1
JEE Main 2022 (Online) 27th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The integral $$\int\limits_0^1 {{1 \over {{7^{\left[ {{1 \over x}} \right]}}}}dx} $$, where [ . ] denotes the greatest integer function, is equal to

A
$$1 + 6{\log _e}\left( {{6 \over 7}} \right)$$
B
$$1 - 6{\log _e}\left( {{6 \over 7}} \right)$$
C
$${\log _e}\left( {{7 \over 6}} \right)$$
D
$$1 - 7{\log _e}\left( {{6 \over 7}} \right)$$
2
JEE Main 2022 (Online) 27th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the solution curve of the differential equation

$$(({\tan ^{ - 1}}y) - x)dy = (1 + {y^2})dx$$ passes through the point (1, 0), then the abscissa of the point on the curve whose ordinate is tan(1), is

A
2e
B
$${2 \over e}$$
C
2
D
$${1 \over e}$$
3
JEE Main 2022 (Online) 27th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the equation of the parabola, whose vertex is at (5, 4) and the directrix is $$3x + y - 29 = 0$$, is $${x^2} + a{y^2} + bxy + cx + dy + k = 0$$, then $$a + b + c + d + k$$ is equal to :

A
575
B
$$-$$575
C
576
D
$$-$$576
4
JEE Main 2022 (Online) 27th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The set of values of k, for which the circle $$C:4{x^2} + 4{y^2} - 12x + 8y + k = 0$$ lies inside the fourth quadrant and the point $$\left( {1, - {1 \over 3}} \right)$$ lies on or inside the circle C, is :

A
an empty set
B
$$\left( {6,{{65} \over 9}} \right]$$
C
$$\left[ {{{80} \over 9},10} \right)$$
D
$$\left( {9,{{92} \over 9}} \right]$$
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