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COMEDK Mock Test - 7 - JEE MCQ

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30 Questions MCQ Test - COMEDK Mock Test - 7

COMEDK Mock Test - 7 for JEE 2025 is part of JEE preparation. The COMEDK Mock Test - 7 questions and answers have been prepared according to the JEE exam syllabus.The COMEDK Mock Test - 7 MCQs are made for JEE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for COMEDK Mock Test - 7 below.

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COMEDK Mock Test - 7 - Question 1

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A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is

Detailed Solution for COMEDK Mock Test - 7 - Question 1

At elongated position (x),
Fradial = mr ω²
∴ kx = m(ℓ + x)ω²

COMEDK Mock Test - 7 - Question 2

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Four identical particles of mass M are located at the corners of a square of side 'a'. What should be their speed if each of them revolves under the influence of other's gravitational field in a circular orbit circumscribing the square?

Detailed Solution for COMEDK Mock Test - 7 - Question 2

Net force on particle towards centre of circle is,

This force will act as centripetal force. Distance of particle from centre of circle is a/√2

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COMEDK Mock Test - 7 - Question 3

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The difference of speed of light in the two media A and B (v_A - v_B) is 2.6 × 10⁷ m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is: (Given: Speed of light in vacuum, c = 3 × 10⁸ ms^-1)

A.
1.303
B.
1.318
C.
1.13
D.
0.12

Detailed Solution for COMEDK Mock Test - 7 - Question 3

Speed of light in a medium,

c is the speed of light and μ is the refractive index.
⇒
= 2.04 × 10⁸ = 20.4 × 10⁷ m/s
∴ v_A - v_B = 2.6 × 10⁷ m/s
∴ v_A = (20.4 + 2.6) × 10⁷ = 23 × 10⁷ m/s
∴

COMEDK Mock Test - 7 - Question 4

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The power factor of an ac circuit having resistance (R) and inductance (L) connected in series and an angular velocity ω is

A. R/ωL
B. R/(R² + ω²L²)^1/2
C. ωL/R
D. R/(R² - ω²L²)^1/2

Detailed Solution for COMEDK Mock Test - 7 - Question 4

Power factor = R/Z

For an LR circuit,

Hence, the power factor is

COMEDK Mock Test - 7 - Question 5

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A radar sends an electromagnetic signal of electric filed (E₀) = 2.25 V/m and magnetic field (B₀) = 1.5 × 10^-8 T which strikes a target on the line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) reflects back towards the radar with the same velocity and by the same path. If the signal was transmitted at time t = 0 from the radar, then after how much time echo will reach to the radar?

A.
2.0 × 10^-5 s
B.
4.0 × 10^-5 s
C.
1.0 × 10^-5 s
D.
8.0 × 10^-5 s

Detailed Solution for COMEDK Mock Test - 7 - Question 5

E₀= 2.25V/m
B₀= 1.5× 10^-8T

COMEDK Mock Test - 7 - Question 6

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A resistor develops 500 J of thermal energy in 20 s when a current of 1.5 A is passed through it. If the current is increased from 1.5 A to 3 A, what will be the energy developed in 20 s?

A.
1500 J
B.
1000 J
C.
500 J
D.
2000 J

Detailed Solution for COMEDK Mock Test - 7 - Question 6

H₂ = 2000 J

COMEDK Mock Test - 7 - Question 7

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The activity of a radioactive sample falls from 700 s^-1 to 500 s^-1 in 30 minutes. Its half life is close to:

A.
66 min
B.
52 min
C.
62 min
D.
72 min

Detailed Solution for COMEDK Mock Test - 7 - Question 7

= 61.8 minute
⇒ T_1/2 ≈ 62 minutes

COMEDK Mock Test - 7 - Question 8

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The energy required to separate the typical middle mass nucleus into its constituent nucleons is:

(Mass of 119.902199amu, mass of proton = 1.007825amu and mass of neutron = 1.008665amu)

A.
921 MeV
B.
821 MeV
C.
1021 MeV
D.
1121 MeV

Detailed Solution for COMEDK Mock Test - 7 - Question 8

Given, Z 50, A - Z = 120 - 50 = 70
Δm = Z.m_p + (A - Z) m_n - M= [50 × 1.007825 +70 × 1.008665 - 119.902199] = 1.095601 MeV
E = 1.095601 × 931.478 MeV = 1020.53 MeV ≈ 1021 MeV

COMEDK Mock Test - 7 - Question 9

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Two spheres A and B of masses m₁ and m₂ respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction.

A.
Same as that of B [2012]
B.
Opposite to that of B
C.
θ = tan^–1 (1/2) to the x-axis
D.
θ = tan^–1 (–1/2) to the x-axis

Detailed Solution for COMEDK Mock Test - 7 - Question 9

Answer :- c

Solution :- Here initially sphere A is at rest and B is moving along x axis with velocity V.

After collision, velocity of sphere B becomes V/2 along direction perpendicular to its initial direction i.e. along Y axis.

Sphere A will move with some velocity u at some angle θ as shown in figure.considering law of conservation of momentum along X−axis.

m2V=m1ucosθ...........(i)

Considering law of conservation of momentum along Y−axis.

m2v/2=m1usinθ............(ii)

From equation i and ii.

1/2=tanθ

θ=tan−1(0.5).

COMEDK Mock Test - 7 - Question 10

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The resistance of the rod is 1 Ω. It is bent in form of a square. What is the resistance across adjacent corners?

A. 1 Ω
B. 3 Ω
C. 3/16 1 Ω
D. 3/4 1 Ω

Detailed Solution for COMEDK Mock Test - 7 - Question 10

When the rod is bent in the form of a square, then each side has a resistance of 1/4 Ω. As shown R₁, R₂ and R₃ are connected in series, so, their equivalent resistance,

Now, R' and R4 are connected in parallel, so, the equivalent resistance of the circuit is

COMEDK Mock Test - 7 - Question 11

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Reaction of acids with alcohols is also known as

A.
Esterification
B.
Saponification
C.
Alkalisation
D.
None

COMEDK Mock Test - 7 - Question 12

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The IUPAC name of (CH₃)₂CHCH₃ is

A.
Dimethylethane
B.
Trimethylmethane
C.
Isopropylmethane
D.
2-Methylpropane

COMEDK Mock Test - 7 - Question 13

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In crystal structure of sodium chloride, the arrangement of Cl^- ions is

A.
fcc
B.
both fcc and bcc
C.
bcc
D.
none of the above

COMEDK Mock Test - 7 - Question 14

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Final product formed on reduction of glycerol by hydriodic acid is

A.
Propane
B.
Propanoic acid
C.
Propene
D.
None of these

COMEDK Mock Test - 7 - Question 15

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Which one of the following compounds is not a vitamin?

A.
Ascorbic acid
B.
Thiamine
C.
Testosterone
D.
Riboflavin

COMEDK Mock Test - 7 - Question 16

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The mass of 112 cm³ of CH₄ gas at STP is

A.
0.16 g
B.
0.8 g
C.
0.08 g
D.
1.6 g

COMEDK Mock Test - 7 - Question 17

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The enthalpy of a solution of KNO₃ is + 35.64 kJ. This denotes

A.
Abosorption of heat
B.
Liberation of heat
C.
No heat change
D.
The electrolyte is unstable

COMEDK Mock Test - 7 - Question 18

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The acid showing salt like character in aqueous solutions is

A.
Acetic acid
B.
Benzoic acid
C.
Formic acid
D.
α-Aminoacetic acid

COMEDK Mock Test - 7 - Question 19

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Let a circle C touch the lines L₁ : 4x - 3y + K₁ = 0 and L₂ : 4x - 3y + K₂ = 0, K₁, K₂ ∈ R. If a line passing through the centre of the circle C intersects L₁ at (-1, 2) and L₂ at (3, -6), then the equation of the circle C is

A.
(x - 1)² + (y - 2)² = 4
B.
(x + 1)² + (y - 2)² = 4
C.
(x - 1)² + (y + 2)² = 16
D.
(x - 1)² + (y - 2)² = 16

Detailed Solution for COMEDK Mock Test - 7 - Question 19

L₁: 4x - 3y + K₁ = 0
L₂: 4x - 3y + K₂ = 0
Now,
-4 - 6 + K₁ = 0
⇒ K1 = 10
12 + 18 + K₂ = 0
⇒ K₂ = -30
⇒ Tangents to the circle are:
4x - 3y + 10 = 0
4x - 3y - 30 = 0
Length of diameter, 2r = = 8
⇒ r = 4
Now, centre is the mid-point of A and B.
x = 1, y = -2
Equation of the circle,
(x - 1)² + (y + 2)² = 16

COMEDK Mock Test - 7 - Question 20

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The set of all values of k for which (tan^-1x)³ + (cot^-1x)³ = kπ³, x ∈ R, is the interval:

Detailed Solution for COMEDK Mock Test - 7 - Question 20

Let tan^-1x = t
cot^-1x = π/2 - t

Max will occur around t = π/2
Range of f(t) =

COMEDK Mock Test - 7 - Question 21

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Let x² + y² + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola y = x² at (2, 4). Then A + C is equal to _______.

A.
16
B.
88/5
C.
72
D.
-8

Detailed Solution for COMEDK Mock Test - 7 - Question 21

For tangent to parabola y = x² at (2, 4):

Equation of tangent is:
y - 4 = 4(x - 2)
⇒ 4x - y - 4 = 0
Family of circle can be given by:
(x - 2)² + (y - 4)² + λ(4x - y - 4) = 0
As it passes through (0, 6),
22 + 22 + λ(-10) = 0
∴ λ = 4/5
Equation of circle is:
(x - 2)² + (y - 4)² + 4/5(4x - y - 4) = 0

So, A + C = 16

COMEDK Mock Test - 7 - Question 22

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The number of values of α for which the system of equations
x + y + z = α
αx + 2αy + 3z = -1
x + 3αy + 5z = 4
is inconsistent, is

A.
0
B.
1
C.
2
D.
3

Detailed Solution for COMEDK Mock Test - 7 - Question 22

= 1(10α - 9α) - 1 (5α - 3) + 1 (3α² - 2α)
= α - 5α + 3 + 3α²- 2α
= 3α² - 6α + 3
For inconsistency, Δ = 0, i.e. α = 1
Now, check for α = 1.
x + y + z = 1 ... (i)
x + 2y + 3z = -1 ... (ii)
x + 3y + 5z = 4 ... (iii)
By (ii) × 2 - (i) × 1:
x + 3y + 5z = -3
So, the equations are inconsistent for α = 1.

COMEDK Mock Test - 7 - Question 23

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The inverse function of

Detailed Solution for COMEDK Mock Test - 7 - Question 23

COMEDK Mock Test - 7 - Question 24

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Let P be a variable point on the parabola y = 4x² + 1. Then the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x is:

A.
(3x - y)² + (x - 3y) + 2 = 0
B.
2(x - 3y)² + (3x - y) + 2 = 0
C.
2(3x - y)² + (x - 3y) + 2 = 0
D.
(3x - y)² + 2(x - 3y) + 2 = 0

Detailed Solution for COMEDK Mock Test - 7 - Question 24

COMEDK Mock Test - 7 - Question 25

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For which of the following ordered pairs (μ, δ), the system of linear equations
x + 2y + 3z = 1
3x + 4y + 5z = μ
4x + 4y + 4z =
is inconsistent?

A.
(4, 3)
B.
(4, 6)
C.
(3, 4)
D.
(1, 0)

Detailed Solution for COMEDK Mock Test - 7 - Question 25

For inconsistent system, we need Δ = 0 and at least one of Δx, Δy, Δz ≠ 0.

∴ (μ, δ) = (4, 3) is the only possible choice among the given ones.

COMEDK Mock Test - 7 - Question 26

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Let . If , then T + n(S) is equal to:

A.
7 + √3
B.
9
C.
8 + √3
D.
10

Detailed Solution for COMEDK Mock Test - 7 - Question 26

tanθ (sinθ + 1) - sin2θ = 0
tanθ (sinθ + 1 - 2cos²θ) = 0
⇒ tanθ = 0 or 2sin²θ + sinθ - 1 = 0
⇒ (2sinθ + 1) (sinθ - 1) = 0
⇒ sinθ = -1/2 or 1
But sinθ = 1 not possible

n(S) = 5

= 4

COMEDK Mock Test - 7 - Question 27

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The lines x = ay - 1 = z - 2 and x = 3y - 2 = bz - 2, (ab ≠ 0) are coplanar, if:

A.
b = 1, a ∈ R - {0}
B.
a = 2, b = 3
C.
a = 2, b = 2
D.
a = 1, b ∈ R - {0}

Detailed Solution for COMEDK Mock Test - 7 - Question 27

Lines are coplanar.

COMEDK Mock Test - 7 - Question 28

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The sum of all the real roots of the equation (e^2x - 4)(6e^2x - 5e^x + 1) = 0 is

A.
log_e3
B.
-log_e3
C.
log_e6
D.
-log_e6

Detailed Solution for COMEDK Mock Test - 7 - Question 28

COMEDK Mock Test - 7 - Question 29

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The sum of absolute maximum and absolute minimum values of the function f(x) = |2x² + 3x - 2| + sinx cosx in the interval [0, 1] is:

Detailed Solution for COMEDK Mock Test - 7 - Question 29

f(x) = |(2x - 1)(x + 2)| +
f(x) = (1 - 2x) (x + 2) +
f'(x) = -4x - 3 + cos2x < 0
For x ≥ 1/2 : f'(x) = 4x + 3 + cos2x > 0
So, minima occurs at x = 1/2.

So, maximum is possible at x = 0 or x = 1
Now checking for x = 0 and x = 1, we can see it attains its maximum value at x = 1

Sum of absolute maximum and minimum value

COMEDK Mock Test - 7 - Question 30

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A random variable X has the following probability distribution:

The value of P(1 < X < 4 | X ≤ 2) is equal to:

A.
4/7
B.
2/3
C.
3/7
D.
4/5

Detailed Solution for COMEDK Mock Test - 7 - Question 30

∵ X is a random variable, k + 2k + 4k + 6k + 8k = 1
∴ k = 1/21
Now, P(1 < X < 4 | X ≤ 2) = 4k/7k = 4/7

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