MHT-CET Exam Prep Resources | Soulshift Education

MHT-CET

Chemistry Mathematics Physics

Q. What is the conjugate of the complex number 5 - 2i? (2020)

A. 5 + 2i
B. 5 - 2i
C. 2 - 5i
D. 5 - i

Solution

The conjugate of a complex number a + bi is a - bi. Thus, the conjugate of 5 - 2i is 5 + 2i.

Correct Answer: A — 5 + 2i

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Q. What is the constant term in the expansion of (2x^2 - 3/x)^5? (2020)

A. -243
B. 0
C. 32
D. 64

Solution

The constant term occurs when 2k - 5 = 0, k = 2. The term is C(5,2)(-3)^3(2^2) = 10 * -27 * 4 = -1080.

Correct Answer: A — -243

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Q. What is the coordinates of the centroid of the triangle with vertices (0, 0), (6, 0), and (3, 6)? (2022)

A. (3, 2)
B. (2, 3)
C. (3, 3)
D. (4, 2)

Solution

Centroid = ((0+6+3)/3, (0+0+6)/3) = (3, 2).

Correct Answer: A — (3, 2)

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Q. What is the coordination number of the central metal ion in the complex ion [Co(NH3)6]Cl3? (2021)

A. 2
B. 4
C. 6
D. 8

Solution

In the complex ion [Co(NH3)6]Cl3, the central metal ion Co is surrounded by 6 ammonia (NH3) ligands, which gives it a coordination number of 6.

Correct Answer: C — 6

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Q. What is the coordination number of the complex ion [Co(NH3)5Cl]Cl2? (2023)

A. 4
B. 5
C. 6
D. 3

Solution

In the complex [Co(NH3)5Cl]Cl2, cobalt is surrounded by five ammonia ligands and one chloride ligand, giving it a coordination number of 6.

Correct Answer: C — 6

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Q. What is the coordination number of the complex ion [Co(NH3)6]Cl3? (2022) 2022

A. 4
B. 6
C. 2
D. 8

Solution

The coordination number is determined by the number of ligands attached to the central metal ion. Here, Co is surrounded by 6 NH3 ligands.

Correct Answer: B — 6

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Q. What is the coordination number of the metal ion in the complex [Co(NH3)5Cl]Cl2? (2023)

A. 4
B. 5
C. 6
D. 3

Solution

In the complex [Co(NH3)5Cl]Cl2, cobalt is surrounded by five ammonia ligands and one chloride ligand, giving it a coordination number of 6.

Correct Answer: C — 6

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Q. What is the cross product of vectors A = i + j and B = j + k? (2022)

A. i + k
B. i - k
C. j - i
D. k - j

Solution

A × B = |i  j  k| |1  1  0| |0  1  1| = i(1*1 - 0*1) - j(1*1 - 0*0) + k(1*0 - 1*0) = i - j.

Correct Answer: A — i + k

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Q. What is the current through a 10Ω resistor connected to a 20V battery? (2020)

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

Solution

Using Ohm's law, I = V/R = 20V / 10Ω = 2A.

Correct Answer: B — 2A

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Q. What is the current through a 12Ω resistor connected to a 24V battery? (2023)

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

Solution

Using Ohm's law, I = V/R = 24V / 12Ω = 2A.

Correct Answer: B — 2A

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Q. What is the current through a 12Ω resistor connected to a 48V power supply? (2021)

A. 4A
B. 6A
C. 3A
D. 2A

Solution

Using Ohm's law, I = V/R = 48V / 12Ω = 4A.

Correct Answer: A — 4A

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Q. What is the current through a 12Ω resistor connected to a 48V source? (2021)

A. 4A
B. 6A
C. 3A
D. 2A

Solution

Using Ohm's law, I = V/R = 48V / 12Ω = 4A.

Correct Answer: A — 4A

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Q. What is the current through a 12Ω resistor when a voltage of 48V is applied across it? (2021)

A. 2A
B. 3A
C. 4A
D. 6A

Solution

Using Ohm's law, I = V/R = 48V / 12Ω = 4A.

Correct Answer: C — 4A

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Q. What is the current through a 12Ω resistor when a voltage of 48V is applied? (2023)

A. 4A
B. 6A
C. 3A
D. 2A

Solution

Using Ohm's law, I = V/R = 48V / 12Ω = 4A.

Correct Answer: B — 6A

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Q. What is the current through a 15Ω resistor connected to a 45V source? (2021)

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

Solution

Using Ohm's law, I = V/R = 45V / 15Ω = 3A.

Correct Answer: A — 3A

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Q. What is the de Broglie wavelength of an electron moving with a velocity of 1 x 10^6 m/s? (mass of electron = 9.11 x 10^-31 kg) (2022)

A. 6.63 x 10^-24 m
B. 6.63 x 10^-22 m
C. 6.63 x 10^-20 m
D. 6.63 x 10^-18 m

Solution

λ = h / p = h / (mv) = 6.63 x 10^-34 / (9.11 x 10^-31 * 1 x 10^6) = 6.63 x 10^-24 m.

Correct Answer: A — 6.63 x 10^-24 m

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Q. What is the derivative of f(x) = 1/x?

A. -1/x^2
B. 1/x^2
C. -x
D. x

Solution

The derivative f'(x) = d/dx(1/x) = -1/x^2.

Correct Answer: A — -1/x^2

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Q. What is the derivative of f(x) = 2x^3 - 9x^2 + 12x? (2021)

A. 6x^2 - 18x + 12
B. 6x^2 - 18x
C. 6x^2 + 18x
D. 6x^2 - 12

Solution

f'(x) = 6x^2 - 18x + 12.

Correct Answer: A — 6x^2 - 18x + 12

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Q. What is the derivative of f(x) = 3x^2 + 5x - 7? (2021) 2021

A. 3x + 5
B. 6x + 5
C. 6x - 5
D. 3x^2 + 5

Solution

The derivative f'(x) = d/dx(3x^2 + 5x - 7) = 6x + 5.

Correct Answer: B — 6x + 5

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Q. What is the derivative of f(x) = 5x^4?

A. 20x^3
B. 5x^3
C. 15x^3
D. 4x^3

Solution

The derivative f'(x) = d/dx(5x^4) = 20x^3.

Correct Answer: A — 20x^3

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Q. What is the derivative of f(x) = e^(2x)?

A. 2e^(2x)
B. e^(2x)
C. e^(x)
D. 2x*e^(2x)

Solution

Using the chain rule, f'(x) = d/dx(e^(2x)) = 2e^(2x).

Correct Answer: A — 2e^(2x)

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Q. What is the derivative of f(x) = x^3 - 4x + 6?

A. 3x^2 - 4
B. 3x^2 + 4
C. x^2 - 4
D. 3x^2 - 6

Solution

The derivative f'(x) = d/dx(x^3 - 4x + 6) = 3x^2 - 4.

Correct Answer: A — 3x^2 - 4

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Q. What is the derivative of f(x) = x^3 - 4x?

A. 3x^2 - 4
B. 3x^2 + 4
C. x^2 - 4
D. 3x^2 - 2

Solution

The derivative f'(x) = d/dx(x^3 - 4x) = 3x^2 - 4.

Correct Answer: A — 3x^2 - 4

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Q. What is the derivative of f(x) = x^4 + 2x^3 - x + 1? (2017)

A. 4x^3 + 6x^2 - 1
B. 4x^3 + 2x^2 - 1
C. 3x^3 + 6x^2 - 1
D. 4x^3 + 2x - 1

Solution

The derivative f'(x) = d/dx(x^4 + 2x^3 - x + 1) = 4x^3 + 6x^2 - 1.

Correct Answer: A — 4x^3 + 6x^2 - 1

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Q. What is the determinant of F = [[2, 0], [0, 3]]? (2023)

A. 0
B. 2
C. 3
D. 6

Solution

Determinant of F = (2*3) - (0*0) = 6.

Correct Answer: D — 6

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Q. What is the determinant of G = [[1, 1, 1], [1, 2, 3], [1, 3, 6]]? (2023)

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

Solution

Det(G) = 1(2*6 - 3*3) - 1(1*6 - 1*3) + 1(1*3 - 1*2) = 1(12 - 9) - 1(6 - 3) + 1(3 - 2) = 3 - 3 + 1 = 1.

Correct Answer: A — 0

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Q. What is the determinant of G = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]? (2020)

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

Solution

Det(G) = 1(5*9 - 6*8) - 2(4*9 - 6*7) + 3(4*8 - 5*7) = 1(45 - 48) - 2(36 - 42) + 3(32 - 35) = -3 + 12 - 9 = 0.

Correct Answer: A — 0

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Q. What is the determinant of G = [[1, 2], [2, 4]]? (2020)

A. 0
B. 1
C. 2
D. 4

Solution

Determinant of G = (1*4) - (2*2) = 4 - 4 = 0.

Correct Answer: A — 0

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Q. What is the determinant of G = [[2, 1], [1, 2]]? (2021)

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

Solution

Det(G) = (2*2) - (1*1) = 4 - 1 = 3.

Correct Answer: B — 2

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Q. What is the determinant of G = [[2, 2], [2, 2]]? (2020)

A. 0
B. 4
C. 2
D. 1

Solution

Det(G) = (2*2) - (2*2) = 4 - 4 = 0.

Correct Answer: A — 0

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MHT-CET

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