JEE Advanced 2014 · 25 May 2014 · Paper 2

Q1.A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the vari …

Q2.A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves fr …

Q3.During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at $40.0cm$ using a standard resistance of $90\Omega$, as shown in the figure. The least count of the scale used in the metre bridge is 1 $mm$. The unknown resistance …

Q4.Charges $Q,2Q$ and $4Q$ are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii $R/2,R$ and $2R$, respectively, as shown in figure. If magnitudes of the electric fields at point P at a distance $R$ from the center of spheres 1, 2 and 3 are …

Q5.A point source $S$ is placed at the bottom of a transparent block of height $10mm$ and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright sp …

Q6.Parallel rays of light of intensity $I=912W{m}^{-2}$ are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant $\sigma =5.7\times 10^{-8}W{m}^{-2}{K}^{-4}$ and assume that the energy exchange with the surroundings is only thr …

Q7.A metal surface is illuminated by light of two different wavelengths $248nm$ and $310nm$. The maximum speeds of the photoelectrons corresponding to these wavelengths are $u_1$ and $u_2$, respectively. If the ratio $u_1:u_2=2:1$ and $hc=1240eVnm$, the wor …

Q8.If ${\lambda }_{Cu}$ is the wavelength of $K_{\alpha }$ X-ray line of copper (atomic number 29) and ${\lambda }_{Mo}$ is the wavelength of the $K_{\alpha }$ X-ray line of molybdenum (atomic number 42), then the ratio ${\lambda }_{Cu}/{\lambda }_{Mo}$ is close to

Q9.A planet of radius $R=\frac{1}{10}\times$ (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth $\frac{R}{5}$ on it and lower a wire of the same length and of linear mass density $10^{-3}kg{m}^{-1}$ into it. If the wire is not touching anywher …

Q10.A glass capillary tube is of the shape of a truncated cone with an apex angle $\alpha$ so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height $h$, where the radius of its cross section is $b$. If the surfa …

Q11.In the figure a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by …

Q12.In the figure a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by …

Q13.A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rise …

Q14.A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rise …

Q15.The figure shows a circular loop of radius $a$ with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is $d$. The loop and the wires are carrying the same current $I$. The current in the loop is i …

Q16.The figure shows a circular loop of radius $a$ with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is $d$. The loop and the wires are carrying the same current $I$. The current in the loop is i …

Q17.Four charges $Q_1,Q_2,Q_3$ and $Q_4$ of same magnitude are fixed along the $x$ axis at $x=-2a,-a,+a$ and $+2a$, respectively. A positive charge $q$ is placed on the positive $y$ axis at a distance $b>0$. Four options of the signs of these charges are g …

Q18.Four combinations of two thin lenses are given in List I. The radius of curvature of all curved surfaces is $r$ and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer using the code g …

Q19.A block of mass $m_1=1kg$ another mass $m_2=2kg$, are placed together (see figure) on an inclined plane with angle of inclination $\theta$. Various values of $\theta$ are given in List I. The coefficient of friction between the block $m_1$ and the plane is alway …

Q20.A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance of $1.2m$ from the person. In the following, state of the lift's motion is gi …

Q1.The acidic hydrolysis of ether (X) shown below is fastest when

Q2.Isomers of hexane, based on their branching, can be divided into three distinct classes as shown in the figure.

I

II

III

The correct order of their boiling point is

Q3.The major product in the following reaction is

Q4.Hydrogen peroxide in its reaction with ${\mathrm{KIO}}_4$ and ${\mathrm{NH}}_2\mathrm{OH}$ respectively, is acting as a

Q5.The product formed in the reaction of ${\mathrm{SOCl}}_2$ with white phosphorous is

Q6.Under ambient conditions, the total number of gases released as products in the final step of the reaction scheme shown below is

Q7.For the identification of $\beta$-naphthol using dye test, it is necessary to use

Q8.For the elementary reaction $\mathbf{M}\to \mathbf{N}$, the rate of disappearance of $\mathbf{M}$ increases by a factor of 8 upon doubling the concentration of $\mathbf{M}$. The order of the reaction with respect to M is

Q9.For the process

at $T=100^{\circ }\mathrm{C}$ and 1 atmosphere pressure, the correct choice is

Q10.Assuming $2s-2p$ mixing is NOT operative, the paramagnetic species among the following is

Q11.Schemes 1 and 2 describe sequential transformation of alkynes M and N. Consider only the major products formed in each step for both the schemes.

1. ${\mathrm{NaNH}}_2$ (excess)

1. ${\mathrm{NaNH}}_2$ (2 equivalent)

The product X is

Q12.Schemes 1 and 2 describe sequential transformation of alkynes M and N. Consider only the major products formed in each step for both the schemes.

1. ${\mathrm{NaNH}}_2$ (excess)

1. ${\mathrm{NaNH}}_2$ (2 equivalent)

The correct statement with respect to product Y is

Q13.An aqueous solution of metal ion $M1$ reacts separately with reagents $\mathbf{Q}$ and $\mathbf{R}$ in excess to give tetrahedral and square planar complexes, respectively. An aqueous solution of another metal ion M2 always forms tetrahedral complexes wit …

Q14.An aqueous solution of metal ion $M1$ reacts separately with reagents $\mathbf{Q}$ and $\mathbf{R}$ in excess to give tetrahedral and square planar complexes, respectively. An aqueous solution of another metal ion M2 always forms tetrahedral complexes wit …

Q15.X and Y are two volatile liquids with molar weights of $10\mathrm{g}{\mathrm{mol}}^{-1}$ and $40\mathrm{g}{\mathrm{mol}}^{-1}$ respectively. Two cotton plugs, one soaked in $\mathbf{X}$ and the other soaked in $\mathbf{Y}$, are simultaneously placed at the ends of a t …

Q16.X and Y are two volatile liquids with molar weights of $10\mathrm{g}{\mathrm{mol}}^{-1}$ and $40\mathrm{g}{\mathrm{mol}}^{-1}$ respectively. Two cotton plugs, one soaked in $\mathbf{X}$ and the other soaked in $\mathbf{Y}$, are simultaneously placed at the ends of a t …

Q17.Different possible thermal decomposition pathways for peroxyesters are shown below. Match each pathway from List I with an appropriate structure from List II and select the correct answer using the code given below the lists.

List-I

P. Pathway P

Q. Pathway Q

R. Pathway R

S. …

Q18.Match the four starting materials (P, Q, R, S) given in List I with the corresponding reaction schemes (I, II, III, IV) provided in List II and select the correct answer using the code given below the lists.

List-I

P. (see structure)

Q. (see structure)

R. (see structure)

S. …

Q19.Match each coordination compound in List-I with an appropriate pair of characteristics from List-II and select the correct answer using the code given below the lists.
{$\mathrm{en}={\mathrm{H}}_2{\mathrm{NCH}}_2{\mathrm{CH}}_2{\mathrm{NH}}_2$; atomic numbers: …

Q20.Match the orbital overlap figures shown in List-I with the description given in List-II and select the correct answer using the code given below the lists.

List-I

P. (see structure)

Q. (see structure)

R. (see structure)

S. (see structure)

List-II

1. $p-d\pi$ antibonding …

Q1.The function $y=f(x)$ is the solution of the differential equation

in $(-1,1)$ satisfying $f(0)=0$. Then

is

Q2.The following integral

is equal to

Q3.Coefficient of $x^{11}$ in the expansion of ${\left(1+x^2\right)}^4{\left(1+x^3\right)}^7{\left(1+x^4\right)}^{12}$ is

Q4.Let $f:[0,2]\to \mathbb{R}$ be a function which is continuous on $[0,2]$ and is differentiable on ( 0,2 ) with $f(0)=1$. Let

for $x\in [0,2]$. If $F^{\prime }(x)=f^{\prime }(x)$ for all $x\in (0,2)$, then $F(2)$ equ …

Q5.The common tangents to the circle $x^2+y^2=2$ and the parabola $y^2=8x$ touch the circle at the points $P,Q$ and the parabola at the points $R,S$. Then the area of the quadrilateral $PQRS$ is

Q6.For $x\in (0,\pi )$, the equation $\sin x+2\sin 2x-\sin 3x=3$ has

Q7.In a triangle the sum of two sides is $x$ and the product of the same two sides is $y$. If $x^2-c^2=y$, where $c$ is the third side of the triangle, then the ratio of the in-radius to the circum-radius of the triangle is

Q8.Six cards and six envelopes are numbered 1,2,3,4,5,6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. The …

Q9.Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is

Q10.The quadratic equation $p(x)=0$ with real coefficients has purely imaginary roots. Then the equation

has

Q11.Let $a,r,s,t$ be nonzero real numbers. Let $P\left(a{t}^2,2at\right),Q,R\left(a{r}^2,2ar\right)$ and $S\left(a{s}^2,2as\right)$ be distinct points on the parabola $y^2=4ax$. Suppose that $PQ$ is the focal chord and lines $QR$ and $PK$ are par …

Q12.Let $a,r,s,t$ be nonzero real numbers. Let $P\left(a{t}^2,2at\right),Q,R\left(a{r}^2,2ar\right)$ and $S\left(a{s}^2,2as\right)$ be distinct points on the parabola $y^2=4ax$. Suppose that $PQ$ is the focal chord and lines $QR$ and $PK$ are par …

Q13.Given that for each $a\in (0,1)$,

exists. Let this limit be $g(a)$. In addition, it is given that the function $g(a)$ is differentiable on (0,1).

The value of $g\left(\frac{1}{2}\right)$ is

Q14.Given that for each $a\in (0,1)$,

exists. Let this limit be $g(a)$. In addition, it is given that the function $g(a)$ is differentiable on (0,1).

The value of $g^{\prime }\left(\frac{1}{2}\right)$ is

Q15.Box 1 contains three cards bearing numbers 1,2,3; box 2 contains five cards bearing numbers 1,2,3,4,5; and box 3 contains seven cards bearing numbers 1,2,3,4,5,6,7. A card is drawn from each of the boxes. Let $x_i$ be the number on the card drawn from the $i^{\text{th }}$ …

Q16.Box 1 contains three cards bearing numbers 1,2,3; box 2 contains five cards bearing numbers 1,2,3,4,5; and box 3 contains seven cards bearing numbers 1,2,3,4,5,6,7. A card is drawn from each of the boxes. Let $x_i$ be the number on the card drawn from the $i^{\text{th }}$ …

Q17.Let $z_k=\cos \left(\frac{2k\pi }{10}\right)+i\sin \left(\frac{2k\pi }{10}\right);k=1,2,\dots ,9$.
| Q. | There exists a …

Q18.| Q. | The number of points in the interval …

Q19.| Q. | Let …

Q20.Let $f_1:\mathbb{R}\to \mathbb{R},f_2:[0,\infty )\to \mathbb{R},f_3:\mathbb{R}\to \mathbb{R}$ and $f_4:\mathbb{R}\to [0,\infty )$ be defined by …