JEE Main 2018 · 08 Apr 2018 · Offline

Q1.Three concentric metal shells A, B and C of respective radii $a,b$ and $c$ ($a<b<c$) have surface charge densities $+\sigma ,-\sigma$ and $+\sigma$ respectively. The potential of shell B is :

Q2.Seven identical circular planar disks, each of mass $M$ and radius $R$ are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :

Q3.From a uniform circular disc of radius $R$ and mass 9 M , a small disc of radius $\frac{\mathrm{R}}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is :

Q4.The reading of the ammeter for a silicon diode in the given circuit is :

Q5.Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A . The intensity of light beyond B is found to be $\frac{\mathrm{I}}{2}$. Now another identical polarizer C is placed between A and B. The intensity beyond B is …

Q6.For an RLC circuit driven with voltage of amplitude $v_{\mathrm{m}}$ and frequency ${\omega }_{\mathrm{o}}=\frac{1}{\sqrt{\mathrm{LC}}}$ the current exibits resonance. The quality factor, Q is given by :

Q7.Two masses ${\mathrm{m}}_1=5\mathrm{kg}$ and ${\mathrm{m}}_2=10\mathrm{kg}$, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15 . The minimum weight $m$ that should …

Q8.In a collinear collision, a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after co …

Q9.A particle is moving with a uniform speed in a circular orbit of radius $R$ in a central force inversely proportional to the ${\mathrm{n}}^{\text{th }}$ power of $R$. If the period of rotation of the particle is T , then :

Q10.Two batteries with e.m.f. 12 V and 13 V are connected in parallel across a load resistor of $10\Omega$. The internal resistances of the two batteries are $1\Omega$ and $2\Omega$ respectively. The voltage across the load lies between :

Q11.In an a.c. circuit, the instantaneous e.m.f. and current are given by


In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively :

Q12.An EM wave from air enters a medium. The electric fields are
${\overrightarrow{\mathrm{E}}}_1={\mathrm{E}}_{01}\hat{x}\cos \left[2\pi \nu \left(\frac{z}{c}-\mathrm{t}\right)\right]$ in air and …

Q13.A telephonic communication service is working at carrier frequency of 10 GHz. Only $10\%$ of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz?

Q14.A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7\times 10^3$ kg/m${}^3$ and its Young's modulus is $9.27\times 10^{10}$ Pa. What will be the fundamental frequency of the longitudinal vibrations?

Q15.It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is $p_d$; while for its similar collision with carbon nucleus at rest, fractional loss of energy is $p_c$. The values of $p_d$ and $p_c$ are respectively:

Q16.The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $1.5\%$ and $1\%$, the maximum error in determining the density is:

Q17.Two moles of an ideal monoatomic gas occupies a volume V at $27^{\circ }$C. The gas expands adiabatically to a volume 2V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

Q18.A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass $m$ is placed on the sur …

Q19.A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant $K=\frac{5}{3}$ is inserted between the plates, the magnitude of the induced charge will be:

Q20.The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is $B_1$. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_2$. The ratio $\frac{B_1}{B_2}$ is:

Q21.An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let ${\lambda }_n$, ${\lambda }_g$ be the de Broglie wavelength of the electron in the $n^{\text{th}}$ state and the ground state respectively. Let ${\Lambda }_n$ be the wavelength of the …

Q22.The mass of a hydrogen molecule is $3.32\times 10^{-27}$ kg. If $10^{23}$ hydrogen molecules strike, per second, a fixed wall of area $2$ cm${}^2$ at an angle of $45^{\circ }$ to the normal, and rebound elastically with a speed of $10^3$ m/s, then the pressure on the wall is nearly …

Q23.All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

Q24.An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $r_e$, $r_p$, $r_{\alpha }$ respectively in a uniform magnetic field $B$. The relation between $r_e$, $r_p$, $r_{\alpha }$ is:

Q25.On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is $1\mathrm{k}\Omega$. How much was the resistance on the left slot before interchanging the resistances?

Q26.In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of $5\Omega$, a balance is found when the cell is connected acro …

Q27.If the series limit frequency of the Lyman series is ${\nu }_L$, then the series limit frequency of the Pfund series is:

Q28.The angular width of the central maximum in a single slit diffraction pattern is $60^{\circ }$. The width of the slit is $1\mu \mathrm{m}$. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a sc …

Q29.A particle is moving in a circular path of radius a under the action of an attractive potential $\mathrm{U}=-\frac{\mathrm{k}}{2{\mathrm{r}}^2}$. Its total energy is:

Q30.A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of $10^{12}/\sec$. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avagadro number …

Q1.For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point ?

Q2.Hydrogen peroxide oxidises ${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{4-}$ to ${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{3-}$ in acidic medium but reduces ${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{3-}$ to ${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{4-}$ in alkaline medium. Th …

Q3.Which of the following compounds will be suitable for Kjeldahl's method for nitrogen estimation ?

Q4.Glucose on prolonged heating with HI gives :

Q5.An alkali is titrated against an acid with methyl orange as indicator, which of the following is a correct combination ?
| (3) | Strong | S …

Q6.The predominant form of histamine present in human blood is (${\mathrm{pK}}_{\mathrm{a}}$, Histidine=6.0)

Q7.The increasing order of basicity of the following compounds is :
(a) (see structure)
(b) (see structure)
(c) (see structure)
(d) (see structure)

Q8.Which of the following lines correctly show the temperature dependence of equilibrium constant, K, for an exothermic reaction?

Q9.How long (approximate) should water be electrolysed by passing through 100 amperes current so that the oxygen released can completely burn 27.66 g of diborane ?
(Atomic weight of $\mathrm{B}=10.8\mathrm{u}$)

Q10.Consider the following reaction and statements :
${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_4{\mathrm{Br}}_2\right]}^{+}+{\mathrm{Br}}^{-}\to \left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_3{\mathrm{Br}}_3\right]+{\mathrm{NH}}_3$
(I) Two isomers are produced if the …

Q11.Phenol reacts with methyl chloroformate in the presence of NaOH to form product A. A reacts with ${\mathrm{Br}}_2$ to form product B. $A$ and $B$ are respectively :

Q12.An aqueous solution contains an unknown concentration of ${\mathrm{Ba}}^{2+}$. When 50 mL of a 1 M solution of ${\mathrm{Na}}_2{\mathrm{SO}}_4$ is added, ${\mathrm{BaSO}}_4$ just begins to precipitate. The final volume is 500 mL . The solubility product of ${\mathrm{BaSO}}_4$ is …

Q13.At $518^{\circ }\mathrm{C}$, the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of 363 Torr, was 1.00 Torr ${\mathrm{s}}^{-1}$ when $5\%$ had reacted and 0.5 Torr ${\mathrm{s}}^{-1}$ when $33\%$ had reacted. The order of the reaction is …

Q14.The combustion of benzene (l) gives ${\mathrm{CO}}_2(\mathrm{g})$ and ${\mathrm{H}}_2\mathrm{O}(\mathrm{l})$. Given that heat of combustion of benzene at constant volume is $-3263.9\mathrm{kJ}{\mathrm{mol}}^{-1}$ at $25^{\circ }\mathrm{C}$; heat of combustion (in …

Q15.The ratio of mass percent of C and H of an organic compound $\left({\mathrm{C}}_{\mathrm{X}}{\mathrm{H}}_{\mathrm{Y}}{\mathrm{O}}_{\mathrm{Z}}\right)$ is $6:1$. If one molecule of the above compound ( ${\mathrm{C}}_{\mathrm{X}}{\mathrm{H}}_{\mathrm{Y}}{\mathrm{O}}_{\mathrm{Z}}$ ) …

Q16.The trans-alkenes are formed by the reduction of alkynes with :

Q17.When metal ' M ' is treated with NaOH , a white gelatinous precipitate ' $X$ ' is obtained, which is soluble in excess of NaOH . Compound ' X ' when heated strongly gives an oxide which is used in chromatography as an adsorbent. The metal ' M ' is :

Q18.According to molecular orbital theory, which of the following will not be a viable molecule?

Q19.Phenol on treatment with ${\mathrm{CO}}_2$ in the presence of NaOH followed by acidification produces compound $X$ as the major product. $X$ on treatment with ${\left({\mathrm{CH}}_3\mathrm{CO}\right)}_2\mathrm{O}$ in the presence of catalytic amount of …

Q20.Which of the following compounds contain(s) no covalent bond(s) ?
$\mathrm{KCl},{\mathrm{PH}}_3,{\mathrm{O}}_2,{\mathrm{B}}_2{\mathrm{H}}_6,{\mathrm{H}}_2{\mathrm{SO}}_4$

Q21.Which type of 'defect' has the presence of cations in the interstitial sites ?

Q22.The compound that does not produce nitrogen gas by the thermal decomposition is :

Q23.An aqueous solution contains $0.10\mathrm{M}{\mathrm{H}}_2\mathrm{S}$ and 0.20 M HCl . If the equilibrium constants for the formation of ${\mathrm{HS}}^{-}$from ${\mathrm{H}}_2\mathrm{S}$ is $1.0\times 10^{-7}$ and that of ${\mathrm{S}}^{2-}$ from ${\mathrm{HS}}^{-}$ …

Q24.The oxidation states of Cr in $\left[\mathrm{Cr}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]{\mathrm{Cl}}_3,\left[\mathrm{Cr}{\left({\mathrm{C}}_6{\mathrm{H}}_6\right)}_2\right]$, and …

Q25.The recommended concentration of fluoride ion in drinking water is up to 1 ppm as fluoride ion is required to make teeth enamel harder by converting $\left[3{\mathrm{Ca}}_3{\left({\mathrm{PO}}_4\right)}_2\cdot \mathrm{Ca}(\mathrm{OH}{)}_2\right]$ to :

Q26.Which of the following salts is the most basic in aqueous solution?

Q27.Total number of lone pair of electrons in ${\mathrm{I}}_3^{-}$ion is :

Q28.Which of the following are Lewis acids?

Q1.If the curves $y^2=6x,9x^2+b{y}^2=16$ intersect each other at right angles, then the value of $b$ is :

Q2.Let $\overrightarrow{\mathrm{u}}$ be a vector coplanar with the vectors $\overrightarrow{\mathrm{a}}=2\hat{i}+3\hat{j}-\hat{k}$ and $\overrightarrow{\mathrm{b}}=\hat{j}+\hat{k}$. If $\overrightarrow{\mathrm{u}}$ is perpendicular to $\vec{a}$ and $\vec{u}\cdot \vec{b}=24$, then …

Q3.For each $t\in \mathbf{R}$, let $[t]$ be the greatest integer less than or equal to $t$. Then
${\lim }_{x\to 0+}x\left(\left[\frac{1}{x}\right]+\left[\frac{2}{x}\right]+\dots ..+\left[\frac{15}{x}\right]\right)$

Q4.If ${\mathrm{L}}_1$ is the line of intersection of the planes $2x-2y+3z-2=0,x-y+z+1=0$ and ${\mathrm{L}}_2$ is the line of intersection of the planes $x+2y-z-3=0,3x-y+2z-1=0$, then the distance of the origin from the plane, containing the lines ${\mathrm{L}}_1$ and …

Q5.The value of ${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}\frac{{\sin }^{2}x}{1+2^x}\mathrm{d}x$ is :

Q6.Let $\mathrm{g}(x)=\cos x^2,f(x)=\sqrt{x}$, and $\alpha ,\beta (\alpha <\beta )$ be the roots of the quadratic equation $18x^2-9\pi x+{\pi }^2=0$. Then the area (in sq. units) bounded by the curve $y=\left(g_{\circ }f\right)(x)$ and the lines $x=\alpha ,x=\beta$ and …

Q7.If sum of all the solutions of the equation $8\cos x\cdot \left(\cos \left(\frac{\pi }{6}+x\right)\cdot \cos \left(\frac{\pi }{6}-x\right)-\frac{1}{2}\right)=1$ in $[0,\pi ]$ is $\mathrm{k}\pi$, then k is equal to :

Q8.Let $f(x)=x^2+\frac{1}{x^2}$ and $\mathrm{g}(x)=x-\frac{1}{x}$, $x\in \mathbf{R}-\{-1,0,1\}$. If $\mathrm{h}(x)=\frac{f(x)}{\mathrm{g}(x)}$, then the local minimum value of $\mathrm{h}(x)$ is :

Q9.The integral
$\int \frac{{\sin }^{2}x{\cos }^{2}x}{{\left({\sin }^{5}x+{\cos }^{3}x{\sin }^{2}x+{\sin }^{3}x{\cos }^{2}x+{\cos }^{5}x\right)}^2}\mathrm{d}x$ is equal to :

Q10.A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn bal …

Q11.Let the orthocentre and centroid of a triangle be $\mathrm{A}(-3,5)$ and $\mathrm{B}(3,3)$ respectively. If $C$ is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is :

Q12.If the tangent at $(1,7)$ to the curve $x^2=y-6$ touches the circle $x^2+y^2+16x+12y+\mathrm{c}=0$ then the value of c is :

Q13.If $\alpha ,\beta \in \mathbf{C}$ are the distinct roots, of the equation $x^2-x+1=0$, then ${\alpha }^{101}+{\beta }^{107}$ is equal to :

Q14.PQR is a triangular park with $\mathrm{PQ}=\mathrm{PR}=200\mathrm{m}$. A T.V. tower stands at the mid-point of QR . If the angles of elevation of the top of the tower at P, Q and R are respectively $45^{\circ },30^{\circ }$ and $30^{\circ }$, then the height of the tower (i …

Q15.If ${\sum }_{i=1}^9\left(x_i-5\right)=9$ and ${\sum }_{i=1}^9{\left(x_i-5\right)}^2=45$, then the standard deviation of the 9 items $x_1,x_2,\dots ..,x_9$ is :

Q16.The sum of the co-efficients of all odd degree terms in the expansion of ${\left(x+\sqrt{x^3-1}\right)}^5+{\left(x-\sqrt{x^3-1}\right)}^5,(x>1)$ is :

Q17.Tangents are drawn to the hyperbola $4x^2-y^2=36$ at the points P and Q . If these tangents intersect at the point $\mathrm{T}(0,3)$ then the area (in sq. units) of $△\mathrm{PTQ}$ is :

Q18.From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

Q19.If the system of linear equations

has a non-zero solution $(x,y,z)$, then $\frac{xz}{y^2}$ is equal to :

Q20.If $\left|\begin{array}{rrr}x-4& 2x& 2x\\ 2x& x-4& 2x\\ 2x& 2x& x-4\end{array}\right|=(\mathrm{A}+\mathrm{B}x)(x-\mathrm{A}{)}^2$, then the ordered pair $(\mathrm{A},\mathrm{B})$ is equal to :

Q21.Two sets A and B are as under : $\mathrm{A}=\{(\mathrm{a},\mathrm{b})\in \mathbf{R}\times \mathbf{R}:|\mathrm{a}-5|<1$ and $|\mathrm{b}-5|<1\};B=\{(a,b)\in \mathbf{R}\times \mathbf{R}:4(a-6{)}^2+9(b-5{)}^2\le 36\}$. Then :

Q22.Tangent and normal are drawn at $\mathrm{P}(16,16)$ on the parabola $y^2=16x$, which intersect the axis of the parabola at A and B , respectively. If C is the centre of the circle through the points $\mathrm{P},\mathrm{A}$ and B and $\angle \mathrm{CPB}=\theta$, then …

Q23.Let $\mathrm{S}=\{\mathrm{t}\in \mathbf{R}:f(x)=|x-\pi |\cdot \left({\mathrm{e}}^{|x|}-1\right)\sin |x|$ is not differentiable at t $\}$. Then the set S is equal to :

Q24.The Boolean expression
$\sim (\mathrm{p}\vee \mathrm{q})\vee (\sim \mathrm{p}\wedge \mathrm{q})$ is equivalent to :

Q25.A straight line through a fixed point $(2,3)$ intersects the coordinate axes at distinct points P and Q . If O is the origin and the rectangle OPRQ is completed, then the locus of R is :

Q26.Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series
$1^2+2\cdot 2^2+3^2+2\cdot 4^2+5^2+2\cdot 6^2+\dots .$.

If $B-2A=100\lambda$, then $\lambda$ is equal to :

Q27.Let $y=y(x)$ be the solution of the differential equation
$\sin x\frac{\mathrm{d}y}{\mathrm{d}x}+y\cos x=4x,x\in (0,\pi )$. If
$y\left(\frac{\pi }{2}\right)=0$, then $y\left(\frac{\pi }{6}\right)$ is equal to :

Q28.The length of the projection of the line segment joining the points $(5,-1,4)$ and $(4,-1,3)$ on the plane, $x+y+z=7$ is :

Q29.Let $\mathrm{S}=\{x\in \mathbf{R}:x⩾0$ and
$2|\sqrt{x}-3|+\sqrt{x}(\sqrt{x}-6)+6=0\}$. Then S :

Q30.Let $a_1,a_2,a_3,\dots .,a_{49}$ be in A.P. such that ${\sum }_{k=0}^{12}{a}_{4k+1}=416$ and $a_9+a_{43}=66$. If ${\mathrm{a}}_1^2+{\mathrm{a}}_2^2+\dots ..+{\mathrm{a}}_{17}^2=140\mathrm{m}$, then m is equal to :