1

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

2

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

then

3

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

$$\mathop {\lim }\limits_{x \to 2} {{f\left( x \right)g\left( x \right)} \over {f'\left( x \right)g'\left( x \right)}} = 1,$$ then

4

JEE Advanced 2015 Paper 2 Offline

MCQ (More than One Correct Answer)

+4

-1

Let $$f, g :$$ $$\left[ { - 1,2} \right] \to R$$ be continuous functions which are twice differentiable on the interval $$(-1, 2)$$. Let the values of f and g at the points $$-1, 0$$ and $$2$$ be as given in the following table:

X = -1 | X = 0 | X = 2 | |
---|---|---|---|

f(x) | 3 | 6 | 0 |

g(x) | 0 | 1 | -1 |

In each of the intervals $$(-1, 0)$$ and $$(0, 2)$$ the function $$(f-3g)''$$ never vanishes. Then the correct statement(s) is (are)

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

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