Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

Q. If 7 - 3x ≥ 1, what is the solution for x?

A. x ≤ 2
B. x ≥ 2
C. x ≤ 3
D. x ≥ 3

Solution

7 - 3x ≥ 1 => -3x ≥ -6 => x ≤ 2.

Correct Answer: B — x ≥ 2

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Q. If 7x + 1 ≥ 15, what is the value of x?

A. x ≥ 2
B. x < 2
C. x > 2
D. x ≤ 2

Solution

7x + 1 ≥ 15 => 7x ≥ 14 => x ≥ 2

Correct Answer: A — x ≥ 2

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Q. If a + b = 10 and ab = 21, what are the values of a and b?

A. 3 and 7
B. 4 and 6
C. 5 and 5
D. 2 and 8

Solution

The roots of the equation x^2 - 10x + 21 = 0 are found using the quadratic formula, yielding a = 3 and b = 7.

Correct Answer: A — 3 and 7

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Q. If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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

Solution

Using the identity a^2 + b^2 = (a + b)^2 - 2ab, we get a^2 + b^2 = 10^2 - 2*21 = 100 - 42 = 58.

Correct Answer: A — 49

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Q. If A = (1, 0) and B = (0, 1), what is the angle between them?

A. 0 degrees
B. 90 degrees
C. 45 degrees
D. 180 degrees

Solution

Angle = cos⁻¹((A·B) / (|A||B|)) = cos⁻¹(0) = 90 degrees

Correct Answer: B — 90 degrees

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Q. If A = (1, 0, -1) and B = (0, 1, 1), what is the scalar product A · B?

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

Solution

A · B = 1*0 + 0*1 + (-1)*1 = 0 + 0 - 1 = -1.

Correct Answer: A — 0

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Q. If A = (1, 0, 0) and B = (0, 1, 0), what is the value of A · B?

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

Solution

A · B = 1*0 + 0*1 + 0*0 = 0.

Correct Answer: A — 0

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Q. If A = (1, 0, 0) and B = (0, 1, 0), what is the vector product A × B?

A. (0, 0, 1)
B. (1, 0, 0)
C. (0, 1, 0)
D. (0, 0, 0)

Solution

A × B = (0, 0, 1) using the right-hand rule.

Correct Answer: A — (0, 0, 1)

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Q. If A = (1, 1, 1) and B = (1, 1, 1), what is the scalar product A · B?

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

Solution

A · B = 1*1 + 1*1 + 1*1 = 3.

Correct Answer: C — 3

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Q. If A = (1, 1, 1) and B = (2, 2, 2), what is A × B?

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

Solution

A × B = (0, 0, 0) since A and B are parallel.

Correct Answer: A — (0, 0, 0)

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

A. 3
B. 6
C. 9
D. 12

Solution

A · B = 1*2 + 1*2 + 1*2 = 2 + 2 + 2 = 6.

Correct Answer: B — 6

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Q. If A = (1, 1, 1) and B = (x, y, z) such that A · B = 3, what is the value of x + y + z?

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

Solution

A · B = 1*x + 1*y + 1*z = x + y + z = 3.

Correct Answer: C — 3

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Q. If A = (1, 2) and B = (3, 4), what is the dot product A · B?

A. 10
B. 11
C. 12
D. 8

Solution

Dot product A · B = 1*3 + 2*4 = 3 + 8 = 11.

Correct Answer: A — 10

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Q. If A = (1, 2) and B = (3, 4), what is the midpoint M of AB?

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

Solution

Midpoint M = ((1+3)/2, (2+4)/2) = (2, 3).

Correct Answer: A — (2, 3)

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Q. If A = (1, 2, 3) and B = (0, 1, 0), what is the direction of the vector product A × B?

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

Solution

A × B = (2, -3, 1) gives direction (2, -3, 1).

Correct Answer: B — (3, 0, -1)

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

A. 0
B. 1
C. 2√2
D. √14

Solution

Magnitude |A × B| = √(1^2 + 2^2 + 3^2) = √14.

Correct Answer: D — √14

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

A. 32
B. 30
C. 28
D. 26

Solution

A · B = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

Correct Answer: B — 30

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Q. If A = (1, 2, 3) and B = (k, k, k) are perpendicular, what is the value of k?

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

Solution

A · B = 1*k + 2*k + 3*k = 6k = 0. Thus, k = 0.

Correct Answer: D — 0

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Q. If A = (1, 2, 3) and B = (x, y, z) are such that A · B = 0, what is the condition for x, y, z?

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

Solution

A · B = 1*x + 2*y + 3*z = 0 gives the condition x + 2y + 3z = 0.

Correct Answer: A — x + 2y + 3z = 0

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Q. If A = (1, 2, 3) and B = (x, y, z) such that A · B = 14, find the value of x + y + z.

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

Solution

A · B = 1*x + 2*y + 3*z = 14. If we assume x = 2, y = 4, z = 2, then x + y + z = 8.

Correct Answer: C — 7

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Q. If A = (2, 0, -1) and B = (0, 3, 4), what is A · B?

A. -4
B. 0
C. 6
D. 8

Solution

A · B = 2*0 + 0*3 + (-1)*4 = 0 - 4 = -4.

Correct Answer: B — 0

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Q. If A = (2, 0, -1) and B = (0, 3, 4), what is the scalar product A · B?

A. -4
B. 0
C. 6
D. 8

Solution

A · B = 2*0 + 0*3 + (-1)*4 = 0 - 4 = -4.

Correct Answer: B — 0

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

A. (2, 2)
B. (2, 3)
C. (4, 5)
D. (6, 8)

Solution

AB = B - A = (4 - 2, 5 - 3) = (2, 2)

Correct Answer: A — (2, 2)

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Q. If A = (2, 3) and B = (4, 7), find the vector AB.

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

Solution

Vector AB = B - A = (4 - 2, 7 - 3) = (2, 4).

Correct Answer: A — (2, 4)

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Q. If A = (2, 3) and B = (k, 1) are such that A · B = 10, find k.

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

Solution

A · B = 2k + 3*1 = 10. Thus, 2k + 3 = 10, leading to 2k = 7, k = 3.5.

Correct Answer: C — 3

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Q. If A = (2, 3, 4) and B = (0, 0, 0), what is A · B?

A. 0
B. 2
C. 3
D. 4

Solution

A · B = 2*0 + 3*0 + 4*0 = 0.

Correct Answer: A — 0

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Q. If A = (2, 3, 4) and B = (1, 0, -1), find the scalar product A · B.

A. -1
B. 0
C. 1
D. 10

Solution

A · B = 2*1 + 3*0 + 4*(-1) = 2 + 0 - 4 = -2.

Correct Answer: A — -1

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Q. If A = (2, 3, 4) and B = (1, 0, -1), find the vector product A × B.

A. (3, 6, -3)
B. (3, 4, -3)
C. (3, -4, 6)
D. (3, -6, 4)

Solution

A × B = |i  j  k|\n|2  3  4|\n|1  0 -1| = (3, 6, -3)

Correct Answer: A — (3, 6, -3)

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Q. If A = (2, 3, 4) and B = (1, 0, -1), what is the scalar product A · B?

A. -1
B. 0
C. 2
D. 10

Solution

A · B = 2*1 + 3*0 + 4*(-1) = 2 + 0 - 4 = -2.

Correct Answer: D — 10

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Q. If A = (2, 3, 4) and B = (k, 0, -1) are perpendicular, find k.

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

Solution

A · B = 2k + 3*0 + 4*(-1) = 0. Thus, 2k - 4 = 0, k = 2.

Correct Answer: A — -4

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Showing 1021 to 1050 of 2847 (95 Pages)

Mathematics Syllabus (JEE Main)

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