UGEE SUPR Mock Test-2 - JEE MCQ

(*) According to Rutherford's α-particles scattering experiment, following observations are made
(i) Most of the α-particles passed through the gold foil undeflected.
(ii) Only about 0.14% of the incident α-particles scattered by an angle greater than 1°.
(iii) About one α-particle in every 8000 α-particles deflects by angle more than 90°.
So, from above observation, we can conclude about the number of α-particle in given figure as,
n_A' > n_C' > n_B' 
i.e., number of a-particle will be maximum in A' and minimum in B'.
No given option is correct.

The process of ß^- decay is shown below

Thus, in this decay a neutron inside the nucleus decays into a proton with the emission of an electron e^- and a particle called anti-neutrino (S').

Given, half-life, T_1/2 = 15 years
Time, t = 30 years
∴ Number of half-life, n = t/T = 30/15 = 2
The number of nuclei left undecayed in 30 years
or 2 half-lives is

:. Fraction of decayed element 
= 3/4 or 0.75

The given circuit is as shown

The truth table for P can be shown as

The truth table for Q can be shown as

Thus, Q is 1 for any value of P. So, the values satisfying given condition are,
P = 0, Q = 1

The magnetic field in between because of each will be in opposite direction.

Given, mass, m (0.3 ± 003) g
Radius, r = (0.5 ± 0.005) mm
Length, I = (6 ± 0.06) cm

Percentage error in ρ,

Let h be the height of platform, then speed of walking (v_g) = h/20
Speed of escalator (v_e) = h/30
Time taken by girl when she walk up on the movin escalator is

The woman is riding a bicycle at a speed of 12 ms^-1 from east to west.

The rain is falling vertically at the same speed of 12 ms^-1.

To determine the direction in which she should hold her umbrella, consider the relative velocity of the rain:

• The horizontal component of the rain's velocity is towards the east at 12 ms^-1 (opposite the woman's direction).
• The vertical component is 12 ms^-1 downwards.

Using these components, the resultant direction of the rain can be calculated:

• The angle can be determined using trigonometry: tan^-1(12/12) = 45°.
• Thus, she should hold her umbrella at 45° towards the west.

(a) Consider a string of length I connected to a particle as shown in figure

As the particle is moving with velocity v in uniform circular motion, so the net force must be equal to the centripetal force, which is provided by the tension in the string.
∴ Net force = Centripetal force (F_C)
= Tension in string (T)
⇒ 

Let in time t, the body will acquire a velocity of v from rest.
As, power (P) = rate of doing work = dW/dt

For motion in one dimension,
P = Fv cos 0° = Fv   .....(i)
From first equation of motion,
v = u + at
v = at   ...(ii)  (∵ u = 0)
From Eqs. (i) and (ii), we get
P = F × at = ma × at ...(ii)     (∵ u = 0)
= ma² t
As ma² is constant.
so, P ∝ t

Given, mass, M = 2 kg
I_x = 0.2 kg -m² 
and I_y = 0.3 kg -m²
According to the perpendicular axis theorem, the moment of inertia of the rectangular plate about an axis passing through O and perpendicular to the plane of plate is
I = I_x + l_y = 0.2 + 0.3
= 0.5kg m²
Also, 1 = Mk²
where, k = radius of gyration.
⇒ 

AM ≥ HM

For minimum value = 0.
Let and   are anti-parallel so

he equation represents a pair of lines if
1·1·4 + 2·f·g·1-1·f²-1·g²- 4·1² = 0
⇒ (f - g)² = 0 ⇒ f = g
The equation becomes (x + y)² + 2g(x + y) + 4 = 0
which represents a pair of parallel lines, which
are real provided (2g)² - 4·4·1 ≥ 0 ⇒ |g| ≥ 2.
This confirms Statement-I is true. Statement-2 is a well-known condition for an equation to represent a pair of real lines, confirming its truth. Thus, both statements are true, and Statement-2 is not a correct explanation for Statement-1.

For (x) to be defined, we must have

Total number of ways = 6 × 6 × ..... to n times = 6ⁿ.
Total number of ways to show only to even number = 3 × 3 × ........ to n times = 3ⁿ.
∴ required number of ways = 6ⁿ - 3ⁿ.

The given relation is xy + y² = tan x + y.
Differentiating both sides with respect to x, we get

Fe³⁺(d⁵) has 5 unpaired electrons therefore magnetic moment
which is maximum among given options. As Sc³⁺ Ti³⁺ , Cr³⁺ and V³⁺ contain 0, 1, 3, and 2 number of unpaired electrons respectively.

Maleic acid and fumaric acids are geometrical isomers.

Gaseous ions, when dissolved in water, get hydrated and heat is evolved (heat of hydration).
Cl^- (g) + aq → Cl^- (aq) is such reaction

Phosphine (PH₃) is produced by the reaction of:

• White phosphorus with NaOH under heat
• Calcium phosphide with water

However, red phosphorus does not react with NaOH to produce PH₃ because:

• It is less reactive
• It requires more stringent conditions

These stringent conditions are typically not met in this reaction.

More will be the electronegativity of X, lesser will be the bond length of X-O bond.

According to the ideal gas law, PV = nRT, where n is the number of moles. The number of molecules is proportional to the number of moles. For the first vessel:

P₁ = 1.5 atm, V₁ = 16.4 L, T₁ = 27°C = 300 K (273 + 27)

For the second vessel:

P₂ = 4.1 atm, V₂ = 5 L, T₂ = 227°C = 500 K (273 + 227)

Using n = PV/RT, the ratio of molecules n₁/n₂ is given by:

(P₁V₁/T₁) / (P₂V₂/T₂) = (1.5 * 16.4 / 300) / (4.1 * 5 / 500)

= (0.082) / (0.041)

= 2

ΔH = ΔU + ΔnRT
Δn = n_P - n_R