1
JEE Main 2021 (Online) 17th March Morning Shift
Numerical
+4
-1
Change Language
The oxygen dissolved in water exerts a partial pressure of 20 kPa in the vapour above water. The molar solubility of oxygen in water is __________ $$\times$$ 10$$-$$5 mol dm$$-$$3. (Round off to the Nearest Integer).

[Given : Henry's law constant = KH = 8.0 $$\times$$ 104 kPa for O2. Density of water with dissolved oxygen = 1.0 kg dm$$-$$3 ]
Your input ____
2
JEE Main 2021 (Online) 17th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
In a triangle PQR, the co-ordinates of the points P and Q are ($$-$$2, 4) and (4, $$-$$2) respectively. If the equation of the perpendicular bisector of PR is 2x $$-$$ y + 2 = 0, then the centre of the circumcircle of the $$\Delta$$PQR is :
A
($$-$$1, 0)
B
(1, 4)
C
(0, 2)
D
($$-$$2, $$-$$2)
3
JEE Main 2021 (Online) 17th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of
$$\mathop {\lim }\limits_{x \to {0^ + }} {{{{\cos }^{ - 1}}(x - {{[x]}^2}).{{\sin }^{ - 1}}(x - {{[x]}^2})} \over {x - {x^3}}}$$, where [ x ] denotes the greatest integer $$ \le $$ x is :
A
$$\pi$$
B
$${\pi \over 4}$$
C
$${\pi \over 2}$$
D
0
4
JEE Main 2021 (Online) 17th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Which of the following statements is correct for the function g($$\alpha$$) for $$\alpha$$ $$\in$$ R such that

$$g(\alpha ) = \int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{{{\sin }^\alpha }x} \over {{{\cos }^\alpha }x + {{\sin }^\alpha }x}}dx} $$
A
$$g(\alpha )$$ is a strictly increasing function
B
$$g(\alpha )$$ is an even function
C
$$g(\alpha )$$ has an inflection point at $$\alpha$$ = $$-$$$${1 \over 2}$$
D
$$g(\alpha )$$ is a strictly decreasing function
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