1
JEE Main 2015 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $${\tan ^{ - 1}}y = {\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right),$$
where $$\left| x \right| < {1 \over {\sqrt 3 }}.$$ Then a value of $$y$$ is :
A
$${{3x - {x^3}} \over {1 + 3{x^2}}}$$
B
$${{3x + {x^3}} \over {1 + 3{x^2}}}$$
C
$${{3x - {x^3}} \over {1 - 3{x^2}}}$$
D
$${{3x + {x^3}} \over {1 - 3{x^2}}}$$
2
JEE Main 2015 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$O$$ be the vertex and $$Q$$ be any point on the parabola, $${{x^2} = 8y}$$. If the point $$P$$ divides the line segment $$OQ$$ internally in the ratio $$1:3$$, then locus of $$P$$ is :
A
$${y^2} = 2x$$
B
$${{x^2} = 2y}$$
C
$${{x^2} = y}$$
D
$${y^2} = x$$
3
JEE Main 2015 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
Locus of the image of the point $$(2, 3)$$ in the line $$\left( {2x - 3y + 4} \right) + k\left( {x - 2y + 3} \right) = 0,\,k \in R,$$ is a :
A
circle of radius $$\sqrt 2 $$.
B
circle of radius $$\sqrt 3 $$.
C
straight line parallel to $$x$$-axis
D
straight line parallel to $$y$$-axis
4
JEE Main 2015 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $$(0, 0)$$ $$(0, 41)$$ and $$(41, 0)$$ is :
A
820
B
780
C
901
D
861
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