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JEE Main2019

JEE Main 2019

90 questions with step-by-step solutions. All free.

Physics

  1. Q1 A gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat flow into the system in path ADB is : …
  2. Q2 A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to : …
  3. Q3 A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time,
  4. Q4 Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio: …
  5. Q5 An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is , then : …
  6. Q6 A mixture of 2 moles of helium gas (atomic mass= 4 u), and 1 mole of argon gas (atomic mass= 40 u) is kept at 300 K in a container. The ratio of their rms speed
  7. Q7When the switch S, in the circuit shown, is closed, then the value of current will be :
  8. Q8A resistance is shown in the figure. Its value and tolerance are given respectively by:
  9. Q9 A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The coactivity of the bar magnet is : …
  10. Q10 A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion . It is observed that an external compressive force F, is applied on each of its …
  11. Q11 A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is: …
  12. Q12 Three charges +Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by + Q, placed at x= 0, is zero, then value of q is: …
  13. Q13 A conducting circular loop made of a thin wire, has area 3.5 × 10–3 m2 and resistance 10. It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T)sin(50t). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to: …
  14. Q14 Two masses m and are connected at the two ends of a massless rigid rod of length …
  15. Q15A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is:
  16. Q16 A parallel plate capacitor is made of two square plates of side 'a', separated by a distance d(d<<a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is: …
  17. Q17 Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an n-type semiconductor, the density of electrons is1019m–3 and their mobility is 1.6 m2/(V.s) then the resistivity of the semiconductor (since it is an n-type semiconductor contribution of holes is ignored) is close to: …
  18. Q18 If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is : …
  19. Q19 A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? …
  20. Q20 Temperature difference of 120°C is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length
  21. Q21 A heavy ball of mass M is suspended from the ceiling of a car by a light string of mass m(m<<M). When the car is at rest, the speed of transverse waves in the string is 60 ms–1. When the car has acceleration a, the wave-speed increases to 60.5 ms–1. The value of a, in terms of gravitational acceleration g, is closest to: …
  22. Q22 A sample of radioactive material A, that has an activity of 10 mCi (1 Ci = 3.7 × 1010 decays/s),has twice the number of nuclei as another sample of a different radioactive material B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively : …
  23. Q23 Consider a tank made of glass(refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index ,. A student finds that, irrespective of what the incident angle (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of is : …
  24. Q24 An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d»a). If the loop applies a force F on the wire then: …
  25. Q25 Surface of certain metal is first illuminated with light of wavelength =350 nm and then, by light of wavelength
  26. Q26A particle is moving with a velocity where K is a constant. The general equation for its path is:
  27. Q27 A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is : …
  28. Q28 For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its centre. The value of h is: …
  29. Q29 Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M. Block A is given an brutal speed v towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically
  30. Q30 Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross section 5 mm2,is v. If the electron density in copper is 9 ×1028/m3 the value of v in mm/s is close to (Take charge of electron to be =1.6 × 10–19C) …

Chemistry

  1. Q1Major product of the following reaction is :
  2. Q2Which one of the following statements regarding Henry's law not correct ?
  3. Q3The correct decreasing order for acid strength is :-
  4. Q4 Two complexes [Cr(H2O6)Cl3] (A) and [Cr(NH3)6]Cl3 (B) are violet and yellow coloured, respectively. The incorrect statement regarding them is : …
  5. Q5 Adsorption of a gas follows Freundlich adsorption isotherm. In the given plot, x is the mass of the gas adsorbed on mass m of the adsorbent at pressure p.
  6. Q6 Correct statements among a to d regarding silicones are: (1) They are polymers with hydrophobic character (2) They are biocompatible. (3) In general, they have high thermal stability and low dielectric strength. (4) Usually, they are resistant to oxidation and used as greases. …
  7. Q7 For emission line of atomic hydrogen from ni = 8 to nf = the plot of wave number
  8. Q8The major product the following reaction is :
  9. Q9The alkaline earth metal nitrate that does not crystallize with water molecules, is:
  10. Q10The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexes is :
  11. Q1120 mL of 0.1 MH2SO4  solution is added to 30mL of 0.2 M NH4OH solution. The pH of the resultant mixture is: [pkb of NH4OH = 4.7].
  12. Q12 0.5 moles of gas A and x moles of gas B exert pressure of 200 Pa in a a container of volume 10 m3  at 1000 K. given R is the gas constant in JK-1 mol-1m, x is: …
  13. Q13In general, the properties that decrease and increase down a group in the periodic table, respectively, are :
  14. Q14 Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures T1 and T2 (T1 < T2). The correct graphical depiction of the dependence of work done (w) on the final volume (V) is: …
  15. Q15The major product of following reaction is :?
  16. Q16A solution of sodium sulfate contains 92 g of Na+ ions per kilogram of water. The molality of Na+ ions in that solution in mol kg.1 is:
  17. Q17 A water sample has ppm level concentration of the following metals: Fe= 0.2; Mn = 5.0; Cu = 3.0;Zn = 5.0. The metal that makes the water sample unsuitable drinking is : …
  18. Q18The increasing order of pKa of the following amino acids in aqueous solution is : Gly, Asp, Lys, Arg
  19. Q19According to molecular orbital theory, which of the following is true with respect to and ?
  20. Q20 The following results were obtained during kinetic studies of the reaction : 2A + B Products The time (in minutes) required to consume half of A is : …
  21. Q21The major product of the following reaction is:
  22. Q22Arrange the following amines in the decreasing order of basicity:
  23. Q23Which amongst the following is the strongest acid ?
  24. Q24 The anodic half-cell of lead-acid battery is recharged using electricity of 0.05 Faraday. The amount of PbSO4 electrolyzed in g during the process in : (Molar mass of PbSO4 = 303g mol-1) …
  25. Q25The one that is extensively used as a piezoelectric material is:
  26. Q26Aluminium is usually found in +3 oxidation stage. In contrasts, thallium exists in +1 and +3 oxidation states. This is due to :
  27. Q27The correct match between Item -I and Item- II is :
  28. Q28The ore that contains both iron and copper is:
  29. Q29The compounds A and B in the following reaction are, respectively:
  30. Q30The isotopes of hydrogen are :

Maths

  1. Q1The area (in sq. units) bounded by the parabola y = x2 – 1, the tangent at the point (2, 3) to it and the y-axis is :
  2. Q2The maximum volume (in cu. m) of the right circular cone having slant height 3m is:
  3. Q3 For
  4. Q4Let and be two roots of the equation x2 + 2x + 2 = 0, then 15 + 15 is equal to :
  5. Q5If y = y(x) is the solution of the differential equation, satisfying then is equal to:
  6. Q6Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is:
  7. Q7 Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class , if there are two specific boys A and B, who refuse to be the members of the same team, is : …
  8. Q8Three circles of radii a, b, c(a < b < c) touch each other externally. If they have x-axis as a common tangent, then :
  9. Q9If the fractional part of the number is , then k is equal to :
  10. Q10 Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it ? …
  11. Q11The plane through the intersection of the planes x + y + z = 1 and 2x + 3y – z + 4 = 0 and parallel to y-axis also passes through the point:
  12. Q12If a, b and c be three distinct real numbers in G. P. and a + b + c = xb, then x cannot be :
  13. Q13Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0. Which one of the following statements is true?
  14. Q14The system of linear equations. x + y + z = 2 2x + 3y + 2z = 5 2x + 3y + (a2 – 1)z = a + 1
  15. Q15Let and be a vector such that and then is equal to :-
  16. Q16Let a1, a2,.........,a30 be an A. P., S = and T=  . If a5 = 27 and S – 2T = 75, then a10 is equal to :
  17. Q17 5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance (in cm2) of the height of these six students is : …
  18. Q18 Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P(X = 2) equals: …
  19. Q19 For
  20. Q20 Let  A = \,\,\left\{ {0 \in \left( { - \,\dfrac{\pi }{2},\pi } \right):\,\,\dfrac{{{\text{3 + 2i sin\theta }}}}{{{\text{1 - 2i sin\theta}}}}{\text{is purely imaginary}}} \right\}Then the sum of the elements in A is : …
  21. Q21 If denotes the acute angle between the curves, y = 10 – x2  and y = 2 + x2  at a point of their intersection, then is equal to : …
  22. Q22 If {\text{A = }}\,\,\left[ {\begin{array}{*{20}{c}} {{\text{cos\,\theta}}}{{\text{ - sin\,\theta}}} \\ {{\text{sin\,\theta}}}{{\text{cos\,\theta}}} \end{array}} \right], then the matrix A–50 when
  23. Q23 Let
  24. Q24 The equation of the line passing through (–4, 3, 1), parallel to the plane x + 2y – z – 5 = 0 and intersecting the line 
  25. Q25For any the expression equals:
  26. Q26If then x is equal to :
  27. Q27If the Boolean expression is equivalent to where  then the ordered pair is :
  28. Q28
  29. Q29 1Let f : R R be a function defined as :
    f\left( x \right)\left\{ {\begin{array}{*{20}{c}} {5,}\,\,\,\,\,\,\,\,\,\,\,\,\,{if}\,\,\,\,\,\,\,\,\,\,{x \leqslant 1} \\ {a + bx,}\,\,\,\,\,\,\,\,\,\,\,\,\,\,{if}\,\,\,\,\,\,\,\,\,\,\,\,\,{1 < x < 3} \\ {b + 5x,}\,\,\,\,\,\,\,\,\,\,\,\,\,{if}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{3 \leqslant x < 5} \\ {30,}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{if}\,\,\,\,\,\,\,\,\,\,\,{x \geqslant 5} \end{array} } \right.                  Then, f is : …
  30. Q30The value of

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