JEE AMU B.Tech Entrance Exam Mock Test- 8 Free Online Test 2026

When key K is kept closed, condenser C is charged to potential V. When plates of capacitors are moved apart, its capacitance, C = ϵ_oA/d decreases.
As potential of condenser remains same, charge Q = CV decreases. So option is correct. Once key K is closed, condenser gets charged, Q = CV.
Now, if key K is opened, battery is disconnected, no more charging can occur i.e. Q remains same.
As plates or capacitor are moved apart, its capacity C = ϵ_oA/d decreases.
Therefore, its potential, V = q/C increases

Power=IV
Where I=V_rms value of current=I_V
And V=V_rms value of voltage=E_V
Therefore, P=E_VI_V

Since the collision is head-on and there are no external forces, both momentum and kinetic energy of the system are conserved.

Let's denote:

• m₁ = 1 kg (mass of the first ball)
• u = initial velocity of the first ball
• v = final velocity of the first ball after collision = -u/3
• m₂ = mass of the second ball (unknown)
• V = velocity of the second ball after collision

From the conservation of momentum:

m₁ × u = m₁ × v + m₂ × V

1 × u = 1 × (-u/3) + m₂ × V

u = -u/3 + m₂ × V

4u/3 = m₂ × V                (1)

From the conservation of kinetic energy:

(1/2) × m₁ × u² = (1/2) × m₁ × (u/3)² + (1/2) × m₂ × V²

(1/2) × u² = (1/2) × u²/9 + (1/2) × m₂ × V²

u² = u²/9 + m₂ × V²

8u²/9 = m₂ × V²         (2)

From equation (1):

V = 4u/(3m₂)

Substitute V in equation (2):

8u²/9 = m₂ × (4u/(3m₂))²

8u²/9 = m₂ × (16u²)/(9m₂²)

8u²/9 = 16u²/(9m₂)

8m₂ = 16

m₂ = 2

Therefore, the mass of the other ball is 2 kg.

Concept:

Newton's law of gravitation: The force of attraction between any objects in the universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

• The force acts along the line joining the two bodies.
• The gravitational force is a central force that is It acts along the line joining the centers of two bodies.
• It is a conservative force. This means that the work done by the gravitational force in displacing a body from one point to another is only dependent on the initial and final positions of the body and is independent of the path followed.

• The moon revolves around the earth in a circular orbit (not perfectly circular). Sun exerts a gravitational force on both, the earth and moon. The major force acting on the moon is due to the gravitational force of attraction of the sun and earth and the moon is not always on the line joining the sun and earth. 
• Two forces acting on the moon have different lines of action or the forces are not central, so it's motion will not be strictly elliptical.

Hence, option (b) is the correct answer.

Sum of masses = 1 + 1.5 + 2 + M = 4.5 + M
x-coordinate;
(1*2 + 1.5*1 + 2*2 – M)/(4.5 + M) = 1
4.5 + M = 7.5 – M
2M = 3
M = 1.5 kg.

The change in velocity (Δv) is the final velocity minus the initial velocity:

Δv = 36km/h − 18km/h = 18km/h

Convert Δv to m/s:

Δv = 18 × 1000 / 3600 m/s ≈ 5m/s

The change in time (Δt) is given as 5 seconds.

Now, use the formula for acceleration:

a = Δv/Δt = 5/5 m/s² = 1m/s²

So, the acceleration of the automobile is 1m/s², and the correct answer is (c) 1 m/s².

  6 means sp³d²

I₃ , SF₄ , and PCl₅ ; all have sp³d hybridization.

Firstly we have to convert mole fraction into molality.

Since the acid is only 0.059% ionized, therefore the concentration of ions in solution = 0.1 x 0.059 / 100 = 0.000059

Ka = [H⁺] [X^–] / [HX] = (0.000059)² / 0.1 = 3.5 x 10^-8

dsp² is square planar geometry.

The correct answer is option C
Relative lowering of vapour pressure:
= lowering of vapour pressure of solution/ vapour pressure of pure solvent
=0.0175/17.5=0.001

Mass of solvent = 1000 g
Molar mass of urea (NH₂CONH₂) = 60gmol⁻¹
0.25 mole of urea = 0.25 × 60 = 15g
Total mass of solution = 100 + 15 = 1.015kg
1.015 kg of solution contain urea = 15g
2.5 kg of solution = 

Cl₂ + 2OH^- → Cl + OCI^- + H₂O is a disproportionation reaction.

Cl⁰ → Cl^-1

Cl⁰ → Cl⁺¹

Hence correct option is B

The correct answer is option A

V₁ = 30 mL, M₁ = 0.5 M, V₂ = 500 mL, M₂ = ?,
M₁V₁ = M₂V₂
0.5 x 30 = M₂ × 500 or M₂ = 0.03 M

Due to e^- withdrawing capacity of fluorideion, it withdraws. from nitrogen in NF₃ make it weakerlig and while presence of e^- donating methyl group makes the nitrogen in N(CH₃)₃ a strong ligand. In aqueous medium, NF₃ furnishes fluorideion.

Presence of electron-withdrawing groups, like -NO₂ and -Cl, on the benzene ring increases the acidic strength of phenol.
-NO₂ has stronger electron-withdrawing effect than -Cl.
Presence of electron-donating groups, like -OCH₃ and -CH₃, decreases the acidic strength of phenol.
-OCH₃ group has stronger electron-donating effect than -CH₃.
Hence, the correct order of acidic strength is: (III) > (I) > (II) > (IV).

We have,



Centre of smallest circle is A
Centre of largest circle is B

Hence,

Hence,
a = 3, b = 2
a + b = 5

Given two circles x² + y² = 1 and (x − 9)² + (y − 12)² = 4
Here, the centres and radii of given circles are C₁(0, 0) & C₂(9, 12) and radii R₁ = 1 & R₂ = 2, respectively.

Thus, the given circles are external to each other.

 

∴ The Shortest distance between given circles are AB = C₁C₂ − (R₁ + R₂).
= 15 − (1 + 2)
= 12

We know that to every square matrix, A = [aij] of order n. We can associate a number called the determinant of square matrix A, where aij = (i, j)th element of A. Thus, the determinant is a number associated with a square matrix.

13, a₁, a₂, a₃, ....a₂₀, 67 are in AP

∴

= 800

Now, AM ≥ GM

∵

∴∴The maximum value of a₁⋅a₂⋅a₃⋅....a₂₀ is (40)²⁰

Focus of parabola y² = 8x is (2,0). Equation of circle with centre (2,0) is (x−2)² + y² = r²
Let AB is common chord and Q is mid point i.e. (1,0)
AQ² = y² = 8x
= 8×1 = 8
∴ r² = AQ² + QS²
= 8 + 1 = 9
So required circle is (x−2)² + y² = 9

Given:

Equation₁ = ax + 9y = 1

Equation₂ = 9y - x - 1 = 0 

Concept used:

If linear equations are a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0. Here, the equations have an infinite number of solutions, if

a₁/a₂ = b₁/b₂ = c₁/c₂

Calculation:

We have equations,

ax + 9y = 1 

⇒ ax + 9y - 1 = 0

and, 9y - x - 1 = 0

⇒ x - 9y + 1 = 0

Here, a₁ = a, b₁ = 9, c₁ = -1

and, a₂ = 1, b₂ = -9, c₂ = 1

As we know that 

a1/a2 = b1/b2 = c1/c₂

⇒ a/1 = 9/-9 = -1/1

⇒ a = -1 = -1

⇒ a = -1

∴ The value of a is -1.

We have


Also for the greatest value of abc² the numbers have to be equal, i.e a = b = c/2
Also given that maximum value = 1/64
so, a + b + c = 1
i.e. a = b = 1/4, c = 1/2