'\left( c \right)$$
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