Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

Q. From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?

A. 100√3 m
B. 50 m
C. 100 m
D. 50√3 m

Solution

Using tan(30°) = height/distance, we have height = distance * tan(30°) = 100 * (1/√3) = 100/√3 = 50 m.

Correct Answer: B — 50 m

Learn More →

Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 20 m, how far is the point from the base of the hill?

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

Solution

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

Correct Answer: A — 20 m

Learn More →

Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill?

A. 100 m
B. 50 m
C. 200 m
D. 150 m

Solution

Using tan(45°) = height/distance, we have distance = height/tan(45°) = 100/1 = 100 m.

Correct Answer: A — 100 m

Learn More →

Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 50 m, how far is the point from the base of the hill?

A. 25 m
B. 50 m
C. 70 m
D. 100 m

Solution

Using tan(45°) = height/distance, we have 1 = 50/distance. Therefore, distance = 50 m.

Correct Answer: B — 50 m

Learn More →

Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the point is 100 meters away from the base of the hill, what is the height of the hill?

A. 100 meters
B. 50 meters
C. 200 meters
D. 150 meters

Solution

Height = distance * tan(angle) = 100 * tan(45°) = 100 meters.

Correct Answer: A — 100 meters

Learn More →

Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 40 m, how far is the point from the base of the hill?

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

Solution

Using tan(45°) = height/distance, we have 1 = 40/distance. Therefore, distance = 40 m.

Correct Answer: B — 40 m

Learn More →

Q. From a point on the ground, the angle of elevation to the top of a tower is 60 degrees. If the tower is 30 m high, how far is the point from the base of the tower?

A. 15 m
B. 30 m
C. 20 m
D. 10 m

Solution

Using tan(60°) = height/distance, we have √3 = 30/distance. Therefore, distance = 30/√3 m.

Correct Answer: A — 15 m

Learn More →

Q. From a set of 8 different books, how many ways can you choose 3 books?

A. 56
B. 84
C. 28
D. 70

Solution

The number of ways to choose 3 books from 8 is given by 8C3 = 56.

Correct Answer: B — 84

Learn More →

Q. From the top of a 20-meter high building, the angle of depression to a car parked on the ground is 60 degrees. How far is the car from the base of the building?

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

Solution

Distance = height / tan(angle) = 20 / tan(60°) = 20 / √3 = 10√3 meters.

Correct Answer: A — 10√3 meters

Learn More →

Q. From the top of a 50 m high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building?

A. 25 m
B. 50 m
C. 70 m
D. 100 m

Solution

Using tan(45°) = height/distance, we have 1 = 50/distance. Therefore, distance = 50 m.

Correct Answer: B — 50 m

Learn More →

Q. From the top of a 50-meter high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building?

A. 50 meters
B. 100 meters
C. 25 meters
D. 70 meters

Solution

Distance = height / tan(angle) = 50 / tan(45°) = 50 meters.

Correct Answer: A — 50 meters

Learn More →

Q. From the top of a 60 m high building, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the building?

A. 60√3 m
B. 30√3 m
C. 60 m
D. 30 m

Solution

Using tan(30°) = height/distance, we have distance = height/tan(30°) = 60/√3 = 60√3 m.

Correct Answer: A — 60√3 m

Learn More →

Q. From the top of a 60 m high cliff, the angle of depression to a boat in the sea is 30 degrees. How far is the boat from the base of the cliff?

A. 60√3 m
B. 30√3 m
C. 60 m
D. 30 m

Solution

Using tan(30°) = height/distance, we have distance = height/tan(30°) = 60/√3 = 60√3 m.

Correct Answer: A — 60√3 m

Learn More →

Q. Given A = 3i + 4j and B = 0i + 0j, find A · B.

A. 0
B. 12
C. 7
D. 3

Solution

A · B = (3)(0) + (4)(0) = 0.

Correct Answer: A — 0

Learn More →

Q. Given vectors A = (2, -1, 3) and B = (4, 0, -2), find A × B.

A. (-1, -10, 4)
B. (1, 10, -4)
C. (10, -1, 4)
D. (10, 1, -4)

Solution

A × B = |i  j  k|\n|2 -1  3|\n|4  0 -2| = (-1, -10, 4)

Correct Answer: A — (-1, -10, 4)

Learn More →

Q. Given vectors A = (x, y, z) and B = (1, 2, 3), if A · B = 14, what is the value of x + 2y + 3z?

A. 14
B. 10
C. 8
D. 6

Solution

A · B = x*1 + y*2 + z*3 = 14, thus x + 2y + 3z = 14.

Correct Answer: A — 14

Learn More →

Q. Given vectors P = (4, 0, -3) and Q = (1, 2, 1), find the scalar product P · Q.

A. -1
B. 5
C. 10
D. 2

Solution

P · Q = 4*1 + 0*2 + (-3)*1 = 4 + 0 - 3 = 1.

Correct Answer: B — 5

Learn More →

Q. Given vectors P = (4, 1, 0) and Q = (0, 2, 3), find the scalar product P · Q.

A. 0
B. 6
C. 8
D. 10

Solution

P · Q = 4*0 + 1*2 + 0*3 = 0 + 2 + 0 = 2.

Correct Answer: B — 6

Learn More →

Q. Given vectors P = (4, 1, 0) and Q = (1, 2, 3), find the scalar product P · Q.

A. 10
B. 11
C. 12
D. 13

Solution

P · Q = 4*1 + 1*2 + 0*3 = 4 + 2 + 0 = 6.

Correct Answer: B — 11

Learn More →

Q. How many different ways can 3 red, 2 blue, and 1 green balls be arranged in a line?

A. 60
B. 120
C. 30
D. 10

Solution

The total arrangements = 6! / (3! * 2! * 1!) = 60.

Correct Answer: B — 120

Learn More →

Q. How many different ways can 4 people be seated at a round table?

A. 6
B. 12
C. 24
D. 30

Solution

The number of arrangements of n people at a round table is (n-1)!. For 4 people, it is 3! = 6.

Correct Answer: B — 12

Learn More →

Q. How many different ways can 4 students be selected from a group of 10?

A. 210
B. 120
C. 100
D. 90

Solution

The number of ways to choose 4 from 10 is given by 10C4 = 210.

Correct Answer: A — 210

Learn More →

Q. How many different ways can 6 people be seated at a round table?

A. 720
B. 120
C. 600
D. 480

Solution

The number of arrangements of 6 people at a round table is (6-1)! = 5! = 120.

Correct Answer: A — 720

Learn More →

Q. How many elements are in the power set of the empty set?

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

Solution

The power set of the empty set contains only one subset, which is the empty set itself. Thus, it has 1 element.

Correct Answer: B — 1

Learn More →

Q. How many relations can be formed from a set with 3 elements?

A. 3
B. 6
C. 8
D. 16

Solution

The number of relations on a set with n elements is 2^(n^2). For n = 3, it is 2^(3^2) = 2^9 = 512.

Correct Answer: C — 8

Learn More →

Q. How many subsets can be formed from the set C = {x, y, z, w}?

A. 4
B. 8
C. 16
D. 2

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 4, so 2^4 = 16.

Correct Answer: B — 8

Learn More →

Q. How many subsets can be formed from the set G = {1, 2, 3, 4, 5, 6}?

A. 32
B. 64
C. 128
D. 256

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 6, so the number of subsets is 2^6 = 64.

Correct Answer: C — 128

Learn More →

Q. How many subsets can be formed from the set H = {a, b, c, d, e, f}?

A. 32
B. 64
C. 128
D. 256

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 6, so 2^6 = 64.

Correct Answer: B — 64

Learn More →

Q. How many subsets can be formed from the set S = {a, b, c, d}?

A. 4
B. 8
C. 16
D. 2

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 4, so the number of subsets is 2^4 = 16.

Correct Answer: B — 8

Learn More →

Q. How many subsets can be formed from the set {1, 2, 3, 4, 5, 6}?

A. 32
B. 64
C. 128
D. 256

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 6, so the number of subsets is 2^6 = 64.

Correct Answer: D — 256

Learn More →

Showing 931 to 960 of 2847 (95 Pages)

Mathematics Syllabus (JEE Main)

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