1
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
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Let, $$f(x) = {{\sin \pi x} \over {{x^2}}}$$, x > 0

Let x1 < x2 < x3 < ... < xn < ... be all the points of local maximum of f and y1 < y2 < y3 < ... < yn < ... be all the points of local minimum of f.

Then which of the following options is/are correct?
A
$$|{x_n} - {y_n}|\, > 1$$
B
$${x_{n + 1}} - {x_n}\, > 2$$ for every n
C
x1 < y1
D
$${x_n} \in \left( {2n,\,2n + {1 \over 2}} \right)$$ for every n
2
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
f : R $$ \to $$ R is a differentiable function such that f'(x) > 2f(x) for all x$$ \in $$R, and f(0) = 1 then
A
f(x) > e2x in (0, $$\infty $$)
B
f'(x) < e2x in (0, $$\infty $$)
C
f(x) is increasing in (0, $$\infty $$)
D
f(x) is decreasing in (0, $$\infty $$)
3
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
If $$f(x) = \left| {\matrix{ {\cos 2x} & {\cos 2x} & {\sin 2x} \cr { - \cos x} & {\cos x} & { - \sin x} \cr {\sin x} & {\sin x} & {\cos x} \cr } } \right|$$,

then
A
f(x) attains its minimum at x = 0
B
f(x) attains its maximum at x = 0
C
f'(x) = 0 at more than three points in ($$-$$$$\pi $$, $$\pi $$)
D
f'(x) = 0 at exactly three points in ($$-$$$$\pi $$, $$\pi $$)
4
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Let f: R $$ \to \left( {0,\infty } \right)$$ and g : R $$ \to $$ R be twice differentiable functions such that f'' and g'' are continuous functions on R. Suppose f'$$(2)$$ $$=$$ g$$(2)=0$$, f''$$(2)$$$$ \ne 0$$ and g'$$(2)$$ $$ \ne 0$$. If
$$\mathop {\lim }\limits_{x \to 2} {{f\left( x \right)g\left( x \right)} \over {f'\left( x \right)g'\left( x \right)}} = 1,$$ then
A
$$f$$ has a local minimum at $$x=2$$
B
$$f$$ has a local maximum at $$x=2$$
C
$$f''(2)>f(2)$$
D
$$f(x)-f''(x)=0$$ for at least one $$x \in R$$
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