JEE Advanced Mix Test 63

Result

JEE Advanced Mix Test 63

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Weekly Quiz Competition

Question 1
4 / -1

A disc of radius R rotating with an angular velocity ω₀ is placed on a rough horizontal surface. If initial velocity of centre of disc is zero, then velocity of centre of disc when it ceases to slip, comes out to be ω₀R/k, value of k is _____.

A
3

B
4

C
5

D
6

Solution
Question 2
4 / -1

A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set into vibrations using an external vibrator of frequency 100 Hz. Find the separation (in cm) between the successive nodes on the string.

A
5

B
6

C
10

D
15

Solution
Question 3
4 / -1

A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is μ. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 μ, then N is

A
10

B
8

C
6

D
5

Solution
Question 4
4 / -1

Steel wire of length L' at 40°C is suspended from the ceiling and then a mass 'm' is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length 'L'. The coefficient of linear thermal expansion of the steel is 10^-5/°C, Young's modulus of steel is 10¹¹N/m² and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of 'm' in kg is

(Round off up to 2 decimal places)

A
3.20

B
3.14

C
3.10

D
3.5

Solution
Question 5
4 / -1

A
5

B
4

C
3

D
1

Solution

It is caprolactam, which on heating polymerises to give polyamide Nylon -6. One monomeric unit of Nylon-6 contain 6 carbon so 2-unit will have 12 carbons.
Question 6
4 / -1

In a mixture of H-He⁺ gas (He⁺ is singly ionised He atom), H atoms and He⁺ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He⁺ ions (by collisions). Assume that the Bohr model of atom is exactly valid.

The quantum number n of the state finally populated in He⁺ ions is

A
4

B
5

C
6

D
10

Solution

When H atoms transfer their excitation energy (10.2 eV) to the electron in He^⊕, it is further excited to say n = n₂.

Thus, 10.2 = 13.6 × 2² × (1/2² - 1/n₂²)

∴ n₂ = 4
Question 7
4 / -1

EDTA^4– is ethylenediaminetetraacetate ion. What is the total number of N–Co–O bond angles in [Co(EDTA)]^1– complex ion?

A
10

B
20

C
15

D
8

Solution

[Co(EDTA)]⁻: Co³⁺, octahedral, EDTA⁴⁻ coordinates via 2 N, 4 O.

Each N forms 4 N–Co–O angles with the 4 O atoms.

Total: 2 × 4 = 8
Question 8
4 / -1

Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2CD.

Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

A
4

B
3

C
2

D
1

Solution
Question 9
4 / -1

The total number of local maxima and local minima of the function

A
3

B
2

C
4

D
5

Solution

Hence, the total number of local maxima and local minima of the function is 2.
Question 10
4 / -1

Let A, B, C be three complex numbers as defined below:

A = {z : Im z ≥ 1}

B = {z : |z - 2 - i| = 3}

C = {z : Re((1 - i)z) = 3√2}

The number of elements in the set A ∩ B ∩ C is

A
4

B
3

C
2

D
1

Solution

Given Sets:

A = {z : Im(z) ≥ 1}

→ Region above (and on) the line Im(z) = 1.

B = {z : |z − (2 + i)| = 3}

→ Circle centered at (2,1) with radius 3.

C = {z : Re((1 − i)z) = 3√2}

→ Line in the complex plane.

(This line was shown graphically in the image and intersects the circle at exactly one point lying above Im(z) = 1.)

From the graph provided:

The line Re((1 − i)z) = 3√2 intersects the circle in two points.

Only one of those points lies in the region where Im(z) ≥ 1.

Hence, only one point lies in A ∩ B ∩ C.