In the following circuit, the current through the resistor R(=2Ω) is I Amperes. The value of I is

In the following circuit, the current through the resisto…

\sum_{k = 1}^{13} \frac{1}{\sin (\frac{π}{4} + \frac{(k - 1) π}{6}) \sin (\frac{π}{4} + \frac{k π}{6})}

is equal to

JEE Advanced 2016 Hard

A line L :

y = m x + 3

meets

y - a x is

at E(0,3) and the arc of the parabola

y^{2} = 16 x, 0 \leq y \leq 6

at the point

F (x_{0}, y_{0})

.The tangent to the parabola at

F (x_{0}, y_{0})

intersects the y-axis at

G (0, y_{1})

.The slope m of the line L is chosen such that the area of the triangle EFG has a local maximum.
Match List I with List II and select the correct answer using the code given below the lists :

	List I		List II
A.	m =	P.	$\frac{1}{2}$
B.	Maximum area of ΔEFG is	Q.	4
C.	y₀ =	R.	2
D.	y₁=	S.	1

JEE Advanced 2013 Medium

Consider the following reaction.

On estimation of bromine in

1.00 g

of

R

using Carius method, the amount of

AgBr

formed (in

g

) is____[Given: Atomic mass of $\text H =1,\text C =12,\text O =16,\text P =31,\text {Br}$ $=80,\text{Ag} =108]$

JEE Advanced 2022 Medium

Paragraph:
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridisation easily explains the ease of sigma donation capability of $\mathrm{NH}_3$ and $\mathrm{PH}_3$. Phosphine is a flammable gas and is prepared from white phosphorus.
Question:
Among the following, the correct statement is

JEE Advanced 2008 Easy

Let

ℓ_{1}

and

ℓ_{2}

be the lines

{\vec{r}}_{1} = λ (\hat{i} + \hat{j} + \hat{k})

and

{\vec{r}}_{2} = (\hat{j} - \hat{k}) + μ (\hat{i} + \hat{k})

, respectively, Let

X

be the set of all the planes

H

that contain the line

ℓ_{1}

. For a plane

H

, let

d (H)

denote the smallest possible distance between the points of

ℓ_{2}

and

H

. Let

H_{0}

be a plane in

X

for which

d (H_{0})

is the maximum value of

d (H)

as

H

varies over all planes in

X

. Match each entry in List-I to the correct entries in List-II.

	List-I		List-II
$(P)$	The value of $d (H_{0})$ is	$(1)$	$\sqrt{3}$
$(Q)$	The distance of the point $(0, 1, 2)$ from $H_{0}$ is	$(2)$	$\frac{1}{\sqrt{3}}$
$(R)$	The distance of origin from $H_{0}$ is	$(3)$	$0$
$(S)$	The distance of origin from the point of intersection of planes $y = z, x = 1$ and $H_{0}$ is	$(4)$	$\sqrt{2}$
		$(5)$	$\frac{1}{\sqrt{2}}$

The correct option is

JEE Advanced 2023 Medium

The total number of alkenes possible by dehydrobromination of 3-bromo-3-cyclopentylhexane using alcoholic $\mathrm{KOH}$ is

JEE Advanced 2011 Hard

	List-I		List-II
(i)	$\frac{1}{\sqrt{2}} (\sin ω t \hat{j} + \cos ω t \hat{k})$	(p)	$0$
(ii)	$\frac{1}{\sqrt{2}} (\sin ω t \hat{i} + \cos ω t \hat{j})$	(q)	$- \frac{α}{4} \hat{i}$
(iii)	$\frac{1}{\sqrt{2}} (\sin ω t \hat{i} + \cos ω t \hat{k})$	(r)	$\frac{3 α}{4} \hat{i}$
(iv)	$\frac{1}{\sqrt{2}} (\cos ω t \hat{j} + \sin ω t \hat{k})$	(s)	$\frac{α}{4} \hat{j}$
		(t)	$- \frac{3 α}{4} \hat{i}$

In the following circuit, the current through the resistor $R (= 2 Ω)$ is $I$ Amperes. The value of $I$ is

Answer & Solution

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