JEE Main 2019 (Online) 10th January Morning Slot

Paper was held on
Thu, Jan 10, 2019 3:30 AM

## Chemistry

The total number of isotopes of hydrogen and number of radioactive isotopes among them, respectively, are :

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Which of the following is not an example of heterogenous catalytic reaction ?

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A process has $$\Delta $$H = 200 J mol–1 and $$\Delta $$S = 40 JK–1 mol–1. Out of the values given below, choose the min

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A mixture of 100 m mol of Ca(OH)2 and 2 g of sodium sulphate was dissolved in water and the volume was made up to 100 mL

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Hall- Heroult's process is given by

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Which premitive unit cell has unequal edge lengths (a $$ \ne $$ b $$ \ne $$ c) and all axial angles different from 90o ?

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The metal used for marking X–ray tube window is :

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The electronegativity of aluminium is similar to :

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The values of Kp/Kc for the following reactions at 300 K are, respectively : (At 300 K, RT = 24.62 dm3 atm mol–1)
N2(g)

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If dichloromethane (DCM) and water (H2O) are used for differential extraction, which one of the following statements is

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The chemical nature of hydrogen peroxide is :

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Wilkinson catalyst is : (Et = C2H5)

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Two pi and half sigma bonds are present in :

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The effect of lanthanoid contraction in the lanthanoid series of elements by and large means :

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Water filled in two glasses A and B have BOD values of 10 and 20, respectively. The correct statement regarding them, is

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Liquids A and B form an ideal solution in the entire composition range. At 350 K, the vaapor pressures of pure A and pur

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Consider the following reduction processes :
Zn2+ + 2e– $$ \to $$ Zn(s) ; Eo = – 0.76 V
Ca2+ + 2e– $$ \to $$ Ca(s); Eo =

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The type of hybridisation and number of lone pair (s) of electrons of Xe in XeOF4, respectively, are:

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Which hydrogen in compound (E) is easily replaceable during bromination reaction in presence of light ?

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The increasing order of the pKa values of the following compounds is :

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Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from

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Consider the given plots for a reaction obeying Arrhenius equation (0oC < T < 300oC) : (K and Ea are rate constant

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Which dicarboxylic acid in presence of a dehydrating agent is least reactive to give an anhydride?

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The major product of the following reaction is

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The major product 'X' formed in the following reaction is :

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The correct structure of product 'P' in the following reactions is :

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The major product of the following reaction is :

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The decreasing order of ease of alkaline hydrolysis for the following esters in

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The total number of isomers for a square planar complex [M(F)(Cl)(SCN)(NO2)] is

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The major product formed in the reaction given below will be :

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## Mathematics

In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is

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Let $$\overrightarrow a = 2\widehat i + {\lambda _1}\widehat j + 3\widehat k,\,\,$$ $$\overrightarrow b =

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Consider the statement : "P(n) : n2 – n + 41 is prime". Then which one of the following is true ?

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If a circle C passing through the point (4, 0) touches the circle x2 + y2 + 4x – 6y = 12 externally at the point (1, – 1

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If the parabolas y2 = 4b(x – c) and y2 = 8ax have a common normal, then which on of the following is a valid choice fo

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The plane passing through the point (4, –1, 2) and parallel to the lines $${{x + 2} \over 3} = {{y - 2} \over

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Let n $$ \ge $$ 2 be a natural number and $$0 < \theta < {\pi \over 2}.$$ Then $$\int {{{{{\left( {{{\sin }^n}\t

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The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, t

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If the system of equations
x + y + z = 5
x + 2y + 3z = 9
x + 3y + az = $$\beta $$
has infinitely many solutions, then $$

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If 5, 5r, 5r2 are the lengths of the sides of a triangle, then r cannot be equal to -

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An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers o

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Let f : R $$ \to $$ R be a function such that f(x) = x3 + x2f'(1) + xf''(2) + f'''(3), x $$ \in $$ R. Then f(2) equals

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The equation of a tangent to the hyperbola 4x2 – 5y2 = 20 parallel to the line x – y = 2 is -

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If $${{dy} \over {dx}} + {3 \over {{{\cos }^2}x}}y = {1 \over {{{\cos }^2}x}},\,\,x \in \left( {{{ - \pi } \over 3

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The shortest distance between the point $$\left( {{3 \over 2},0} \right)$$ and the curve y = $$\s

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Consider a triangular plot ABC with sides AB = 7m, BC = 5m and CA = 6m. A vertical lamp-post at the mid point D of AC su

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Let $${\rm I} = \int\limits_a^b {\left( {{x^4} - 2{x^2}} \right)} dx.$$ If I is minimum then the ordere

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Let z1 and z2 be any two non-zero complex numbers such that $$3\left| {{z_1}} \right| = 4\left| {{z_2}} \rig

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If $${\sum\limits_{i = 1}^{20} {\left( {{{{}^{20}{C_{i - 1}}} \over {{}^{20}{C_i} + {}^{20}{C_{i - 1}}}}} \ri

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A point P moves on the line 2x – 3y + 4 = 0. If Q(1, 4) and R (3, – 2) are fixed points, then the locus of the centroid

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For each t $$ \in $$ R , let [t] be the greatest integer less than or equal to t
Then $$\mathop {\lim }\limit

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If the area enclosed between the curves y = kx2 and x = ky2, (k > 0), is 1 square unit. Then k is -

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Consider the quadratic equation (c – 5)x2 – 2cx + (c – 4) = 0, c $$ \ne $$ 5. Let S be the set of all integral values of

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The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is -

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If the line 3x + 4y – 24 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of th

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Let d $$ \in $$ R, and
$$A = \left[ {\matrix{
{ - 2} & {4 + d} & {\left( {\sin \theta } \rig

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If the third term in the binomial expansion of $${\left( {1 + {x^{{{\log }_2}x}}} \right)^5}$$ equals 2560, then a possi

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Let $$f\left( x \right) = \left\{ {\matrix{
{\max \left\{ {\left| x \right|,{x^2}} \right\}} & {\left|

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Let A be a point on the line $$\overrightarrow r = \left( {1 - 3\mu } \right)\widehat i + \left( {\mu - 1} \right)\wid

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The sum of all values of $$\theta $$ $$ \in $$$$\left( {0,{\pi \over 2}} \right)$$ satisfying sin2 2$$\theta $$ + cos4

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## Physics

Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they ar

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A heat source at T = 103 K is connected to another heat reservoir at T = 102 K by a copper slab which is 1 mthick. Given

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A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from

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A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximum dista

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A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered b

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In the cube of side ‘a’ shown in the figure, the vector from the central point of the face ABOD to the central point of

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To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rot

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A parallel plate capacitor is of area 6 cm2
and a separation 3 mm. The gap is filled with three dielectric
materials of

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A magnet of total magnetic moment 10-2$${\widehat i}$$A-m2 is placed in a time varying magnetic field, B$${\widehat i}$$

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Water flows into a large tank with flat bottom at the rate of 10–4m3s–1. Water is also leaking out of a hole ofarea 1 cm

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In a Young’s double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle $${1 \over {40}}

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A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There is a unif

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The density of a material in SI units is 128 kg m–3
. In certain units in which the unit of length is 25 cm and the unit

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Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600

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A uniform metallic wire has a resistance of 18 $$\Omega $$ and is bent into an equilateral triangle. Then, the resistanc

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An insulating thin rod of length $$l$$ has a linear charge density $$\rho \left( x \right)$$ = $${\rho _0}{x \over l}$$

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A plano convex lens of refractive index $$\mu $$1 and focal length ƒ1 is kept in contact with another plano concave lens

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In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To r

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A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vi

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A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assumi

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A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be pas

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If the magnetic field of a plane electromagnetic wave is given by (the speed of light = 3 × 108 B = 100 × 10–6
sin $$\l

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A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surf

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A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0

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Two electric dipoles, A, B with respective dipole moments $${\overrightarrow d _A} = - 4qai$$ and $${\overrightarrow d

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A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in figure

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In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing through resistance R1 an

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To get output 1 at R, for the given logic gate circuit the input values must be

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Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see

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A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf $$\varepsilon $$ and internal r

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