# CBSE Class 10 Maths Question Paper | 2018

###### Class 10 Board Paper Solution | 2 Mark Questions | Section B

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).

1. Given that √2 is irrational , prove that (5 + 3√2) is an irrational number.

Hint to solve this irrational numbers question

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

2. In the figure given below, ABCD is a rectangle. Find the values of x and y. Hint to solve this Linear Equations problem

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.

3. Find the sum of first 8 multiples of 3.

Hint to solve this Arithmetic Progressions problem

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.

4. 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.

Hint to solve this Coordinate Geometry problem

Approach: Let point P divide the segment AB in the ratio m1 : m2.
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.

5. 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

Hint to solve this CBSE 2018 1 mark Probability question

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.

6. 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

Hint to solve this CBSE 2018 maths 1 mark Probability problem

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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