JEE Main Question Paper 30 January 2024 Shift 1(Memory Based) Available

Chemistry

1. What happen to freezing point of benzene when small quantity of naphthalene is added to benzene?
2. Find out the maximum number of hybrid orbitals formed when 2s and 2p orbitals are mixed.
3. Identify the given reaction. C₆H₆-C=O-CI -> (in the presence of H2, Pd/BaSO4) -> Product
   i. Etard Reaction
   ii. Stephen's Reaction
   iii. Wolff Kishner Reduction
   iv. Rosenmund Reaction
4. Find out the sum of the coefficients of all the species involved in the balanced equation:
   2MnO₄ + I^- → (in the presence of a slightly alkaline medium) → Product
5. Which of the following compounds does not pass the Fehling Test
   a)Lactose
   b)Maltose
   c)Sucrose
   d)Glucose
6. Find out the work done in Joules for the cyclic process ABCA such that PA = 30 kPa, VA = 10 dm3, Pg = 10 kPa, Vg = 30 dm3, Pc = 10 kPa, Vc= 10 dm3 (as per the given graph).
7. Identify the halogen which has allylic halogen. (A diagrammatic representation of compounds was given).
8. Find the final product when C6H6-Br reacts with - i. Mg, Dry Ether, ii. CO2, H+, iii. NH3, heat, and iv. Br2, KOH
9. Identify the correct structure for the compound named "3-Methylpent-2-enal" as per IUPAC nomenclature.
10. Identify the most stable compound/ion among the given options.
11. Statement I: For hydrogen atoms, 3p and 3d are degenerate. Statement II: Degenerate orbitals have the same energy.
    i. Both statements I and II are correct.
    ii. Both statements I and II are incorrect.
    iii. Statement I is correct and statement II is incorrect.
    iv. Statement I is incorrect and statement II is correct.
12. What is the geometry of Aluminium chloride in an aqueous solution?
    i. Square planar
    ii. Octahedral
    iii. Tetrahedral
    iv. Square pyramidal
13. The number of atoms in a silver plate having an area of 0.05 cm2 and a thickness of 0.05 cm is m x 1019. If the density of silver is 7.9 g/cm3, find the value of m.
14. What is the group number of unununnium?
15. Match the following:
    i. BrF5       a. Sea-Saw
    ii. H2O      b. T-Shape
    iii. CIF3     c. Bent
    iv. SF4       d. Square Pyramidal
16. If a 250 mL solution of CH3COONa of molarity 0.35 M is to be prepared, what is the mass of CH3COONa required in grams? Round off the answer to the nearest integer.
17. Which of the following sets contain both diamagnetic ions?
    i. Ni2+, Cu2+
    ii. Eu3+, Gd3+
    iii. Cu+, Zn2+
    iv. Ce4+, Pm3+

Physics

1. A ball that is dropped from a height of 10m, after collision with earth surface, rises back to a height of 5m. In that case, find the impulse on the ball by earth surface if mass of the ball is 100gm.
2. Two current carrying ring (radius R) are perpendicular to each other and their centres coincide. Then, find magnetic field at centre 'O'.
3. The Young's modulus of a material of length L and cross sectional area A is given by 'Y". What will the Young's modulus be if the length is doubled and cross sectional area is halved?
4. Find the temperature at which the r.m.s velocity of hydrogen molecule is equal to that of oxygen molecule at 47°C.
5. The electro static potential due to an electron at a distance r varies as:
   a) 1/r
   b) 1/r²
   c) r
   d) r²
6. What is the ratio of magnitude of the kinetic energy to potential energy of an electron in the 5th orbit of hydrogen atom?
7. In a convex lens the distance between object and image is 45 cm, and magnification produced by lens is two. Find focal length of the lens.
8. A particle of mass m is projected at an angle of 30° with initial velocity u. Find its angular momentum about point of projection at maximum height.
9. Work function of a metal is 3 eV. Find its threshold wavelength.
10. Find the acceleration of a 2 kg block on a fixed inclined surface at 37° with the horizontal. The block is tied with a rope that passes over two pulleys (represented through a diagram) such that pulley 1 rests at the top of the inclined surface and pulley 2 carries a weight of 4 kg. Neglect friction.
11. Find the potential difference Vo across the 700 resistance. A diagram was given in which three resistances 3.5 kOhm, 2 Ohm, and 700 Ohm are connected in series across a 7 V battery.
12. A ball is released from a height of 1 m on a fixed smooth hemispherical surface. Find its velocity when it is at a height of 0.5 m from the ground. Take g = 10 m/s2.

Mathematics

1. Let (a, ẞ, y) be the foot of perpendicular form the point (1,2,3) on the line (x+3)/5 = (y-1)/2 = (z+4)/3. Find (a+ẞ+y).
2. In an arithametic progression, the sum of the first 20 numbers in 790 and the first 10 numbers is 145. Find S₁₅-S₅
3. Find the value of the maximum area possible (in sq.units) of triangle ABC with vertices A(0, 0), B(x, y) and C(-x, y) such that y = - 2x² + 54x.
4. What is the range of r for which circles (x + 1)²+(y+ 2)² = 12 and x²+ y²-4x-4y+4=0 coincide at two distinct points.
5. Find the eccentricity of an ellipse whose length of the minor axis is equal to half of the length between foci.