VITEEE PCME Mock Test - 8 - JEE MCQ

P₁ + λP₂ = 0
(2x - y - 4) + λ(y + 2z - 4) = 0
It passes through (1, 1, 0)
⇒ 1 + λ = 0
⇒ λ = -1
Equation of plane is x - y - z = 0

Let 

Similarly, 

domain = R - {0,-2)

Since, 
Also, 

Hence f is one - one

Side =

a₁, a₂, .......... a₁₆ are in A.P.
a₁ + a₄ + a₇ + a₁₀ + a₁₃ + a₁₆ = 114
a₁ + a₁₆ = a₄ + a₁₃ = a₇ + a₁₀ = a₅ + a₁₂
3(a₅ + a₁₂) = 114
a₅ + a₁₂ = 38
(a₁ + a₅ + a₁₂ + a₁₆) = 2(a₅ + a₁₂) = 2 × 38 = 76

In circuit (1), on closing the switch, the current in the inductor is zero due to self induction, i.e., i₁ = 0.
In circuit (2), on closing the switch, the current in the inductor is zero due to self induction.

Therefore,

In circuit (3), on closing the switch, the current in the inductor is again zero due to the same reason.

Therefore,

Thus, it is obvious that,
i₂ > i₃ > i₁ (= 0)

We know that any moving charge will produce magnetic field. Thus, a current-carrying conductor will also produce a magnetic field which is given by Biot-Savart's law,

where,  is the proportionality constant,
r is the distance of the point where the magnetic field is to be determined,
i is the current flowing in the conductor,
dl is the length of the conductor in consideration and its direction is considered to be in direction of the flow of current.
Thus, from the above equation, we find that, B ∝ i.

Given:
Inductance, L = 1 mH = 1 × 10⁻³ H
Capacitance, C = 10 μF = 10 × 10⁻⁶ F
Resistance, R = 50 Ω

Since the reactance of the inductor and capacitor are the same:
X_L = X_C
ωL = 1 / (ωC)

Squaring both sides:
ω² = 1 / (LC)

Substituting values:
ω = √(1 / (L × C))
= √(1 / (10⁻³ × 10 × 10⁻⁶))
= 10⁴ rad/s

Now, reactance of either component:
X_L = ωL = (10⁴) × (10⁻³) = 10 Ω

Therefore, X_C = 10 Ω.

According to Gauss's law, the total electric flux Φ through a closed surface enclosing a charge q is given by:
Φ = q / ε₀

Since the charge +q is placed at the center of the cube, the entire charge is enclosed within the surface. Thus, the total electric flux emerging from the cube is:
Φ = q / ε₀
Correct answer: A) q / ε₀

Saturation current is proportional to intensity while stopping potential increases with increase in frequency.
Hence, f_a = f_b while I_a < I_b

The convection is process of heat transfer via medium but when glass surface is heated due to filament of bulb, it heated only due to radiation. It is because when glass bulb is manufactured, inside glass bulb, vacuum is maintained means there is no medium inside the bulb.

Reading = Potential gradient × length
= 0.01 × 0.5
= 5 × 10^-3 V
= 5 mV

Rate = K [A]^x [B]^y
r₁ = k[A]₁^x [B]₁^y
r₂ = k[A]₂^x [B]₂^y

8 = 2¹2^y
2^y = 4
∴ y = 2
∴ R = k[A] [B]²

Aluminium will form a gel-like precipitate when we add NH₄Cl and NH₄OH. Also, Al(OH)₃ forms gelatinous mass.

Molecular formula C₂BrClFI has one degree of unsaturation.
It exists in three positional isomeric forms, each of which exists as two geometrical isomers (E-Z forms).
For example:

Both [Ti(H₂O)₆]⁴⁺ and [Sc(H₂O)₆]³⁺ are colourless due to the absence of free electrons in 3d− subshell. d-d transition is not possible because d-orbital is vacant, and all other electrons are completely paired.
so, statement I is false and statement II is correct.

When there is a change in the optical rotation due to the change in the equilibrium between two anomers, then the corresponding stereocenters interconvert, and it is called as mutarotation.
When either of glucose's two forms is dissolved in the water, there is a change in the rotation till the equilibrium value of +52.5°. 

Cellobiose is the repeating disaccharide unit of cellulose having the glyocosidic linkage β (1→4); its full name is thus 4-O-β-D-glucopyranosyl D-α- glucopyranose

Apply Kohlrausch's law, which states that at an infinite dilution the equivalent conductivity of an electrolyte is equal to the sum of the equivalent conductances of anions and cations. So, we can calculate the equivalent conductance only for ions. Hence, the equivalent conductance of Al₂(SO₄)₃ at infinite dilution is,

Silicon is used for making a transistor because the introduction of a small amount of impurities like phosphorus, arsenic, gallium increases the conductivity of Silicon. This process is called as doping.

This is an example of azotisation reaction and the product is p-Amino azobenzene.
Hence, the correct answer is:

From II, we get that Rajesh ranks 23^rd from the bottom, i.e. 18^th from the top, as it is a class of 40 students.
From I and II, we find that Meera is 3 ranks below 18^th rank from the top, i.e. she ranks 21^st from the top.
From II and III, we find that Meera is 3 ranks below 23^rd rank from the bottom, i.e. she ranks 20^th from the bottom. So, she ranks 21^th from the top.
Therefore, either I and II or II and III are sufficient to answer the question.

The least number that must be added to 752 so that the sum is completely divisible by 59 will be 15 as when we divide 752 by 59, we get 44 as the remainder.
The required number will be obtained by subtracting the remainder from the divisor = 59 − 44 = 15

According to the given data:

• The female literacy rate was at its lowest in 1951, at 8.86%.
• From 1951 to 2011, the female literacy rate showed a consistent increasing trend, rising from 8.86% in 1951 to 65.46% in 2011.

Thus, the correct answer is 1951.