JEE AMU B.Tech Entrance Exam Mock Test- 4 Free Online Test 2026

Given: T/2 = 0.5 s
T = Is
Frequency, f = 1/T = 1/1 = 1 Hz
If A is the amplitude, then
2A = 50cm ⇒ A = 25cm

The time when the kinetic energy and potential energy of the system become equal can be determined as follows:

The condition for equal kinetic and potential energy is given by:
Kinetic Energy (KE) = Potential Energy (PE)

⇒  A² = 2x²

The displacement X is given by: X = A sin(ωt)

Solving these equations, 

A² = 2x²

X = A sinωt

x = 8 sec

Drift velocity is directly proportional to potential difference.
Drift velocity is defined as the average velocity with which free electrons get drifted towards the positive end of the conductor under the influence of an external electric field.
Drift velocity is given by
v_d​= eEτ​/ m
But, E=V/l​
(if l is length of the conductor and V is constant potential difference applied across the ends of the conductor)
∴v_d​= eVτ​/ml
⇒v_d​∝V
So, when the potential difference is doubled the drift velocity will be doubled.
Note - Current flowing through a conductor is directly proportional to the drift velocity.

The FBD of blocks is as shown

From Newton's second law

4mg - 2T cos θ = 4mA    ....(1)

and T - mg = ma     .....(2)

 and from constraint we get a = A cos θ   ... (3)

solving equation (1) , (2) and (3)

we get acceleration of block of mass 4 m, a = 5g/11 downwards.

Explanation:

Hydrogen is a diatomic gas. (C_P = 3.5R)

energy transferred by heat to the gas

Q=nCPΔT=1×3.5×8.31×120=3490J=3.49KJ

Maximum acceleration of a particle in the simple harmonic motion is directly proportional to the square of angular frequency i.e.

From Pascal’s law: P₁ ​= P₂​

⇒ F₁/A₁ ​​= ​F₂/A₂​​
⇒ F₁/πr_1​²​ ​= F₂/πr₂​² ​​
⇒ F₁ = (F₂ * r_1​² ) / r₂​²  = 1350 * 9.8 * (5 * 10^-2)² / (15 * 10^-2)² = 1470 N ​= 1.47 * 10³ N

We have, (1/v)−(1/−90)=1/f⇒(1.5−1)(1/30)=1/60
∴ v=180 cm
∴|m|=∣v/u∣=180/90=2.0

ma=Bil−mg
a=0.3×100×2×10⁻²−10×6×10⁻³​/ m
a= 0.6−0.06​/6×10⁻³
=100−10
=90ms⁻²

According to the second law the orbital radius and angular velocity of the planet in the elliptical orbit will vary. The planet travels faster when closer to the Sun, then slower when farther from the Sun. Hence we can say that the transverse acceleration is zero while radial and longitudinal accelerations are not zero.

According to question P ∝ T³
But as we know for an adiabatic process the pressure 

 [NEET 2013]

According to Bernoulli’s theorem,

= constant and Av = constant

If A is minimum, v is maximum, P is minimum. NEET Kar. 2013]

The correct answer is option B

The general formula C_nH_2nO₂ could be for open chain carboxylic acids. For example, ethanoic acid: C₂H₄O₂.

Since the product of oxidation reacts with phenyl hydrazine, it is a carbonyl compound. Since it does not answer silver mirror test, it must be a ketone. Ketones are produced by the oxidation of secondary alcohols. So the compound X is isopropyl alcohol

The correct answer is Option B
Let x M be the equilibrium concentration of PCl₃​.
The equilibrium reaction is shown below.
PCl₅​(g) ⇌ PCl₃​(g) + Cl₂​(g)
The equilibrium concentrations of PCl₅​, PCl_3​ and Cl₂​ are 0.5×10⁻²M, x and x respectively.
The expression of the equilibrium constant is 
K_c​= ( [PCl3​][Cl2​] ​) / [PCl3​].
Substitute values in the above expression.
8.3 × 10⁻³  = x² / (0.5 × 10⁻¹​)
x² = 4.15m × 10⁻⁴
x ≃ 0.02M.

As OP lies on XZ plane so y co-ordinate is 0.

QP = r cos α 

PR = r sin α 

Co-ordinate of P = (rcosα,0,rsinα) 

Option a is correct.

The standard deviation of a set remains unchanged if each data is increased or decreased by a constant.
However, it changes similarly when data is multiplied or divided by a constant.
∴ The SD for the new data set will be = −2 × 3.5 = −7

Now   is real ⇒  Im  = 0

⇒  

⇒​  Im [(x² – y² + 2ixy) (x – 1) – iy)] = 0

⇒  2xy (x – 1) – y (x² – y²) = 0

⇒ y(x² + y² – 2x) = 0 ⇒  y = 0;  x² + y² – 2x = 0

∴ z lies either on real axis or on a circle through origin.

Let the number of children in each family be n.
Thus, the total number of children in both the families is 2n.
Now, it is given that tickets are distributed amongst the children of the families.
If all the tickets are distributed to the children in the families, the probability that all the three tickets go to the children in family B is given by:

n = 5

Q(-1, 3, 4), where Q is the midpoint of PR.
The normal to the plane is:

Equation of plane is:
2x - y - z + d = 0
Since the plane passes through the point (-1, 3, 4), d = 9
Hence, the equation of plane is:
2x - y - z + 9 = 0
From the given options; (-3, 2, 1) satisfies it.

Let P = (2t, t²)
For the distance between point P and centre of circle to be minimum, line drawn from the centre of circle to point P must be normal to the parabola at P.
The equation normal at P to x² = 4y:
y - t² = -1/t (x - 2t)
It passes through (-3, 0).
0 - t² = -1/t (-3 - 2t)
t³ + 2t + 3 = 0
(t + 1)(t² - t + 3) = 0
⇒ t = -1
Point P is (-2, 1).
The equation of tangent to x² = 4y at (x', y') is:
xx' = 2(y + y')
So, at P(-2, 1),
x(-2) = 2(y + 1)
x + y + 1 = 0