JEE Main Part Test - 2

Question 1

A particle is projected upward from the surface of earth (radius = R) with a speed equal to the orbital speed of a satellite near the earth’s surface. The height to which it would rise is

Accepted Answer

R

Answer

&#8730;2R

Answer

R/&#8730;2

Answer

2R

Question 2

A spherical hole is made in a solid sphere of radius R. The mass of the original sphere was M.The gravitational field at the centre of the hole due to the remaining mass is

Accepted Answer

GM/2R2

Answer

zero

Answer

GM/8R2

Answer

GM/R2

Question 3

Three particles P, Q and R placed as per given figure. Masses of P, Q and R are √3 m, √3 m and m respectively. The gravitational force on a fourth particle ‘S’ of mass m is equal to

Accepted Answer

in SQ direction only

Answer

is ST direction only

Answer

is SQ direction and in SU direction

Answer

Question 4

A cylindrical tank has a hole of diameter 2r in its bottom. The hole is covered wooden cylindrical block of diameter 4r, height h and density ρ/3.

Situation I : Initially, the tank is filled with water of density ρ to a height such that the height of water above the top of the block is h₁ (measured from the top of the block).

Situation II : The water is removed from the tank to a height h₂ (measured from the bottom of the block), as shown in the figure.
The height h₂ is smaller than h (height of the block) and thus the block is exposed to the atmosphere.

Q. Find the minimum value of height h₁ (in situation 1), for which the block just starts to move up?

Accepted Answer

5h/3

Answer

2h/3

Answer

5h/4

Answer

5h/2

Question 5

A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container.
As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm respectively. The upper end of the container is open to the atmosphere.

Q. If the piston is pushed at a speed of 5 mms^–1, the air comes out of the nozzle with a speed of

Accepted Answer

2 ms&ndash;1

Answer

0.1 ms^–1

Answer

1 ms&ndash;1

Answer

8 ms&ndash;1

Question 6

If the elastic limit of copper is 1.5 × 10⁸ N/ m², determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.

Accepted Answer

0.912 mm

Answer

1.012 mm

Answer

0.712 mm

Answer

0.812 mm

Question 7

A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire? Young's modulus for steel: E = 20 × 10¹⁰ Pa .

Accepted Answer

1.4 mm

Answer

10 mm

Answer

1.5 mm

Answer

12.4 mm

Question 8

Water is flowing continuously from a tap having an internal diameter 8 × 10^-3m. The water velocity as it leaves the tap is 0.4 ms^-1. The diameter of the water stream at a distance 2 × 10^-1 m below the tap is close to

[AIEEE 2011]

Accepted Answer

3.6 × 10^-3 m

Answer

7.5 × 10^-3 m

Answer

9.6 × 10^-3 m

Answer

5.0 × 10^-3 m

Question 9

There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to

Accepted Answer

h &#160; &#160;

Answer

&#8730;h &#160;

Answer

h3/2 &#160;

Answer

h2

Question 10

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively, are T₂ and T₁ (T₂ >T₁) . The rate of heat transfer through the slab, in a steady state is with f equal to

Accepted Answer

1/3

Question 11

In which case change of oxidation number of V is maximum?

Accepted Answer

Answer

Answer

Answer

Equal in each case

Question 12

The complex [Fe(H₂O)₅NO]²⁺ is formed in the ring-test for nitrate ion when freshly prepared FeSO₄ solution is added to aqueous solution of followed by the addition of conc. H₂SO₄. NO exists as NO⁺(nitrosyl).

Q. Magnetic moment of Fe in the ring is

Accepted Answer

Question 13

The pK_a of a weak acid, HA, is 4.80. The pK_b of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be -

[AIEEE-2008]

Accepted Answer

7.01

Answer

4.79

Answer

9.22

Answer

9.58

Question 14

In aqueous solution the ionization constants for carbonic acid are K₁ = 4.2 x 10^-7 and K₂ = 4.8 x 10^-11 Selection the correct statement for a saturated 0.034 M solution of the carbonic acid.

[AIEEE-2010]

Accepted Answer

The concentration of H⁺ and are approximately equal.

Answer

The concentration of H⁺ is double that of

Answer

The concentration of is 0.034 M.

Answer

The concentration of is greater than that of

Question 15

How many litres of water must be added to litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2?

[AIEEE-2013]

Accepted Answer

9.0 L

Answer

2.0 L

Answer

0.1 L

Answer

0.9 L

Question 16

For the following electrochemical cell reaction at 298 K:

Zn(s) + Cu²⁺(aq) ⇌ Cu(s) + Zn²⁺(aq),

Given that the standard cell potential (E° cell) is +1.10 V.

Accepted Answer

37.22

Answer

0.027

Answer

0.012

Answer

85.73

Question 17

A 0.10 M solution of a weak acid, HX, is 0.059% ionized. Evaluate K_a for the acid.

Accepted Answer

3.5 x 10^-8

Answer

4.2 x 10^-6

Answer

3.8 x 10^-9

Answer

7.0 x 10^-6

Question 18

AgCI(s)is sparingly soluble salt,

AgCl (s) Ag⁺(aq) + Cl^-(aq)

There is

Accepted Answer

increase in solubility if NH₃(aq) is added

Answer

increase in solubility if NaCI or AgNO₃ is added

Answer

increase in solubility if KCI is added

Answer

decrease in solubility if H₂O is added

Question 19

Which one of the following is the approximate pH of 0.01 M solution of NaOH at 298 k?

Accepted Answer

12

Answer

10-2

Answer

2.5

Answer

2

Question 20

In the expansion of (1+x)⁶⁰, the sum of coefficients of odd powers of x is

Accepted Answer

259

Answer

261

Answer

260

Answer

none of these.

Question 21

The middle term in the expansion of (1+x)²ⁿ is

Accepted Answer

Answer

2ⁿC_n−1xⁿ⁻¹

Answer

2ⁿC_n+1xⁿ⁺¹

Answer

2nCn

Question 22

Accepted Answer

a rational number

Answer

a negative integer

Answer

an irrational number

Answer

none of these

Question 23

The mid points of the sides of a triangle are (5, 0), (5, 12) and (0, 12), then orthocentre of this triangle is

Accepted Answer

(0, 0)

Answer

(0, 24)

Answer

(10, 0)

Answer

Question 24

Area of a triangle whose vertices are (a cos q, b sinq), (–a sin q, b cos q) and (–a cos q, –b sin q) is

Accepted Answer

Ab

Answer

Ab sin q cos q

Answer

A cos q sin q

Answer

1/2 ab

Question 25

If A(cosa, sina), B(sina, – cosa), C(1, 2) are the vertices of a ΔABC, then as a varies, the locus of its centroid is

Accepted Answer

3(x² + y²) – 2x – 4y+1=0

Answer

x² + y² – 2x – 4y+3=0

Answer

x²+y² – 2x–4y+1 = 0

Answer

None of these

Question 26

Two perpendicular tangents to the circle x²+y² = r² meet at P. The locus of P is

Accepted Answer

x²+ y² = 2r²

Answer

x + y = r

Answer

x2+y2 = <img src="https://cn.edurev.in/ApplicationImages/Temp/59_ea4b5163-69cf-4154-af8f-d145c5b4aff4_lg.PNG" />

Answer

x²+y² = 4r²

Question 27

The locus of a variable point whose distance from the point (2, 0) is 2/3 times its distance from the line x = 9/2 is

Accepted Answer

an ellipse

Answer

a parabola

Answer

a hyperbola

Answer

a circle

Question 28

The locus of a point such that two tangents drawn from it to the parabola y² = 4ax are such that the slope of one is double the other is

Accepted Answer

y² = 9/2 ax

Answer

y² = 9/4 ax

Answer

y2 = 9ax

Answer

x2 = 4ay

Question 29

The focus of the parabola x² - 8x + 2y + 7 = 0 is

Accepted Answer

(4, 4)

Answer

(4, 9/2)

Answer

Answer

Question 30

is equal to

Accepted Answer

Answer

Answer

Answer

None of the above

JEE Main Part Test - 2 Free Online Test 2026

MCQ Practice Test & Solutions: JEE Main Part Test - 2 (75 Questions)

A particle is projected upward from the surface of earth (radius = R) with a speed equal to the orbital speed of a satellite near the earth’s surface. The height to which it would rise is

A spherical hole is made in a solid sphere of radius R. The mass of the original sphere was M.The gravitational field at the centre of the hole due to the remaining mass is

Three particles P, Q and R placed as per given figure. Masses of P, Q and R are √3 m, √3 m and m respectively. The gravitational force on a fourth particle ‘S’ of mass m is equal to

If the elastic limit of copper is 1.5 × 10⁸ N/ m², determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.

A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire? Young's modulus for steel: E = 20 × 10¹⁰ Pa .

Water is flowing continuously from a tap having an internal diameter 8 × 10^-3m. The water velocity as it leaves the tap is 0.4 ms^-1. The diameter of the water stream at a distance 2 × 10^-1 m below the tap is close to
[AIEEE 2011]

There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively, are T₂ and T₁ (T₂ >T₁) . The rate of heat transfer through the slab, in a steady state is with f equal to

In which case change of oxidation number of V is maximum?

The complex [Fe(H₂O)₅NO]²⁺ is formed in the ring-test for nitrate ion when freshly prepared FeSO₄ solution is added to aqueous solution of followed by the addition of conc. H₂SO₄. NO exists as NO⁺(nitrosyl).
Q. Magnetic moment of Fe in the ring is

The pK_a of a weak acid, HA, is 4.80. The pK_b of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be -
[AIEEE-2008]

In aqueous solution the ionization constants for carbonic acid are K₁ = 4.2 x 10^-7 and K₂ = 4.8 x 10^-11 Selection the correct statement for a saturated 0.034 M solution of the carbonic acid.
[AIEEE-2010]

How many litres of water must be added to litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2?
[AIEEE-2013]

For the following electrochemical cell reaction at 298 K:
Zn(s) + Cu²⁺(aq) ⇌ Cu(s) + Zn²⁺(aq),
Given that the standard cell potential (E° cell) is +1.10 V.

A 0.10 M solution of a weak acid, HX, is 0.059% ionized. Evaluate K_a for the acid.

AgCI(s)is sparingly soluble salt,
AgCl (s) Ag⁺(aq) + Cl^-(aq)

There is

Which one of the following is the approximate pH of 0.01 M solution of NaOH at 298 k?

In the expansion of (1+x)⁶⁰, the sum of coefficients of odd powers of x is

The middle term in the expansion of (1+x)²ⁿ is

The mid points of the sides of a triangle are (5, 0), (5, 12) and (0, 12), then orthocentre of this triangle is

Area of a triangle whose vertices are (a cos q, b sinq), (–a sin q, b cos q) and (–a cos q, –b sin q) is

If A(cosa, sina), B(sina, – cosa), C(1, 2) are the vertices of a ΔABC, then as a varies, the locus of its centroid is

Two perpendicular tangents to the circle x²+y² = r² meet at P. The locus of P is

The locus of a variable point whose distance from the point (2, 0) is 2/3 times its distance from the line x = 9/2 is

The locus of a point such that two tangents drawn from it to the parabola y² = 4ax are such that the slope of one is double the other is

The focus of the parabola x² - 8x + 2y + 7 = 0 is

is equal to

Mock Tests for JEE Main and Advanced 2026

Mock Tests for JEE Main and Advanced 2026

Top Courses for JEE

About this JEE Practice Test

Explore more JEE Study Resources

JEE Main Part Test - 2 Free Online Test 2026

MCQ Practice Test & Solutions: JEE Main Part Test - 2 (75 Questions)

A particle is projected upward from the surface of earth (radius = R) with a speed equal to the orbital speed of a satellite near the earth’s surface. The height to which it would rise is

A spherical hole is made in a solid sphere of radius R. The mass of the original sphere was M.The gravitational field at the centre of the hole due to the remaining mass is

Three particles P, Q and R placed as per given figure. Masses of P, Q and R are √3 m, √3 m and m respectively. The gravitational force on a fourth particle ‘S’ of mass m is equal to

If the elastic limit of copper is 1.5 × 108 N/ m2, determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.

A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire? Young's modulus for steel: E = 20 × 1010 Pa .

Water is flowing continuously from a tap having an internal diameter 8 × 10-3m. The water velocity as it leaves the tap is 0.4 ms-1. The diameter of the water stream at a distance 2 × 10-1 m below the tap is close to[AIEEE 2011]

There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively, are T2 and T1 (T2 >T1) . The rate of heat transfer through the slab, in a steady state is with f equal to

In which case change of oxidation number of V is maximum?

The complex [Fe(H2O)5NO]2+ is formed in the ring-test for nitrate ion when freshly prepared FeSO4 solution is added to aqueous solution of followed by the addition of conc. H2SO4. NO exists as NO+ (nitrosyl).Q. Magnetic moment of Fe in the ring is

The pKa of a weak acid, HA, is 4.80. The pKb of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be - [AIEEE-2008]

In aqueous solution the ionization constants for carbonic acid are K1 = 4.2 x 10-7 and K2 = 4.8 x 10-11 Selection the correct statement for a saturated 0.034 M solution of the carbonic acid. [AIEEE-2010]

How many litres of water must be added to litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2? [AIEEE-2013]

For the following electrochemical cell reaction at 298 K:Zn(s) + Cu²⁺(aq) ⇌ Cu(s) + Zn²⁺(aq),Given that the standard cell potential (E° cell) is +1.10 V.

A 0.10 M solution of a weak acid, HX, is 0.059% ionized. Evaluate Ka for the acid.

AgCI(s)is sparingly soluble salt,AgCl (s) Ag+(aq) + Cl-(aq) There is

Which one of the following is the approximate pH of 0.01 M solution of NaOH at 298 k?

In the expansion of (1+x)60, the sum of coefficients of odd powers of x is

The middle term in the expansion of (1+x)2n is

The mid points of the sides of a triangle are (5, 0), (5, 12) and (0, 12), then orthocentre of this triangle is

Area of a triangle whose vertices are (a cos q, b sinq), (–a sin q, b cos q) and (–a cos q, –b sin q) is

If A(cosa, sina), B(sina, – cosa), C(1, 2) are the vertices of a ΔABC, then as a varies, the locus of its centroid is

Two perpendicular tangents to the circle x2+y2 = r2 meet at P. The locus of P is

The locus of a variable point whose distance from the point (2, 0) is 2/3 times its distance from the line x = 9/2 is

The locus of a point such that two tangents drawn from it to the parabola y2 = 4ax are such that the slope of one is double the other is

The focus of the parabola x2 - 8x + 2y + 7 = 0 is

is equal to

Mock Tests for JEE Main and Advanced 2026

Mock Tests for JEE Main and Advanced 2026

Top Courses for JEE

About this JEE Practice Test

Explore more JEE Study Resources

If the elastic limit of copper is 1.5 × 10⁸ N/ m², determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.

A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire? Young's modulus for steel: E = 20 × 10¹⁰ Pa .

Water is flowing continuously from a tap having an internal diameter 8 × 10^-3m. The water velocity as it leaves the tap is 0.4 ms^-1. The diameter of the water stream at a distance 2 × 10^-1 m below the tap is close to
[AIEEE 2011]

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively, are T₂ and T₁ (T₂ >T₁) . The rate of heat transfer through the slab, in a steady state is with f equal to

The complex [Fe(H₂O)₅NO]²⁺ is formed in the ring-test for nitrate ion when freshly prepared FeSO₄ solution is added to aqueous solution of followed by the addition of conc. H₂SO₄. NO exists as NO⁺(nitrosyl).
Q. Magnetic moment of Fe in the ring is

The pK_a of a weak acid, HA, is 4.80. The pK_b of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be -
[AIEEE-2008]

In aqueous solution the ionization constants for carbonic acid are K₁ = 4.2 x 10^-7 and K₂ = 4.8 x 10^-11 Selection the correct statement for a saturated 0.034 M solution of the carbonic acid.
[AIEEE-2010]

How many litres of water must be added to litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2?
[AIEEE-2013]

For the following electrochemical cell reaction at 298 K:
Zn(s) + Cu²⁺(aq) ⇌ Cu(s) + Zn²⁺(aq),
Given that the standard cell potential (E° cell) is +1.10 V.

A 0.10 M solution of a weak acid, HX, is 0.059% ionized. Evaluate K_a for the acid.

AgCI(s)is sparingly soluble salt,
AgCl (s) Ag⁺(aq) + Cl^-(aq)

There is

In the expansion of (1+x)⁶⁰, the sum of coefficients of odd powers of x is

The middle term in the expansion of (1+x)²ⁿ is

Two perpendicular tangents to the circle x²+y² = r² meet at P. The locus of P is

The locus of a point such that two tangents drawn from it to the parabola y² = 4ax are such that the slope of one is double the other is

The focus of the parabola x² - 8x + 2y + 7 = 0 is