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 2018 CBSE Class 10 Board Exam maths paper. The questions appeared from the following topics: Real numbers (irrational numbers), Linear Equations (Linear equations in 2 variables), Arithmetic Progressions (sum of an AP), Coordinate Geometry (section formula), and Probability (probability of rolling dice and picking numbers).
Given that √2 is irrational , prove that (5 + 3√2) is an irrational number.
A 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 √2 in terms of the expressed fraction and deduce if that can be done, √2 is also rational
In the figure given below, ABCD is a rectangle. Find the values of x and y.
An easy 2 mark question that appeared in CBSE class 10 maths paper 2018.
Concept: Opposite sides of a rectangle are equal
Approach: Step 1: Equate the length given in terms of x and y to the value of the length. You will get a linear equation in two variables.
Step 2: Equate the width given in terms of x and y to the value of the width. You will get a second linear equation in two variables.
Step 3: Solve the system of linear equations in two variables to find the answer to x and y.
Find the sum of first 8 multiples of 3.
Concept: The first 8 multiples of 3 are in an AP with a common difference of 3. The first term of the arithmetic progression is 3.
Approach: Now that we know the first term, common difference and the number of terms, susbtitute these values in the sum of arithmetic progression formula to find the answer.
Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, - 3). Hence, find m.
Approach: Let point P divide the segment AB in the ratio m_{1} : m_{2}.
Step 1: Apply the section formula on the x coordinate of point P to compute the ratio in which point P divides the line segment AB.
Step 2: Apply the section formula with the value of the ratio computed in step 2 to find the y coordinate of point P. That gives the value of m.
Two different dice are tossed together, Find the probability:
(i) of getting a doublet
(ii) of getting a sum 10, of the numbers on the two dice
Step 1: Compute the total number of outcomes when two dice are tossed together.
Step 2: What is a doublet? An outcome such as (1, 1) or (5, 5) is a doublet. Compute the number of such outcomes when two dice are tossed together.
Step 2: What is a doublet? An outcome such as (1, 1) or (5, 5) is a doublet. Compute the number of such outcomes when two dice are tossed together.
Step 3: The ratio of the values that you got in step 2 to step 1 is the required probability for part (i).
Step 4: List down outcomes that will result in a sum of 10.
Step 5: The value of step 4 divided by the alue of step 1 is the answer to part (ii) of this CBSE Class 10 maths section A question.
An integer is chosen at random between 1 and 100. Find the probability that it is:
(i) divisible by 8
(ii) not divisible by 8
Step 1: Compute the number of numbers between 1 and 100. Note: The count will not include 1 and 100.
Step 2 - Part (i): Compute the number of multiples of 8 between 1 and 100.
Step 3: The value obtained in step 2 divided by the value obtained in step 1 is the answer to part (i) of this 2018 CBSE class 10 maths section A question.
Step 4 - part (ii): Events given in part (i) and part (ii) are mutually exclusive and collectively exhaustive events. Therefore, answer for part (ii) = 1 - answer for part (i)
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1. Section A | 2018 CBSE Class 10 Maths 1 Mark Questions 1 to 6
2. Section B | 2018 CBSE Class 10 Maths 2 Mark Question 7 | Real Numbers - Irrational Numbers
3. Section B | 2018 CBSE Class 10 Maths 2 Mark Question 8 | Linear Equations in 2 variables
4. Section B | 2018 CBSE Class 10 Maths 2 Mark Question 9 | Sum of Arithmetic Progressions
5. Section B | 2018 CBSE Class 10 Maths 2 Mark Question 10 | Coordinate Geometry Section Formula
6. Section B | 2018 CBSE Class 10 Maths 2 Mark Question 11 | Probability of Rolling 2 dice
7. Section B | 2018 CBSE Class 10 Maths 2 Mark Question 12 | Probability of selecting numbers
8. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 13 | Real Numbers - LCM & HCF
9. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 14 | Polynomial Factorization
10. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 15A | Coordinate Geometry - Parallelogram
11. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 15B | Coordinate Geometry - Area of Triangles
12. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 16 | Quadratic Equations - Speed Time Distance
13. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 17 | Similar & Congruent Triangles
14. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 19 | Trigonometric Ratios
15. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 20 | Areas related to circles - sector area
16. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 21 | Surface Areas & Volumes - Cylinder, hemisphere and cone
17. Section C | 2018 CBSE Class 10 Maths 3 Mark Question 22 | Statistics - Median
18. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 23 | Quadratic Equations _ Speed Distance Time
19. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 24 | Arithmetic Progressions
20. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 25A | Equilateral & Right Triangles and Congruence
21. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 25B | Pythagoram Theorem Proof
22. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 27 | Trigonometric Ratios & Identities
23. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 28 | Surface Area of Frustum
24. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 29 | Applications of Trigonometry - Heights & Distances
25. Section D | 2018 CBSE Class 10 Maths 4 Mark Question 30 | Statistics - 2 Alternatives
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