JEE Main DPP 31 December 2024: Daily practice problems for 2025 aspirants

JEE Main DPP 31 December 2024

JEE Main DPP 31 December 2024: JEE Main Session 1 2025 will take place from January 22 to 31. Applicants preparing for the exam must focus on practising the JEE Main sample papers. Hence, here are some daily practice questions with answers for JEE Main DPP 31 December  2024, including five questions from each subject: Mathematics, Physics, and Chemistry.

Also Read | NEET Daily Practice Questions 31 December 2024: DPP for 2025 aspirants

JEE Main DPP 31 December 2024: Physics

Candidates can check out the JEE Main DPP 31 December  2024 daily practice problems for 2025 aspirants from the Physics section:

Question 1: Two projectiles are thrown with the same initial velocity making an angle of 45° and 30° with the horizontal respectively. The ratio of their respective ranges will be

(A) 1:(2)^½

(B) (2)^½:1

(C) 2:(3)^½

(D) (3)^½:2

Answer (C)

Question 2: A ball of mass 0.15 kg hits the wall with its initial speed of 12 ms–1 and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N, calculate the time duration of the contact of the ball with the wall.

(A) 0.018 s

(B) 0.036 s

(C) 0.009 s

(D) 0.072 s

Answer (B)

Question 3: I n a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 mm. While measuring the diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6th Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be

(A) 3.02 cm

(B) 3.06 cm

(C) 3.10 cm

(D) 3.20 cm

Answer (C)

Question 4: A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be

(A) 1:1

(B) 2:1

(C) 1:4

(D) 4:1

Answer (B)

Question 5: Two uniformly charged spherical conductors A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of the sphere A and B will be

(A) 1:2

(B) 2:1

(C) 1:1

(D) 1:4

Answer (B)

JEE Main DPP 31 December 2024: Chemistry

Candidates can check out the JEE Main DPP 31 December  2024 daily practice problems for 2025 aspirants from the Chemistry section:

Question 1: Haemoglobin contains 0.34% of iron by mass. The number of Fe atoms in 3.3 g of haemoglobin is

(Given : Atomic mass of Fe is 56 u, NA = 6.022 × 1023 mol–1)

(A) 1.21 × 10^5

(B) 12.0 × 10^16

(C) 1.21 × 10^20

(D) 3.4 × 10^22

Answer (C)

Question 2: Arrange the following in increasing order of their covalent character.

A. CaF2

B. CaCl2

C. CaBr2

D. CaI2

Choose the correct answer from the option given below.

(A) B < A < C < D

(B) A < B < C < D

(C) A < B < D < C

(D) A < C < B < D

Answer (B)

Question 3: Class XII students were asked to prepare one litre of buffer solution of pH 8.26 by their Chemistry teacher. The amount of ammonium chloride to be dissolved by the student in 0.2 M ammonia solution to make one litre of the buffer is

(Given : pKb (NH3) = 4.74, Molar mass of NH3 = 17 g mol–1, Molar mass of NH4Cl = 53.5 g mol–1)

(A) 53.5 g

(B) 72.3 g

(C)107.0 g

(D) 126.0 g

Answer (C)

Question 4: At 30ºC, the half life for the decomposition of AB2 is 200 s and is independent of the initial concentration of AB2. The time required for 80% of the AB2 to decompose is

(Given : log 2 = 0.30, log 3 = 0.48)

(A) 200 s

(B) 323 s

(C) 467 s

(D) 532 s

Answer (C)

Question 5: The metal that has very low melting point and its periodic position is closer to a metalloid is

(A)  Al

(B) Ga

(C) Se

(D) ln

Answer (B)

JEE Main DPP 31 December 2024: Mathematics

Candidates can check out the JEE Main DPP 31 December 2024 daily practice problems for 2025 aspirants from Maths section:

Problem 1: Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be along  the straight line x + y = 3. If R and r be the radius of circumcircle and incircle respectively of DABC, then (R + r) is

(1) 3(2)^½

(2) 2(2)^½

(3) 9/(2)^½

(4) 7(2)^½

Solution (3)

Problem 2: Let in a series of 2n observations, half of them are equal to a and the remaining half are equal to –a. Also by adding a constant b in each of these observations, the mean and standard deviation of the new set become 5 and 20, respectively. Then the value of a2 + b2 is equal to :

(1) 925

(2) 650

(3) 425

(4) 250

Solution (3)

Problem 3: If 15sin4a + 10cos4a = 6, for some a Î R, then the value of 27sec6a + 8cosec6a is equal to :

(1) 350

(2) 250

(3) 300

(4) 500

Solution (2)

Problem 4: Define a relation R over a class of n × n real matrices A and B as “ARB iff there exists a non- singular matrix P such that PAP–1 = B”. Then which of the following is true?

(1)   R is reflexive, symmetric but not transitive

(2)   R is an equivalence relation

(3)   R is symmetric, transitive but not reflexive

(4)   R is reflexive, transitive but not symmetric

Solution (2)

Problem 5: Let S1 be the sum of the first 2n terms of an arithmetic progression. Let S2 be the sum of first in terms of the same arithmetic progression. If (S2 – S1) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to :

(1) 7000

(2) 5000

(3) 3000

(4) 1000

Solution (3)