1
JEE Main 2019 (Online) 10th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of   $$\int\limits_{ - \pi /2}^{\pi /2} {{{dx} \over {\left[ x \right] + \left[ {\sin x} \right] + 4}}} ,$$  where [t] denotes the greatest integer less than or equal to t, is
A
$${1 \over {12}}\left( {7\pi - 5} \right)$$
B
$${1 \over {12}}\left( {7\pi + 5} \right)$$
C
$${3 \over {10}}\left( {4\pi - 3} \right)$$
D
$${3 \over {20}}\left( {4\pi - 3} \right)$$
2
JEE Main 2019 (Online) 10th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let S = $$\left\{ {\left( {x,y} \right) \in {R^2}:{{{y^2}} \over {1 + r}} - {{{x^2}} \over {1 - r}}} \right\};r \ne \pm 1.$$ Then S represents :
A
an ellipse whose eccentricity is $${1 \over {\sqrt {r + 1} }},$$ where r > 1
B
an ellipse whose eccentricity is $${2 \over {\sqrt {r + 1} }},$$ where 0 < r < 1
C
an ellipse whose eccentricity is $${2 \over {\sqrt {r - 1} }},$$ where 0 < r < 1
D
an ellipse whose eccentricity is $$\sqrt {{2 \over {r + 1}}}$$, where r > 1
3
JEE Main 2019 (Online) 10th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If  $$\int\limits_0^x \, $$f(t) dt = x2 + $$\int\limits_x^1 \, $$ t2f(t) dt then f '$$\left( {{1 \over 2}} \right)$$ is -
A
$${{18} \over {25}}$$
B
$${{6} \over {25}}$$
C
$${{24} \over {25}}$$
D
$${{4} \over {5}}$$
4
JEE Main 2019 (Online) 10th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let A = $$\left[ {\matrix{ 2 & b & 1 \cr b & {{b^2} + 1} & b \cr 1 & b & 2 \cr } } \right]$$ where b > 0.

Then the minimum value of $${{\det \left( A \right)} \over b}$$ is -
A
$$\sqrt 3 $$
B
$$-$$ $$2\sqrt 3 $$
C
$$ - \sqrt 3 $$
D
$$2\sqrt 3 $$
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