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MET Mock Test - 4 - JEE MCQ

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30 Questions MCQ Test - MET Mock Test - 4

MET Mock Test - 4 for JEE 2024 is part of JEE preparation. The MET Mock Test - 4 questions and answers have been prepared according to the JEE exam syllabus.The MET Mock Test - 4 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MET Mock Test - 4 below.

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MET Mock Test - 4 - Question 1

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A particle falls from a height 'h' on a fixed horizontal plane and rebounds. If 'e' is the coefficient of restitution, the total distance travelled by the particle before it stops is

Detailed Solution for MET Mock Test - 4 - Question 1

Total distance travelled si

Hence the correct choice is (a)

MET Mock Test - 4 - Question 2

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A disc of radius r is connected to a string of length L. The string is tied to a point on the circumference of the disc. This system is made to oscillate in vertical plane of the disc with a small angular amplitude θ₀. Find the speed of the lowest point of the disc at the moment the string become vertical.

Detailed Solution for MET Mock Test - 4 - Question 2

This is a compound pendulum with angular frequency is:

Angular displacement can be expressed as a function of time θ = θ₀ sin (ωt)
∴ dθ/dt = θ₀ cos (ωt)
When the string is vertical θ = 0 ∴ sin (ωt) = 0 and cos (ωt) = 1
∴ dθ/dt = θ₀ω
∴ speed of lowest point is:

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MET Mock Test - 4 - Question 3

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A long cylindrical volume contains a uniformly distributed charge of density ρ. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is:

Detailed Solution for MET Mock Test - 4 - Question 3

MET Mock Test - 4 - Question 4

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If and are two vectors satisfying the relation . Then the value of will be:

Detailed Solution for MET Mock Test - 4 - Question 4

AB cosθ = AB sinθ ⇒ θ = 45°

*Answer can only contain numeric values

MET Mock Test - 4 - Question 5

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A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from 60° to 30° at point B. The block is initially at least at A. Assume that collisions between the block and the incline are totally inelastic. (g = 10 m/s²)

If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline, is

Detailed Solution for MET Mock Test - 4 - Question 5

In case of elastic collision, component of v₁ parallel to BC will remain unchanged, while component perpendicular to BC will remain unchanged in magnitude but reverse in its direction.

Now, the vertical component of velocity of the block is given by:

Now the vertical component of velocity of the block is,

v' = v_T cos 30° - v₂ cos 60°

= 0

*Answer can only contain numeric values

MET Mock Test - 4 - Question 6

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A wire of length 2.5 m and area of cross section 1×10^–6 m² has a mass of 15 kg hanging on it. What is the extension produced? How much is the energy stored in the standard wire if Young’s modulus of wire is 2×10¹¹ Nm^–2.

Detailed Solution for MET Mock Test - 4 - Question 6

Here,

Length of wire l = 2.5m

Area of cross-section, A = 1×10^–6 m²

Hanging mass, m = 15 kg

Elongation, e = ?

Energy stored in the wire, E = ?

Young’s modulus of steel, Y = 2×10¹¹ Nm^–2.

We have,

Young’s modulus of elasticity,

e = 1.875 ×10^-3 m

Again,

Energy stored in the stretched wire,

E = 1/2 .F .e

Or, E = 1/2 × mg × e

Or, E = 1/2 × 15×10 ×1.875 ×10^-3

∴∴ E = 0.141 J

*Answer can only contain numeric values

MET Mock Test - 4 - Question 7

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Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m². The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m. Find the ratio n_A/n_B, where n_A and n_B are the number of moles of air in bubbles A and B, respectively. [Neglect the effect of gravity.]

(Round off upto 2 decimal places)

Detailed Solution for MET Mock Test - 4 - Question 7

Excess pressure above atmospheric pressure, due to surface tension in a bubble = 4T/r

Surrounding pressure, P₀ = 8 N/m²

MET Mock Test - 4 - Question 8

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In presence of alkali, C₂H₅OH reacts with Cl₂ to give

A.
Ethane
B.
Ethyl chloride
C.
Chloroform
D.
Pyrene

MET Mock Test - 4 - Question 9

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At room temperature formaldehyde is

A.
Gas
B.
Liquid
C.
Solid
D.
None of the above

MET Mock Test - 4 - Question 10

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How many monochlorobutanes will be obtained on chlorination of n-butane?

A.
1
B.
2
C.
3
D.
4

Detailed Solution for MET Mock Test - 4 - Question 10

MET Mock Test - 4 - Question 11

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The ratio of the molar amounts of H₂S needed to precipitate the metal ions from 20 mL each of 1M Cd(NO₃)₂ and 0.5 M CuSO₄ is

A.
1 : 1
B.
2 : 1
C.
1 : 2
D.
Indefinite

Detailed Solution for MET Mock Test - 4 - Question 11

As Cd²⁺ and Cu²⁺, both are dipositive ions but Cu²⁺ has one half of the concentration compared to that of the Cd²⁺. Thus, the molar amount of the H₂S used to precipitate the metals ions Cd²⁺ and Cu²⁺ is 2 : 1.

*Answer can only contain numeric values

MET Mock Test - 4 - Question 12

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At 345 K, the half life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa was 340 s. When the pressure was 27.8 kPa, the half life was found to be 170 s. The order of the reaction is ________. [integer answer]

Detailed Solution for MET Mock Test - 4 - Question 12

2 = (2)¹ - n
1 - n = 1
n = 0

*Answer can only contain numeric values

MET Mock Test - 4 - Question 13

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The difference in oxidation state of chromium in chromate and dichromate salts is ______. (in integer)

Detailed Solution for MET Mock Test - 4 - Question 13

Chromate ion → , oxidation state of Cr = +6
Dichromate ion → , oxidation state of Cr = +6
Difference in oxidation state = zero

*Answer can only contain numeric values

MET Mock Test - 4 - Question 14

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The vapour pressures of A and B at 25°C are 90 mm Hg and 15 mm Hg, respectively. If A and B are mixed such that the mole fraction of A in the mixture is 0.6, then the mole fraction of B in the vapour phase is x × 10^-1. The value of x is _________. (Nearest integer)

Detailed Solution for MET Mock Test - 4 - Question 14

x_A = 0.6
PT = xAPA^o + xBPB^o
= 0.6 × 90 + 0.4 × 15
= 54 + 6 = 60
xAPA^o = yAPT
0.6 × 90 = y_A(60)
y_A = 0.9
y_B = 0.1 = 1 × 10^-1
∴ x = 1

MET Mock Test - 4 - Question 15

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If the slope of the normal to the curve x³ = 8a²y, a > 0, at a point in the first quadrant is - 2/3, then the point is

A.
(2a, -a)
B.
(2a, a)
C.
(a, 2a)
D.
(-a, a)

MET Mock Test - 4 - Question 16

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Area bounded by parabola y² = x and st.line 2 y = x is

A.
4/3
B.
1
C.
2/3
D.
1/3

MET Mock Test - 4 - Question 17

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If | z₁ − 1 | < 1 , | z₂ − 2 | < 2 , | z₃ − 3 | < 3 then | z₁ + z₂ + z₃ |

A.
is less than 6
B.
is more than 3
C.
is less than 12
D.
lies between 6 and 12

MET Mock Test - 4 - Question 18

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The order of the differential equation y(dy/dx)=x/(dy/dx)+(dy/dx)³ is

A.
1
B.
2
C.
3
D.
4

MET Mock Test - 4 - Question 19

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The solution of the equation xdy-ydx=0 is

A.
Rectangular hyperbola
B.
Straight line passing (0,0)
C.
Parabola with vertex at (0,0)
D.
Circle with centre at (0,0)

MET Mock Test - 4 - Question 20

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The order of differential equation (d²y/dx²)²= (1+dy/dx)^1/2 is

A.
2
B.
3
C.
1/2
D.
6

*Answer can only contain numeric values

MET Mock Test - 4 - Question 21

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The number of solutions of the equation log_{(x + 1)}(2x² + 7x + 5) + log_{(2x + 5)}(x + 1)² - 4 = 0, x > 0, is ________.

Detailed Solution for MET Mock Test - 4 - Question 21

log(x + 1) (2x² + 7x + 5) + log_{(2x + 5)} (x + 1)² - 4 = 0
log_{(x + 1)} (2x + 5) (x + 1) + 2log_{(2x + 5)} (x + 1) = 4
log_{(x + 1)} (2x + 5) + 1 + 2 log_{(2x + 5)} (x + 1) = 4
Put log(_{x + 1)} (2x + 5) = t

t = 1, 2
log(x + 1) (2x + 5) = 1 and log(x + 1) (2x + 5) = 2
x + 1 = 2x + 3 and 2x + 5 = (x + 1)²
x = -4 (rejected) x² = 4 ⇒ x = 2, -2 (rejected)
So, x = 2
No. of solutions = 1

*Answer can only contain numeric values

MET Mock Test - 4 - Question 22

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Let A = and B = Then the number of elements in the set {(n, m) : n, m ∈ {1, 2 ..., 10} and nAⁿ + mB^m = l} is ___________.

Detailed Solution for MET Mock Test - 4 - Question 22

⇒ A^K = A, K ∈ l
nAⁿ + mB^m = nA + mB

So, 2n - m = 1,
-n + m = 0,
2m - n = 1
Hence, (m, n) = (1, 1)

*Answer can only contain numeric values

MET Mock Test - 4 - Question 23

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Let f(θ) = . Then the value of is _______. (in integer)

Detailed Solution for MET Mock Test - 4 - Question 23

Clearly, f(θ) = asinsθ + bcosθ
Where a = 1 + dt
⇒ a = 1 + 2b ... (1)
and b = (at sint + bt cos t) dt
⇒ b = 2a ... (2)
From (1) and (2), we get

So, f(θ) =

*Answer can only contain numeric values

MET Mock Test - 4 - Question 24

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If and , , then tan is equal to ________.

Detailed Solution for MET Mock Test - 4 - Question 24

Now,

MET Mock Test - 4 - Question 25

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Find the synonym of RUPTURE

A.
gap
B.
damage
C.
break
D.
breach

MET Mock Test - 4 - Question 26

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Improve the sentence by choosing best alternative for capitalised part of the sentence.

Despite his old age, his movements were as spirited as A YOUNG MAN

A.
a young man's
B.
if a young man
C.
those of a young man
D.
of a young man

MET Mock Test - 4 - Question 27

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Find the antonym of CORPULENT

A.
belligerent
B.
gaunt
C.
garrulous
D.
fat

MET Mock Test - 4 - Question 28

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Find the Synonym of LANGUISHING

A.
enjoying
B.
avoiding
C.
suffering
D.
convicted

MET Mock Test - 4 - Question 29

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Choose the alternative which best expresses the meaning of the idiom/phrase.

To be under a cloud

A.
to be in the dark
B.
to be hidden
C.
to be suspicious
D.
to be in disgrace

MET Mock Test - 4 - Question 30

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Improve the sentence by choosing best alternative for capitalised part of the sentence.

He has very good command ON English.

A.
of
B.
over
C.
in
D.
No improvement

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