Mathematics Syllabus for JEE Main

Mathematics Syllabus (JEE Main)

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

Q. The pair of straight lines represented by the equation x^2 - 4xy + y^2 = 0 are:

A. Parallel
B. Perpendicular
C. Coincident
D. Intersecting at a point

Solution

The given equation can be factored as (x - 2y)(x - 2y) = 0, indicating that the lines are perpendicular.

Correct Answer: B — Perpendicular

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Q. The parabola y = -3(x - 2)^2 + 5 opens in which direction?

A. Upwards
B. Downwards
C. Left
D. Right

Solution

Since the coefficient of (x - 2)^2 is negative, the parabola opens downwards.

Correct Answer: B — Downwards

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Q. The product of the roots of the equation x^2 + 7x + 10 = 0 is:

A. 10
B. 7
C. 5
D. 3

Solution

The product of the roots is given by c/a = 10/1 = 10.

Correct Answer: A — 10

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Q. The product of the roots of the equation x^2 - 7x + k = 0 is 10. What is the value of k?

A. 10
B. 17
C. 20
D. 30

Solution

Using Vieta's formulas, the product of the roots is k = 10. Thus, k = 17.

Correct Answer: B — 17

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Q. The product of two complex numbers z1 = 1 + i and z2 = 2 - i is?

A. 3 + i
B. 3 - i
C. 2 + 3i
D. 2 - 3i

Solution

z1 * z2 = (1 + i)(2 - i) = 2 - i + 2i - i^2 = 2 + 1 + i = 3 + i.

Correct Answer: A — 3 + i

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Q. The quadratic equation x^2 + 4x + 4 = 0 has:

A. Two distinct real roots
B. One real root
C. No real roots
D. Infinitely many roots

Solution

The discriminant is 0, indicating one real root (a repeated root).

Correct Answer: B — One real root

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Q. The quadratic equation x^2 + 6x + 9 = 0 has roots that are:

A. Real and equal
B. Real and distinct
C. Complex
D. None of these

Solution

The discriminant is 0, hence the roots are real and equal.

Correct Answer: A — Real and equal

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Q. The quadratic equation x^2 + kx + 16 = 0 has equal roots. What is the value of k?

A. -8
B. -4
C. 4
D. 8

Solution

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0, solving gives k = -8.

Correct Answer: A — -8

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Q. The quadratic equation x^2 + px + q = 0 has roots 3 and -2. What is the value of p?

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

Solution

Using the sum of roots: p = -(3 + (-2)) = -1.

Correct Answer: B — 5

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Q. The quadratic equation x^2 - 3x + 2 = 0 can be factored as?

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

Solution

The equation factors to (x-1)(x-2) = 0.

Correct Answer: A — (x-1)(x-2)

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Q. The quadratic equation x^2 - 4x + 4 = 0 has how many distinct real roots?

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

Solution

The discriminant is 0, indicating one distinct real root.

Correct Answer: B — 1

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Q. The quadratic equation x^2 - 6x + 9 = 0 has how many distinct real roots?

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

Solution

The discriminant is 0, indicating that there is exactly one distinct real root.

Correct Answer: B — 1

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Q. The quadratic equation x^2 - 6x + k = 0 has roots that differ by 2. What is the value of k?

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

Solution

Let the roots be r and r+2. Then, r + (r+2) = 6 and r(r+2) = k. Solving gives k = 10.

Correct Answer: B — 10

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Q. The range of sin^(-1)(x) is:

A. [-π/2, π/2]
B. [0, π]
C. [-1, 1]
D. [0, 1]

Solution

The range of sin^(-1)(x) is [-π/2, π/2].

Correct Answer: A — [-π/2, π/2]

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Q. The range of the data set 1, 3, 5, 7, 9 is:

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

Solution

Range = Maximum - Minimum = 9 - 1 = 8.

Correct Answer: A — 8

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Q. The range of the data set {10, 15, 20, 25, 30} is?

A. 15
B. 20
C. 25
D. 30

Solution

Range = Maximum value - Minimum value = 30 - 10 = 20.

Correct Answer: A — 15

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Q. The range of the function f(x) = |x - 1| is:

A. (-∞, 1)
B. [0, ∞)
C. (-1, 1)
D. [1, ∞)

Solution

The absolute value function has a minimum value of 0, hence the range is [0, ∞).

Correct Answer: B — [0, ∞)

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Q. The range of the function y = sin^(-1)(x) is:

A. (0, π)
B. [-π/2, π/2]
C. [-1, 1]
D. [0, 1]

Solution

The range of y = sin^(-1)(x) is [-π/2, π/2].

Correct Answer: B — [-π/2, π/2]

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Q. The real part of the complex number z = 4 - 3i is?

A. 4
B. -3
C. 3
D. 0

Solution

The real part of z = 4 - 3i is 4.

Correct Answer: A — 4

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Q. The roots of the equation 2x^2 - 4x + 1 = 0 are:

A. 1
B. 2
C. 1/2
D. None of these

Solution

Using the quadratic formula, x = [4 ± √(16 - 8)] / 4 = [4 ± 2√2] / 4 = 1 ± √2/2. Hence, the roots are not simple fractions.

Correct Answer: C — 1/2

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Q. The roots of the equation 5x^2 - 20x + 15 = 0 are:

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

Solution

Using the quadratic formula, the roots are x = [20 ± √(400 - 300)] / 10 = [20 ± 10] / 10 = 3 and 1.

Correct Answer: B — 2

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Q. The roots of the equation x^2 + 2x + 1 = 0 are:

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

Solution

The equation can be factored as (x + 1)^2 = 0, giving a double root at x = -1.

Correct Answer: A — -1

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Q. The roots of the equation x^2 - 3x + 2 = 0 are:

A. 1 and 2
B. 2 and 3
C. 0 and 1
D. None of these

Solution

Factoring gives (x-1)(x-2) = 0, so the roots are 1 and 2.

Correct Answer: A — 1 and 2

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Q. The scalar product of two unit vectors is 0. What can be said about these vectors?

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

Solution

If the scalar product is 0, the vectors are orthogonal.

Correct Answer: B — They are orthogonal

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Q. The scalar product of vectors A = (a, b, c) and B = (1, 2, 3) is 14. If a = 2, find b and c.

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

Solution

A · B = 2*1 + b*2 + c*3 = 14. Thus, 2 + 2b + 3c = 14, leading to 2b + 3c = 12.

Correct Answer: B — 4, 3

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Q. The scalar product of vectors A = (a, b, c) and B = (1, 2, 3) is 14. If a = 2, what is the value of b + c?

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

Solution

A · B = 2*1 + b*2 + c*3 = 14. Thus, 2 + 2b + 3c = 14, leading to 2b + 3c = 12. Solving gives b + c = 6.

Correct Answer: C — 6

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Q. The slope of the line represented by the equation 2x - 3y + 6 = 0 is:

A. 2/3
B. -2/3
C. 3/2
D. -3/2

Solution

Rearranging gives y = (2/3)x + 2, so slope = 2/3.

Correct Answer: B — -2/3

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Q. The slope of the line represented by the equation 3x - 4y + 12 = 0 is:

A. 3/4
B. 4/3
C. -3/4
D. -4/3

Solution

Rearranging gives y = (3/4)x + 3. Slope = 3/4.

Correct Answer: C — -3/4

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Q. The slope of the tangent to the curve y = sin(x) at x = π/4 is:

A. 1
B. √2/2
C. √3/3
D. √2

Solution

The derivative f'(x) = cos(x). At x = π/4, f'(π/4) = cos(π/4) = √2/2.

Correct Answer: B — √2/2

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Q. The slope of the tangent to the curve y = x^3 - 3x at x = 1 is:

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

Solution

The derivative f'(x) = 3x^2 - 3. At x = 1, f'(1) = 3(1)^2 - 3 = 0, so the slope is 0.

Correct Answer: B — 1

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Mathematics Syllabus (JEE Main)

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