JEE Main 2018 (Online) 15th April Morning Slot | Limits, Continuity and Differentiability Question 161 | Mathematics

JEE Main 2018 (Online) 15th April Morning Slot

MCQ (Single Correct Answer)

-1

If $$f\left( x \right) = \left| {\matrix{ {\cos x} & x & 1 \cr {2\sin x} & {{x^2}} & {2x} \cr {\tan x} & x & 1 \cr } } \right|,$$ then $$\mathop {\lim }\limits_{x \to 0} {{f'\left( x \right)} \over x}$$

does not exist.

exists and is equal to 2.

existsand is equal to 0.

exists and is equal to $$-$$ 2.

JEE Main 2018 (Online) 15th April Morning Slot

MCQ (Single Correct Answer)

-1

If x² + y² + sin y = 4, then the value of $${{{d^2}y} \over {d{x^2}}}$$ at the point ($$-$$2,0) is :

$$-$$ 34

$$-$$ 32

$$-$$ 2

JEE Main 2018 (Online) 15th April Morning Slot

MCQ (Single Correct Answer)

-1

Let S = {($$\lambda $$, $$\mu $$) $$ \in $$ R $$ \times $$ R : f(t) = (|$$\lambda $$| e^|t| $$-$$ $$\mu $$). sin (2|t|), t $$ \in $$ R, is a differentiable function}. Then S is a subset of :

R $$ \times $$ [0, $$\infty $$)

[0, $$\infty $$) $$ \times $$ R

R $$ \times $$ ($$-$$ $$\infty $$, 0)

($$-$$ $$\infty $$, 0) $$ \times $$ R

JEE Main 2017 (Online) 9th April Morning Slot

MCQ (Single Correct Answer)

-1

The value of k for which the function

$$f\left( x \right) = \left\{ {\matrix{ {{{\left( {{4 \over 5}} \right)}^{{{\tan \,4x} \over {\tan \,5x}}}}\,\,,} & {0 < x < {\pi \over 2}} \cr {k + {2 \over 5}\,\,\,,} & {x = {\pi \over 2}} \cr } } \right.$$

is continuous at x = $${\pi \over 2},$$ is :

$${{17} \over {20}}$$

$${{2} \over {5}}$$

$${{3} \over {5}}$$

$$-$$ $${{2} \over {5}}$$

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