Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

Q. What is the value of the limit: lim (x -> ∞) (1/x)?

A. 0
B. 1
C. Infinity
D. Undefined

Solution

As x approaches infinity, 1/x approaches 0.

Correct Answer: A — 0

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Q. What is the value of the series 1 + 1/2 + 1/3 + ... + 1/n as n approaches infinity?

A. 0
B. 1
C. ∞
D. undefined

Solution

The series diverges to infinity as n approaches infinity.

Correct Answer: C — ∞

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Q. What is the value of x if 2x + 3 = 11?

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

Solution

Subtract 3 from both sides: 2x = 8. Then divide by 2: x = 4.

Correct Answer: C — 4

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Q. What is the value of x if 3x - 5 = 16?

A. 7
B. 5
C. 4
D. 3

Solution

Solving for x: 3x = 21 => x = 7.

Correct Answer: A — 7

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Q. What is the value of x in the equation 2x^2 - 8x + 6 = 0?

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

Solution

Using the quadratic formula, x = [8 ± sqrt(64 - 48)] / 4 = [8 ± 4] / 4, giving x = 3 or x = 1.

Correct Answer: C — 3

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Q. What is the value of x in the equation 3x - 5 = 7?

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

Solution

Solving for x: 3x = 12, thus x = 4.

Correct Answer: A — 4

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Q. What is the value of x in the equation 5(x - 2) = 3x + 4?

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

Solution

Expanding gives 5x - 10 = 3x + 4. Rearranging gives 2x = 14, thus x = 7.

Correct Answer: A — -1

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Q. What is the value of x in the equation 5x - 3 = 2x + 12?

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

Solution

Rearranging gives 5x - 2x = 12 + 3 => 3x = 15 => x = 5.

Correct Answer: B — 4

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Q. What is the value of x in the equation 5x - 3 = 2x + 6?

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

Solution

Rearranging gives 5x - 2x = 6 + 3 => 3x = 9 => x = 3.

Correct Answer: B — 2

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Q. What is the value of z if z^2 = -1?

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

Solution

The solutions to z^2 = -1 are z = i and z = -i.

Correct Answer: A — i

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Q. What is the value of \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{vmatrix} \)?

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

Solution

The determinant is 0 because the first column is repeated.

Correct Answer: A — 0

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Q. What is the value of \( \tan(\tan^{-1}(3)) \)?

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

Solution

By definition, \( \tan(\tan^{-1}(x)) = x \). Therefore, \( \tan(\tan^{-1}(3)) = 3 \).

Correct Answer: C — 3

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Q. What is the value of |z| if z = -3 + 4i?

A. 5
B. 7
C. 4
D. 3

Solution

|z| = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

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Q. What is the value of |z| if z = 4 - 3i?

A. 5
B. 7
C. 4
D. 3

Solution

|z| = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5.

Correct Answer: A — 5

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Q. What is the value of |z| if z = 4e^(iπ/3)?

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

Solution

The modulus |z| = 4, as it is the coefficient in the polar form.

Correct Answer: A — 4

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Q. What is the value of |z|^2 if z = 4 - 3i?

A. 25
B. 16
C. 7
D. 12

Solution

|z|^2 = 4^2 + (-3)^2 = 16 + 9 = 25.

Correct Answer: A — 25

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Q. What is the variance of the data set {4, 8, 6, 5, 3}?

A. 2.5
B. 3
C. 4
D. 5

Solution

Mean = 5.2; Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²] / 5 = 2.56.

Correct Answer: A — 2.5

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Q. What is the variance of the data set: 1, 2, 3, 4, 5?

A. 2
B. 1.5
C. 1
D. 0.5

Solution

Mean = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.

Correct Answer: B — 1.5

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Q. What is the variance of the data set: 2, 4, 4, 4, 5, 5, 7, 9?

A. 2.5
B. 3.5
C. 4.5
D. 5.5

Solution

Mean = 5.0; Variance = [(2-5)^2 + (4-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2] / 8 = 2.5.

Correct Answer: A — 2.5

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Q. What is the variance of the following data set: {5, 7, 8, 9, 10}?

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

Solution

Mean = 7.8, Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²] / 5 = 3.

Correct Answer: B — 3

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Q. What is the vertex of the parabola defined by the equation y = -2(x - 1)^2 + 4?

A. (1, 4)
B. (1, -4)
C. (4, 1)
D. (-1, 4)

Solution

The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).

Correct Answer: A — (1, 4)

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Q. What is the vertex of the parabola given by the equation y = -2(x - 1)^2 + 4?

A. (1, 4)
B. (1, -4)
C. (4, 1)
D. (-1, 4)

Solution

The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).

Correct Answer: A — (1, 4)

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Q. What is the vertex of the parabola represented by the equation y = -2(x - 1)^2 + 4?

A. (1, 4)
B. (1, -4)
C. (-1, 4)
D. (-1, -4)

Solution

The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).

Correct Answer: A — (1, 4)

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Q. What is the vertex of the parabola represented by the equation y = 2x^2 - 8x + 5?

A. (2, -3)
B. (2, -7)
C. (4, -3)
D. (4, -7)

Solution

The vertex can be found using x = -b/(2a) = 4. Substituting x = 4 into the equation gives y = -3.

Correct Answer: A — (2, -3)

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Q. What is the weighted mean of the scores 70, 80, 90 with weights 1, 2, 3 respectively?

A. 80
B. 85
C. 90
D. 75

Solution

Weighted mean = (70*1 + 80*2 + 90*3) / (1 + 2 + 3) = 85.

Correct Answer: B — 85

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Q. What is the weighted mean of the scores 70, 80, and 90 with weights 1, 2, and 3 respectively?

A. 80
B. 85
C. 90
D. 75

Solution

Weighted mean = (70*1 + 80*2 + 90*3) / (1 + 2 + 3) = 85.

Correct Answer: B — 85

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Q. What is the weighted mean of the scores 80, 90, and 70 with weights 1, 2, and 1 respectively?

A. 80
B. 85
C. 90
D. 75

Solution

Weighted mean = (80*1 + 90*2 + 70*1) / (1 + 2 + 1) = 85.

Correct Answer: B — 85

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Q. What is the x-intercept of the line 3x + 4y - 12 = 0?

A. 0
B. 3
C. 4
D. 12

Solution

To find the x-intercept, set y = 0. Thus, 3x - 12 = 0 gives x = 4.

Correct Answer: B — 3

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Q. What is the y-intercept of the line 5x + 2y - 10 = 0?

A. 5
B. 10
C. 2
D. 0

Solution

Setting x = 0 in the equation gives 2y - 10 = 0, thus y = 5.

Correct Answer: C — 2

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Q. What is the y-intercept of the line represented by the equation 5x + 2y = 10?

A. 5
B. 2
C. 0
D. 10

Solution

Set x = 0: 2y = 10 => y = 5. The y-intercept is (0, 5).

Correct Answer: B — 2

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Mathematics Syllabus (JEE Main)

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