1
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
All the pairs (x, y) that satisfy the inequality
$${2^{\sqrt {{{\sin }^2}x - 2\sin x + 5} }}.{1 \over {{4^{{{\sin }^2}y}}}} \le 1$$
also satisfy the equation
A
sin x = |sin y|
B
sin x = 2sin y
C
2 sin x = sin y
D
2 |sin x | = 3 sin y
2
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The region represented by| x – y | $$ \le $$ 2 and | x + y| $$ \le $$ 2 is bounded by a :
A
rhombus of area 8$$\sqrt 2 $$ sq. units
B
square of side length 2$$\sqrt 2 $$ units
C
square of area 16 sq. units
D
rhombus of side length 2 units
3
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If$$f(x) = \left\{ {\matrix{ {{{\sin (p + 1)x + \sin x} \over x}} & {,x < 0} \cr q & {,x = 0} \cr {{{\sqrt {x + {x^2}} - \sqrt x } \over {{x^{{\raise0.5ex\hbox{$\scriptstyle 3$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}}}}} & {,x > 0} \cr } } \right.$$
is continuous at x = 0, then the ordered pair (p, q) is equal to
A
$$\left( { - {3 \over 2}, - {1 \over 2}} \right)$$
B
$$\left( { - {1 \over 2},{3 \over 2}} \right)$$
C
$$\left( { - {3 \over 2}, {1 \over 2}} \right)$$
D
$$\left( { {5 \over 2}, {1 \over 2}} \right)$$
4
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f(x) = ex – x and g(x) = x2 – x, $$\forall $$ x $$ \in $$ R. Then the set of all x $$ \in $$ R, where the function h(x) = (fog) (x) is increasing, is :
A
[0, $$\infty $$)
B
$$\left[ { - 1, - {1 \over 2}} \right] \cup \left[ {{1 \over 2},\infty } \right)$$
C
$$\left[ { - {1 \over 2},0} \right] \cup \left[ {1,\infty } \right)$$
D
$$\left[ {0,{1 \over 2}} \right] \cup \left[ {1,\infty } \right)$$
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