Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

Q. If the area of triangle JKL is 30 cm² and the base JK is 10 cm, what is the height from point L?

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

Solution

Area = 1/2 * base * height. 30 = 1/2 * 10 * height. Therefore, height = 6 cm.

Correct Answer: C — 5 cm

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Q. If the center of a circle is at (0, 0) and it passes through the point (3, 4), what is the equation of the circle?

A. x² + y² = 25
B. x² + y² = 12
C. x² + y² = 7
D. x² + y² = 16

Solution

The radius is 5 (distance from (0,0) to (3,4)), so the equation is x² + y² = 5² = 25.

Correct Answer: A — x² + y² = 25

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Q. If the center of a circle is at (0, 0) and it passes through the point (3, 4), what is the radius of the circle?

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

Solution

The radius is the distance from the center to the point, which is √(3² + 4²) = √25 = 5.

Correct Answer: A — 5

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Q. If the circumradius of triangle ABC is 10 cm and the area is 48 cm², what is the length of the side opposite to angle A?

A. 12 cm
B. 14 cm
C. 16 cm
D. 18 cm

Solution

Using the formula R = (abc)/(4 * Area), we can find the side opposite to angle A. Let a = side opposite to A. Then, a = (4 * Area * R) / (bc) = (4 * 48 * 10) / (b * c).

Correct Answer: B — 14 cm

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Q. If the circumradius R of triangle ABC is 5 cm, what is the maximum area of the triangle?

A. 12.5 cm²
B. 15 cm²
C. 20 cm²
D. 25 cm²

Solution

The maximum area of a triangle with circumradius R is given by the formula Area = (abc)/(4R). For maximum area, the triangle should be equilateral, thus Area = (3√3/4) * (R^2) = (3√3/4) * (5^2) = 25√3/4 cm².

Correct Answer: C — 20 cm²

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Q. If the coordinates of the vertices of a triangle are (1, 1), (4, 5), and (7, 2), what is the perimeter of the triangle?

A. 12
B. 14
C. 16
D. 18

Solution

Calculate distances AB, BC, CA and sum them: AB = 5, BC = 5, CA = 7. Perimeter = 5 + 5 + 7 = 17.

Correct Answer: B — 14

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Q. If the coordinates of the vertices of a triangle are (1, 2), (3, 4), and (5, 2), what is the perimeter of the triangle?

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

Solution

Perimeter = AB + BC + CA = √[(3-1)² + (4-2)²] + √[(5-3)² + (2-4)²] + √[(1-5)² + (2-2)²] = 2.83 + 2.83 + 4 = 10.

Correct Answer: B — 10

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Q. If the coordinates of the vertices of a triangle are (1, 2), (4, 6), and (7, 2), what is the perimeter of the triangle?

A. 12
B. 14
C. 16
D. 18

Solution

Perimeter = AB + BC + CA = √[(4-1)² + (6-2)²] + √[(7-4)² + (2-6)²] + √[(1-7)² + (2-2)²] = 3 + √(9 + 16) + 6 = 3 + 5 + 6 = 14.

Correct Answer: B — 14

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Q. If the coordinates of the vertices of a triangle are A(1, 1), B(4, 5), and C(7, 2), what is the area of the triangle?

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

Solution

Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 1/2 | 1(5-2) + 4(2-1) + 7(1-5) | = 1/2 | 3 + 4 - 28 | = 1/2 * 21 = 10.5.

Correct Answer: B — 12

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Q. If the data set has a mean of 30 and a median of 25, what does this indicate?

A. Data is symmetrical
B. Data is positively skewed
C. Data is negatively skewed
D. Data is uniform

Solution

Since the mean is greater than the median, the data is positively skewed.

Correct Answer: B — Data is positively skewed

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Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of the value 40?

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

Solution

Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1

Correct Answer: C — 2

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Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of a value 40?

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

Solution

Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1.

Correct Answer: C — 2

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Q. If the data set has a mean of 30 and a variance of 16, what is the standard deviation?

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

Solution

Standard Deviation = √Variance = √16 = 4.

Correct Answer: A — 4

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Q. If the data set has a mean of 50 and a median of 45, what can be said about the data distribution?

A. Symmetric
B. Positively skewed
C. Negatively skewed
D. Uniform

Solution

Since the mean is greater than the median, the distribution is positively skewed.

Correct Answer: B — Positively skewed

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Q. If the data set has a mean of 50 and a standard deviation of 10, what is the z-score of the value 70?

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

Solution

Z-score = (X - Mean) / Standard Deviation = (70 - 50) / 10 = 2.

Correct Answer: B — 2

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Q. If the data set has a mean of 50 and a variance of 16, what is the standard deviation?

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

Solution

Standard Deviation = √Variance = √16 = 4.

Correct Answer: B — 4

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Q. If the data set is 1, 2, 2, 3, 4, 4, 4, 5, what is the mode?

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

Solution

Mode = 4 (most frequent value).

Correct Answer: C — 4

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Q. If the data set is 4, 4, 4, 5, 5, 6, what is the mode?

A. 4
B. 5
C. 6
D. None

Solution

Mode = 4 (most frequent value).

Correct Answer: A — 4

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Q. If the data set is {5, 7, 7, 8, 10}, what is the mode?

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

Solution

Mode = 7 (most frequently occurring value).

Correct Answer: B — 7

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Q. If the data set is {5, 7, 8, 9, 10}, what is the interquartile range?

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

Solution

Q1 = 7, Q3 = 9; Interquartile Range = Q3 - Q1 = 9 - 7 = 2.

Correct Answer: B — 3

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Q. If the data set is {5, 7, 8, 9, 10}, what is the standard deviation?

A. 1.58
B. 2.58
C. 3.58
D. 4.58

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 = 2.5. Standard Deviation = √2.5 ≈ 1.58.

Correct Answer: A — 1.58

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Q. If the data set is: 3, 7, 7, 19, what is the median?

A. 7
B. 10
C. 11
D. 12

Solution

Median = (7 + 7) / 2 = 7.

Correct Answer: A — 7

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Q. If the data set is: 5, 7, 8, 9, 10, what is the median?

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

Solution

Median is the middle value. Here, the middle values are 7 and 8, so Median = (7+8)/2 = 7.5.

Correct Answer: B — 8

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Q. If the data set {1, 2, 3, 4, 5} is transformed to {2, 3, 4, 5, 6}, what happens to the standard deviation?

A. Increases
B. Decreases
C. Remains the same
D. Cannot be determined

Solution

The standard deviation remains the same because the transformation is a shift.

Correct Answer: C — Remains the same

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Q. If the data set {10, 20, 30, 40, 50} is transformed to {x + 5}, what happens to the standard deviation?

A. Increases
B. Decreases
C. Remains the same
D. Cannot be determined

Solution

Standard deviation remains the same as adding a constant does not affect dispersion.

Correct Answer: C — Remains the same

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Q. If the data set {3, 7, 8, 12, 14} has a median of 8, what is the first quartile?

A. 3
B. 7
C. 8
D. 12

Solution

Q1 is the median of the first half of the data set {3, 7}, which is 7.

Correct Answer: B — 7

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Q. If the data set {3, 7, 8, 12, 14} is given, what is the median?

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

Solution

Median is the middle value, which is 8.

Correct Answer: A — 8

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Q. If the data set {5, 7, 8, 9, 10} has a mean of 7.8, what is the sum of the deviations from the mean?

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

Solution

The sum of deviations from the mean is always 0.

Correct Answer: A — 0

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Q. If the determinant | x 2 | | 3 4 | = 0, find x.

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

Solution

Setting the determinant to zero gives x*4 - 2*3 = 0, thus x = 1.5.

Correct Answer: B — 2

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Q. If the directrix of a parabola is given by the equation y = -p, what is the equation of the parabola?

A. y^2 = 4px
B. x^2 = 4py
C. y^2 = -4px
D. x^2 = -4py

Solution

The equation of a parabola with directrix y = -p is y^2 = -4px.

Correct Answer: C — y^2 = -4px

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Mathematics Syllabus (JEE Main)

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