2019 Class 10 Maths Sample Question Paper

Section B contains 6 questions of 2 marks each. Scroll down for explanatory answer and video solution to all six 2-mark questions that appeared in 2019 CBSE Class 10 maths sample question paper. The questions appeared from the following topics: Real numbers (LCM and HCF; irrational numbers), Arithmetic Progressions (nth term of an AP), Coordinate Geometry (section formula), Linear Equations (Linear equations in 2 variables)and Probability (probability of rolling dice and drawing cards).

7. Question 7 | Internal Choice A

   The HCF and LCM of two numbers are 9 and 360 respectively. If one number is 45, find the other number.

   Hint to solve this Real numbers question

   A classic text book question.
   Concept: Product of two numbers is equal to the product of the LCM and HCF of the two numbers.

   Solution Video Solution Real Numbers
   OR

   Question 7 | Internal Choice B

   Show that 7 − √5 is irrational, given that √5 is irrational.

   Hint to solve this Real numbers question

   Another classic text book question.
   Step 1: Assume the contrary to what is to be proved. i.e., assume that the given number is rational.
   Step 2: If the converse is true, we should be able to express the number as a fraction.
   Step 3: Derive √5 in terms of the expressed fraction and deduce if that can be done, √5 is also rational

   Solution Video Solution Real Numbers

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8. Question 8 | Internal Choice A

   Find the 20th term from the last term of the AP: 3, 8, 13, .... , 253

   Hint to solve this Arithmetic Progressions question

   Step 1: The common difference is 5. The last term is 253.
   Step 2: The 20th term from the last will be 19 common differences lesser than the last term.
   Step 3: Subtract 19 common differences from the last term to find the 20th term from the last.

   Solution Video Solution Arithmetic Progressions
   OR

   Question 8 | Internal Choice B

   If 7 times the 7th term of an A.P is equal to 11 times its 11th term, then find its 18th term.

   Hint to solve this Arithmetic Progressions question

   Concept: nth term of an AP a_n = a₁ + (n - 1)d
   Approach: Step 1: Express 7th term and 11th term in terms of a₁ and d.
   Step 2: Equate the 7 times 7th term to 11 times the 11th term (both terms expressed in terms of a₁ and d) and find a₁ and d.
   Step 3: Substitute values of a₁ and d to find the value of a₁₈.

   Solution Video Solution Arithmetic Progressions

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9. Question 9

   Find the coordinates of the point P which divides the line segment joining the points A(-2, 5) and B(3, -5) in the ratio 2 : 3.

   Hint to solve this Coordinate Geometry question

   Approach: Substitute coordinates of points A and B in the section formula to find the coordinates of point P.

   Solution Video Solution Coordinate Geometry

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10. Question 10

    A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting neither a red card nor a queen.

    Hint to solve this Probability question

    Step 1: Denominator is the total number of ways of drawing a card from a well shuffled deck of 52 cards.
    Step 2: Numerator is the number of cards that are neither red nor queen in a pack of cards.
    Step 3: The ratio between the values obtained in step 2 and step 1 is the required probability.

    Solution Video Solution Probability

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11. Question 11

    Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is a prime number.

    Hint to solve this Probability question

    Step 1 - Compute Denominator: Compute the total number of outcomes when two dice are thrown together.
    Step 2 & 3 - Compute Numerator: When will the product be a prime number?
    When one of the numbers is 1 and the other number is a prime number, the product will be prime.
    Step 3: List down all such possibilities.
    Step 4 - Compute Probability: The ratio of the values that you got in step 3 to step 2 is the required probability.

    Solution Video Solution Probability

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12. Question 12

    For what value of p will the following pair of linear equations have infinitely many solutions: (p - 3)x + 3y = p and px + py = 12

    Hint to solve this Linear Equations question

    Concept: A pair of linear equations in two variables a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 will have infinintely many solutions when \\frac{a_1}{a_2}) = \\frac{b_1}{b_2}) = \\frac{c_1}{c_2}).
    Step 1: Substitute values of a₁, a₂, b₁, b₂, c₁, and c₂ in the above expression.
    Step 2: Solve for p and find the answer.

    Solution Video Solution Linear Equations

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