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).

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.ORQuestion 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

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.ORQuestion 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}= a_{1}+ (n - 1)d

**Approach: Step 1**: Express 7th term and 11th term in terms of a_{1}and d.

**Step 2:**Equate the 7 times 7th term to 11 times the 11th term (both terms expressed in terms of a_{1}and d) and find a_{1}and d.

**Step 3:**Substitute values of a_{1}and d to find the value of a_{18}.

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.

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.

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.

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 a_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2}= 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 a_{1}, a_{2}, b_{1}, b_{2}, c_{1}, and c_{2}in the above expression.

**Step 2**: Solve for p and find the answer.

Class 10 Maths

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CBSE Class 10 Maths - 2021

- Real Numbers Revision Class
- Polynomials Revision Videos
- Linear Equations Revision Class
- Quadratic Equations Revision Class
- Arithmetic Progressions Revision Video
- Triangles Revision
- Coordinate Geometry Revision
- Trigonometry Revision Class
- Appl of Trigonometry
- Circles Revision Class
- Areas Related to Circles Revision Videos

1. Section A | 2018 CBSE Class 10 Maths 1 Mark **Questions 1 to 2** ▶

2. Section A | 2019 CBSE Class 10 Maths 1 Mark **Question 3 to 4** ▶

3. Section A | 2019 CBSE Class 10 Maths 1 Mark **Question 5 to 6** ▶

4. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 7** | Real Numbers ▶

5. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 8** | Arithmetic Progressions ▶

6. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 9** | Coordinate Geometry ▶

7. Section B | 2019 CBSE Class 10 Maths 2 Mark **Question 10** | Probability ▶

8. Section B | 2019 CBSE Class 10 Maths 3 Mark **Question 11** | Probability ▶

9. Section B | 2019 CBSE Class 10 Maths 3 Mark **Question 12** | Linear Equations ▶

10. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 13** | Real Numbers & HCF ▶

11. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 14** | Polynomials ▶

12. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 15** | Linear Equations ▶

13. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 16** | Coordinate Geometry ▶

14. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 17** | Trigonometric Ratios ▶

15. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 18** | Circles ▶

16. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 19** | Triangles ▶

17. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 20** | Areas Related to Circles ▶

18. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 21** | Statistics - Median ▶

19. Section C | 2019 CBSE Class 10 Maths 3 Mark **Question 22** | Statistics ▶

20. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 23** | Quadratic Equations ▶

21. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 24** | Arithmetic Progressions ▶

22. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 25** | Triangles ▶

23. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 27** | Trigonometry ▶

24. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 28** | Statistics ▶

25. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 29** | Surface Areas ▶

26. Section D | 2019 CBSE Class 10 Maths 4 Mark **Question 30** | Trigonometry ▶

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