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 roots of the equation x^2 - kx + 8 = 0 are equal, what is the value of k?

A. 4
B. 8
C. 16
D. 0

Solution

For equal roots, the discriminant must be zero: k^2 - 4*1*8 = 0, solving gives k = 4.

Correct Answer: A — 4

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Q. If the roots of the quadratic equation ax^2 + bx + c = 0 are 3 and -2, what is the value of c if a = 1 and b = -1?

A. -6
B. 6
C. 5
D. 1

Solution

Using the product of the roots, c = 3 * (-2) = -6.

Correct Answer: A — -6

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Q. If the roots of the quadratic equation ax^2 + bx + c = 0 are equal, what is the condition on a, b, and c?

A. b^2 - 4ac > 0
B. b^2 - 4ac = 0
C. b^2 - 4ac < 0
D. a + b + c = 0

Solution

The condition for equal roots is given by the discriminant b^2 - 4ac = 0.

Correct Answer: B — b^2 - 4ac = 0

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Q. If the roots of the quadratic equation x^2 + mx + n = 0 are 3 and 4, what is the value of m?

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

Solution

The sum of the roots is 3 + 4 = 7, hence m = -7.

Correct Answer: A — 7

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Q. If the roots of the quadratic equation x^2 + px + q = 0 are equal, what is the relationship between p and q?

A. p^2 = 4q
B. p^2 > 4q
C. p^2 < 4q
D. p + q = 0

Solution

For equal roots, the discriminant must be zero: p^2 - 4q = 0, hence p^2 = 4q.

Correct Answer: A — p^2 = 4q

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Q. If the roots of the quadratic equation x^2 - 3x + p = 0 are 1 and 2, what is the value of p?

A. 1
B. 2
C. 3
D. 6

Solution

Using Vieta's formulas, sum of roots = 1 + 2 = 3 and product of roots = 1*2 = 2. Thus, p = 2.

Correct Answer: D — 6

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Q. If the scalar product of two vectors A and B is 0, what can be said about the vectors?

A. They are parallel
B. They are orthogonal
C. They are equal
D. They are collinear

Solution

If A · B = 0, then the vectors are orthogonal.

Correct Answer: B — They are orthogonal

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Q. If the scalar product of vectors A = (x, y, z) and B = (2, -1, 3) is 10, what is the equation?

A. 2x - y + 3z = 10
B. 2x + y + 3z = 10
C. 2x - y - 3z = 10
D. 2x + y - 3z = 10

Solution

A · B = 2x - y + 3z = 10.

Correct Answer: A — 2x - y + 3z = 10

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Q. If the scores of 10 students are: 50, 60, 70, 80, 90, 100, 50, 60, 70, 80, what is the mode?

A. 50
B. 60
C. 70
D. 80

Solution

Mode is the value that appears most frequently. Here, 50, 60, 70, and 80 all appear twice, but 50 is the smallest.

Correct Answer: A — 50

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Q. If the scores of 5 students are 10, 20, 30, 40, and x, and the mean is 30, what is the value of x?

A. 30
B. 40
C. 50
D. 60

Solution

Mean = (10 + 20 + 30 + 40 + x) / 5 = 30. Solving gives x = 50.

Correct Answer: C — 50

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Q. If the scores of 7 students are 50, 60, 70, 80, 90, 100, and 110, what is the median score?

A. 70
B. 80
C. 90
D. 100

Solution

Arranging the scores: 50, 60, 70, 80, 90, 100, 110. Median = 80 (4th value).

Correct Answer: B — 80

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Q. If the scores of a student are 50, 60, 70, 80, and 90, what is the mode?

A. 50
B. 60
C. 70
D. No mode

Solution

All scores occur only once, so there is no mode.

Correct Answer: D — No mode

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Q. If the scores of a student in five subjects are 60, 70, 80, 90, and 100, what is the median score?

A. 70
B. 80
C. 90
D. 100

Solution

Arranging the scores: 60, 70, 80, 90, 100. Median = 80 (middle value).

Correct Answer: B — 80

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Q. If the scores of a student in five subjects are 70, 80, 90, 100, and 60, what is the median score?

A. 70
B. 80
C. 90
D. 100

Solution

Median = 80 (middle value when arranged: 60, 70, 80, 90, 100).

Correct Answer: B — 80

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Q. If the sides of triangle ABC are 7 cm, 24 cm, and 25 cm, what is the perimeter of the triangle?

A. 50 cm
B. 55 cm
C. 60 cm
D. 65 cm

Solution

Perimeter = a + b + c = 7 + 24 + 25 = 56 cm.

Correct Answer: A — 50 cm

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Q. If the sides of triangle ABC are in the ratio 3:4:5, what type of triangle is it?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.

Correct Answer: C — Right

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Q. If the standard deviation of a data set is 0, what can be said about the data?

A. All values are different
B. All values are the same
C. Values are in a range
D. Data is not valid

Solution

A standard deviation of 0 indicates that all values in the data set are the same.

Correct Answer: B — All values are the same

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Q. If the standard deviation of a data set is 3, what is the variance?

A. 3
B. 6
C. 9
D. 12

Solution

Variance = (Standard Deviation)^2 = 3^2 = 9.

Correct Answer: C — 9

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Q. If the standard deviation of a data set is 4, what is the variance?

A. 8
B. 16
C. 4
D. 12

Solution

Variance = (Standard Deviation)² = 4² = 16.

Correct Answer: B — 16

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Q. If the standard deviation of a data set is 5, what is the variance?

A. 5
B. 10
C. 25
D. 30

Solution

Variance is the square of the standard deviation. Variance = 5² = 25.

Correct Answer: C — 25

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Q. If the sum of the first n terms of a geometric series is 81, and the first term is 3, what is the common ratio?

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

Solution

Using the formula S_n = a(1 - r^n) / (1 - r), we have 81 = 3(1 - r^n) / (1 - r). Solving gives r = 3.

Correct Answer: B — 3

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Q. If the sum of the first n terms of a geometric series is given by S_n = a(1 - r^n)/(1 - r), what is the sum when r = 1?

A. na
B. a
C. 0
D. undefined

Solution

When r = 1, S_n = a(1 - 1^n)/(1 - 1) is indeterminate, but the sum of n terms is na.

Correct Answer: A — na

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Q. If the sum of the first n terms of an arithmetic series is given by S_n = 3n^2 + 2n, what is the 4th term?

A. 26
B. 30
C. 22
D. 24

Solution

The 4th term a_4 = S_4 - S_3 = (3(4^2) + 2(4)) - (3(3^2) + 2(3)) = (48 + 8) - (27 + 6) = 56 - 33 = 23.

Correct Answer: A — 26

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Q. If the sum of the first n terms of an arithmetic series is given by S_n = 5n^2 + 3n, what is the 5th term?

A. 38
B. 43
C. 48
D. 53

Solution

The 5th term can be found using a_n = S_n - S_(n-1). Calculate S_5 and S_4, then find a_5 = S_5 - S_4 = (5(5^2) + 3(5)) - (5(4^2) + 3(4)) = 38.

Correct Answer: A — 38

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Q. If the sum of the roots of the equation x^2 - 3x + p = 0 is 3, what is the value of p?

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

Solution

The sum of the roots is given by -b/a = 3. Here, -(-3)/1 = 3, so p can be any value.

Correct Answer: A — 0

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Q. If the universal set U = {1, 2, 3, 4, 5} and A = {1, 2}, what is A'?

A. {3, 4, 5}
B. {1, 2}
C. {1, 2, 3}
D. {2, 3, 4, 5}

Solution

The complement of A, denoted A', includes all elements in U that are not in A. Thus, A' = {3, 4, 5}.

Correct Answer: A — {3, 4, 5}

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

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

Solution

Standard deviation = √variance = √16 = 4.

Correct Answer: A — 4

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Q. If the vector A = (1, 2) and B = (2, 1), what is the angle between them?

A. 0 degrees
B. 90 degrees
C. 45 degrees
D. 180 degrees

Solution

Cosine of angle = (A · B) / (|A| |B|) = (1*2 + 2*1) / (√5 * √5) = 4/5, angle = cos^(-1)(4/5).

Correct Answer: C — 45 degrees

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Q. If the vector a = (1, 2) and b = (3, 4), find the angle between them using the dot product.

A. 0 degrees
B. 90 degrees
C. 45 degrees
D. 60 degrees

Solution

cos(θ) = (a · b) / (|a| |b|). a · b = 1*3 + 2*4 = 11, |a| = √(1^2 + 2^2) = √5, |b| = √(3^2 + 4^2) = 5. Thus, cos(θ) = 11 / (√5 * 5) = 11 / (5√5), θ = 60 degrees.

Correct Answer: D — 60 degrees

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Q. If the vector a = (2, -1) and b = (1, 3), what is a + b?

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

Solution

a + b = (2 + 1, -1 + 3) = (3, 2)

Correct Answer: A — (3, 2)

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Mathematics Syllabus (JEE Main)

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