1
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language

The system of linear equations

$$\matrix{ {x + \lambda y - z = 0} \cr {\lambda x - y - z = 0} \cr {x + y - \lambda z = 0} \cr } $$

has a non-trivial solution for :
A
infinitely many values of $$\lambda .$$
B
exactly one value of $$\lambda .$$
C
exactly two values of $$\lambda .$$
D
exactly three values of $$\lambda .$$
2
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
The integral $$\int {{{2{x^{12}} + 5{x^9}} \over {{{\left( {{x^5} + {x^3} + 1} \right)}^3}}}} dx$$ is equal to :
A
$${{{x^5}} \over {2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + C$$
B
$${{ - {x^{10}}} \over {2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + C$$
C
$${{{-x^5}} \over {{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + C$$
D
$${{ {x^{10}}} \over {2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + C$$
3
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
The area (in sq. units) of the region $$\left\{ {\left( {x,y} \right):{y^2} \ge 2x\,\,\,and\,\,\,{x^2} + {y^2} \le 4x,x \ge 0,y \ge 0} \right\}$$ is :
A
$$\pi - {{4\sqrt 2 } \over 3}$$
B
$${\pi \over 2} - {{2\sqrt 2 } \over 3}$$
C
$$\pi - {4 \over 3}$$
D
$$\pi - {8 \over 3}$$
4
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
If a curve $$y=f(x)$$ passes through the point $$(1,-1)$$ and satisfies the differential equation, $$y(1+xy) dx=x$$ $$dy$$, then $$f\left( { - {1 \over 2}} \right)$$ is equal to :
A
$${2 \over 5}$$
B
$${4 \over 5}$$
C
$$-{2 \over 5}$$
D
$$-{4 \over 5}$$
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