JEE Advanced Mix Test 62

Result

JEE Advanced Mix Test 62

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Weekly Quiz Competition

Question 1
4 / -1

Answer the following by appropriately matching the lists based on the information given:

List I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as λ_f. Match each system with statements given in List II describing the nature and wavelength of the standing waves.

A
(A) - (p) and (t)

B
(A) - (p) and (s)

C
(B) - (p) and (t)

D
(B) - (u) and (t)

Solution
Question 2
4 / -1

One mole of an ideal monatomic gas undergoes the thermodynamic process, whose PV diagram is given as below:

The process BC is isothermal in nature. Heat taken out or taken in during the process is given in column I. Work done during the process is given in the column II and the change in the internal energy is given in the column III.

Calculate the heat supplied, work done and the change in the internal energy in the isobaric process.

A
(i) - (B) - (Q)

B
(ii) - (C) - (P)

C
(iii) - (B) - (S)

D
(iv) - (C) - (R)

Solution
Question 3
4 / -1

One mole of an ideal monatomic gas undergoes the thermodynamic process, whose PV diagram is given as below:

The process BC is isothermal in nature. Heat taken out or taken in during the process is given in column I. Work done during the process is given in the column II and the change in the internal energy is given in the column III.

Calculate the heat supplied, work done and the change in the internal energy in the isochoric process.

A
(i) - (B) - (R)

B
(ii) - (D) - (S)

C
(iii) - (A) - (R)

D
(iv) - (A) - (Q)

Solution
Question 4
4 / -1

Match the names in List - 1 with their reactions in List - 2, and choose the correct option.

A
1-R, 2-S, 3-Q, 4-P

B
1-P, 2-R, 3-Q, 4-T

C
1-S, 2-Q, 3-R, 4-P

D
1-R, 2-S, 3-T, 4-Q

Solution

Dehydrohalogenation: It is an elimination reaction that eliminates (removes) a hydrogen halide from a substrate.
Question 5
4 / -1

Match the ions of 3d series of d-block elements in the modern periodic table in List - 1 with their values of magnetic moment in List - 2, and choose the correct option.

A
1-S, 2-R, 3-P, 4-Q

B
1-R, 2-S, 3-P, 4-T

C
1-T, 2-R, 3-P, 4-Q

D
1-S, 2-T, 3-P, 4-R

Solution
Question 6
4 / -1

Match the coordination compounds in List - 1 with their shapes/geometries and magnetic characters in List - 2, and choose the correct option.

A
1-S, 2-P, 3-Q, 4-R

B
1-P, 2-S, 3-Q, 4-T

C
1-S, 2-T, 3-Q, 4-P

D
1-R, 2-P, 3-Q, 4-P

Solution
Question 7
4 / -1

Which of the following is the correct option?

A
(i) - (D), (ii) - (D), (iii) - (B), (iv) - (C)

B
(i) - (E), (ii) - (C), (iii) - (B), (iv) - (D)

C
(i) - (D), (ii) - (C), (iii) - (A), (iv) - (E)

D
(i) - (D), (ii) - (E), (iii) - (A), (iv) - (C)

Solution

1. For integral (i):

∫(dx / (1 + x²)) from 0 to 1

This integral is standard, the integral of 1/(1+x²) is arctan(x).

So, we have: = [arctan(x)] from 0 to 1

= arctan(1) - arctan(0)

= π/4 - 0

= π/4

Thus, integral (i) matches (D).

2. For integral (ii):

∫(dx / √(1 - x²)) from 0 to 1/2

This integral is standard, the integral of 1/√(1-x²) is arcsin(x).

Thus: = [arcsin(x)] from 0 to 1/2

= arcsin(1/2) - arcsin(0)

= π/6 - 0

= π/6

Thus, integral (ii) matches (C).

3. For integral (iii):

∫(dx / (1 - x²)) from 0 to 1/2

We recognize this integral:

The integral of 1/(1 - x²) is (1/2) ln|(1+x)/(1-x)|.

Thus: = [(1/2) ln|(1+x)/(1-x)|] from 0 to 1/2

= (1/2) ln((1+1/2)/(1-1/2)) - (1/2) ln(1)

= (1/2) ln((3/2)/(1/2)) - 0

= (1/2) ln(3)

Thus, integral (iii) matches (A).

4. For integral (iv):

∫(dx / √(x - x²)) from 0 to 1

Simplify first:

= ∫[dx / √(x(1 - x))] from 0 to 1

This integral is standard and equals π.

This is a known standard integral: ∫[dx / √(x(1 - x))] from 0 to 1 = π

Thus, integral (iv) matches (E).
Question 8
4 / -1

Let (x, y) be such that sin^-1(ax) + cos^-1(y) + cos^-1(bxy) = π/2

Which of the following options correctly matches the statements in Column I with the statements in Column II?

A
(A) → (q), (B)→ (r) , (C) → (p), (D) → (s)

B
(A) → (p), (B)→ (q) , (C) → (p), (D)→ (s)

C
(A) → (q), (B)→ (p) , (C) → (s), (D) → (s)

D
(A) → (p), (B)→ (q) , (C) → (s), (D) → (p)

Solution
Question 9
4 / -1

Consider the lines given by:

L₁ : x + 3y - 5 = 0, L₂ : 3x - ky - 1 = 0, L₃ : 5x + 2y - 12 = 0

Which of the following options correctly matches the statements in Column I with the statements in Column II?

A
(A) → (p), (B) → (r), (C) → (s), (D) → (q)

B
(A) → (r), (B) → (p), (C) → (s), (D)→ (t)

C
(A) → (r), (B) → (p), (C) → (q), (D) → (t)

D
(A) → (p), (B)→ (r), (C) → (q), (D) → (s)

Solution

Given equation of lines are L₁ : x + 3y - 5 = 0, L₂ : 3x - ky - 1 = 0, L₃ : 5x + 2y - 12 = 0
Question 10
4 / -1

Directions For Questions

Directions: Answer the following question by appropriately matching the information given in the three columns in the following table.

Here,

Column I contains equation of first line

Column II contains equation of second line

Column III contains angle between the first and the second line

...view full instructions

Which of the following options is an incorrect combination?

A
(i) (III) (B)

B
(ii) (I) (C)

C
(iii) (IV) (A)

D
(iv) (II) (C)