1
JEE Main 2023 (Online) 13th April Morning Shift
Numerical
+4
-1
Change Language

$$25.0 \mathrm{~mL}$$ of $$0.050 ~\mathrm{M} ~\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}$$ is mixed with $$25.0 \mathrm{~mL}$$ of $$0.020 ~\mathrm{M} ~\mathrm{NaF} . \mathrm{K}_{\mathrm{Sp}}$$ of $$\mathrm{BaF}_{2}$$ is $$0.5 \times 10^{-6}$$ at $$298 \mathrm{~K}$$. The ratio of $$\left[\mathrm{Ba}^{2+}\right]\left[\mathrm{F}^{-}\right]^{2}$$ and $$\mathrm{K}_{\mathrm{sp}}$$ is ___________.

(Nearest integer)

Your input ____
2
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area of the region enclosed by the curve $$f(x)=\max \{\sin x, \cos x\},-\pi \leq x \leq \pi$$ and the $$x$$-axis is

A
$$2 \sqrt{2}(\sqrt{2}+1)$$
B
4
C
$$2(\sqrt{2}+1)$$
D
$$4(\sqrt{2})$$
3
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\mathrm{PQ}$$ be a focal chord of the parabola $$y^{2}=36 x$$ of length 100 , making an acute angle with the positive $$x$$-axis. Let the ordinate of $$\mathrm{P}$$ be positive and $$\mathrm{M}$$ be the point on the line segment PQ such that PM : MQ = 3 : 1. Then which of the following points does NOT lie on the line passing through M and perpendicular to the line $$\mathrm{PQ}$$?

A
$$(6,29)$$
B
$$(-3,43)$$
C
$$(3,33)$$
D
$$(-6,45)$$
4
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the equation of plane passing through the line of intersection of the planes $$x+2 y+a z=2$$ and $$x-y+z=3$$ be $$5 x-11 y+b z=6 a-1$$. For $$c \in \mathbb{Z}$$, if the distance of this plane from the point $$(a,-c, c)$$ is $$\frac{2}{\sqrt{a}}$$, then $$\frac{a+b}{c}$$ is equal to :

A
$$-$$2
B
4
C
2
D
$$-$$4
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