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 maximum slope of the function f(x) = -x^2 + 4x?

A. 4
B. 2
C. 0
D. 1

Solution

f'(x) = -2x + 4. Setting f'(x) = 0 gives x = 2. The maximum slope occurs at x = 2, f'(2) = 2.

Correct Answer: A — 4

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Q. What is the maximum value of f(x) = -x^2 + 4x?

A. 4
B. 8
C. 6
D. 10

Solution

The vertex form gives the maximum at x = -b/(2a) = 4/2 = 2, f(2) = -2^2 + 4*2 = 4.

Correct Answer: A — 4

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Q. What is the maximum value of the function f(x) = -x^2 + 4x + 1?

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

Solution

The vertex occurs at x = -b/(2a) = 4/(-2) = 2. f(2) = -2^2 + 4*2 + 1 = 6.

Correct Answer: B — 6

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Q. What is the maximum value of the quadratic function f(x) = -x^2 + 4x + 1?

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

Solution

The vertex form gives the maximum value at x = 2, f(2) = 5.

Correct Answer: A — 5

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Q. What is the maximum value of the quadratic function f(x) = -x^2 + 6x - 8?

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

Solution

The vertex form gives the maximum value at x = 3, f(3) = -3^2 + 6*3 - 8 = 4.

Correct Answer: C — 4

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Q. What is the mean of the data set: 2, 4, 6, 8, 10?

A. 4
B. 5
C. 6
D. 8

Solution

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.

Correct Answer: C — 6

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Q. What is the mean of the data set: 5, 10, 15, 20, 25?

A. 10
B. 15
C. 20
D. 25

Solution

Mean = (5 + 10 + 15 + 20 + 25) / 5 = 75 / 5 = 15.

Correct Answer: B — 15

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Q. What is the mean of the first five prime numbers?

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

Solution

Mean = (2 + 3 + 5 + 7 + 11) / 5 = 28 / 5 = 5.6.

Correct Answer: B — 6

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Q. What is the mean of the following data set: 2, 4, 6, 8, 10?

A. 4
B. 5
C. 6
D. 7

Solution

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.

Correct Answer: C — 6

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Q. What is the mean of the following data set: 5, 10, 15, 20, 25?

A. 10
B. 15
C. 20
D. 25

Solution

Mean = (5 + 10 + 15 + 20 + 25) / 5 = 75 / 5 = 15

Correct Answer: B — 15

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Q. What is the mean of the following data: 2, 4, 6, 8, 10?

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

Solution

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.

Correct Answer: B — 6

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Q. What is the mean of the following numbers: 1, 1, 1, 1, 1?

A. 1
B. 2
C. 0
D. 5

Solution

Mean = (1 + 1 + 1 + 1 + 1) / 5 = 5 / 5 = 1.

Correct Answer: A — 1

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Q. What is the mean of the following numbers: 2, 4, 6, 8, 10, 12?

A. 6
B. 7
C. 8
D. 9

Solution

Mean = (2 + 4 + 6 + 8 + 10 + 12) / 6 = 42 / 6 = 7.

Correct Answer: C — 8

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Q. What is the mean of the following numbers: 2, 4, 6, 8, 10?

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

Solution

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.

Correct Answer: B — 6

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Q. What is the mean of the following numbers: 4, 8, 12, 16, 20?

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

Solution

Mean = (4 + 8 + 12 + 16 + 20) / 5 = 60 / 5 = 12.

Correct Answer: B — 12

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Q. What is the mean of the following numbers: 4, 8, 12, 16?

A. 8
B. 10
C. 12
D. 14

Solution

Mean = (4 + 8 + 12 + 16) / 4 = 40 / 4 = 10.

Correct Answer: B — 10

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Q. What is the median of the data set {7, 3, 5, 9, 1}?

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

Solution

First, arrange the data: {1, 3, 5, 7, 9}. The median is the middle value, which is 5.

Correct Answer: A — 5

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Q. What is the median of the following data set: 1, 3, 3, 6, 7, 8, 9?

A. 3
B. 6
C. 7
D. 8

Solution

Median = 6 (middle value of the ordered set).

Correct Answer: B — 6

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

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

Solution

Sorted data: 1, 2, 3, 4, 5. Median = 3 (middle value).

Correct Answer: B — 3

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Q. What is the median of the following data set: 3, 5, 7, 9, 11, 13, 15?

A. 7
B. 8
C. 9
D. 10

Solution

Median = 9 (middle value).

Correct Answer: C — 9

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Q. What is the median of the following numbers: 1, 3, 3, 6, 7, 8, 9?

A. 3
B. 6
C. 7
D. 8

Solution

Median = 6 (middle value of the ordered set).

Correct Answer: B — 6

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Q. What is the median of the following numbers: 12, 15, 14, 10, 18?

A. 12
B. 14
C. 15
D. 18

Solution

Arranging the numbers: 10, 12, 14, 15, 18. Median = 14.

Correct Answer: B — 14

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Q. What is the median of the following numbers: 3, 1, 4, 2, 5?

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

Solution

Arranging in order: 1, 2, 3, 4, 5. Median = 3.

Correct Answer: B — 3

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Q. What is the median of the following numbers: 3, 7, 8, 12, 14?

A. 7
B. 8
C. 10
D. 12

Solution

Median = 8 (middle value in ordered list).

Correct Answer: B — 8

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Q. What is the median of the following numbers: 7, 9, 12, 15, 18, 20?

A. 12
B. 13
C. 14
D. 15

Solution

Median = (12 + 15) / 2 = 27 / 2 = 13.5.

Correct Answer: A — 12

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Q. What is the middle term in the expansion of (x + 2)^8?

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

Solution

The middle term is T(5) = C(8,4) * (2)^4 = 70 * 16 = 1120.

Correct Answer: A — 128

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Q. What is the midpoint of the line segment joining the points (1, 2) and (3, 4)?

A. (2, 3)
B. (1, 2)
C. (3, 4)
D. (4, 6)

Solution

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

Correct Answer: A — (2, 3)

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Q. What is the midpoint of the line segment joining the points (2, 3) and (4, 7)?

A. (3, 5)
B. (2, 5)
C. (4, 3)
D. (5, 7)

Solution

Midpoint = ((2+4)/2, (3+7)/2) = (3, 5).

Correct Answer: A — (3, 5)

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Q. What is the minimum value of the function f(x) = 2x^2 - 8x + 10?

A. 2
B. 4
C. 6
D. 8

Solution

The vertex form gives the minimum at x = 2. f(2) = 2(2^2) - 8(2) + 10 = 6.

Correct Answer: B — 4

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Q. What is the minimum value of the function f(x) = x^2 - 4x + 5?

A. 1
B. 0
C. 2
D. 4

Solution

The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4(2) + 5 = 1.

Correct Answer: A — 1

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Mathematics Syllabus (JEE Main)

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