Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

Q. Calculate the determinant: | 2 3 1 | | 1 0 4 | | 0 5 2 |.

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

Solution

Using the determinant formula, we find that the determinant evaluates to 0.

Correct Answer: A — -1

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Q. Calculate the integral ∫ (x^2 + 2x + 1) dx.

A. (1/3)x^3 + x^2 + x + C
B. (1/3)x^3 + x^2 + C
C. (1/3)x^3 + 2x^2 + C
D. (1/3)x^3 + x^2 + x

Solution

The integral of x^2 is (1/3)x^3, the integral of 2x is x^2, and the integral of 1 is x. Thus, ∫ (x^2 + 2x + 1) dx = (1/3)x^3 + x^2 + x + C.

Correct Answer: A — (1/3)x^3 + x^2 + x + C

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Q. Calculate the integral ∫ (x^2 + 2x + 1)/(x + 1) dx.

A. (1/3)x^3 + x^2 + C
B. x^2 + 2x + C
C. x^2 + x + C
D. (1/3)x^3 + (1/2)x^2 + C

Solution

The integrand simplifies to x + 1. Therefore, ∫ (x + 1) dx = (1/2)x^2 + x + C.

Correct Answer: A — (1/3)x^3 + x^2 + C

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Q. Calculate the integral ∫ (x^3 - 4x) dx.

A. (1/4)x^4 - 2x^2 + C
B. (1/4)x^4 - 2x^2
C. (1/4)x^4 - 4x^2 + C
D. (1/4)x^4 - 2x^2 + 1

Solution

The integral of x^3 is (1/4)x^4 and the integral of -4x is -2x^2. Therefore, ∫ (x^3 - 4x) dx = (1/4)x^4 - 2x^2 + C.

Correct Answer: A — (1/4)x^4 - 2x^2 + C

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Q. Calculate the integral ∫ cos^2(x) dx.

A. (1/2)x + (1/4)sin(2x) + C
B. (1/2)x + C
C. (1/2)x - (1/4)sin(2x) + C
D. (1/2)x + (1/2)sin(2x) + C

Solution

Using the identity cos^2(x) = (1 + cos(2x))/2, we find that ∫ cos^2(x) dx = (1/2)x + (1/4)sin(2x) + C.

Correct Answer: A — (1/2)x + (1/4)sin(2x) + C

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Q. Calculate the integral ∫ from 0 to π of sin(x) dx.

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

Solution

The integral evaluates to [-cos(x)] from 0 to π = [1 - (-1)] = 2.

Correct Answer: C — 2

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Q. Calculate the interquartile range (IQR) for the data set: 1, 3, 7, 8, 9, 10.

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

Solution

Q1 = 3, Q3 = 9; IQR = Q3 - Q1 = 9 - 3 = 6.

Correct Answer: A — 4

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Q. Calculate the limit: lim (x -> 0) (1 - cos(x))/(x^2)

A. 0
B. 1/2
C. 1
D. Infinity

Solution

Using the identity 1 - cos(x) = 2sin^2(x/2), we have lim (x -> 0) (2sin^2(x/2))/(x^2) = 1.

Correct Answer: B — 1/2

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Q. Calculate the limit: lim (x -> 0) (e^x - 1)/x

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

Solution

Using the definition of the derivative of e^x at x = 0, we find that lim (x -> 0) (e^x - 1)/x = e^0 = 1.

Correct Answer: B — 1

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Q. Calculate the limit: lim (x -> 0) (tan(3x)/x)

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

Solution

Using the standard limit lim (x -> 0) (tan(kx)/x) = k, we have k = 3, so the limit is 3.

Correct Answer: A — 3

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Q. Calculate the limit: lim (x -> 1) (x^2 - 1)/(x - 1)

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

Solution

This is an indeterminate form (0/0). Factor the numerator: (x-1)(x+1)/(x-1) = x + 1. Thus, lim (x -> 1) (x + 1) = 2.

Correct Answer: C — 2

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Q. Calculate the limit: lim (x -> 1) (x^2 - 1)/(x - 1)^2

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

Solution

Factoring gives (x - 1)(x + 1)/(x - 1)^2 = (x + 1)/(x - 1). Thus, lim (x -> 1) (x + 1)/(x - 1) = 2.

Correct Answer: C — 2

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Q. Calculate the limit: lim (x -> 1) (x^3 - 1)/(x - 1)

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

Solution

Factoring gives (x - 1)(x^2 + x + 1)/(x - 1). Canceling (x - 1) gives lim (x -> 1) (x^2 + x + 1) = 3.

Correct Answer: C — 3

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Q. Calculate the limit: lim (x -> 2) (x^2 - 2x)/(x - 2)

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

Solution

Factoring gives (x(x - 2))/(x - 2), canceling gives lim (x -> 2) x = 2.

Correct Answer: D — Undefined

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Q. Calculate the mean absolute deviation for the data set: 1, 2, 3, 4, 5.

A. 1
B. 1.5
C. 2
D. 2.5

Solution

Mean = 3. Mean Absolute Deviation = (|1-3| + |2-3| + |3-3| + |4-3| + |5-3|)/5 = (2 + 1 + 0 + 1 + 2)/5 = 1.5.

Correct Answer: B — 1.5

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Q. Calculate the mean of the following data: 5, 10, 15, 20.

A. 10
B. 12.5
C. 15
D. 17.5

Solution

Mean = (5 + 10 + 15 + 20) / 4 = 50 / 4 = 12.5.

Correct Answer: B — 12.5

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Q. Calculate the mean of the following numbers: 10, 20, 30, 40, 50.

A. 30
B. 35
C. 40
D. 45

Solution

Mean = (10 + 20 + 30 + 40 + 50) / 5 = 150 / 5 = 30.

Correct Answer: A — 30

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Q. Calculate 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: C — 14

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Q. Calculate the range of the data set: 12, 15, 22, 30, 5.

A. 25
B. 27
C. 30
D. 22

Solution

Range = Maximum - Minimum = 30 - 5 = 25.

Correct Answer: A — 25

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Q. Calculate the range of the data set: 4, 8, 15, 16, 23, 42.

A. 38
B. 36
C. 34
D. 32

Solution

Range = Maximum - Minimum = 42 - 4 = 38.

Correct Answer: A — 38

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Q. Calculate the range of the data set: 8, 12, 15, 20, 22.

A. 10
B. 12
C. 14
D. 15

Solution

Range = Max - Min = 22 - 8 = 14.

Correct Answer: A — 10

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Q. Calculate the range of the following data set: 12, 15, 20, 22, 30.

A. 10
B. 12
C. 18
D. 20

Solution

Range = Maximum - Minimum = 30 - 12 = 18.

Correct Answer: C — 18

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Q. Calculate the range of the following data set: 15, 22, 8, 19, 30.

A. 7
B. 15
C. 22
D. 30

Solution

Range = max - min = 30 - 8 = 22.

Correct Answer: D — 30

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Q. Calculate the range of the following data set: 4, 8, 15, 16, 23, 42.

A. 38
B. 36
C. 34
D. 32

Solution

Range = Maximum - Minimum = 42 - 4 = 38.

Correct Answer: A — 38

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Q. Calculate the range of the following data set: 8, 12, 15, 7, 10.

A. 5
B. 8
C. 10
D. 12

Solution

Range = Maximum - Minimum = 15 - 7 = 8.

Correct Answer: A — 5

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Q. Calculate the scalar product of A = (1, 1, 1) and B = (2, 2, 2).

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

Solution

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

Correct Answer: D — 6

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Q. Calculate the scalar product of the vectors (1, 0, 0) and (0, 1, 0).

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

Solution

Scalar product = 1*0 + 0*1 + 0*0 = 0.

Correct Answer: A — 0

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Q. Calculate the scalar product of the vectors (1, 2, 3) and (4, 5, 6).

A. 32
B. 33
C. 34
D. 35

Solution

Scalar product = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

Correct Answer: A — 32

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Q. Calculate the scalar product of the vectors (2, 3, 4) and (4, 3, 2).

A. 28
B. 29
C. 30
D. 31

Solution

Scalar product = 2*4 + 3*3 + 4*2 = 8 + 9 + 8 = 25.

Correct Answer: A — 28

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Q. Calculate the scalar product of the vectors (3, 0, -3) and (1, 2, 1).

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

Solution

Scalar product = 3*1 + 0*2 + (-3)*1 = 3 + 0 - 3 = 0.

Correct Answer: A — 0

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Mathematics Syllabus (JEE Main)

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