1
JEE Main 2015 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
The set of all values of $$\lambda $$ for which the system of linear equations:

$$\matrix{ {2{x_1} - 2{x_2} + {x_3} = \lambda {x_1}} \cr {2{x_1} - 3{x_2} + 2{x_3} = \lambda {x_2}} \cr { - {x_1} + 2{x_2} = \lambda {x_3}} \cr } $$

has a non-trivial solution
A
contains two elements
B
contains more than two elements
C
in an empty set
D
is a singleton
2
JEE Main 2015 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$f(x)$$ be a polynomial of degree four having extreme values
at $$x=1$$ and $$x=2$$. If $$\mathop {\lim }\limits_{x \to 0} \left[ {1 + {{f\left( x \right)} \over {{x^2}}}} \right] = 3$$, then f$$(2)$$ is equal to :
A
$$0$$
B
$$4$$
C
$$-8$$
D
$$-4$$
3
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
$${{3x + {x^3}} \over {1 - 3{x^2}}}$$
4
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
$${y^2} = x$$
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