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Arihant CBSE Chapterwise Question Bank Mathematics For Class 10th 2027

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  • Q1
    What is the Fundamental Theorem of Arithmetic?
    A1

    It states every composite number can be expressed (factorised) as a product of primes, and this factorization is unique, apart from the order in which the prime factors occur.

  • Q2
    What is the relationship between the zeros and coefficients of a quadratic polynomial?
    A2

    For polynomial ax² + bx + c, the sum of zeros = -b/a, and the product of zeros = c/a.

  • Q3
    How many solutions do a pair of linear equations with intersecting lines have?
    A3

    A pair of linear equations whose graphical representation is a pair of intersecting lines has a unique solution and is consistent.

  • Q4
    What is the formula for the sum of the first n terms of an arithmetic progression?
    A4

    The sum is given by Sn = n/2 [2a + (n-1)d], where 'a' is the first term and 'd' is the common difference.

  • Q5
    What is the theorem regarding a line drawn parallel to one side of a triangle?
    A5

    If a line is drawn parallel to one side of a triangle to intersect the other two sides, it divides the other two sides in the same ratio (Basic Proportionality Theorem).

  • Q6
    What is the relationship between a tangent to a circle and the radius at the point of contact?
    A6

    The tangent at any point of a circle is perpendicular to the radius through the point of contact.

  • Q7
    What are the trigonometric ratios for an acute angle θ in a right triangle?
    A7

    The six ratios are sin θ, cos θ, tan θ, cot θ, sec θ, and cosec θ.

  • Q8
    What is meant by the angle of elevation?
    A8

    It is the angle formed by the line of sight with the horizontal when the object viewed is above the observer.

  • Q9
    Define the mode of grouped data.
    A9

    The mode is the value that appears most frequently in a data set. For grouped data, it is calculated using a specific formula.

  • Q10
    What is the classical definition of probability?
    A10

    Probability of an event = (Number of favourable outcomes) / (Total number of possible outcomes), assuming all outcomes are equally likely.

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  • Q1
    What is the Fundamental Theorem of Arithmetic?
    A1

    It states every composite number can be expressed (factorised) as a product of primes, and this factorization is unique, apart from the order in which the prime factors occur.

  • Q2
    What is the relationship between the zeros and coefficients of a quadratic polynomial?
    A2

    For polynomial ax² + bx + c, the sum of zeros = -b/a, and the product of zeros = c/a.

  • Q3
    How many solutions do a pair of linear equations with intersecting lines have?
    A3

    A pair of linear equations whose graphical representation is a pair of intersecting lines has a unique solution and is consistent.

  • Q4
    What is the formula for the sum of the first n terms of an arithmetic progression?
    A4

    The sum is given by Sn = n/2 [2a + (n-1)d], where 'a' is the first term and 'd' is the common difference.

  • Q5
    What is the theorem regarding a line drawn parallel to one side of a triangle?
    A5

    If a line is drawn parallel to one side of a triangle to intersect the other two sides, it divides the other two sides in the same ratio (Basic Proportionality Theorem).

  • Q6
    What is the relationship between a tangent to a circle and the radius at the point of contact?
    A6

    The tangent at any point of a circle is perpendicular to the radius through the point of contact.

  • Q7
    What are the trigonometric ratios for an acute angle θ in a right triangle?
    A7

    The six ratios are sin θ, cos θ, tan θ, cot θ, sec θ, and cosec θ.

  • Q8
    What is meant by the angle of elevation?
    A8

    It is the angle formed by the line of sight with the horizontal when the object viewed is above the observer.

  • Q9
    Define the mode of grouped data.
    A9

    The mode is the value that appears most frequently in a data set. For grouped data, it is calculated using a specific formula.

  • Q10
    What is the classical definition of probability?
    A10

    Probability of an event = (Number of favourable outcomes) / (Total number of possible outcomes), assuming all outcomes are equally likely.

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