1
JEE Advanced 2019 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language
A line y = mx + 1 intersects the circle $${(x - 3)^2} + {(y + 2)^2}$$ = 25 at the points P and Q. If the midpoint of the line segment PQ has x-coordinate $$ - {3 \over 5}$$, then which one of the following options is correct?
A
6 $$ \le $$ m < 8
B
$$ - $$3 $$ \le $$ m < $$ - $$1
C
4 $$ \le $$ m < 6
D
2 $$ \le $$ m < 4
2
JEE Advanced 2019 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language
The area of the region

{(x, y) : xy $$ \le $$ 8, 1 $$ \le $$ y $$ \le $$ x2} is
A
$$8{\log _e}2 - {{14} \over 3}$$
B
$$8{\log _e}2 - {{7} \over 3}$$
C
$$16{\log _e}2 - {{14} \over 3}$$
D
$$16{\log _e}2 - 6$$
3
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
Let $$\Gamma $$ denote a curve y = y(x) which is in the first quadrant and let the point (1, 0) lie on it. Let the tangent to I` at a point P intersect the y-axis at YP. If PYP has length 1 for each point P on I`, then which of the following options is/are correct?
A
$$xy' + \sqrt {1 - {x^2}} = 0$$
B
$$xy' - \sqrt {1 - {x^2}} = 0$$
C
$$y = {\log _e}\left( {{{1 + \sqrt {1 - {x^2}} } \over x}} \right) - \sqrt {1 - {x^2}} $$
D
$$y = - {\log _e}\left( {{{1 + \sqrt {1 - {x^2}} } \over x}} \right) + \sqrt {1 - {x^2}} $$
4
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
Define the collections {E1, E2, E3, ...} of ellipses and {R1, R2, R3.....} of rectangles as follows :

$${E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$

R1 : rectangle of largest area, with sides parallel to the axes, inscribed in E1;

En : ellipse $${{{x^2}} \over {a_n^2}} + {{{y^2}} \over {b_n^2}} = 1$$ of the largest area inscribed in $${R_{n - 1}},n > 1$$;

Rn : rectangle of largest area, with sides parallel to the axes, inscribed in En, n > 1.

Then which of the following options is/are correct?
A
The eccentricities of E18 and E19 are not equal.
B
The distance of a focus from the centre in E9 is $${{\sqrt 5 } \over {32}}$$.
C
$$\sum\limits_{n = 1}^N {(area\,of\,{R_n})} $$ < 24, for each positive integer N.
D
The length of latusrectum of E9 is $${1 \over 6}$$
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