Class 10th Maths notes
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Channel Class 10th Maths notes (@class_10_math_notes) in the English language segment is an active participant. Currently, the community unites 15 808 subscribers, ranking 12 937 in the Education category and 25 334 in the India region.
π Audience metrics and dynamics
Since its creation on Π½Π΅Π²ΡΠ΄ΠΎΠΌΠΎ, the project has demonstrated rapid growth, gathering an audience of 15 808 subscribers.
According to the latest data from 29 October, 2026, the channel demonstrates stable activity. Although there has been a change in the number of participants by -305 over the last 30 days and by -14 over the last 24 hours, overall reach remains high.
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- Engagement rate (ER): The average audience engagement rate is 5.47%. Within the first 24 hours after publication, content typically collects 1.00% reactions from the total number of subscribers.
- Post reach: On average, each post receives 865 views. Within the first day, a publication typically gains 158 views.
- Reactions and interaction: The audience actively supports content: the average number of reactions per post is 1.
- Thematic interests: Content is focused on key topics such as cbse, sample, syllabus, pattern, 11th.
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Thanks to the high frequency of updates (latest data received on 30 October, 2026), the channel maintains relevance and a high level of publication reach. Analytics show that the audience actively interacts with content, making it an important point of influence in the Education category.
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15 808
π Quiz Completed! π
Thank you for participating in today's quiz! π
Stay tuned for more educational content! π
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π QUIZ EXPLANATION
β Question: The roots of xΒ² - 4x + 4 = 0 are:
β
Correct Answer: 2, 2
π‘ Explanation:
The correct answer is 2, 2.
Reason - This factors as (x - 2)Β² = 0, giving a double root at x = 2.
Concept - This is a perfect square trinomial where both roots are the same, confirming that the discriminant is zero.
Fact - Using the quadratic formula: x = (4 Β± β(16-16))/2 = (4 Β± 0)/2 = 2, giving the repeated root x = 2.
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π QUIZ EXPLANATION
β Question: If the discriminant of a quadratic equation is zero, the roots are:
β
Correct Answer: Real and equal
π‘ Explanation:
The correct answer is Real and equal.
Reason - When Ξ = bΒ² - 4ac = 0, the quadratic formula gives x = -b/2a twice, resulting in one repeated real root.
Concept - This means the parabola touches the x-axis at exactly one point (the vertex), making it a perfect square trinomial.
Fact - Examples include xΒ² - 4x + 4 = 0, where Ξ = 16 - 16 = 0, giving the double root x = 2.
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If the discriminant of a quadratic equation is zero, the roots are:
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π QUIZ EXPLANATION
β Question: The discriminant of the quadratic equation axΒ² + bx + c = 0 is:
β
Correct Answer: bΒ² - 4ac
π‘ Explanation:
The correct answer is bΒ² - 4ac.
Reason - The discriminant (Ξ) is defined as bΒ² - 4ac and determines the nature of roots in the quadratic formula.
Concept - The discriminant tells us about the roots: if Ξ > 0 (two distinct real roots), Ξ = 0 (one repeated real root), or Ξ < 0 (no real roots).
Fact - This expression appears under the square root in the quadratic formula: x = (-b Β± β(bΒ² - 4ac))/2a.
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The discriminant of the quadratic equation axΒ² + bx + c = 0 is:
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π QUIZ EXPLANATION
β Question: The solution of x + y = 5 and x - y = 1 is:
β
Correct Answer: (3, 2)
π‘ Explanation:
The correct answer is (3, 2).
Reason - Adding the equations: (x + y) + (x - y) = 5 + 1 gives 2x = 6, so x = 3. Substituting: 3 + y = 5, so y = 2.
Concept - This uses the elimination method to solve simultaneous linear equations by eliminating one variable.
Fact - Verification: 3 + 2 = 5 β and 3 - 2 = 1 β, confirming that (3, 2) satisfies both equations.
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π QUIZ EXPLANATION
β Question: A pair of linear equations has unique solution when:
β
Correct Answer: aβ/aβ β bβ/bβ
π‘ Explanation:
The correct answer is aβ/aβ β bβ/bβ.
Reason - When the ratios of coefficients are unequal, the lines intersect at exactly one point, giving a unique solution to the system.
Concept - This condition ensures that the two linear equations represent different, non-parallel lines that must intersect at one point.
Fact - If aβ/aβ = bβ/bβ but β cβ/cβ, the lines are parallel (no solution), and if aβ/aβ = bβ/bβ = cβ/cβ, the lines are identical (infinitely many solutions).
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π QUIZ EXPLANATION
β Question: The zeroes of the polynomial xΒ² - 5x + 6 are:
β
Correct Answer: 2, 3
π‘ Explanation:
The correct answer is 2, 3.
Reason - Setting xΒ² - 5x + 6 = 0 and factoring gives (x - 2)(x - 3) = 0, so x = 2 or x = 3.
Concept - Zeroes are the values of x that make the polynomial equal to zero, and they correspond to the x-intercepts of the polynomial's graph.
Fact - This can be verified by substitution: (2)Β² - 5(2) + 6 = 4 - 10 + 6 = 0, and (3)Β² - 5(3) + 6 = 9 - 15 + 6 = 0.
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π QUIZ EXPLANATION
β Question: What is the degree of the polynomial 3xΒ² + 2x + 1?
β
Correct Answer: 2
π‘ Explanation:
The correct answer is 2.
Reason - The degree of a polynomial is the highest power of the variable, and in 3xΒ² + 2x + 1, the highest power of x is 2.
Concept - The degree determines many properties of the polynomial, including the maximum number of roots and the general shape of its graph.
Fact - This is a quadratic polynomial (degree 2), which means its graph is a parabola and it can have at most 2 real roots.
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π QUIZ EXPLANATION
β Question: The decimal expansion of a rational number is:
β
Correct Answer: Either terminating or non-terminating repeating
π‘ Explanation:
The correct answer is Either terminating or non-terminating repeating.
Reason - Rational numbers in decimal form either terminate (like 1/2 = 0.5) or have infinitely repeating patterns (like 1/3 = 0.333...).
Concept - The nature of decimal expansion depends on the prime factorization of the denominator when the fraction is in lowest terms - only factors of 2 and 5 give terminating decimals.
Fact - Examples include 3/4 = 0.75 (terminating) and 2/3 = 0.666... (non-terminating repeating), while irrational numbers like Ο have non-terminating, non-repeating expansions.
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π QUIZ EXPLANATION
β Question: Which of the following is an irrational number?
β
Correct Answer: β2
π‘ Explanation:
The correct answer is β2.
Reason - β2 is an irrational number because it cannot be expressed as a ratio of two integers and its decimal expansion is non-terminating and non-recurring.
Concept - Irrational numbers are real numbers that cannot be written as fractions (p/q where p and q are integers and q β 0).
Fact - 2/3 and 0.5 are rational numbers, while Ο/Ο = 1, which is also rational. Only β2 among the given options is irrational.
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