JEE Main Mock Test - 2 - JEE MCQ

By the principle of superposition of fields

Here  = net field at the centre of hole due to entire mass

 = field due to remaining mass

 = field due to mass in hole = 0

Consider the equilibrium of wooden block.
Forces acting in the downward direction are

(a) Weight of wooden cylinder

(b) Force due to pressure (P₁) created by liquid of height h₁ above the wooden block is
= P₁ × π (2r)² = [P₀ + h₁rg] × π (2r)²
Force acting on the upward direction due to pressure P₂ exerted from below the wooden block and atmospheric pressure is

At the verge of rising

So heat is given by 

H = I² Rt

time is fixed, unit time, Resistance of wire will remain the same. 

H ∝ I² 

So,

H = k I²    ---(1)

if the current becomes twice'

H' = k (2I)²    ---(2)

(2) divided by (1) we get

So, H' : H = 4 : 1

So we see, the heat generated in unit time becomes 4 times of its initial value.

The motion of the particles is roughly sketched in figure. By symmetry they will meet at the centroid O of the triangle. As the speed of all the particles is equal they will cover equal distance in any given interval of time.
If we join the instantaneous position of the particle at any time, the particles will form an equilateral triangle of same centroid as initial triangle.

Let us consider the motion of any one particle say A. At any instant, its velocity makes an angle 30° with line AO.

The component of the velocity along AO is vcos 30^∘. This component will be equal to the rate of change of distance between A and O.
At t = 0, distance between A and O

At time t = T, the separation between A and O is zero. Hence, time taken for AO to become zero,

The P − V equation is given as

putting P = P₀, we get


P attains the maximum value at V = 3V₀/2

Resultant amplitude

∴   I ∝ A²
⇒   I ∝ 4a² 

Given:

The particle have initial velocity zero, So electric field will be responsible for to move in opposite direction of electric field.
Magnetic force on the particle does not increase the speed of the particle since

Since acceleration is constant applying the onedimensional kinematics equation:
v² − u² = 2a²   

u = −15
f = 30 cm
from lens formula,

So distance from plane mirror is
u₂ = 30 + 15 = 45 cm
So u₂ = v₂ for plane mirror
So from the lens 45 + 15 = 60 cm to the right of it.

Maximum range 
= 25.3 × 103 m = 25.3 km
Hence the correct choice is (b).

(i) Kirchhoff's law states that the total current entering into the junction is equal to the total current leaving the junction and it is based on energy conservation. As long as the energy is conserved,  it doesn't matters whether the current is AC or DC. 
(iv) Emf of a cell depends upon the following factors-
(a) Emf is inversely proportional to the area of electrode.
(b) Emf is directly proportional to the distance of separation between the two electrodes.
(c) Emf is inversely proportional to the temperature of electrodes.
(d) Emf is inversely proprtional to the concentation of electrolytes. 

pH = −log(H⁺) = −log10⁻⁸ = 8
As the solution is acidic, pH<7. This is because [H⁺]from H₂₀[10⁻⁷] cannot be neglected in comparison to 10⁻⁸.
It is not possible for acid, so it is [H⁺], the [H⁺]of water is also added
Total [H⁺] in solution
= [H⁺] of HCl⁺[H⁺] of water
= (1 × 10⁻⁸ + 1 × 10⁻⁷)M
= (1 + 10) × 10⁻⁸ = 11 × 10⁻⁸M
∴ pH = −log[H⁺] = −log11 × 10⁻⁸
= −log11 + 8log10 = −1.0414 + 8 = 6.9586

Hydrolysis of substituted chlorosilanes yield corresponding silanols which undergo polymerisation.

Polymerisation of dialkyl silandiol yields linear thermoplastic polymer.

The reaction follows first-order kinetics. Hence k = 0.693/_t1/2 = 0.693/(80 s). For the reaction to be 80%, [A]_t/[A]₀ = 0.2. Hence

(i) Since H₂O is highly polar in nature and aniline is highly reactive towards electrophilic substitution.
Thus, Br₂ in H₂O gives: 2, 4, 6 tribromo aniline as main product i.e.


and as a result only mono-substituted bromine at p-position is the major product i.e.,

Nucleosides are the structural subunit of nucleic acids such as DNA and RNA. A nucleoside, composed of a nucleobase, is either a pyrimidine (cytosine, thymine or uracil) or a purine (adenine or guanine), a five carbon sugar which is either ribose or deoxyribose. The base connected to sugar at  position. Nucleotides are building blocks of nucleic acids DNA and RNA. Nucleotides are composed of a nitrogenous base, a five-carbon sugar (ribose or deoxyribose), and at least one phosphate group. Thus, a nucleoside plus a phosphate group yields a nucleotide.

The −NH₂ group of aniline is a very strong electron donor (+ M effect), hence it activates the benzene ring thoroughly and the electrophilic aromatic substitutions on the benzene ring are very easy to take place at ortho and para-positions.

Given :

ΔH = 400 J mol⁻¹

ΔS = 0.2 J K⁻¹ mol⁻¹

T = 298 K

We know that ΔG = ΔH − TΔS

At equilibrium, ΔG = 0

∴ TΔS = ΔH

T = ΔH / ΔS = ( 400 J mol⁻¹ ) / ( 0.2 Jk⁻¹ mol⁻¹)

T = 2000K

ΔG = 400 − (2000 × 0.2)

 = 0

if T > 2000K ΔG will be negative

The reaction would be spontaneous only beyond 2000K

Given, 2 sec2α = tanβ + cotβ 

Equation of directrix is x + y = 0


On simplifying we get-
(x − y)² = 8(x + y − 2)

We have,

On integrating both sides,

On integrating both sides,