1
JEE Main 2018 (Online) 15th April Morning Slot
+4
-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 $$\mathop {\lim }\limits_{x \to 0} {{f'\left( x \right)} \over x}$$
A
does not exist.
B
exists and is equal to 2.
C
existsand is equal to 0.
D
exists and is equal to $$-$$ 2.
2
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
If   x2 + y2 + sin y = 4, then the value of $${{{d^2}y} \over {d{x^2}}}$$ at the point ($$-$$2,0) is :
A
$$-$$ 34
B
$$-$$ 32
C
4
D
$$-$$ 2
3
JEE Main 2018 (Online) 15th April Morning Slot
+4
-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 :
A
R $$\times$$ [0, $$\infty$$)
B
[0, $$\infty$$) $$\times$$ R
C
R $$\times$$ ($$-$$ $$\infty$$, 0)
D
($$-$$ $$\infty$$, 0) $$\times$$ R
4
JEE Main 2017 (Online) 9th April Morning Slot
+4
-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 :
A
$${{17} \over {20}}$$
B
$${{2} \over {5}}$$
C
$${{3} \over {5}}$$
D
$$-$$ $${{2} \over {5}}$$
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