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 quadratic equation x^2 + 6x + 9 = 0 is solved, what is the nature of the roots?

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

Solution

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

Correct Answer: B — Real and equal

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Q. If the quadratic equation x^2 + 6x + k = 0 has roots -2 and -4, what is the value of k?

A. 8
B. 12
C. 16
D. 20

Solution

Using Vieta's formulas, k = (-2)(-4) = 8.

Correct Answer: B — 12

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Q. If the quadratic equation x^2 + 6x + k = 0 has roots that are both negative, what is the condition for k?

A. k > 9
B. k < 9
C. k = 9
D. k < 0

Solution

For both roots to be negative, k must be greater than the square of half the coefficient of x, hence k > 9.

Correct Answer: A — k > 9

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Q. If the quadratic equation x^2 + bx + 9 = 0 has roots 3 and -3, what is the value of b?

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

Solution

The sum of the roots is 3 + (-3) = 0, so b = -0.

Correct Answer: C — -6

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Q. If 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, thus k = -8.

Correct Answer: A — -8

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

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

Solution

Using Vieta's formulas, the product of the roots is n = 1 * (-3) = -3.

Correct Answer: A — -3

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Q. If the quadratic equation x^2 + mx + n = 0 has roots 1 and -3, what is the value of m?

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

Solution

Using Vieta's formulas, m = -(1 + (-3)) = 2.

Correct Answer: A — 2

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

A. -1
B. 5
C. 1
D. 3

Solution

Using Vieta's formulas, m = -(-1) = 1 and n = 2*(-3) = -6, thus m + n = 1 - 6 = -5.

Correct Answer: B — 5

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Q. If the quadratic equation x^2 + px + q = 0 has roots 2 and 3, what is the value of p?

A. -5
B. -6
C. -7
D. -8

Solution

The sum of the roots is -p = 2 + 3 = 5, so p = -5.

Correct Answer: A — -5

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Q. If the quadratic equation x^2 + px + q = 0 has roots 2 and 3, what is the value of p + q?

A. 5
B. 6
C. 7
D. 8

Solution

Using Vieta's formulas, p = -(2 + 3) = -5 and q = 2*3 = 6. Thus, p + q = -5 + 6 = 1.

Correct Answer: C — 7

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Q. If the quadratic equation x^2 - kx + 9 = 0 has equal roots, what is the value of k?

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

Solution

For equal roots, the discriminant must be zero: k^2 - 36 = 0, hence k = 6.

Correct Answer: A — 6

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Q. If the range of a data set is 15 and the minimum value is 5, what is the maximum value?

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

Solution

Range = Maximum - Minimum. Therefore, Maximum = Range + Minimum = 15 + 5 = 20.

Correct Answer: C — 20

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Q. If the relation R on set A = {1, 2, 3} is defined as R = {(1, 1), (2, 2), (3, 3)}, is R reflexive?

A. Yes
B. No
C. Only for 1
D. Only for 2

Solution

A relation is reflexive if every element in the set is related to itself. Here, R includes (1, 1), (2, 2), and (3, 3), so R is reflexive.

Correct Answer: A — Yes

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Q. If the relation R on set A = {1, 2, 3} is defined as R = {(1, 2), (2, 3)}, is R reflexive?

A. Yes
B. No
C. Depends on A
D. None of the above

Solution

A relation is reflexive if every element is related to itself. Here, (1,1), (2,2), and (3,3) are not in R, so R is not reflexive.

Correct Answer: B — No

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Q. If the roots of the equation ax^2 + bx + c = 0 are 3 and -2, what is the value of a if b = 5 and c = -6?

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

Solution

Using Vieta's formulas, a = 1 since the product of the roots (3 * -2) = -6 and sum (3 + -2) = 1.

Correct Answer: A — 1

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Q. If the roots of the equation ax^2 + bx + c = 0 are 3 and -2, what is the value of b if a = 1 and c = -6?

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

Solution

Using the sum of roots (-b/a = 3 + (-2) = 1), we find b = -1.

Correct Answer: A — -1

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Q. If the roots of the equation x^2 + 4x + k = 0 are real and distinct, what is the condition on k?

A. k < 16
B. k > 16
C. k = 16
D. k <= 16

Solution

The discriminant must be greater than zero: 4^2 - 4*1*k > 0 => 16 - 4k > 0 => k < 4.

Correct Answer: A — k < 16

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Q. If the roots of the equation x^2 + 4x + k = 0 are real and equal, what is the minimum value of k?

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

Solution

For real and equal roots, the discriminant must be zero: 16 - 4k = 0, thus k = 4.

Correct Answer: B — -4

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Q. If the roots of the equation x^2 + 5x + 6 = 0 are a and b, what is the value of a + b?

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

Solution

Using Vieta's formulas, the sum of the roots is -b/a = -5/1 = -5.

Correct Answer: A — 5

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Q. If the roots of the equation x^2 + 6x + k = 0 are -2 and -4, what is the value of k?

A. 4
B. 8
C. 10
D. 12

Solution

Using the sum and product of roots: -2 + -4 = -6 and -2*-4 = k => k = 8.

Correct Answer: C — 10

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

A. -5
B. -6
C. -7
D. -8

Solution

The sum of the roots is -(-2 - 3) = 5, so m = 5. The product of the roots is (-2)(-3) = 6, so n = 6. Thus, m + n = 5 + 6 = 11.

Correct Answer: C — -7

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

A. 5
B. 6
C. 7
D. 8

Solution

Using Vieta's formulas, p = -(-2 - 3) = 5.

Correct Answer: A — 5

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

A. -5
B. -6
C. -7
D. -8

Solution

Using Vieta's formulas, p = -(-2 - 3) = 5 and q = (-2)(-3) = 6. Therefore, p + q = 5 + 6 = 11.

Correct Answer: C — -7

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

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

Solution

The sum of the roots is 0, hence p = -sum = 0.

Correct Answer: A — 0

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Q. If the roots of the 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 equation x^2 - 5x + k = 0 are equal, what is the value of k?

A. 0
B. 5
C. 6
D. 25

Solution

For the roots to be equal, the discriminant must be zero. Thus, b^2 - 4ac = 0 => 25 - 4k = 0 => k = 25.

Correct Answer: C — 6

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Q. If the roots of the equation x^2 - 5x + k = 0 are real and equal, what is the minimum value of k?

A. 0
B. 5
C. 6
D. 10

Solution

The minimum value of k is 6, as the discriminant must be zero.

Correct Answer: C — 6

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Q. If the roots of the equation x^2 - 5x + k = 0 are real and equal, what is the value of k?

A. 0
B. 5
C. 6
D. 25

Solution

For real and equal roots, the discriminant must be zero: 25 - 4k = 0, thus k = 6.

Correct Answer: C — 6

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Q. If the roots of the equation x^2 - 7x + p = 0 are 3 and 4, what is the value of p?

A. 12
B. 15
C. 16
D. 20

Solution

Using Vieta's formulas, the sum of the roots is 7 and the product is p. Thus, 3 * 4 = p, so p = 12.

Correct Answer: C — 16

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Q. If the roots of the equation x^2 - 7x + p = 0 are in the ratio 3:4, what is the value of p?

A. 12
B. 16
C. 20
D. 24

Solution

Let the roots be 3k and 4k. Then, 3k + 4k = 7 => 7k = 7 => k = 1. The product of the roots is 3k * 4k = 12k^2 = p => p = 12.

Correct Answer: C — 20

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Mathematics Syllabus (JEE Main)

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