JEE Advanced 2018

JEE Advanced Physics 2018 Answer Key with Solution

A

$|\vec{\tau} | = \frac{1}{3} N \ m$

B

The torque $\vec{\tau}$ is in the direction of the unit vector + $\hat{k}$

C

The velocity of the body at $t = 1 \ s $ is $\vec{v} = \frac{1}{2} (\hat{i} + 2 \hat{j}) m \ s^{-1}$

D

The magnitude of displacement of the body at $t = 1 \ s $ is $\frac{1}{6} m $

A

For a given material of the capillary tube, $h$ decreases with increase in $r$

B

For a given material of the capillary tube, $h$ is independent of $\sigma$

C

If this experiment is performed in a lift going up with a constant acceleration, then $h$ decreases

D

$h$ is proportional to contact angle $\theta$

A

Process I is an isochoric process

B

In process II, gas absorbs heat

C

In process IV, gas releases heat

D

Processes I and III are not isobaric

A

The force applied on the particle is constant

B

The speed of the particle is proportional to time

C

The distance of the particle from the origin increases linearly with time

D

The force is conservative

A

The resistive force of liquid on the plate is inversely proportional to $h$

B

The resistive force of liquid on the plate is independent of the area of the plate

C

The tangential (shear) stress on the floor of the tank increases with $u_0$

D

The tangential (shear) stress on the plate varies linearly with the viscosity $\eta$ of the liquid

A

The electric flux through the shell is $\sqrt{3} R \lambda / \in_0$

B

The $z$-component of the electric field is zero at all the points on the surface of the shell

C

The electric flux through the shell is $\sqrt{2} R \lambda / \in_0$

D

The electric field is normal to the surface of the shell at all points

A

The speed of sound determined from this experiment is $332 \ m \ s^{-1}$

B

The end correction in this experiment is $0.9 \ cm$

C

The wavelength of the sound wave is $66.4 \ cm $

D

The resonance at $50.7 \ cm $ corresponds to the fundamental harmonic

JEE Advanced Chemistry 2018 Answer Key with Solution

A

$\ce{NH_4NO_3}$

B

$\ce{(NH_4)_2Cr_2O_7}$

C

$\ce{Ba(N_3)_2}$

D

$\ce{Mg_3N_2}$

A

Total number of valence shell electrons at metal centre in $\ce{Fe(CO)_5}$ or $\ce{Ni(CO)_4}$ is 16

B

These are predominantly low spin in nature

C

Metal–carbon bond strengthens when the oxidation state of the metal is lowered

D

The carbonyl Cβˆ’O bond weakens when the oxidation state of the metal is increased

A

$\ce{Bi_2O_5}$ is more basic than $\ce{N_2O_5}$

B

$\ce{NF_3}$ is more covalent than $\ce{BiF_3}$

C

$\ce{PH_3}$ boils at lower temperature than $\ce{NH_3}$

D

The Nβˆ’N single bond is stronger than the Pβˆ’P single bond

A

$q_{AC} = \Delta U_{BC}$ and $W_{AB} = P_2 (V_2 - V_1)$

B

$W_{BC} = P_2 (V_2 - V_1) and q_{BC} = \Delta H_{AC}$

C

$\Delta H_{CA} < \Delta U_{CA}$ and $q_{AC} = \Delta U_{BC}$

D

$q_{BC} = \Delta H_{AC}$ and $\Delta H_{CA} > \Delta U_{CA}$

A

It has two geometrical isomers

B

It will have three geometrical isomers if bidentate β€˜en’ is replaced by two cyanide ligands

C

It is paramagnetic

D

It absorbs light at longer wavelength as compared to $\ce{[Co(en)(NH3)4]^{3+}}$

A

$\ce{Mn^{2+}}$ shows the characteristic green colour in the flame test

B

Only $\ce{Cu^{2+}}$ shows the formation of precipitate by passing $\ce{H_2S}$ in acidic medium

C

Only $\ce{Mn^{2+}}$ shows the formation of precipitate by passing $\ce{H_2S}$ in faintly basic medium

D

$\ce{Cu^{2+} /Cu}$ has higher reduction potential than $\ce{Mn^{2+} /Mn}$ (measured under similar conditions)

A

P $\to$ 1; Q $\to$ 2,3; R $\to$ 1,4; S $\to$ 2,4

B

P $\to$ 1,5; Q $\to$ 3,4; R $\to$ 4,5; S $\to$ 3

C

P $\to$ 1,5; Q $\to$ 3,4; R $\to$ 5; S $\to$ 2,4

D

P $\to$ 1,5; Q $\to$ 2,3; R $\to$ 1,5; S $\to$ 2,3

A

P $\to$ 1,5; Q $\to$ 2; R $\to$ 3; S $\to$ 4

B

P $\to$ 1,4; Q $\to$ 2; R $\to$ 4; S $\to$ 3

C

P $\to$ 1,4; Q $\to$ 1,2; R $\to$ 3,4; S $\to$ 4

D

P $\to$ 4,5; Q $\to$ 4; R $\to$ 4; S $\to$ 3,4

JEE Advanced Mathematics 2018 Answer Key with Solution

A

arg(βˆ’1 βˆ’ i) = $\frac{\pi}{4}$, where $i = \sqrt{-1}$

B

The function $f : \mathbb R \to (βˆ’ \pi , \pi ]$, defined by $f (t) $ = arg $(βˆ’1 + it )$ for all $t \in \mathbb R$ , is continuous at all points of $\mathbb R$, where $ i = \sqrt{βˆ’1}$

C

For any two non-zero complex numbers $z_1$ and $z_2, arg \left(\frac{z_1}{z_2}\right) - arg (z_1) + arg (z_2)$ is an integer multiple of $2 \pi $

D

For any three given distinct complex numbers $z_1, z_2$ and $z_3$, the locus of the point $z$ satisfying the condition $arg \left( \frac{(z - z_1)(z_2 - z_2)}{(z - z_3)(z_2 - z_1)}\right) = \pi $, lies on a straight line

A

$\angle QPR = 45^{\circ} $

B

The area of the triangle $PQR$ is $25 \sqrt{3}$ and $\angle QPR = 120^{\circ} $

C

The radius of the incircle of the triangle $PQR $ is $10 \sqrt{3} - 15$

D

The area of the circumcircle of the triangle $PQR$ is $100 \ \pi $

A

The line of intersection of $P_1$ and $P_2$ has direction ratios 1, 2, βˆ’1

B

The line $\frac{3x - 4}{9} = \frac{1 - 3y}{9} = \frac{z}{3}$ is perpendicular to the line of intersection of $P_1$ and $P_2$

C

The acute angle between $P_1$ and $P_2$ is $60^{\circ}$

D

If $P_3$ is the plane passing through the point (4, 2, βˆ’2) and perpendicular to the line of intersection of $P_1$ and $P_2$, then the distance of the point (2, 1, 1) from the plane $P_3$ is $\frac{2 }{\sqrt{3}}$

A

There exist $r, s \in \mathbb R$, where $r < s$, such that $f$ is one-one on the open interval $(r ,s)$

B

There exists $x 0 \in (βˆ’4, 0)$ such that $|𝑓′(x0)| \leq 1$

C

$\lim_{x \to \infty} f(x) = 1 $

D

There exists $\alpha \in (βˆ’4, 4)$ such that $f (\alpha ) + fβ€²β€²(\alpha) = 0$ and $𝑓′(\alpha) \neq 0$

A

The curve $y = f(x)$ passes through the point (1, 2)

B

The curve $y = f(x)$ passes through the point (2, βˆ’1)

C

The area of the region $\{(x, y) \in [0, 1] \times \mathbb R ∢ f(x) \leq y \leq \sqrt{1 βˆ’ x^2} \}$ is $\frac{\pi - 2}{4}$

D

The area of the region $\{(x, y) \in [0, 1] \times \mathbb R ∢ f(x) \leq y \leq \sqrt{1 βˆ’ x^2} \}$ is $\frac{\pi - 1}{4}$

A

$\sum_{j =1}^5 \ \tan^2 (f_j (0)) = 55 $

B

$\sum^{10}_{j=1} (1 + f'_j (0)) \sec^2 (f_j (0)) = 1 0$

C

For any fixed positive integer $n , \lim_{x \to \infty} \tan \ (f_n(x)) = \frac{1}{n}$

D

For any fixed positive integer $n , \lim_{x \to \infty} \sec^2 \ (f_n(x)) = 1 $

A

For the ellipse, the eccentricity is $\frac{1}{\sqrt{2}}$ and the length of the latus rectum is 1

B

For the ellipse, the eccentricity is $\frac{1}{2}$ and the length of the latus rectum is $\frac{1}{2}$

C

The area of the region bounded by the ellipse between the lines $x = \frac{1}{\sqrt{2}}$ and $x = 1$ is $\frac{1}{4 \sqrt{2}} (\pi - 2)$

D

The area of the region bounded by the ellipse between the lines $x = \frac{1}{\sqrt{2}}$ and $x = 1$ is $\frac{1}{16} (\pi - 2)$

A

If $L$ has exactly one element, then $|s| \neq |t|$

B

If $|s| = |t|$, then $L$ has infinitely many elements

C

The number of elements in $L \cap \{z : | z -1 + i| = 5 \}$ is at most 2

D

If $L$ has more than one element, then $L$ has infinitely many elements

A

$f\left(\frac{\pi}{4}\right) = \frac{\pi}{4\sqrt{2}} $

B

$f\left(x\right) < \frac{x^{4}}{6} -x^{2} $ for all $x \in (0, \pi)$

C

There exists $\alpha \in (0, \pi)$ such that $f'(\alpha) = 0 $

D

$f" \left(\frac{\pi}{2}\right) + f\left(\frac{\pi}{2}\right) = 0 $

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