1
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$\int {{{dx} \over {{{\left( {{x^2} - 2x + 10} \right)}^2}}}} = A\left( {{{\tan }^{ - 1}}\left( {{{x - 1} \over 3}} \right) + {{f\left( x \right)} \over {{x^2} - 2x + 10}}} \right) + C$$

where C is a constant of integration then :
A
A =$${1 \over {54}}$$ and f(x) = 9(x–1)2
B
A =$${1 \over {54}}$$ and f(x) = 3(x–1)
C
A =$${1 \over {81}}$$ and f(x) = 3(x–1)
D
A =$${1 \over {27}}$$ and f(x) = 9(x–1)2
2
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f : R $$ \to $$ R be differentiable at c $$ \in $$ R and f(c) = 0. If g(x) = |f(x)| , then at x = c, g is :
A
differentiable if f '(c) = 0
B
differentiable if f '(c) $$ \ne $$ 0
C
not differentiable
D
not differentiable if f '(c) = 0
3
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of $$\int\limits_0^{2\pi } {\left[ {\sin 2x\left( {1 + \cos 3x} \right)} \right]} dx$$,
where [t] denotes the greatest integer function is :
A
2$$\pi $$
B
$$\pi $$
C
-2$$\pi $$
D
-$$\pi $$
4
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If a directrix of a hyperbola centred at the origin and passing through the point (4, –2$$\sqrt 3 $$ ) is 5x = 4$$\sqrt 5 $$ and its eccentricity is e, then :
A
4e4 – 24e2 + 27 = 0
B
4e4 – 24e2 + 35 = 0
C
4e4 – 12e2 - 27 = 0
D
4e4 + 8e2 - 35 = 0
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