1
JEE Main 2021 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The locus of the centroid of the triangle formed by any point P on the hyperbola $$16{x^2} - 9{y^2} + 32x + 36y - 164 = 0$$, and its foci is :
A
$$16{x^2} - 9{y^2} + 32x + 36y - 36 = 0$$
B
$$9{x^2} - 16{y^2} + 36x + 32y - 144 = 0$$
C
$$16{x^2} - 9{y^2} + 32x + 36y - 144 = 0$$
D
$$9{x^2} - 16{y^2} + 36x + 32y - 36 = 0$$
2
JEE Main 2021 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f : R $$\to$$ R be defined as

$$f(x) = \left\{ {\matrix{ {{{\lambda \left| {{x^2} - 5x + 6} \right|} \over {\mu (5x - {x^2} - 6)}},} & {x < 2} \cr {{e^{{{\tan (x - 2)} \over {x - [x]}}}},} & {x > 2} \cr {\mu ,} & {x = 2} \cr } } \right.$$

where [x] is the greatest integer is than or equal to x. If f is continuous at x = 2, then $$\lambda$$ + $$\mu$$ is equal to :
A
e($$-$$e + 1)
B
e(e $$-$$ 2)
C
1
D
2e $$-$$ 1
3
JEE Main 2021 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of the definite integral $$\int\limits_{\pi /24}^{5\pi /24} {{{dx} \over {1 + \root 3 \of {\tan 2x} }}} $$ is :
A
$${\pi \over 3}$$
B
$${\pi \over 6}$$
C
$${\pi \over {12}}$$
D
$${\pi \over {18}}$$
4
JEE Main 2021 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If b is very small as compared to the value of a, so that the cube and other higher powers of $${b \over a}$$ can be neglected in the identity $${1 \over {a - b}} + {1 \over {a - 2b}} + {1 \over {a - 3b}} + ..... + {1 \over {a - nb}} = \alpha n + \beta {n^2} + \gamma {n^3}$$, then the value of $$\gamma$$ is :
A
$${{{a^2} + b} \over {3{a^3}}}$$
B
$${{a + b} \over {3{a^2}}}$$
C
$${{{b^2}} \over {3{a^3}}}$$
D
$${{a + {b^2}} \over {3{a^3}}}$$
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