BITSAT Mock Test - 4 - JEE MCQ

Magnetic field of 1 A turn/m = 4π × 10^-7 T

or V = 6 volt
To nullify the horizontal component of magnetic field of earth, plane of the coil should be normal to magnetic meridian.

According to the law of conservation of momentum,
l_ω = constant
When viscous fluid of mass m is dropped and starts spreading out, then its moment of inertia increases and angular velocity decreases. But when it starts falling, then its moment of inertia again starts decreasing and angular velocity increases.

Potential difference between two equipotential surfaces A and B,


or 

or t₁ ∝ r_A r_B    
Similarly, t₂ ∝ rB rC
Since r_A < r_B < r_C, therefore r_A r_B < r_B r_C,
∴  t₁ < t₂.

When considering the behaviour of the point charges, it's important to understand the concepts of force and potential energy.

• The point charges at (a, 0) and (-a, 0) exert forces on the charge at the origin.
• In equilibrium, there is a balance of forces acting on the charge at the origin.
• This balance results in the charge experiencing minimum force because it is not accelerating.
• At this equilibrium point, the potential energy is also at a minimum level, as potential energy is lowest when forces are balanced.

Thus, the charge at the origin in equilibrium will have minimum force and minimum potential energy.

Unit of magnetic field intensity is Am^-1.
Unit of magnetic flux is Wb (weber)
Unit of magnetic potential is Wbm^-1.
Unit of magnetic induction is Wbm^-2.

Weight decreases by 1% at height h 

For height: 

thus

At depth h:
 
Weight decreases by 0.5%.

From the Gibb's-Helmholtz equation
ΔG = ΔH - TΔS_, at equilibrium Δ​​​​​​​H = T Δ S
Hence, ΔG - 0
T = ΔH / Δ S
Δ H = 30.56 kJ mol^-1= 30,560 J mol^-1
Δ S = 66.0 JK^-1 mol^-1
∴ T = 30560 / 66.0 = 463 K

The structure of diborane is as follows.

Thus, H-B-H angles are nearly 97° and 120°.

Ni and RhCI(PPH₃)₂ are used as catalysts in hydrogenation.
TiCI₄ + AI(C₂H₅)₃ is a Ziegler-Natta catalyst used in polymerisation reaction.
In Haber-Bosch process, for the manufacture of NH₃, finely divided iron + molybdenum (as promoter) is used as catalyst.
N₂ + 3H₂ ⇌ 2NH₃
V₂O₅ is used in contact process as a catalyst for the conversion of SO₂ into SO₃.
2SO₂ + O₂ ⇌ 2SO₃

Let the formula of oxide = M_xO_y
Molar mass of metal oxide = 2 x 32 = 64 g
Mass of metal = 3.2g
Mass of oxygen = 3.6 - 3.2 = 0.4 g
According to law of constant proportions:
(64 X x) / (16 X y) = 3.2 / 0.4;
= x/y = 2/1
Thus, formula of metal oxide = M₂O

According to Gibb's equation:
ΔGº = ΔHº - T Δ Sº
The reaction becomes spontaneous at a temperature at which ΔGº is a negative value.
At 298K:
ΔGº = 176000 - 298 x 160 = 128320 J mol^-1
Since ΔGº is positive, the reaction is not spontaneous at this temperature.
Let ΔGº = 0; at T K
0 = 176000 - T x 160
T = 176000 / 160 = 1100 K
Hence, the reaction is spontaneous above 1100 K or 827^oC.

The oxidation state of sulphur in Na₂S₄O₆ is 5/2.
Let the oxidation state of sulphur be x.
2 + 4x – 12 = 0
4x = +10
x = 10/4
x = 5/2

Few' means next to none; 'a few' means some; 'the few' is specific to the group already referred to. As there is no comparison and no specification, option 3 is the correct usage.

There are 10 straight lines in the first Question Figure, 9 straight lines in the second, 8 straight lines in the third and 7 straight lines in the fourth. The number of lines is decreasing by one in every step, so the next figure must have 6 straight lines.
Hence, option (1) is correct.

The following sentence, 'Hybrids use two types of propulsion in order to use gasoline more efficiently than conventional vehicles do' justifies the correct choice.
Thus, option (2) is the correct answer.

Block' means to obstruct (someone or something) by placing obstacles in the way. 'Facilitate' means to assist the progress of a person. The sentence mentions that the fallen trees obstructed/blocked the passage. 'Facilitate' implies that instead of being blocked, the subjects were assisted to pass through. Thus, option 1 is the answer.

Problem figure 2 is the water image of Problem figure 1. Similarly, Answer figure (b) is the water image of Problem figure (3). Hence, Answer figure (b) is correct.

Zealous' means someone who works with enthusiasm, and 'indifferent' is someone marked by lack of interest. Hence, it would be the correct answer.

Distance can be calculated by using formula

Let (h, k) be any point in the set, then the equation of the circle is:

Since (h, k) lies on x² + y² = 25
we have:

Thus, the distance between the centers of the two circles satisfies:

Given (z - 1) / (z + 1) is purely imaginary, the real part must be zero:
Re (z - 1) / (z + 1) = 0

Multiply by the conjugate of the denominator:

The numerator must be zero (denominator ≠ 0 since x ≠ -1):

Expand:

Let α, α + 1 be roots
α + α + 1 = b
α(α + 1) = c
∴ b² - 4c = (2α + 1)² - 4α(α + 1) = 1.

Let

The equation of sphere =
Centre of sphere = (-1/2, -1/2, 1/2)
The position vector of centre of sphere =

C₁(0,0) R₁ = r
C₂(5,0) R₂ = 3
The two circles intersect at real and distinct points
|R₁ - R₂| < C₁C₂ < |R₁ + R₂|
r - 3 < 5 < r + 3
2 < r & r < 8
2 < r < 8

Let slope of required line L be m.
Given line is L₁: √3x + y = 1
Slope of line (m₁) = - Coefficient of x / Coefficient of v = √3 / 1 = -√3
Angle between L and L₁ is 60°.


As line passes through (3, -2), hence equation of L is given by:

Probability that a man will live 10 more years = 1/4
Probability that man will not live 10 more years = 1 - 1/4 = 3/4
Probability that his wife will live 10 more years = 1/3
Probability that his wife will not live 10 more years = 1 - 1/3 = 2/3
Then, probability that neither will be alive in 10 years = (3/4) x (2/3) = 1/2