Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

Q. A tower is 50 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. What is the distance from the point to the base of the tower?

A. 25√3 m
B. 50 m
C. 25 m
D. 50√3 m

Solution

Using tan(30°) = height/distance, we have distance = height/tan(30°) = 50/√3 = 25√3 m.

Correct Answer: A — 25√3 m

Learn More →

Q. A tower is 60 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower?

A. 30 meters
B. 60 meters
C. 45 meters
D. 75 meters

Solution

Distance = height / tan(angle) = 60 / 1 = 60 meters.

Correct Answer: B — 60 meters

Learn More →

Q. A tower is 80 meters high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower?

A. 40 m
B. 80 m
C. 20 m
D. 60 m

Solution

Distance = height / tan(angle) = 80 / √3 = 40 m.

Correct Answer: A — 40 m

Learn More →

Q. A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 10√3 meters, how far is the point from the base of the tower?

A. 10 m
B. 20 m
C. 30 m
D. 40 m

Solution

Using tan(30°) = height/distance, we have 1/√3 = 10√3/distance. Therefore, distance = 10√3 * √3 = 30 m.

Correct Answer: B — 20 m

Learn More →

Q. A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 50 meters, how far is the point from the base of the tower?

A. 50√3 m
B. 100 m
C. 50 m
D. 100√3 m

Solution

Using tan(30°) = height/distance, we have distance = height/tan(30°) = 50/(1/√3) = 50√3 m.

Correct Answer: A — 50√3 m

Learn More →

Q. A tower is standing on a horizontal ground. The angle of elevation of the top of the tower from a point on the ground is 30 degrees. If the height of the tower is 10√3 m, how far is the point from the base of the tower?

A. 10 m
B. 5 m
C. 15 m
D. 20 m

Solution

Using tan(30°) = height/distance, we have 1/√3 = 10√3/distance. Therefore, distance = 10√3 * √3 = 30 m.

Correct Answer: A — 10 m

Learn More →

Q. A tree casts a shadow of 20 m when the angle of elevation of the sun is 30 degrees. What is the height of the tree?

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

Solution

Using tan(30°) = height/20, we have 1/√3 = height/20. Therefore, height = 20/√3 ≈ 11.55 m.

Correct Answer: A — 10 m

Learn More →

Q. A tree casts a shadow of 20 m when the angle of elevation of the sun is 45 degrees. What is the height of the tree?

A. 10 m
B. 20 m
C. 30 m
D. 40 m

Solution

Using tan(45°) = height/shadow, we have 1 = height/20. Therefore, height = 20 m.

Correct Answer: B — 20 m

Learn More →

Q. A tree casts a shadow of 20 meters when the angle of elevation of the sun is 30 degrees. What is the height of the tree?

A. 20√3 meters
B. 10√3 meters
C. 30 meters
D. 40 meters

Solution

Height = shadow * tan(angle) = 20 * tan(30°) = 20 * (1/√3) = 20√3 meters.

Correct Answer: A — 20√3 meters

Learn More →

Q. A tree is 15 meters tall. From a point on the ground, the angle of elevation to the top of the tree is 30 degrees. How far is the point from the base of the tree?

A. 15√3 meters
B. 30 meters
C. 45 meters
D. 10 meters

Solution

Distance = height / tan(angle) = 15 / tan(30°) = 15√3 meters.

Correct Answer: A — 15√3 meters

Learn More →

Q. Calculate the area between the curves y = x and y = x^2 from x = 0 to x = 1.

A. 0.25
B. 0.5
C. 0.75
D. 1

Solution

The area is given by the integral from 0 to 1 of (x - x^2) dx. This evaluates to [x^2/2 - x^3/3] from 0 to 1 = (1/2 - 1/3) = 1/6 = 0.5.

Correct Answer: B — 0.5

Learn More →

Q. Calculate the area between the curves y = x^2 and y = 2x from x = 0 to x = 2.

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

Solution

The area is given by the integral from 0 to 2 of (2x - x^2) dx. This evaluates to [x^2 - x^3/3] from 0 to 2 = (4 - 8/3) = 4/3.

Correct Answer: A — 2

Learn More →

Q. Calculate the area between the curves y = x^2 and y = 4 from x = 0 to x = 2.

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

Solution

The area is given by the integral from 0 to 2 of (4 - x^2) dx. This evaluates to [4x - x^3/3] from 0 to 2 = (8 - 8/3) = 16/3.

Correct Answer: A — 4

Learn More →

Q. Calculate the area under the curve y = cos(x) from x = 0 to x = π/2.

A. 1
B. 0
C. π/2
D. 2

Solution

The area under the curve y = cos(x) from x = 0 to x = π/2 is given by ∫(from 0 to π/2) cos(x) dx = [sin(x)] from 0 to π/2 = 1 - 0 = 1.

Correct Answer: A — 1

Learn More →

Q. Calculate the area under the curve y = x^2 + 2x from x = 0 to x = 2.

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

Solution

The area under the curve is given by ∫(from 0 to 2) (x^2 + 2x) dx = [x^3/3 + x^2] from 0 to 2 = (8/3 + 4) = 20/3.

Correct Answer: B — 6

Learn More →

Q. Calculate the area under the curve y = x^4 from x = 0 to x = 2.

A. 4
B. 8
C. 16
D. 32

Solution

The area under the curve y = x^4 from x = 0 to x = 2 is given by ∫(from 0 to 2) x^4 dx = [x^5/5] from 0 to 2 = (32/5) - 0 = 32/5.

Correct Answer: B — 8

Learn More →

Q. Calculate the derivative of f(x) = e^(2x).

A. 2e^(2x)
B. e^(2x)
C. 2xe^(2x)
D. e^(x)

Solution

Using the chain rule, f'(x) = d/dx(e^(2x)) = 2e^(2x).

Correct Answer: A — 2e^(2x)

Learn More →

Q. Calculate the derivative of f(x) = x^2 * e^x.

A. (2x + x^2)e^x
B. 2xe^x
C. x^2e^x
D. (x^2 + 2x)e^x

Solution

Using the product rule, f'(x) = d/dx(x^2 * e^x) = (x^2 + 2x)e^x.

Correct Answer: D — (x^2 + 2x)e^x

Learn More →

Q. Calculate the determinant of the matrix [[1, 2], [3, 4]].

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

Solution

Determinant = (1*4) - (2*3) = 4 - 6 = -2.

Correct Answer: A — -2

Learn More →

Q. Calculate the determinant of the matrix \( B = \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \).

A. -1
B. 1
C. 7
D. 10

Solution

The determinant is calculated as \( 2*7 - 3*5 = 14 - 15 = -1 \).

Correct Answer: D — 10

Learn More →

Q. Calculate the determinant of the matrix \( G = \begin{pmatrix} 2 & 1 & 3 \\ 1 & 0 & 1 \\ 3 & 1 & 2 \end{pmatrix} \).

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

Solution

The determinant is calculated as \( 2(0*2 - 1*1) - 1(1*2 - 3*1) + 3(1*1 - 3*0) = 0 \).

Correct Answer: A — -1

Learn More →

Q. Calculate the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \).

A. 5
B. 10
C. 7
D. 8

Solution

The determinant is calculated as \( 2*4 - 3*1 = 8 - 3 = 5 \).

Correct Answer: A — 5

Learn More →

Q. Calculate the determinant of the matrix \( \begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \).

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

Solution

The determinant is calculated as (2*7) - (3*5) = 14 - 15 = -1.

Correct Answer: A — 1

Learn More →

Q. Calculate the determinant of the matrix: | 1 1 1 | | 2 2 2 | | 3 3 3 |

A. 0
B. 3
C. 6
D. 9

Solution

The rows are linearly dependent, hence the determinant is 0.

Correct Answer: A — 0

Learn More →

Q. Calculate the determinant \( \begin{vmatrix} 1 & 2 & 1 \\ 2 & 3 & 1 \\ 3 & 4 & 1 \end{vmatrix} \).

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

Solution

The determinant is 0 because the rows are linearly dependent.

Correct Answer: A — 0

Learn More →

Q. Calculate the determinant \( \begin{vmatrix} 2 & 3 \\ 5 & 7 \end{vmatrix} \)

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

Solution

The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).

Correct Answer: A — 1

Learn More →

Q. Calculate the determinant \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \)

A. ad - bc
B. ab + cd
C. ac - bd
D. bc - ad

Solution

The determinant is calculated as \( ad - bc \).

Correct Answer: A — ad - bc

Learn More →

Q. Calculate the determinant | 1 0 0 | | 0 1 0 | | 0 0 1 |.

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

Solution

The determinant of the identity matrix is 1.

Correct Answer: B — 1

Learn More →

Q. Calculate the determinant | 2 3 | | 4 5 | + | 1 1 | | 1 1 |.

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

Solution

The first determinant is -2 and the second is 0, so the total is -2 + 0 = -2.

Correct Answer: B — 1

Learn More →

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

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

Solution

The determinant evaluates to 0 as the rows are linearly dependent.

Correct Answer: A — -1

Learn More →

Showing 121 to 150 of 2847 (95 Pages)

Mathematics Syllabus (JEE Main)

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?