JEE Main 2016 · 03 Apr 2016 · Offline

Q1.A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is : (take $g=10{\mathrm{ms}}^{-2}$)

Q2.A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supp …

Q3.A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals $\mu$. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, …

Q4.Two identical wires A and B, each of length '$\ell$', carry the same current I. Wire A is bent into a circle of radius $R$ and wire B is bent to form a square of side 'a'. If $B_A$ and $B_B$ are the values of magnetic field at the centres of the circle and square respectively …

Q5.A galvanometer having a coil resistance of $100\Omega$ gives a full scale deflection, when a current of 1 mA is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of 10 A is :

Q6.An observer looks at a distant tree of height 10 m with a telescope of magnifying power of 20. To the observer the tree appears :

Q7.The temperature dependence of resistances of Cu and undoped Si in the temperature range 300-400 K, is best described by :

Q8.Choose the correct statement :

Q9.Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be :

Q10.'n' moles of an ideal gas undergoes a process $A\to B$ as shown in the figure. The maximum temperature of the gas during the process will be :

Q11.An arc lamp requires a direct current of 10 A and 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to :

Q12.A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :

Q13.The box of pin hole camera, of length L, has a hole of radius $a$. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength $\lambda$ the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and …

Q14.A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the $4\mu \mathrm{F}$ and $9\mu \mathrm{F}$ capacitors), at a point distant 30 m from it, would e …

Q15.Arrange the following electromagnetic radiations per quantum in the order of increasing energy :
A : Blue light
B : Yellow light
C : X-ray
D : Radiowave

Q16.Hysteresis loops for two magnetic materials A and B are given below :

These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use :

Q17.A pendulum clock loses 12 s a day if the temperature is $40^{\circ }\mathrm{C}$ and gains 4 s a day if the temperature is $20^{\circ }\mathrm{C}$. The temperature at which the clock will show correct time, and the co-efficient of linear expansion ($\alpha$) of the metal of …

Q18.The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density $\rho =\frac{A}{r}$, where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such th …

Q19.In an experiment for determination of refractive index of glass of a prism by $\mathrm{i}-\delta$, plot, it was found that a ray incident at angle $35^{\circ }$, suffers a deviation of $40^{\circ }$ and that it emerges at angle $79^{\circ }$. In that case which of the follow …

Q20.A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91s, 95s and 92s. If the minimum division in the measuring clock is 1s, then the reported mean time should be :

Q21.Identify the semiconductor devices whose characteristics are given below, in the order (a), (b), (c), (d) :

Q22.Radiation of wavelength $\lambda$, is incident on a photocell. The fastest emitted electron has speed v. If the wavelength is changed to $\frac{3\lambda }{4}$, the speed of the fastest emitted electron will be :

Q23.A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at a distance $\frac{2\mathrm{A}}{3}$ from equilibrium position. The new amplitude of the motion is :

Q24.A particle of mass $m$ is moving along the side of a square of side 'a', with a uniform speed v in the $\mathrm{x}-\mathrm{y}$ plane as shown in the figure :

Which of the following statements is false for the angular momentum $\overrightarrow{\mathrm{L}}$ about the origin?

Q25.An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by ${\mathrm{PV}}^{\mathrm{n}}=$ constant, then n is given by (Here ${\mathrm{C}}_{\mathrm{P}}$ and …

Q26.A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the $45^{\text{th}}$ division …

Q27.A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so …

Q28.If $\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}$ are inputs to a gate and x is its output, then, as per the following time graph, the gate is:

Q29.For a common emitter configuration, if $\alpha$ and $\beta$ have their usual meanings, the incorrect relationship between $\alpha$ and $\beta$ is:

Q30.A satellite is revolving in a circular orbit at a height 'h' from the earth's surface (radius of earth $R$; $h\ll R$). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to: (Neglect the effect …

Q1.A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference $V$ esu. If $e$ and $m$ are charge and mass of an electron, respectively, then the value of $h/\lambda$ (where $\lambda$ is wavelength associated with electron wave …

Q2.2-chloro-2-methylpentane on reaction with sodium methoxide in methanol yields :

Q3.Which of the following statements about low density polythene is FALSE ?

Q4.For a linear plot of $\log (x/m)$ versus $\log p$ in a Freundlich adsorption isotherm, which of the following statements is correct ? ( k and n are constants)

Q5.The heats of combustion of carbon and carbon monoxide are -393.5 and $-283.5\mathrm{kJ}{\mathrm{mol}}^{-1}$, respectively. The heat of formation (in kJ ) of carbon monoxide per mole is :

Q6.The hottest region of Bunsen flame shown in the figure below is :

Q7.Which of the following is an anionic detergent ?

Q8.18 g glucose $(\mathrm{C}{}_6\mathrm{H}{}_{12}\mathrm{O}{}_6)$ is added to 178.2 g water. The vapour pressure of water (in torr) for this aqueous solution is :

Q9.The distillation technique most suited for separating glycerol from spent-lye in the soap industry is :

Q10.The species in which the N atom is in a state of $sp$ hybridization is :

Q11.Decomposition of ${\mathrm{H}}_2{\mathrm{O}}_2$ follows a first order reaction. In fifty minutes the concentration of ${\mathrm{H}}_2{\mathrm{O}}_2$ decreases from 0.5 to 0.125 M in one such decomposition. When the concentration of ${\mathrm{H}}_2{\mathrm{O}}_2$ reaches …

Q12.The pair having the same magnetic moment is :
[At. No.: $\mathrm{Cr}=24,\mathrm{Mn}=25,\mathrm{Fe}=26,\mathrm{Co}=27$ ]

Q13.The absolute configuration of

Q14.The equilibrium constant at 298 K for a reaction $\mathrm{A}+\mathrm{B}\rightleftharpoons \mathrm{C}+\mathrm{D}$ is 100 . If the initial concentration of all the four species were 1 M each, then equilibrium concentration of D (in $\mathrm{mol}{\mathrm{L}}^{-1}$ ) will be:

Q15.Which one of the following ores is best concentrated by froth floatation method?

Q16.The pair in which phosphorous atoms have a formal oxidation state of +3 is:

Q17.Which one of the following complexes shows optical isomerism?
(en = ethylenediamine)

Q18.The reaction of zinc with dilute and concentrated nitric acid, respectively, produces:

Q19.Which one of the following statements about water is FALSE?

Q20.The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake was found to be $1000\mathrm{ppb},40\mathrm{ppb},100\mathrm{ppm}$ and 0.2 ppm , respectively. This water is unsuitable for drinking due to high concentration of :

Q21.The main oxides formed on combustion of $\mathrm{Li},\mathrm{Na}$ and K in excess of air are, respectively:

Q22.Thiol group is present in :

Q23.Galvanization is applying a coating of:

Q24.Which of the following atoms has the highest first ionization energy?

Q25.In the Hofmann bromamide degradation reaction, the number of moles of NaOH and ${\mathrm{Br}}_2$ used per mole of amine produced are:

Q26.Two closed bulbs of equal volume ($V$) containing an ideal gas initially at pressure $p_{\mathrm{i}}$ and temperature $T_1$ are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to …

Q27.The reaction of propene with $\mathrm{HOCl}\left({\mathrm{Cl}}_2+{\mathrm{H}}_2\mathrm{O}\right)$ proceeds through the intermediate:

Q28.The product of the reaction given below is:

Q1.Two sides of a rhombus are along the lines, $x-y+1=0$ and $7x-y-5=0$. If its diagonals intersect at $(-1,-2)$, then which one of the following is a vertex of this rhombus?

Q2.If the $2^{\text{nd }}$, $5^{\text{th }}$ and $9^{\text{th }}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

Q3.Let P be the point on the parabola, ${\mathrm{y}}^2=8\mathrm{x}$ which is at a minimum distance from the centre C of the circle, $x^2+(y+6{)}^2=1$. Then the equation of the circle, passing through $C$ and having its centre at $P$ is:

Q4.The system of linear equations
$\mathrm{x}+\lambda \mathrm{y}-\mathrm{z}=0$
$\lambda \mathrm{x}-\mathrm{y}-\mathrm{z}=0$
$\mathrm{x}+\mathrm{y}-\lambda \mathrm{z}=0$
has a non-trivial solution for :

Q5.If $\mathrm{f}(\mathrm{x})+2\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=3\mathrm{x},\mathrm{x}\ne 0$, and $\mathrm{S}=\{\mathrm{x}\in \mathrm{R}:\mathrm{f}(\mathrm{x})=\mathrm{f}(-\mathrm{x})\}$; then S :

Q6.Let $\mathrm{p}={\lim }_{\mathrm{x}\to 0+}{\left(1+{\tan }^2\sqrt{\mathrm{x}}\right)}^{\frac{1}{2\mathrm{x}}}$ then $\log \mathrm{p}$ is equal to:

Q7.A value of $\theta$ for which $\frac{2+3i\sin \theta }{1-2i\sin \theta }$ is purely imaginary, is:

Q8.The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal half of the distance between its foci, is:

Q9.If the standard deviation of the numbers 2,3, a and 11 is 3.5, then which of the following is true?

Q10.The integral $\int \frac{2{\mathrm{x}}^{12}+5{\mathrm{x}}^9}{{\left({\mathrm{x}}^5+{\mathrm{x}}^3+1\right)}^3}\mathrm{dx}$ is equal to:

Q11.If the line, $\frac{\mathrm{x}-3}{2}=\frac{\mathrm{y}+2}{-1}=\frac{\mathrm{z}+4}{3}$ lies in the plane, $l\mathrm{x}+\mathrm{my}-\mathrm{z}=9$, then $l^2+{\mathrm{m}}^2$ is equal to:

Q12.If $0\le x<2\pi$, then the number of real values of $x$, which satisfy the equation $\cos \mathrm{x}+\cos 2\mathrm{x}+\cos 3\mathrm{x}+\cos 4\mathrm{x}=0$ is:

Q13.The area (in sq. units) of the region $\{(x,y):y^2\ge 2x$ and $x^2+y^2\le 4x,x\ge 0,y\ge 0\}$ is:

Q14.Let $\vec{a},\vec{b}$ and $\vec{c}$ be three unit vectors such that $\vec{a}\times (\vec{b}\times \vec{c})=\frac{\sqrt{3}}{2}(\vec{b}+\vec{c})$. If $\vec{b}$ is not parallel to $\vec{c}$, then the angle between $\vec{a}$ and $\vec{b}$ is:

Q15.A wire of length 2 units is cut into two parts which are bent respectively to form a square of side $=x$ units and a circle of radius $=r$ units. If the sum of the areas of the square and the circle so formed is minimum, then:

Q16.The distance of the point $(1,-5,9)$ from the plane $x-y+z=5$ measured along the line $x=y=z$ is:

Q17.If a curve $y=f(x)$ passes through the point (1,-1) and satisfies the differential equation, $y(1+xy)dx=xdy$, then $f\left(-\frac{1}{2}\right)$ is equal to:

Q18.If the number of terms in the expansion of ${\left(1-\frac{2}{x}+\frac{4}{x^2}\right)}^n,x\ne 0$, is 28, then the sum of the coefficients of all the terms in this expansion, is:

Q19.Consider $f(x)={\tan }^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right),x\in \left(0,\frac{\pi }{2}\right)$. A normal to $y=f(x)$ at $x=\frac{\pi }{6}$ also passes through the point:

Q20.For $x\in \mathbf{R},f(x)=|\log 2-\sin x|$ and $g(x)=f(f(x))$, then:

Q21.Let two fair six-faced dice A and B be thrown simultaneously. If $E_1$ is the event that die A shows up four, $E_2$ is the event that die B shows up two and $E_3$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT t …

Q22.If $A=\left[\begin{array}{cc}5a& -b\\ 3& 2\end{array}\right]$ and A adj $A=A{A}^T$, then $5a+b$ is equal to:

Q23.The Boolean Expression $(p\wedge \sim q)\vee q\vee (\sim p\wedge q)$ is equivalent to:

Q24.The sum of all real values of x satisfying the equation ${\left(x^2-5x+5\right)}^{x^2+4x-60}=1$ is

Q25.The centres of those circles which touch the circle, $x^2+y^2-8x-8y-4=0$, externally and also touch the x-axis, lie on:

Q26.If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:

Q27.${\lim }_{n\to \infty }{\left(\frac{(n+1)(n+2)\dots 3n}{n^{2n}}\right)}^{1/n}$ is equal to:

Q28.If the sum of the first ten terms of the series ${\left(1\frac{3}{5}\right)}^2+{\left(2\frac{2}{5}\right)}^2+{\left(3\frac{1}{5}\right)}^2+4^2+{\left(4\frac{4}{5}\right)}^2+\dots$, is $\frac{16}{5}m$, then m is equal to:

Q29.If one of the diameters of the circle, given by the equation, $x^2+y^2-4x+6y-12=0$, is a chord of a circle S, whose centre is at $(-3,2)$, then the radius of S is:

Q30.A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is $30^{\circ }$. After walking for 10 minutes from A in the same direction, at a point B, he obser …