JEE Main 2017 (Offline)

Paper was held on
Sun, Apr 2, 2017 9:30 AM

## Chemistry

1 gram of a carbonate (M2CO3) on treatment with excess HCl produces 0.01186 mole of CO2. The molar mass of M2CO3 in g mo

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The radius of the second Bohr orbit for hydrogen atom is:
(Planck’s Const. h = 6.6262 × 10-34 Js; mass of electron = 9.1

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Which of the following species is not paramagnetic?

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A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest
approach

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The most abundant elements by mass in the body of a healthy human adult are: Oxygen (61.4%); Carbon
(22.9%), Hydrogen (1

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$$\Delta $$U is equal to :

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The group having isoelectronic species is:

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The freezing point of benzene decreases by 0.450C when 0.2 g of acetic acid is added to 20g of benzene. If
acetic acid a

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Given, $${C_{(graphite)}} + {O_2} \to C{O_2}(g)$$;
$${\Delta _r}{H^o}$$ = - 393.5 kJ mol-1
$${{\rm H}_2}(g)$$ + $${1 \ov

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Given
$$E_{C{l_2}/C{l^ - }}^o$$ = 1.36 V, $$E_{C{r^{3 + }}/Cr}^o$$ = - 0.74 V
$$E_{C{r_2}{O_7}^{2 - }/C{r^{3 + }}}^o$$ =

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pKa of a weak acid (HA) and pKb of a weak base (BOH) are 3.2 and 3.4, respectively. The pH of their salt (AB) solution i

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Which of the following reactions is an example of a redox reaction?

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Two reactions R1 and R2 have identical pre-exponential factors. Activation energy of R1 exceeds that of R2 by 10 kJ mol–

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The Tyndall effect is observed only when following conditions are satisfied:
(a) The diameter of the dispersed particles

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Both lithium and magnesium display several similar properties due to the diagonal relationship; however,
the one which i

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In the following reactions, ZnO is respectively acting as a/an :
(a) ZnO + Na2O $$\to$$ Na2ZnO2
(b) ZnO + CO2 $$\to$$ Zn

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The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are :

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On treatment of 100 mL of 0.1 M solution of CoCl3. 6H2O with excess AgNO3; 1.2 $$\times$$ 1022 ions are precipitated. Th

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A water sample has ppm level concentration of following anions
F- = 10; $$SO_4^{2-}$$ = 100; $$NO_3^-$$ = 50
The anion/a

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Which of the following molecules is least resonance stabilized?

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Which of the following compounds will form significant amount of meta product during mono-nitration
reaction?

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The increasing order of the reactivity of the following halides for the SN1 reaction is :

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3-Methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product. The number
of possible stere

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Which of the following, upon treatment with tert-BuONa followed by addition of bromine water, fails to
decolorize the co

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The major product obtained in the following reaction is :

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Sodium salt of an organic acid ‘X’ produces effervescence with conc. H2SO4. ‘X’ reacts with the acidified
aqueous CaCl2

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The major product obtained in the following reaction is :

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The correct sequence of reagents for the following conversion will be :

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The formation of which of the following polymers involves hydrolysis reaction?

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Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution?

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## Mathematics

The function $$f:R \to \left[ { - {1 \over 2},{1 \over 2}} \right]$$ defined as
$$f\left( x \right) = {x \over {1 + {x^2

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Let $$\omega $$ be a complex number such that 2$$\omega $$ + 1 = z where z = $$\sqrt {-3} $$. If
$$\left| {\matrix{
1

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If $$A = \left[ {\matrix{
2 & { - 3} \cr
{ - 4} & 1 \cr
} } \right]$$,
then adj(3A2 + 12A) is equal

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If S is the set of distinct values of 'b' for which the following system of linear equations
x + y + z = 1
x + ay + z =

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If for a positive integer n, the quadratic equation
$$x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \ri

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A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are
ladies and 4 are

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The value of $$\left( {{}^{21}{C_1} - {}^{10}{C_1}} \right) + \left( {{}^{21}{C_2} - {}^{10}{C_2}} \right) + \left( {{}^

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Let $$a$$, b, c $$ \in R$$. If $$f$$(x) = ax2 + bx + c is such that
$$a$$ + b + c = 3 and $$f$$(x + y) = $$f$$(x) + $$f$

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For any three positive real numbers a, b and c,
9(25$${a^2}$$ + b2) + 25(c2 - 3$$a$$c) = 15b(3$$a$$ + c).
Then

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$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\cot x - \cos x} \over {{{\left( {\pi - 2x} \right)}^3}}}$$ equals

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If for $$x \in \left( {0,{1 \over 4}} \right)$$, the derivatives of
$${\tan ^{ - 1}}\left( {{{6x\sqrt x } \over {1 - 9{x

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Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the
maximum area

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The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes
through the po

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The integral $$\int\limits_{{\pi \over 4}}^{{{3\pi } \over 4}} {{{dx} \over {1 + \cos x}}} $$ is equal to

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Let $${I_n} = \int {{{\tan }^n}x\,dx} ,\,\left( {n > 1} \right).$$
If $${I_4} + {I_6}$$ = $$a{\tan ^5}x + b{x^5} + C$

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The area (in sq. units) of the region
$$\left\{ {\left( {x,y} \right):x \ge 0,x + y \le 3,{x^2} \le 4y\,and\,y \le 1 + \

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If $$\left( {2 + \sin x} \right){{dy} \over {dx}} + \left( {y + 1} \right)\cos x = 0$$ and y(0) = 1,
then $$y\left( {{\p

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The radius of a circle, having minimum area, which touches the curve y = 4 – x2 and the lines, y = |x| is :

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A hyperbola passes through the point P$$\left( {\sqrt 2 ,\sqrt 3 } \right)$$ and has foci at $$\left( { \pm 2,0} \right)

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If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to the line,
$${x \over 1} =

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Let k be an integer such that the triangle with vertices (k, – 3k), (5, k) and (–k, 2) has area 28 sq. units. Then the o

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The distance of the point (1, 3, – 7) from the plane passing through the point (1, –1, – 1), having normal
perpendicular

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The eccentricity of an ellipse whose centre is at the origin is $${1 \over 2}$$. If one of its directrices is x = – 4, t

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Let $$\overrightarrow a = 2\widehat i + \widehat j -2 \widehat k$$ and $$\overrightarrow b = \widehat i + \widehat j$$

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For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P
(Exactly one of C or

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If two different numbers are taken from the set {0, 1, 2, 3, ........, 10}; then the probability that their sum as
well

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A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with
replacement, then the vari

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Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point
on the ground

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If $$5\left( {{{\tan }^2}x - {{\cos }^2}x} \right) = 2\cos 2x + 9$$,
then the value of $$\cos 4x$$ is :

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The following statement
$$\left( {p \to q} \right) \to \left[ {\left( { \sim p \to q} \right) \to q} \right]$$ is :

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## Physics

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs
time?

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A body of mass m = 10–2 kg is moving in a medium and experiences a frictional force F = –kv2. Its initial speed is v0 =

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A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done
by the fo

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The moment of inertia of a uniform cylinder of length $$l$$ and radius R about its perpendicular bisector is $$I$$.
What

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A slender uniform rod of mass M and length $$l$$ is pivoted at one end so that it
can rotate in a vertical plane (see fi

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A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his
density remains sa

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The variation of acceleration due to gravity $$g$$ with distance d from centre of the earth is best represented by
(R =

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A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm,
filled with 17

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An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the
bulk modulu

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The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressur

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CP and Cv are specific heats at constant pressure and constant volume respectively. It is observed that CP – Cv = a for

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A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of
equilibrium

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A capacitance of 2 $$\mu $$F is required in an electrical circuit across a potential difference of 1.0 kV. A large
numbe

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An electric dipole has a fixed dipole moment $$\overrightarrow p $$, which makes angle $$\theta$$ with respect to x-axis

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In the given circuit diagram when the current reaches steady state in the
circuit, the charge on the capacitor of capaci

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Which of the following statements is false?

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In the given circuit, the current in each resistance is:

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A magnetic needle of magnetic moment 6.7 $$\times$$ 10-2 A m2 and moment of inertia 7.5 $$\times$$ 10-6 kg m2 is
perform

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When a current of 5 mA is passed through a galvanometer having a coil of resistance 15$$\Omega $$, it shows full
scale d

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In a coil of resistance 100 $$\Omega $$, a current is induced by changing
the magnetic flux through it as shown in the f

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An observer is moving with half the speed of light towards a stationary microwave source emitting waves
at frequency 10

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In a Young’s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away.
A beam of ligh

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A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15cm from a converging
lens of magnitud

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An electron beam is accelerated by a potential difference V to hit a metallic target to produce X–rays. It
produces cont

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A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The
collision is

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Some energy levels of a molecule are shown in the figure. The
ratio of the wavelengths r = $${{\lambda _1}}$$/$${{\lambd

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A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At
sometime t, the

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In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and
the output v

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In amplitude modulation, sinusoidal carrier frequency used is denoted by $${\omega _c}$$ and the signal frequency is
den

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The following observations were taken for determining surface tension T of water by capillary method:
diameter of capill

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