JEE Main 2014 · 06 Apr 2014 · Offline

Q1.The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by $100^{\circ }\mathrm{C}$ is :
(For steel Young's modulus is $2\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}$ and coefficient of thermal exp …

Q2.A conductor lies along the z-axis at $-1.5\le \mathrm{z}<1.5\mathrm{m}$ and carries a fixed current of 10.0 A in $-{\hat{\mathrm{a}}}_{\mathrm{z}}$ direction (see figure). For a field …

Q3.A bob of mass m attached to an inextensible string of length $\ell$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega \mathrm{rad}/\mathrm{s}$ about the vertical. About the point of suspension :

Q4.The current voltage relation of diode is given by $I=\left(e^{1000\mathrm{V}/\mathrm{T}}-1\right)\mathrm{mA}$, where the applied voltage $V$ is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring $\pm 0.01\mathrm{V}$ while measuring th …

Q5.An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. What will be length of the air column above mercury in the t …

Q6.Match List-I (Electromagnetic wave type) with List-II (Its association / application) and select the correct option from the choices given below the lists:

Q7.A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is $3\times 10^4\mathrm{V}/\mathrm{m}$, the charge density of the positive pla …

Q8.A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

Q9.Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is :

Q10.In a large building, there are 15 bulbs of $40\mathrm{W}$, 5 bulbs of $100\mathrm{W}$, 5 fans of 80 W and 1 heater of 1 kW. The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be :

Q11.A particle moves with simple harmonic motion in a straight line. In first $\tau \mathrm{s}$, after starting from rest it travels a distance a, and in next $\tau \mathrm{s}$ it travels 2a, in same direction, then :

Q12.The coercivity of a small magnet where the ferromagnet gets demagnetized is $3\times 10^3{\mathrm{Am}}^{-1}$. The current required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets demagnetized when inside the solenoid, is:

Q13.The forward biased diode connection is:

Q14.During the propagation of electromagnetic waves in a medium:

Q15.In the circuit shown here, the point 'C' is kept connected to point 'A' till the current flowing through the circuit becomes constant. Afterward, suddenly, point 'C' is disconnected from point 'A' and connected to point 'B' at time $t=0$. Ratio of the voltage across resistance an …

Q16.A mass 'm' is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

Q17.One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement:

Q18.From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

Q19.A thin convex lens made from crown glass $\left(\mu =\frac{3}{2}\right)$ has focal length f. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$, it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation betw …

Q20.Three rods of Copper, Brass and Steel are welded together to from a Y-shaped structure. Area of cross section of each rod $=4{\mathrm{cm}}^2$. End of copper rod is maintained at $100^{\circ }\mathrm{C}$ where as ends of brass and steel are kept at $0^{\circ }\mathrm{C}$. Lengths o …

Q21.A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is $340\mathrm{m}/\mathrm{s}$.

Q22.There is a circular tube in a vertical plane. Two liquids which do not mix and of densities ${\mathrm{d}}_1$ and ${\mathrm{d}}_2$ are filled in the tube. Each liquid subtends $90^{\circ }$ angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical. ratio …

Q23.A green light is incident from the water to the air-water interface at the critical angle ($\theta$). Select the correct statement

Q24.Hydrogen $\left({}_1{\mathrm{H}}^1\right)$, Deuterium $\left({}_1{\mathrm{H}}^2\right)$, singly ionised Helium ${\left({}_2{\mathrm{He}}^4\right)}^{+}$ and doubly ionised lithium ${\left({}_3{\mathrm{Li}}^6\right)}^{++}$ all have one electron around the nucleus. Consider an e …

Q25.The radiation corresponding to $3\to 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3\times 10^{-4}\mathrm{T}$. If the radius of the largest circular path followed by these elec …

Q26.A block of mass $m$ is placed on a surface with a vertical cross section given by $y=x^3/6$. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is:

Q27.When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude $\mathrm{F}=\mathrm{ax}+{\mathrm{bx}}^2$ where a and b are constants. The work done in stretching the unstretched rubber band by L is:

Q28.On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius $r$ with the bottom of the vessel. If $r\ll R$, and the surface tension of water is T, value of r just before bu …

Q29.Two beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of Polaroid through $30^0$ makes the two beams appear …

Q30.Assume that an electric field $\vec{E}=30x^2\hat{i}$ exists in space. Then the potential difference $V_A-V_O$, where $V_O$ is the potential at the origin and ${\mathrm{V}}_{\mathrm{A}}$ the potential at $\mathrm{x}=2\mathrm{m}$ is:

Q1.Which one of the following properties is not shown by NO?

Q2.If Z is a compressibility factor, van der Waals equation at low pressure can be written as:

Q3.The metal that cannot be obtained by electrolysis of an aqueous solution of its salts is:

Q4.Resistance of 0.2 M solution of an electrolyte is $50\Omega$. The specific conductance of the solution is $1.4\mathrm{S}{\mathrm{m}}^{-1}$. The resistance of 0.5 M solution of the same electrolyte is $280\Omega$. The molar conductivity of 0.5 M solution of the electrolyte in …

Q5.CsCl crystallises in body centred cubic lattice. If 'a' is its edge length then which of the following expressions is correct?

Q6.Consider separate solutions of $0.500\mathrm{M}{\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}(\mathrm{aq}),0.100\mathrm{M}{\mathrm{Mg}}_3({\mathrm{PO}}_4{)}_2(\mathrm{aq}),0.250\mathrm{M}\mathrm{KBr}(\mathrm{aq})$ and 0.125 …

Q7.In which of the following reactions ${\mathrm{H}}_2{\mathrm{O}}_2$ acts as a reducing agent?
(a) ${\mathrm{H}}_2{\mathrm{O}}_2+2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}⟶2{\mathrm{H}}_2\mathrm{O}$
(b) …

Q8.In ${\mathrm{S}}_{\mathrm{N}}2$ reactions, the correct order of reactivity for the following compounds: ${\mathrm{CH}}_3\mathrm{Cl},{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Cl},({\mathrm{CH}}_3{)}_2\mathrm{CHCl}$ and $({\mathrm{CH}}_3{)}_3\mathrm{CCl}$ is:

Q9.The octahedral complex of a metal ion ${\mathrm{M}}^{3+}$ with four monodentate ligands ${\mathrm{L}}_1,{\mathrm{L}}_2,{\mathrm{L}}_3$ and ${\mathrm{L}}_4$ absorb wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of …

Q10.For the estimation of nitrogen, 1.4 g of organic compound was digested by Kjeldahl method and the evolved ammonia was absorbed in 60 mL of $\frac{\mathrm{M}}{10}$ sulphuric acid. The unreacted acid required 20 ml of $\frac{\mathrm{M}}{10}$ sodium hydroxide for complete neutraliza …

Q11.The equivalent conductance of NaCl at concentration C and at infinite dilution are ${\lambda }_{\mathrm{C}}$ and ${\lambda }_{\infty }$, respectively. The correct relationship between ${\lambda }_{\mathrm{C}}$ and ${\lambda }_{\infty }$ is given as:
(where the constant B is positive)

Q12.For the reaction, ${\mathrm{SO}}_{2(\mathrm{g})}+\frac{1}{2}{\mathrm{O}}_{2(\mathrm{g})}\rightleftharpoons {\mathrm{SO}}_{3(\mathrm{g})}$, if ${\mathrm{K}}_{\mathrm{P}}={\mathrm{K}}_{\mathrm{C}}(\mathrm{RT}{)}^{\mathrm{x}}$ where the symbols have usual meaning then the value of x is: (a …

Q13.In the reaction,

the product C is:

Q14.Sodium phenoxide when heated with CO₂ under pressure at 125°C yields a product which on acetylation produces C.

The major product C would be:

Q15.On heating an aliphatic primary amine with chloroform and ethanolic potassium hydroxide, the organic compound formed is:

Q16.The correct statement for the molecule, CsI₃ is:

Q17.The equation which is balanced and represents the correct product(s) is:

Q18.For which of the following molecule significant μ ≠ 0?
(a)

(b)

(c)

(d)

Q19.For the non-stoichiometric reaction 2A + B → C + D, the following kinetic data were obtained in three separate experiments, all at 298 K.
| Initial Concentration (A) | Initial Concentration (B) | Initial rate of formation of C (mol L⁻¹s⁻¹) ||---------------------------|-------- …

Q20.Which series of reactions correctly represents chemical reactions related to iron and its compound?

Q21.Considering the basic strength of amines in aqueous solution, which one has the smallest pKb value?

Q22.Which one of the following bases is not present in DNA?

Q23.The correct set of four quantum numbers for the valence electrons of rubidium atom (Z = 37) is:

Q24.The major organic compound formed by the reaction of 1,1,1-trichloroethane with silver powder is:

Q25.Given below are the half-cell reactions:
${\mathrm{Mn}}^{2+}+2{\mathrm{e}}^{-}⟶\mathrm{Mn};{\mathrm{E}}^0=-1.18\mathrm{V}$
$2\left({\mathrm{Mn}}^{3+}+{\mathrm{e}}^{-}⟶{\mathrm{Mn}}^{2+}\right);{\mathrm{E}}^0=+1.51\mathrm{V}$
The …

Q26.The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is $1:4$. The ratio of number of their molecule is:

Q27.Which one is classified as a condensation polymer?

Q28.Among the following oxoacids, the correct decreasing order of acid strength is:

Q29.For complete combustion of ethanol, ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}(\ell )+3{\mathrm{O}}_2(\mathrm{g})⟶2{\mathrm{CO}}_2(\mathrm{g})+3{\mathrm{H}}_2\mathrm{O}(\ell )$, the amount of heat produced as measured in bomb calorimeter, is …

Q30.The most suitable reagent for the conversion of $\mathrm{R}-{\mathrm{CH}}_2-\mathrm{OH}⟶\mathrm{R}-\mathrm{CHO}$ is:

Q1.The image of the line $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}$ in the plane $2x-y+z+3=0$ is the line

Q2.If the coefficients of $x^3$ and $x^4$ in the expansion of $(1+ax+b{x}^2)(1-2x{)}^{18}$ in powers of $x$ are both zero, then $(a,b)$ is equal to

Q3.If $a\in \mathbb{R}$ and the equation $-3(x-[x]{)}^2+2(x-[x])+a^2=0$ (where $[x]$ denotes the greatest integer $\le x$) has no integral solution, then all possible values of $a$ lie in the interval

Q4.If $[\vec{a}\times \vec{b}\vec{b}\times \vec{c}\vec{c}\times \vec{a}]=\lambda [\vec{a}\vec{b}\vec{c}{]}^2$, then $\lambda$ is equal to

Q5.The variance of first 50 even natural numbers is

Q6.A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is $45^{\circ }$. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to $30^{\circ }$. Then the speed (in m/ …

Q7.The integral ${\int }_0^{\pi }\sqrt{1+4{\sin }^2\frac{x}{2}-4\sin \frac{x}{2}}dx$ equals

Q8.The statement $\sim (p\leftrightarrow \sim q)$ is

Q9.If A is an $3\times 3$ non-singular matrix such that $A{A}^{\prime }=A^{\prime }A$ and $B=A^{-1}{A}^{\prime }$, then $B{B}^{\prime }$ equals

Q10.The integral $\int \left(1+x-\frac{1}{x}\right)e^{x+\frac{1}{x}}dx$ is equal to

Q11.If z is a complex number such that $|z|\ge 2$, then the minimum value of $\left|z+\frac{1}{2}\right|$

Q12.If $g$ is the inverse of a function $f$ and $f^{\prime }(x)=\frac{1}{1+x^5}$, then $g^{\prime }(x)$ is equal to

Q13.If $\alpha ,\beta \ne 0$, and $f(n)={\alpha }^n+{\beta }^n$ and $\left|\begin{array}{ccc}3& 1+f(1)& 1+f(2)\\ 1+f(1)& 1+f(2)& 1+f(3)\\ 1+f(2)& 1+f(3)& 1+f(4)\end{array}\right|=\mathrm{K}(1-\alpha {)}^2(1-\beta {)}^2(\alpha -\beta {)}^2$, then K is equal to

Q14.Let $f_K(x)=\frac{1}{k}\left({\sin }^{k}x+{\cos }^{k}x\right)$ where $x\in \mathrm{R}$ and $k\ge 1$. Then $f_4(x)-f_6(x)$ equals

Q15.Let $\alpha$ and $\beta$ be the roots of equation $p{x}^2+qx+r=0,p\ne 0$. If $p,q,r$ are in A.P. and $\frac{1}{\alpha }+\frac{1}{\beta }=4$, then the value of $|\alpha -\beta |$ is

Q16.Let A and B be two events such that $P(\overline{A\cup B})=\frac{1}{6},P(A\cap B)=\frac{1}{4}$ and $P(\bar{A})=\frac{1}{4}$, where $\bar{A}$ stands for the complement of the event A. Then the events A and B are

Q17.If $f$ and $g$ are differentiable functions in $[0,1]$ satisfying $\mathrm{f}(0)=2=g(1),g(0)=0$ and $f(1)=6$, then for some $\mathrm{c}\in ]0,1[$

Q18.Let the population of rabbits surviving at a time $t$ be governed by the differential equation $\frac{dp(t)}{dt}=\frac{1}{2}p(t)-200$. If $\mathrm{p}(0)=100$, then $p(t)$ equals

Q19.Let C be the circle with centre at $(1,1)$ and radius $=1$. If T is the circle centred at $(0,y)$, passing through origin and touching the circle C externally, then the radius of T is equal to

Q20.The area of the region described by $\mathrm{A}=\{(x,y):x^2+y^2\le 1$ and $y^2\le 1-x\}$ is

Q21.Let $a,b,c$ and d be non-zero numbers. If the point of intersection of the lines $4ax+2ay+c=0$ and $5bx+2by+d=0$ lies in the fourth quadrant and is equidistant from the two axes then

Q22.Let PS be the median of the triangle with vertices $\mathrm{P}(2,2),\mathrm{Q}(6,-1)$ and $\mathrm{R}(7,3)$. The equation of the line passing through $(1,-1)$ and parallel to PS is

Q23.${\lim }_{x\to 0}\frac{\sin \left(\pi {\cos }^{2}x\right)}{x^2}$ is equal to

Q24.If $\mathrm{X}=\left\{4^{\mathrm{n}}-3n-1:\mathrm{n}\in \mathrm{N}\right\}$ and $\mathrm{Y}=\{9(n-1):n\in \mathrm{N}\}$, where N is the set of natural numbers, then $\mathrm{X}\cup \mathrm{Y}$ is equal to

Q25.The locus of the foot of perpendicular drawn from the centre of the ellipse $x^2+3y^2=6$ on any tangent to it is

Q26.Three positive numbers from an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is

Q27.If $(10{)}^9+2(11{)}^1(10{)}^8+3(11{)}^2(10{)}^7+\dots +10(11{)}^9=k(10{)}^9$, then $k$ is equal to

Q28.The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^2=m^2+n^2$ is

Q29.The slope of the line touching both the parabolas $y^2=4x$ and $x^2=-32y$ is

Q30.If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x$, then