MHT-CET Exam Prep Resources | Soulshift Education

MHT-CET

Chemistry Mathematics Physics

Q. What is the value of 9 - 3 × 2? (2015)

A. 3
B. 6
C. 0
D. 9

Solution

Using BODMAS, 3 × 2 = 6, so 9 - 6 = 3.

Correct Answer: B — 6

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Q. What is the value of 9 × 9? (2014)

A. 81
B. 72
C. 90
D. 99

Solution

9 × 9 = 81.

Correct Answer: A — 81

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Q. What is the value of 9^2 - 4^2? (2016)

A. 65
B. 77
C. 81
D. 45

Solution

9^2 = 81 and 4^2 = 16, so 81 - 16 = 65.

Correct Answer: A — 65

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Q. What is the value of cot(45°)?

A. 0
B. 1
C. √3
D. ∞

Solution

cot(45°) = 1/tan(45°) = 1/1 = 1

Correct Answer: B — 1

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Q. What is the value of cot(90°)? (2018)

A. 0
B. 1
C. undefined
D. ∞

Solution

cot(90°) = 1/tan(90°) = 1/0 = undefined.

Correct Answer: C — undefined

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Q. What is the value of k for which the equation x² - 6x + k = 0 has roots 2 and 4? (2022)

A. 8
B. 12
C. 10
D. 6

Solution

The product of the roots is k = 2 * 4 = 8.

Correct Answer: B — 12

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Q. What is the value of k if the equation x² + kx + 16 = 0 has no real roots? (2022)

A. -8
B. -4
C. 4
D. 8

Solution

For no real roots, the discriminant must be less than zero: k² - 4*1*16 < 0, thus k < -8 or k > 8.

Correct Answer: A — -8

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Q. What is the value of k if the equation x² - 4x + k = 0 has no real roots? (2021)

A. 5
B. 6
C. 7
D. 8

Solution

For no real roots, the discriminant must be less than zero: (-4)² - 4*1*k < 0, hence k > 4.

Correct Answer: B — 6

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Q. What is the value of k if the equation x² - kx + 16 = 0 has roots 4 and 4? (2021)

A. 8
B. 16
C. 4
D. 12

Solution

Since the roots are equal, k = 4 + 4 = 8.

Correct Answer: A — 8

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Q. What is the value of sec(0°)?

A. 0
B. 1
C. √2
D. ∞

Solution

sec(0°) = 1/cos(0°) = 1/1 = 1

Correct Answer: B — 1

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Q. What is the value of sec(30°)? (2015)

A. √3/2
B. 2/√3
C. 2
D. √3

Solution

sec(30°) = 1/cos(30°) = 1/(√3/2) = 2/√3 = √3

Correct Answer: D — √3

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Q. What is the value of sec(45°)? (2019)

A. 1
B. √2
C. 2
D. √3

Solution

sec(45°) = 1/cos(45°) = 1/(√2/2) = √2.

Correct Answer: B — √2

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Q. What is the value of sin(45°)? (2016)

A. 1/√2
B. 1/2
C. √3/2
D. 1

Solution

sin(45°) = 1/√2

Correct Answer: A — 1/√2

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Q. What is the value of tan(0°)? (2018)

A. 0
B. 1
C. undefined
D. ∞

Solution

tan(0°) = 0

Correct Answer: A — 0

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Q. What is the value of tan(90°)? (2022)

A. 0
B. 1
C. undefined
D. ∞

Solution

tan(90°) is undefined.

Correct Answer: C — undefined

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Q. What is the value of the 5th term in the expansion of (3x - 2)^6? (2023)

A. -540
B. 540
C. 720
D. 360

Solution

The 5th term is given by C(6,4) * (3x)^4 * (-2)^2 = 15 * 81 * 4 = -4860.

Correct Answer: A — -540

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Q. What is the value of the azimuthal quantum number (l) for a d orbital? (2021) 2021

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

Solution

The azimuthal quantum number l for d orbitals is 2.

Correct Answer: C — 2

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Q. What is the value of the azimuthal quantum number (l) for a p-orbital? (2015)

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

Solution

The azimuthal quantum number (l) for a p-orbital is 1.

Correct Answer: B — 1

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Q. What is the value of the coefficient of x^5 in the expansion of (x + 2)^7?

A. 21
B. 42
C. 56
D. 70

Solution

The coefficient of x^5 is given by 7C5 * (2)^2 = 21 * 4 = 84.

Correct Answer: C — 56

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Q. What is the value of the determinant of the matrix B = [[2, 3], [5, 7]]? (2020)

A. 1
B. 4
C. 11
D. 14

Solution

Determinant of B = (2*7) - (3*5) = 14 - 15 = -1.

Correct Answer: C — 11

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Q. What is the value of the determinant of the matrix B = [[5, 1], [2, 3]]? (2022)

A. 10
B. 15
C. 7
D. 5

Solution

Determinant of B = (5*3) - (1*2) = 15 - 2 = 13.

Correct Answer: A — 10

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Q. What is the value of the term containing x^5 in the expansion of (x + 1/2)^8? (2020)

A. 8
B. 56
C. 112
D. 128

Solution

The term containing x^5 is C(8,5)(1/2)^3 = 56 * 1/8 = 7.

Correct Answer: B — 56

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Q. What is the value of the term containing x^5 in the expansion of (x + 2)^8? (2020)

A. 112
B. 128
C. 256
D. 64

Solution

The term containing x^5 is C(8,5)(2)^3 = 56 * 8 = 448.

Correct Answer: B — 128

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Q. What is the value of x where f(x) = x^3 - 3x has a local maximum? (2022)

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

Solution

f'(x) = 3x^2 - 3. Setting f'(x) = 0 gives x = ±1. f(1) = -2.

Correct Answer: C — 1

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Q. What is the value of \( |D| \) for the matrix \( D = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \)? (2023)

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

Solution

The determinant is \( 0*0 - 1*1 = 0 - 1 = -1 \).

Correct Answer: A — 1

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Q. What is the vertex of the parabola represented by the equation y = x² - 4x + 3? (2022)

A. (2, -1)
B. (2, 1)
C. (1, 2)
D. (3, 0)

Solution

The vertex can be found using the formula x = -b/2a. Here, x = 2, and substituting back gives y = -1.

Correct Answer: A — (2, -1)

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Q. What is the vertex of the parabola represented by the equation y = x² - 6x + 8? (2023)

A. (3, -1)
B. (3, -5)
C. (2, -4)
D. (2, -2)

Solution

The vertex can be found using the formula x = -b/2a = 6/2 = 3. Substituting x = 3 into the equation gives y = -1.

Correct Answer: A — (3, -1)

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Q. What is the voltage across a 10Ω resistor carrying a current of 3A? (2022)

A. 30V
B. 20V
C. 10V
D. 15V

Solution

Using Ohm's law, V = IR = 3A * 10Ω = 30V.

Correct Answer: A — 30V

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Q. What is the voltage across a 12Ω resistor carrying a current of 1.5A? (2023)

A. 18V
B. 12V
C. 6V
D. 24V

Solution

Using Ohm's law, V = IR = 1.5A * 12Ω = 18V.

Correct Answer: A — 18V

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Q. What is the voltage across a 12Ω resistor carrying a current of 3A? (2023)

A. 36V
B. 24V
C. 12V
D. 18V

Solution

Using Ohm's law, V = IR = 3A * 12Ω = 36V.

Correct Answer: A — 36V

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MHT-CET

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