JEE Main 2024 April 4 Questions LIVE Updates: Day 1 paper moderate, mathematics tough

06 30 PM IST - 04 Apr'24

JEE Main 4 April 2024 Exam Question 16 for Physics

The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is

(a) R/2

(b) R/3

(c) 2R

(d) 3R

06 15 PM IST - 04 Apr'24

JEE Main 4 April 2024 Exam Question 15 for Mathematics

If the slope of a line passing through point A (3, 2) is 3/4, then the points on the line which are 5 units away from A, are ________.

06 00 PM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Exam Practice Question 15

A 5.2 molal aqueous solution of methyl alcohol, CH3OH, is supplied. What is the mole fraction of methyl alcohol in the solution?

(1) 0.086

(2) 0.050

(3) 0.100

(4) 0.190

05 45 PM IST - 04 Apr'24

JEE Main 4 April 2024 Exam Question 15 for Physics

An artificial satellite moving in a circular orbit around the earth has a total (K.E. + P.E.) energy E0. Its potential energy is

(a) – E0

(b) 1.5 E0

(c) 2 E0

(d) E0

05 30 PM IST - 04 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 14

The equation of the lines, which passes through the point (3, – 2) and are inclined at 60o to the line √3x + y = 1 ____________.

05 15 PM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 14

10 mL of 2(M) NaOH solution is added to 200 mL of 0.5 (M) of NaOH solution. What is the final concentration?

(1) 0.57 M

(2) 5.7 M

(3) 11.4 M

(4) 1.14 M

05 00 PM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 14

The mass of a spaceship is 1000 kg. It is to be launched from the earth’s surface out into free space. The value of ‘g’ and ‘R’ (radius of the earth) is 10 m/s2 and 6400 km respectively. The required energy for this work will be

(a) 6.4 x 1010 Joules

(b) 6.4 x 1011 Joules

(c) 6.4 x 108 Joules

(d) 6.4 x 109 Joules

04 45 PM IST - 04 Apr'24

JEE Main 2024 Question Paper April 4: Mathematics Important Question 14

The points (1, 3) and (5, 1) are the opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c, then the value of c will be __________.

04 30 PM IST - 04 Apr'24

JEE Main April 4 2024 Chemistry Question Paper: Important Question 14

A transition metal M forms a volatile chloride which has a vapour density of 94.8. If it contains 74.75% of chlorine the formula of the metal chloride will be

(1) MCl2

(2) MCl4

(3) MCl5

(4) MCl3

04 15 PM IST - 04 Apr'24

JEE Main April 4 2024 Question Paper: Physics Important Question 14

If the distance between the earth and the sun were half its present value, the number of days in a year would have been

(a) 64.5

(b) 129

(c) 182.5

(d) 730

04 00 PM IST - 04 Apr'24

JEE Main 4 April 2024 Exam Question 14 for Mathematics

The equation of the line which bisects the obtuse angle between the lines x − 2y + 4 = 0 and 4x − 3y + 2 = 0, is _________.

03 45 PM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Exam Practice Question 14

Given a solution of HNO3 of density 1.4 g/mL and 63% w/w. Determine the molarity of HNO3 solution.

03 30 PM IST - 04 Apr'24

JEE Main 4 April 2024 Exam Question 14 for Physics

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then

(a) T ∝ R3/2

(b) T ∝ R(n/2)+1

(c) T ∝ R(n+1)/2

(d) T ∝ Rn/2

03 15 PM IST - 04 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 13

Line L has intercepts a and b on the co-ordinate axes. When the axes are rotated through a given angle keeping the origin fixed, the same line L has intercepts p and q, find the relation between a,b and p,q.

03 00 PM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 13

Calculate the mass of FeSO4.7H2O which must be added in 100 kg of wheat to get 10 PPM of Fe.

02 45 PM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 13

Suppose that the angular velocity of rotation of earth is increased. Then,as a consequence

(a) There will be no change in weight anywhere on the earth

(b) Weight of the object, everywhere on the earth, will increase

(c) Except at poles, weight of the object on the earth will decrease

(d) Weight of the object, everywhere on the earth, will decrease.

02 30 PM IST - 04 Apr'24

JEE Main 2024 Question Paper April 4: Mathematics Important Question 13

The line 2x + 3y = 12 meets the x-axis at A and y-axis at B. The line through (5, 5) perpendicular to AB meets the x-axis, y-axis, and the AB at C, D, and E, respectively. If O is the origin of coordinates, then the area of OCEB is _______.

02 15 PM IST - 04 Apr'24

JEE Main April 4 2024 Chemistry Question Paper: Important Question 13

0.6 g of urea on strong heating with NaOH evolves NH3. Liberated NH3 will combine with which of the following HCl solution?

(1) 100 mL of 0.2 N HCl

(2) 400 mL of 0.2 N HCl

(3) 100 mL of 0.1 N HCl

(4) 200 mL of 0.2 N HCl

02 00 PM IST - 04 Apr'24

JEE Main April 4 2024 Question Paper: Physics Important Question 13

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

(a) 5GmM/6R

(b) 2GmM/3R

(c) GmM/2R

(d) GmM/3R

01 45 PM IST - 04 Apr'24

JEE Main 4 April 2024 Mathematics Exam Practice Question 13

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is ________.

01 30 PM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Exam Practice Question 13

The density of 3M solution of sodium chloride is 1.252 g mL-1. The molality of the solution will be (molar mass, NaCl = 58.5 g mol-1)

(1) 2.18 m

(2) 3.00 m

(3) 2.60 m

(4) 2.79 m

01 15 PM IST - 04 Apr'24

JEE Main 4 April 2024 Exam Question 13 for Physics

Three particles, each of mass m, are situated at the vertices of an equilateral triangle of side length a. The only forces acting on the particles are their mutual gravitational forces. lt is desired that each particle moves in a circle while maintaining the original mutual separation a. Find the initial velocity that should be given to each particle and also the period of the circular motion. (F = Gm1m2/r2)

01 00 PM IST - 04 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 12

The area of a parallelogram formed by the lines ax ± by ± c = 0, is __________.

12 45 PM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 12

An open vessel at 300 K is heated till ⅖ th of the air in it is expelled. Assuming that the volume of the vessel remains constant, the temperature to which the vessel is heated is :

(1) 750 K

(2) 400 K

(3) 500 K

(4) 1500K

12 30 PM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 12

A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass “m” is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is

(a) 1/2 mV2

(b) mV2

(c) 3/2 mV2

(d) 2 mV2

12 15 PM IST - 04 Apr'24

JEE Main 2024 Question Paper April 4: Mathematics Important Question 12

The locus of a point P, which divides the line joining (1, 0) and (2 cos θ, 2 sin θ) internally in the ratio 2 : 3 for all θ, is a ________.

12 00 PM IST - 04 Apr'24

JEE Main April 4 2024 Chemistry Question Paper: Important Question 12

When CO2 (g) is passed over red hot coke it partially gets reduced to CO(g). Upon passing 0.5 litre of CO2 (g) over red hot coke, the total volume of the gases increased to 700 mL. The composition of the gaseous mixture at STP is :

(1) CO2 = 200 mL: CO = 500mL

(2) CO2 = 350 mL: CO = 350mL

(3) CO2 = 0.0 mL: CO = 700mL

(4) CO2 = 300 mL: CO = 400mL

11 45 AM IST - 04 Apr'24

JEE Main April 4 2024 Question Paper: Physics Important Question 12

A Binary star system consists of two stars A and B which have time periods TA and TB, radii RA and RB and masses MA and MB. Then

(a) TA ＞TB then RA ＞RB

(b) TA ＞TB then MA ＞MB

(c) (TA/TB)2 = (RA/RB)2

(d) TA = TB

11 30 AM IST - 04 Apr'24

JEE Main 4 April 2024 Mathematics Exam Practice Question 12

 The area enclosed within the curve |x|+|y|= 1 is ____________.

11 20 AM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Exam Practice Question 12

The ratio of number of oxygen atoms (O) in 16.0g oxygen (O), 28.0 g carbon monoxide (CO) and 32.0g oxygen (O2) is :

(Atomic mass :C =12, O =16 and Avogadro’s constant NA = 6.0 * 1023 mol-1)

(1) 3 : 1 : 1

(2) 1 : 1 : 2

(3) 3 : 1 : 2

(4) 1 : 1 : 1

11 10 AM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Practice Question 12

Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is

(a) -6Gm/r

(b) -9Gm/r

(c) Zero

(d) -4Gm/r

11 00 AM IST - 04 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 11

A variable line passes through a fixed point P. If the algebraic sum of the perpendicular drawn from (2, 0), (0, 2) and (1, 1) on the line is zero, then what are the coordinates of the P?

10 50 AM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 11

The density of a solution prepared by dissolving 120 g of urea (mol. mass = 60 u) in 1000 g of water is 1.15 g/mL. The molarity of this solution is

(1) 2.05 M

(2) 0.50 M

(3) 1.78 M

(4) 1.02 M

10 40 AM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 11

A geostationary satellite orbits around the earth in a circular orbit of radius 36,000km. Then, the time period of a spy satellite orbiting a few hundred km above the earth’s surface (R =6,400km) will approximately be

(a) (l/2)hr

(b) 1 hr

(c) 2 hr

(d) 4 hr

10 30 AM IST - 04 Apr'24

JEE Main 2024 Question Paper April 4: Mathematics Important Question 11

In what direction can a line be drawn through the point (1, 2) so that its points of intersection with the line x + y = 4 is at a distance √6 / 3 from the given point?

10 20 AM IST - 04 Apr'24

JEE Main April 4 2024 Chemistry Question Paper: Important Question 11

3g of activated charcoal was added to 50 mL of acetic acid solution (0.06N) in a flask. After an hour it was filtered and the strength of the filtrate was found to be 0.042 N. The amount of acetic acid adsorbed (per gram of charcoal) is :

(1) 42 mg

(2) 54 mg

(3) 18 mg

(4) 36 mg

10 10 AM IST - 04 Apr'24

JEE Main April 4 2024 Question Paper: Physics Important Question 11

A simple pendulum has a time period T1 when on the earth’s surface, and T2 when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of T2/T1 is

(a) 1

(b) 3

(c) 4

(d) 2

10 00 AM IST - 04 Apr'24

JEE Main 4 April 2024 Mathematics Exam Practice Question 11

The graph of the function cos x cos (x + 2) − cos2 (x + 1) is

A) A straight line passing through (0, − sin2 1) with slope 2

B) A straight line passing through (0, 0)

C) A parabola with vertex 75°

D) A straight line passing through the point (π/2, −sin2 1) and parallel to the x-axis

09 50 AM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Exam Practice Question 11

The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of their molecule is :

(1) 1 : 8

(2) 3 : 16

(3) 1 : 4

(4) 7 : 32

09 40 AM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Practice Question 11

The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is

(a) R/2

(b) R/3

(c) 2R

(d) 3R

09 30 AM IST - 04 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 10

The graph of the function cos x cos (x + 2) − cos2 (x + 1) is

A) A straight line passing through (0, − sin2 1) with slope 2

B) A straight line passing through (0, 0)

C) A parabola with vertex 75°

D) A straight line passing through the point (π/2, −sin2 1) and parallel to the x-axis

09 20 AM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 10

The concentrated sulphuric acid that is peddled commercially is 95% H2SO4 by weight. If the density of this commercial acid is 1.834 g cm-3, the molarity of this solution is :-

(1) 17.8 M

(2) 15.7 M

(3) 10.5 M

(4) 12.0 M

09 10 AM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 10

An artificial satellite moving in a circular orbit around the earth has a total (K.E. + P.E.) energy E0. Its potential energy is

(a) – E0

(b) 1.5 E0

(c) 2 E0

(d) E0

09 00 AM IST - 04 Apr'24

JEE Main 2024 Question Paper April 4: Mathematics Important Question 10

The equations of two equal sides of an isosceles triangle are 7x − y + 3 = 0 and x + y − 3 = 0, and the third side passes through the point (1, -10). The equation of the third side is ___________.

08 50 AM IST - 04 Apr'24

JEE Main April 4 2024 Chemistry Question Paper: Important Question 10

The ratio of mass percent of C and H of an organic compound (CxHyOz) is 6 : 1. If one molecule of the above compound ( CxHyOZ ) contains half as much oxygen as required to burn one molecule of compound CXHY completely to CO2 and H2O. The empirical formula of compound CxHyOz is :

(1) C2H4O

(2) C3H4O2

(3) C2H4O3

(4) C3H6O3

08 40 AM IST - 04 Apr'24

JEE Main April 4 2024 Question Paper: Physics Important Question 10

The mass of a spaceship is 1000 kg. It is to be launched from the earth’s surface out into free space. The value of ‘g’ and ‘R’ (radius of the earth) is 10 m/s2 and 6400 km respectively. The required energy for this work will be

(a) 6.4 x 1010 Joules

(b) 6.4 x 1011 Joules

(c) 6.4 x 108 Joules

(d) 6.4 x 109 Joules

08 30 AM IST - 04 Apr'24

JEE Main 4 April 2024 Mathematics Exam Practice Question 10

A-line through A (−5, − 4) meets the lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x − y − 5 = 0 at B, C and D, respectively. If (15 / AB)2 + (10 / AC)2 = (6 / AD)2, then the equation of the line is _________.

08 20 AM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Exam Practice Question 10

Number of atoms in the following samples of substances is the largest in :

(1) 127.0g of iodine

(2) 48.0g of magnesium

(3) 71.0g of chlorine

(4) 4.0g of hydrogen

08 10 AM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Practice Question 10

If the distance between the earth and the sun were half its present value, the number of days in a year would have been

(a) 64.5

(b) 129

(c) 182.5

(d) 730

08 00 AM IST - 04 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 9

If the roots of the equation x2 + 2ax + b = 0 are real and distinct and they differ by at most 2m then b lies in what interval?

07 50 AM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 9

The states of hybridization of boron and oxygen atoms in boric acid (H3B03) are respectively

(1) sp2 and sp2 (2) sp3 and sp3

(3) sp3 and sp2 (4) sp2 and sp3

07 40 AM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 9

A bob of mass m attached to an inextensible string of length is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical. About the point of suspension

(a) Angular momentum changes in direction but not in magnitude

(b) Angular momentum changes both in direction and magnitude

(c) Angular momentum is conserved

(d) Angular momentum changes in magnitude but not in direction.

07 30 AM IST - 04 Apr'24

JEE Main 2024 Question Paper April 4: Mathematics Important Question 9

 If ([1 + i] / [1 − i])^m = 1, then what is the least integral value of m?

07 20 AM IST - 04 Apr'24

JEE Main April 4 2024 Chemistry Question Paper: Important Question 9

The maximum number of 90° angles between bond pair of electrons is observed in

(1) dsp3 hybridization

(2) sp3d2 hybridization

(3) dsp2 hybridization

(4) sp3d hybridization

07 10 AM IST - 04 Apr'24

JEE Main April 4 2024 Question Paper: Physics Important Question 9

A particle is confined to rotate in a circular path with decreasing linear speed. Then which of the following is correct?

1. angular momentum is conserved about the centre
2. only the direction of L is conserved
3. it spirals towards the centre
4. its acceleration is towards the centre

07 00 AM IST - 04 Apr'24

JEE Main 4 April 2024 Mathematics Exam Practice Question 9

If (1 − i) x + (1 + i) y = 1 − 3i, then (x, y) = ______________.

06 50 AM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Exam Practice Question 9

Which of the following are arranged in an increasing order of their bond strengths?

(1) O2– < O2 < O2+ < O22-

(2) O22- < O2– < O2 < O2+

(3) O2– < O22- < O2 < O2+

(4) O2+ < O2 < O2– < O22-

06 40 AM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Practice Question 9

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is

1. 2K
2. K/2
3. K/4
4. 4K

06 30 AM IST - 04 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 8

 [3 + 2i sinθ] / [1 − 2i sinθ] will be purely imaginary if θ = ___________.

06 00 AM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 8

Bond order and magnetic nature of CN– are respectively

(1) 3, diamagnetic

(2) 2.5, paramagnetic

(3) 3, paramagnetic

(4) 2.5, diamagnetic

05 30 AM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 8

A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved?

1. centre of the circle
2. on the circumference of the circle
3. inside the circle
4. outside the circle

05 00 AM IST - 04 Apr'24

JEE Main 2024 Question Paper April 4: Mathematics Important Question 8

The real values of x and y for which the equation is (x + iy) (2 − 3i) = 4 + i is satisfied, are __________.

04 30 AM IST - 04 Apr'24

JEE Main April 4 2024 Chemistry Question Paper: Important Question 8

The bond order in NO is 2.5 while that in NO+ is 3. Which of the following statements is true for these two species?

(1)Bond length in NO+ is greater than in NO

(2)Bond length is unpredictable

(3)Bond length in NO+ in equal to that in NO

(4)Bond length in NO is greater than in NO+

04 00 AM IST - 04 Apr'24

JEE Main April 4 2024 Question Paper: Physics Important Question 8

A particle of mass m moving in the x-direction with speed 2v is hit by another particle of mass 2m moving in the y-direction with speed v. If the collisions are perfectly inelastic, the percentage loss in the energy during the collision is close to

(a) 56%

(b) 62%

(c) 44%

(d) 50%

03 30 AM IST - 04 Apr'24

JEE Main 4 April 2024 Mathematics Exam Practice Question 8

Suppose z1, z2, z3 are the vertices of an equilateral triangle inscribed in the circle |z| = 2. If z1 = 1 + i√3, then find the values of z3 and z2.

02 30 AM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Practice Question 8

Statement 1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.

Statement 2: Principle of conservation of momentum holds true for all kinds of collisions.

(a) Statement–1 is true, Statement–2 is false

(b) Statement–1 is true, Statement–2 is true; Statement–2 is the correct explanation of Statement–1

(c) Statement–1 is true, Statement–2 is true; Statement–2 is not the correct explanation of Statement–1

(d) Statement–1 is false, Statement–2 is true

02 00 AM IST - 04 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 7

For any two complex numbers z1 and z2 and any real numbers a and b; |(az1 − bz2)|2 + |(bz1 + az2)|2 = ___________.

01 30 AM IST - 04 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 7

The hybridisation of orbitals of N atom in NO3–, NO2+, NH4+ are respectively:

(1) sp2, sp3, sp

(2) sp, sp3, sp2

(3) sp, sp2, sp3

(4) sp2, sp, sp3

01 00 AM IST - 04 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 7

A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms4. Which of the following statements(s) are correct for the system of these two masses

(a)The total momentum of the system is 3 kg ms-1

(b) The momentum of 5kg mass after the collision is 4kg ms-1

(c) The kinetic energy of the centre of mass is 0.75 J

(d) The total kinetic energy of the system is 4 J

12 00 AM IST - 04 Apr'24

JEE Main April 4 2024 Chemistry Question Paper: Important Question 7

Among the following, the species having the smallest bond is :

(1) NO

(2) NO+

(3) O2

(4) NO–

11 30 PM IST - 03 Apr'24

JEE Main April 4 2024 Question Paper: Physics Important Question 7

Two particles A and B, initially at rest, move to­wards each other under the mutual force of attraction. At the instant when the speed of A is v and the speed of B is 2v, the speed of the centre of mass of the system is

(a) 3v

(b) v

(c) 1.5v

(d) zero

11 00 PM IST - 03 Apr'24

JEE Main 4 April 2024 Mathematics Exam Practice Question 7

If z is a complex number, then the minimum value of |z| + |z − 1| is ______.

10 50 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Exam Practice Question 7

Using MO theory, predict which of the following species has the shortest bond length?

(1) O2–

(2) O22-

(3) O22+

(4) O2+

10 40 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Practice Question 7

Two blocks of masses 10 kg and 4 kg are con­nected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocity of the centre of mass is

(a) 30 m/s

(b) 20 m/s

(c) 10 m/s

(d) 5 m/s

10 30 PM IST - 03 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 6

 If (1 + i) (1 + 2i) (1 + 3i) ….. (1 + ni) = a + ib, then what is 2 * 5 * 10….(1 + n2) is equal to?

10 20 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 6

Among the following species which two have a trigonal bipyramidal shape?

(1) NI3 (2) I3– (3) SO32- (4) NO3–

(1) II and III

(2) III and IV

(3) I and IV

(4) I and III

10 10 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 6

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 force during the first 1 sec. will be :

(a) 9 J

(b) 18 J

(c) 4.5 J

(d) 22 J

10 00 PM IST - 03 Apr'24

JEE Main 2024 Question Paper (April 4): Mathematics Important Question 6

The shortest distance between the lines is?
(x - 1)/2 = (y + 1)/4 = (z - 1)/3 and (2x - 1)/5 = (y - 2)/3 = z/3

09 50 PM IST - 03 Apr'24

JEE Main April 4 2024 Chemistry Question Paper: Important Question 6

The bond dissociation energy of B–F in BF3 is 646 kJ mol-1 whereas that of C–F in CF4 is 515 kJ mol–1. The correct reason for higher B–F bond dissociation energy as compared to that of C–F is

(1) Significant pπ – pπ interaction between B and F in BF3 whereas there is no possibility of such interaction between C and F in CF4.

(2) Lower degree of pπ – pπ interaction between B and F in BF3 than that between C and F in CF4

(3) Smaller size of B-atom as compared to that of C-atom

(4) Stronger bond between B and F in BF3 as compared to that between C and F in CF4.

09 40 PM IST - 03 Apr'24

JEE Main April 4 2024 Question Paper: Physics Important Question 6

A particle performing simple harmonic motion according to x = A sin ωt. Then its kinetic energy (KE), potential energy (PE) and speed (v) at position x = A/2 are?

09 30 PM IST - 03 Apr'24

JEE Main 4 April 2024 Mathematics Exam Practice Question 6

Which of the following statements is incorrect?
i. ΔG = 0 for reversible reaction
ii. ΔG < 0 for spontaneous process
iii. ΔG > 0 for spontaneous process
iv. ΔG < 0 for non-spontaneous process

09 20 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Exam Practice Question 6

Assertion: Boron is a Hard Element.
Reason: Boron has an unusually high melting point due to its crystalline structure.
i. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
ii. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
iii. A is true, R is not
iv. R is true, A is not

09 10 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Practice Question 6

A series of steps has 0.5 m tread and 0.5 m riser. If a ball is thrown from a point on the ground beside the first step, then find the minimum speed required by the ball to directly jump to the 5th step.

09 00 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 5

The group having isoelectronic species is;

(1) O2-, F–, Na+, Mg2+

(2) O–, F–, Na , Mg+

(3) O2-, F–, Na , Mg2+

(4) O– , F–, Na+, Mg2+

08 50 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 5

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 = 10ms-1. If, after 10 s, its energy is, the value of k will be

(a) 10-4 kg m-1

(b) 10-1 kg m-1s-1

(c) 10-3 kg m-1

(d) 10-3 kg s-1

08 40 PM IST - 03 Apr'24

JEE Main 2024 Question Paper (April 4): Mathematics Important Question 5

Let z1 and z2 be nth roots of unity, which are the ends of a line segment that subtends a right angle at the origin. Then n must be of the form ____________.

08 30 PM IST - 03 Apr'24

JEE Main April 4 2024 Chemistry Question Paper: Important Question 5

Which is the correct order of second ionization potential of C, N, O and F in the following?

(1) O > F > N > C

(2) O > N > F > C

(3) C > N > O > F

(4) F > O > N > C

08 20 PM IST - 03 Apr'24

JEE Main April 4 2024 Question Paper: Physics Important Question 5

A person trying to lose weight by burning fat lifts a mass of 10 kg up to a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies 3.8 X 107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 m/s2

(a) 12.89 X 10-3kg

(b) 2.45 X 10-3 kg

(c) 6.45 X 10-3 kg

(d) 9.89 X 10-3 kg

08 10 PM IST - 03 Apr'24

JEE Main 4 April 2024 Mathematics Exam Practice Question 5

Shortest distance between the parabola y2 = 4x and x2 + y2 - 4x - 16y + 64 = 0 is equal to?

08 00 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Exam Practice Question 5

Among the following, the number of meta-directing groups is:
-CN, -NO2, -COOH, CH3, -SO3H, NH3+, -F

07 45 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Practice Question 5

If the diameter of the earth becomes half while keeping mass constant, then the acceleration due to gravity at the surface of the earth becomes?

07 30 PM IST - 03 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 4

If a = cos (2π / 7) + i sin (2π / 7), then the quadratic equation whose roots are α = a + a2 + a4 and β = a3 + a5 + a6 is _____________.

07 20 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 4

Beryllium and aluminium exhibit many properties which are similar. But the two elements differ in

(1) exhibiting maximum covalency in compound

(2) exhibiting amphoteric nature in their oxides

(3) forming covalent halides

(4) forming polymeric hydrides

07 10 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 4

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F =ax + bx2 where a and b are constants. The work done in stretching the unstretched rubber-band by L is

(a) aL2/2 +bL3/3

(b) ½ (aL2/2 +bL3/3)

(c ) aL2 +bL3

(d) ½ (aL2 +bL3)

07 00 PM IST - 03 Apr'24

JEE Main 2024 Question Paper (April 4): Mathematics Important Question 4

 If 1, ω, ω2, ω3……., ωn−1 are the n, nth roots of unity, then (1 − ω) (1 − ω2) …..

(1 − ωn − 1) = ____________.

06 50 PM IST - 03 Apr'24

JEE Main April 4 2024 Chemistry Question Paper: Important Question 4

According to the Periodic Law of elements, the variation in properties of elements is related to their.

(1) nuclear masses

(2) atomic numbers

(3) nuclear neutron-proton number ratios

(4) atomic masses

06 40 PM IST - 03 Apr'24

JEE Main April 4 2024 Question Paper: Physics Important Question 4

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time ‘t’ as ac = k2rt2 where ‘k’ is a constant. The power delivered to the particle by the force acting on it is

(a) 2πmk2r2t

(b) mk2r2t

(c) mk4r2t5/3

(d) zero

06 30 PM IST - 03 Apr'24

JEE Main 4 April 2024 Mathematics Exam Practice Question 4

If the cube roots of unity are 1, ω, ω2, then find the roots of the equation (x − 1)3 + 8 = 0.

06 15 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Exam Practice Question 4

The first ionisation potential of Na is 5.1 eV. The value of electron gain enthalpy of Na+ will be?

(1) – 2.55 eV

(2) – 5.1 eV

(3) – 10.2 eV

(4) + 2.55 eV

06 00 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Practice Question 4

At time t = 0 s particle starts moving along the x-axis. If its kinetic energy increases uniformly with time ‘t’, the net force acting on it must be proportional to

(a) √t

(b) constant

(c) t

(d) 1/√t

05 50 PM IST - 03 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 3

If cosα + cos β + cos γ = sin α + sin β + sin γ = 0 then what is the value of cos 3α + cos 3β + cos 3γ?

05 40 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 3

The increasing order of the ionic radii of the given isoelectronic species is?

(1) K+, S2-, Ca2+, Cl–

(2) Cl–, Ca2+, K+,S2-

(3) S2-, Cl–, Ca2+, K+

(4) Ca2+, K+, Cl–, S2-

05 30 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 3

If a machine is lubricated with oil

(a) the mechanical advantage of the machine increases

(b) the mechanical efficiency of the machine increases

(c) both its mechanical advantage and efficiency increase

(d) its efficiency increases, but its mechanical advantage decreases.

05 10 PM IST - 03 Apr'24

JEE Main 2024 Question Paper (April 4): Mathematics Important Question 3

Suppose z1, z2, z3 are the vertices of an equilateral triangle inscribed in the circle |z| = 2. If z1 = 1 + i√3, then find the values of z3 and z2.

05 00 PM IST - 03 Apr'24

JEE Main April 4 2024 Chemistry Question Paper: Important Question 3

The radius of La3+ (Atomic number of La=57) is 1.06A. Which one of the following given values will be closest to the radius of Lu3+ (Atomic number of Lu = 71)?

(1) 40 A

(2) 1.06 A

(3) 0.85 A

(4) 1.60 A

04 50 PM IST - 03 Apr'24

JEE Main April 4 2024 Question Paper: Physics Important Question 3

Two masses of 1 g and 4g are moving with equal kinetic energy. The ratio of the magnitudes of their momenta is

(a) 4: 1

(b) √2: 1

(c) 1: 2

(d) 1: 16

04 40 PM IST - 03 Apr'24

JEE Main 4 April 2024 Mathematics Exam Question 3

If f (x) = cos (log x), then find the value of f (x) * f (4) − [1 / 2] * [f (x / 4) + f (4x)].

04 30 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Exam Model Question 3

The frequency of light emitted for the transition n = 4 to n = 2 of He+ is equal to the transition in H atom corresponding to which of the following

(1) n = 3 to n = 1

(2) n = 2 to n = 1

(3) n = 3 to n = 2

(4) n = 4 to n = 3

04 20 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 3

Consider a car moving on a straight road with a speed of 100 m/s. The distance at which a car can be stopped is : (μk = 0.5)

(a) 800 m

(b) 1000 m

(c) 100 m

(d) 400 m

04 10 PM IST - 03 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 2

Let a relation R be defined by R = {(4, 5); (1, 4); (4, 6); (7, 6); (3, 7)} then R−1 o R is ________.

04 00 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 2

The energy required to break one mole of Cl–Cl bonds in Cl2 is 242 kJ mol-1. The longest wavelength of light capable of breaking a single Cl–Cl bond is

(C = 3×108 m/s and NA = 6.02×1023 mol-1)

(1) 494 nm

(2) 594 nm

(3) 640 nm

(4) 700 nm

03 45 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 2

The upper half of an inclined plane with inclination Φ is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by

(a) 2 sinΦ

(b) 2 cosΦ

(c) 2 tanΦ

(d) tanΦ

03 30 PM IST - 03 Apr'24

JEE Main 4 April 2024 Exam Mathematics Model Question 2

Let R be the relation on the set R of all real numbers defined by a R b if and only if |a − b| ≤ 1. Then R is __________.

03 20 PM IST - 03 Apr'24

JEE Main 4 April 2024 Important Chemistry Model Question 2

 The radius of the second Bohr orbit for the hydrogen atom is :

(Planck’s constant, h = 6.262×10-34Js: Mass of electron = 9.1091×10-31kg; Charge of electron e = 1.60210×10-19C; permittivity of vacuum ε0 = 8.854185×10-12kg-1m-3A2)

(1) 1.65 A

(2) 4.76 A

(3) 0.529 A

(4) 2.12 A

03 10 PM IST - 03 Apr'24

JEE Main April 4 2024 Exam Physics Important Question 2

A block rests on a rough inclined plane making an angle of 300 with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is : (taken g =10 m/s2)

(a) 2.0

(b) 4.0

(c) 1.6

(d) 2.5

03 00 PM IST - 03 Apr'24

JEE Main 4 April 2024 Mathematics Exam Model Question 2

In a college of 300 students, every student reads 5 newspapers, and every newspaper is read by 60 students. The number of newspapers is ________.

02 50 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Exam Model Question 2

If the kinetic energy of an electron is increased four times, the wavelength of the de-Broglie wave associated with it would become

(1) Two times

(2) Half

(3) One fourth

(4) Four times

02 40 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 2

A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is-

(a) 20 N

(b) 50 N

(c) 100 N

(d) 2 N

02 20 PM IST - 03 Apr'24

JEE Main April 4 Mathematics Exam 2024 Model Question 1

The vertices of a triangle ABC are A(1,2), B(- 3, 4), and C(5,8), then the orthocentre of △ABC is?

02 10 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Model Question 1

What is the correct IUPAC name of the following compound?

i. 1 - ethyl - 3,3-dimethyl cyclohexane
ii. 3 - ethyl -1,1-dimethyl cyclohexane
iii. 1 - ethyl - 3,3-dimethyl cyclohexene
iv. 3 - ethyl - 1,1-dimethyl cyclohexene

02 00 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 1

4 objects of mass 1 kg are kept on vertices of a square of side 2 metres and an axis is passing perpendicular to the plane through one of the vertices, then calculate the Moment of Inertia about this axis.

01 50 PM IST - 03 Apr'24

JEE Main 4 April 2024 Exam Mathematics Practice Question 1

If a line L = 4x + 5y = 20 trisects two other lines L1 and L2 that pass through the origin, then find the tangent made by the line L.

01 40 PM IST - 03 Apr'24

JEE Main 4 April 2024 Important Chemistry Question 1

The compound (CH₂)₄C₂H₂ is:
i. Alicyclic
ii. Aromatic
iii. Antiaromatic
iv. Acyclic

01 30 PM IST - 03 Apr'24

JEE Main April 4 2024 Exam Physics Important Question 1

A block of mass 0.1 kg is held against a wall applying a horizontal force of 5N on the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is

01 20 PM IST - 03 Apr'24

JEE Main 4 April 2024 Mathematics Exam Practice Question 1

Find p if:
3 + (3 + p)/4 + (3 + 2p)/42 + ...∞ = 8

01 10 PM IST - 03 Apr'24

JEE Main 4 April 2024 Chemistry Exam Model Question 1

Which of the following compounds are polar?
i. CC_l4
ii. CH₂ = CH2
iii. CO₂
iv. CH₃Cl

01 00 PM IST - 03 Apr'24

JEE Main 4 April 2024 Physics Exam Model Question 1

A body of mass 1000 kg has a velocity of 6 m/s. If an extra 2000 kg mass is embedded in it, then what will be the velocity of the combined mass?

12 30 AM IST - 03 Apr'24

JEE Main 2024 Question Paper (April 4): Mathematics Important Question 7

If z is a complex number, then the minimum value of |z| + |z − 1| is ______.