1
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
A wire of length $$2$$ units is cut into two parts which are bent respectively to form a square of side $$=x$$ units and a circle of radius $$=r$$ units. If the sum of the areas of the square and the circle so formed is minimum, then:
A
$$x=2r$$
B
$$2x=r$$
C
$$2x = \left( {\pi + 4} \right)r$$
D
$$\left( {4 - \pi } \right)x = \pi \,\, r$$
2
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Consider :
f $$\left( x \right) = {\tan ^{ - 1}}\left( {\sqrt {{{1 + \sin x} \over {1 - \sin x}}} } \right),x \in \left( {0,{\pi \over 2}} \right).$$

A normal to $$y = $$ f$$\left( x \right)$$ at $$x = {\pi \over 6}$$ also passes through the point:

A
$$\left( {{\pi \over 6},0} \right)$$
B
$$\left( {{\pi \over 4},0} \right)$$
C
$$(0,0)$$
D
$$\left( {0,{{2\pi } \over 3}} \right)$$
3
JEE Main 2016 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$A = \left[ {\matrix{ {5a} & { - b} \cr 3 & 2 \cr } } \right]$$ and $$A$$ adj $$A=A$$ $${A^T},$$ then $$5a+b$$ is equal to :
A
$$4$$
B
$$13$$
C
$$-1$$
D
$$5$$
4
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 $$\lambda .$$
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