Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

Algebra Calculus Coordinate Geometry Sets, Relations & Functions Statistics & Probability Trigonometry Vector & 3D Geometry

Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is the vector A - B?

A. (-3, -3, -3)
B. (3, 3, 3)
C. (5, 7, 9)
D. (0, 0, 0)

Solution

A - B = (1-4, 2-5, 3-6) = (-3, -3, -3).

Correct Answer: A — (-3, -3, -3)

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Q. If vector A = (2, 2, 2) and vector B = (1, 1, 1), what is the scalar triple product A . (B × A)?

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

Solution

A . (B × A) = 0, since B × A = 0.

Correct Answer: A — 0

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Q. If vector A = (3, -2, 1) and vector B = (1, 4, -3), what is the cross product A × B?

A. (-5, -10, 14)
B. (5, 10, -14)
C. (10, 14, 5)
D. (14, -5, 10)

Solution

A × B = |i  j  k|\n|3 -2  1|\n|1  4 -3| = (-5, -10, 14).

Correct Answer: A — (-5, -10, 14)

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Q. If vectors A = (x, 2, 3) and B = (1, y, 4) are perpendicular, what is the value of x + y?

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

Solution

A · B = x*1 + 2*y + 3*4 = 0. Thus, x + 2y + 12 = 0. Solving gives x + y = -6.

Correct Answer: B — 2

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Q. If vectors A = 3i + 4j and B = 2i - j, what is the scalar product A · B?

A. -1
B. 2
C. 10
D. 11

Solution

A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.

Correct Answer: C — 10

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Q. If x + 2y = 10 and 2x - y = 3, what is the value of x?

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

Solution

From the first equation, x = 10 - 2y. Substituting into the second gives 2(10 - 2y) - y = 3, solving gives y = 4, x = 2.

Correct Answer: C — 3

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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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Q. If x = sin^(-1)(3/5), what is cos(x)?

A. 4/5
B. 3/5
C. 5/4
D. 1/5

Solution

Using the identity cos^2(x) + sin^2(x) = 1, we find cos(x) = √(1 - (3/5)^2) = 4/5.

Correct Answer: A — 4/5

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Q. If x = sin^(-1)(3/5), what is the value of cos(x)?

A. 4/5
B. 3/5
C. 2/5
D. 1/5

Solution

Using the identity cos(x) = sqrt(1 - sin^2(x)), we have cos(x) = sqrt(1 - (3/5)^2) = sqrt(16/25) = 4/5.

Correct Answer: A — 4/5

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

A. π/4
B. π/2
C. 0
D. 1

Solution

tan^(-1)(1) = π/4.

Correct Answer: A — π/4

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

A. π/4
B. π/3
C. π/6
D. 0

Solution

tan^(-1)(1) = π/4, since tan(π/4) = 1.

Correct Answer: A — π/4

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

A. π/6
B. π/4
C. π/3
D. 0

Solution

tan^(-1)(1/√3) = π/6, since tan(π/6) = 1/√3.

Correct Answer: A — π/6

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

A. π/3
B. π/4
C. π/2
D. π/6

Solution

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

Correct Answer: A — π/3

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Mathematics Syllabus (JEE Main)

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