SRMJEE Mock Test - 8 (Engineering) - JEE MCQ

Magnetic field around the straight current carrying wire is given by:

B ∝ 1/r

Wires A and B carry current 5 A each coming out of the plane of the page, as shown in the figure. The magnitude of magnetic field at point P due to wire A is equal to that due to wire B, i.e.

The direction of field B_A is perpendicular to PA and that of field B_B is perpendicular to PB. Therefore, the angle between the two fields is θ = 60°. The magnitude of the resultant field at P is given by

Number of nuclei left undecayed after time t is given by,

Where n is number of half lives in time t.

According to question, N = N₀/e

Substituting in (i), we get

Taking log on both sides, we get

Activity of the sample reduces to half at its half life.

 and  are the position vectors of A and B.
Let the position vector of C be .

Now, from the given question, 

Δl = 1 - 0.99970 = 0.00030 cm
Δl = αl Δt
Δt = Δl / (αl) = 0.0003 / (1.1 × 10⁻⁵ × 0.9997) = 27.3°C.
So, the plate temperature must be raised to 30°C + 27.3°C = 57.3°C.

For a 1^st order chemical reaction,


Arrhenius equation:

[A = Pre-exponential factor]
In a 1^st order reaction, the unit of the pre-exponential factor is reciprocal second.
Because the pre-exponential factor depends on the frequency of collisions, it is related to collision theory and transition state theory.

Step 1:
Bromination of aniline takes place, where the Br⁺ ion attacks it at the ortho and para positions, to produce 2,4,6-tribromoaniline (X).

Step 2:
2,4,6-tribromoaniline, on treatment with nitrous acid at 0°C, undergoes diazotization to form 2,4,6-tribromobenzene diazonium chloride (Y).

Step 3:
2,4,6-tribromobenzene diazonium chloride (Y), on treatment with cuprous chloride (CuCl), will produce 2,4,6-tribromochlorobenzene (Z). This is known as the Sandmeyer reaction.

Antibiotics which kills or inhibit a wide range of gram-positive and gram-negative bacteria are said to be broad spectrum antibiotics.
So Broad-spectrum antibiotics act on different antigens.

We are given the reaction:

A(g) → B(g)

The time taken for the partial pressure of A to decrease:

• From 1.0 atm to 0.5 atm = 10 seconds
• From 0.5 atm to 0.25 atm = 10 seconds

Since the time required for the concentration to reduce to half remains the same (10 seconds), this indicates a first-order reaction because the half-life (t₁/₂) remains constant in a first-order reaction.

Conclusion:

The reaction follows first-order kinetics.

Answer: Option D (Order = 1).

The given determinant is .
Minor of element a_ij is M_ij ​
∴ M₁₁​ = minor of element a₁₁ = 3
M₁₂ ​ = minor of element a₁₂ = 0
M₂₁ ​ = minor of element a₂₁ = −4
M₂₂ ​ = minor of element a₂₂ = 2

Hence, minor and co- factor of a₂₂ is 2 and 2 respectively.

Let A be an invertible symmetric matrix.
We have AA^–1 = A^–1A = I_n
⇒ (AA^–1)' = (A^–1A)' = (I_n)'
⇒ (A^–1)' A' = A'(A^–1)' = I_n
⇒ (A^–1)' A = A(A^–1)' = I_n
(A^–1)' = A^–1 [inverse of a matrix is unique]

z₁, z₂, z₃, ... zₙ are in G.P., and z₁ = 1.

So, the vertices of an n-sided polygon are:
1, α, α², ... αⁿ⁻¹

Given, 1 + α + α² + ... + αⁿ⁻¹ = 0

⇒ (αⁿ - 1) / (α - 1) = 0
⇒ αⁿ = 1

Thus, z₁, z₂, z₃, z₄, ... zₙ are the roots of αⁿ = 1, i.e., the n-th roots of unity.

So, these form the vertices of an n-sided regular polygon.

The distance between the incentre and circumcentre = 0.

Given:

x² + (y - 1)y² = 0

The given curve is symmetrical about the y-axis and forms a loop.

x² = (1 - y)y²

Since x², y² ≥ 0, we get 1 - y ≥ 0.

⇒ y ≤ 1

Thus, for the loop, y ∈ [0, 1].

Therefore, the required area is...

Let three consecutive terms are T_r, T_r+1, T_r+2
So,  and 

Using property , we have

Solving both equations, n = 6, r = 4
Hence, the greatest coefficient will be of middle term, which is = ⁿ⁺⁵C₅ = ¹¹C₅ = 462

Applying the property

Adding Equations (i) and (ii),

Standard deviation(σ) = 16 x 25 / 100 = 4
Required variance = (4)² = 16

Given,

Expanding with respect to R₁

⇒ x³ + y³ + z³ − 3xyz = 0
⇒ (x + y + z)(x² + y² + z² − xy − yz − zx) = 0
⇒ (x + y + z){x² + y² + z² + xy(ω + ω²) + yz(ω + ω²) + xz(ω + ω²)} = 0
⇒ (x + y + z)(x + yω + zω²)(x + yω² + zω) = 0
⇒ The determinant vanishes, i.e., the value of the determinant is zero if x = y = z or x + yω + zω² = 0.

Let the age of Guri and Shuri five years ago be x and y, respectively.
According to the question,
x + y = 36
x = 36 - y ... (i)
Also,x - y = 4
Putting the value of x as given in (i) we get,
36 - y - y = 4
36 - 2y = 4
-2y = 4 - 36
-2y = -32
2y = 32
y = 32 ÷ 2
y = 16
Therefore, the age of Shuri, 5 years ago = 16 years
Putting y = 16 in the equation x - y = 4,
x - 16 = 4
x = 4 + 16
x = 20
Hence, age of Guri, 5 years ago = 20 years
Present age of Guri = 20 + 5 = 25 years
Present age of Shuri = 16 + 5 = 21 years
Age of Guri and Shuri, 7 years from now, will be 32 years and 28 years, respectively.
Required ratio = 32 : 28
= 8 : 7

Given equations: 15p – 45q = 24 and 6p – 18q = 48/5
We will compare these equations with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0.
15/6 = =
5/2 = 5/2 = 5/2
This implies

So, the given pair of equations has infinite solutions.

Let the number be x.

As per the given condition:
If the number is divided by 3, it is reduced by 34.

That means,
x - x/3 = 34

Simplifying:
2x/3 = 34

Multiplying both sides by 3/2:
x = 34 × 3/2

x = 51

Thus, the number is 51.

Hence, option A is the correct answer.

Let the ten’s digit be T.

Then, the unit digit = 2T, and the hundred’s digit = (2T) ÷ 1.5.

According to the question:

T + 2T + [2T ÷ 1.5] = 13
1.5T + 3T + 2T/1.5 = 13
(1.5T + 3T + 2T) = 13 × 1.5
1.5T + 3T + 2T = 19.5
6.5T = 19.5
T = 19.5 ÷ 6.5
T = 3

So, the unit digit = 6, the ten’s digit = 3, and the hundred’s digit = 4.

Therefore, the number is 436.

Height of platform = 5 m
Relative height of tower from the platform = 40 m
Elevation of tower = 30°
Distance of platform from tower D
tan30° = height/base

D = 40√3 m

The minister suggested the king to make a declaration that whoever has he dog who used to live at the royal elephant's shed will be penalized. 
Hence, it is the correct option.

The elephant was actually missing the dog.The minister diagnosed that the elephant was feeling lonely due to the loss of his dear friend. 
Hence, it is the correct option.