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Q. If x + y = 10 and xy = 21, what is the value of x^2 + y^2? (2021)

A. 49
B. 59
C. 61
D. 41

Solution

We know that x^2 + y^2 = (x + y)^2 - 2xy. Substituting the values, we get (10)^2 - 2(21) = 100 - 42 = 58.

Correct Answer: A — 49

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Q. If x = -3, what is the value of |x| + x?

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

Solution

|-3| = 3, so |x| + x = 3 - 3 = 0.

Correct Answer: B — -3

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Q. If x = -5, what is the value of |x|?

A. -5
B. 0
C. 5
D. 10

Solution

The absolute value |x| of -5 is 5.

Correct Answer: C — 5

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Q. If x = 2 and y = 3, what is the value of x^y + y^x?

A. 11
B. 17
C. 19
D. 25

Solution

Calculating, we find 2^3 + 3^2 = 8 + 9 = 17.

Correct Answer: B — 17

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Q. If x = 2^3 and y = 2^2, what is the value of x/y? (2023)

A. 2
B. 4
C. 1
D. 8

Solution

We have x = 8 and y = 4. Thus, x/y = 8/4 = 2.

Correct Answer: A — 2

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Q. If x = 3 and y = 4, what is the value of x² + y²?

A. 25
B. 20
C. 15
D. 12

Solution

x² + y² = 3² + 4² = 9 + 16 = 25.

Correct Answer: A — 25

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Q. If x = 3, what is the value of 2x^2 - 5x + 1? (2022)

A. -2
B. 0
C. 4
D. 6

Solution

2(3^2) - 5(3) + 1 = 18 - 15 + 1 = 4.

Correct Answer: D — 6

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Q. If x = 4, what is the value of 2x - 3? (2022)

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

Solution

2x - 3 = 2(4) - 3 = 8 - 3 = 5.

Correct Answer: C — 7

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Q. If x = 4, what is the value of 3x - 2? (2019)

A. 10
B. 12
C. 14
D. 16

Solution

3x - 2 = 3(4) - 2 = 12 - 2 = 10.

Correct Answer: B — 12

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Q. If x = 5, what is the value of (x - 1)²?

A. 16
B. 20
C. 25
D. 36

Solution

(x - 1)² = (5 - 1)² = 4² = 16.

Correct Answer: A — 16

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Q. If x = 5, what is the value of 2x + 3? (2022)

A. 10
B. 13
C. 8
D. 15

Solution

Substituting x = 5, we get 2(5) + 3 = 10 + 3 = 13.

Correct Answer: B — 13

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Q. If x = 5, what is the value of 3x + 2? (2022)

A. 17
B. 15
C. 20
D. 18

Solution

3(5) + 2 = 15 + 2 = 17.

Correct Answer: A — 17

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Q. If x = cos^(-1)(-1/2), what is the value of x?

A. π/3
B. 2π/3
C. π/4
D. π/6

Solution

x = cos^(-1)(-1/2) = 2π/3

Correct Answer: B — 2π/3

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Q. If x = cos^(-1)(1/2), then the value of sin(x) is:

A. 1/2
B. √3/2
C. 1
D. 0

Solution

If x = cos^(-1)(1/2), then x = π/3. Therefore, sin(x) = sin(π/3) = √3/2.

Correct Answer: B — √3/2

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Q. If x = cos^(-1)(1/2), then what is the value of sin(x)?

A. 1/2
B. √3/2
C. 1
D. 0

Solution

If x = cos^(-1)(1/2), then cos(x) = 1/2, which corresponds to x = π/3. Therefore, sin(x) = sin(π/3) = √3/2.

Correct Answer: B — √3/2

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Q. If x = cos^(-1)(1/2), then what is the value of sin^(-1)(x)?

A. π/3
B. π/6
C. π/4
D. 0

Solution

Since x = cos^(-1)(1/2) = π/3, then sin^(-1)(1/2) = π/6.

Correct Answer: B — π/6

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Q. If x = cos^(-1)(1/2), then what is the value of sin^(-1)(√(1 - (1/2)^2))?

A. π/3
B. π/4
C. π/2
D. 0

Solution

Since cos^(-1)(1/2) = π/3, we have sin^(-1)(√(1 - (1/2)^2)) = sin^(-1)(√(3/4)) = π/3.

Correct Answer: A — π/3

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Q. If x = cos^(-1)(1/2), then what is the value of x?

A. π/3
B. π/4
C. π/2
D. 0

Solution

cos^(-1)(1/2) = π/3.

Correct Answer: A — π/3

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Q. If x = cos^(-1)(1/2), what is sin(x)?

A. √3/2
B. 1/2
C. 0
D. 1

Solution

If x = cos^(-1)(1/2), then x = π/3, thus sin(x) = sin(π/3) = √3/2.

Correct Answer: A — √3/2

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Q. If x = cos^(-1)(1/2), what is the value of sin(x)?

A. √3/2
B. 1/2
C. 0
D. 1

Solution

Using the identity sin(x) = sqrt(1 - cos^2(x)), we have sin(x) = sqrt(1 - (1/2)^2) = √3/2.

Correct Answer: A — √3/2

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Q. If x = sin^(-1)(-1), then the value of x is:

A. -π/2
B. π/2
C. 0
D. π

Solution

sin^(-1)(-1) corresponds to the angle -π/2.

Correct Answer: A — -π/2

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Q. If x = sin^(-1)(-1), what is the value of x?

A. -π/2
B. 0
C. π/2
D. π

Solution

sin^(-1)(-1) corresponds to the angle -π/2.

Correct Answer: A — -π/2

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Q. If x = sin^(-1)(-1/2), then what is the value of x?

A. -π/6
B. π/6
C. -π/3
D. π/3

Solution

sin^(-1)(-1/2) = -π/6, since sin(-π/6) = -1/2.

Correct Answer: A — -π/6

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Q. If x = sin^(-1)(-1/2), what is the value of x?

A. -π/6
B. π/6
C. π/4
D. 0

Solution

sin^(-1)(-1/2) = -π/6, since sin(-π/6) = -1/2.

Correct Answer: A — -π/6

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Q. If x = sin^(-1)(1/2), then the value of cos(x) is:

A. 1/2
B. √3/2
C. 1
D. 0

Solution

If x = sin^(-1)(1/2), then x = π/6. Therefore, cos(x) = cos(π/6) = √3/2.

Correct Answer: B — √3/2

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Q. If x = sin^(-1)(1/2), what is the value of cos(x)?

A. 1/2
B. √3/2
C. 1
D. 0

Solution

If x = sin^(-1)(1/2), then x = π/6. Therefore, cos(x) = cos(π/6) = √3/2.

Correct Answer: B — √3/2

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Q. If x = sin^(-1)(1/3), then what is the value of cos(x)?

A. √(8)/3
B. √(2)/3
C. 1/3
D. 2/3

Solution

Using the identity cos(x) = √(1 - sin^2(x)), we find cos(sin^(-1)(1/3)) = √(1 - (1/3)^2) = √(8)/3.

Correct Answer: A — √(8)/3

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Q. If x = sin^(-1)(1/3), then what is the value of cos^(-1)(√(1 - (1/3)^2))?

A. π/3
B. π/2
C. 2π/3
D. π/4

Solution

Using the identity cos^(-1)(√(1 - sin^2(x))) = π/2 - x, we find that cos^(-1)(√(1 - (1/3)^2)) = π/2 - sin^(-1)(1/3).

Correct Answer: B — π/2

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Q. If x = sin^(-1)(1/√2), then what is the value of cos(x)?

A. 1/2
B. √2/2
C. √3/2
D. 1

Solution

If x = sin^(-1)(1/√2), then sin(x) = 1/√2. Therefore, cos(x) = √(1 - sin^2(x)) = √(1 - (1/√2)^2) = √(1/2) = √2/2.

Correct Answer: B — √2/2

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Q. If x = sin^(-1)(1/√2), then what is the value of cos^(-1)(x)?

A. π/4
B. π/3
C. π/2
D. π/6

Solution

Since x = sin^(-1)(1/√2) = π/4, then cos^(-1)(x) = π/2 - π/4 = π/4.

Correct Answer: A — π/4

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Major Competitive Exams

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