# 2019 Class 10 Maths Sample Question Paper

#### Solution & Videos | 2 Mark Questions | Section B | 6 Questions

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).

1. 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.

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

2. 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.

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 an = 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.

3. 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.

4. 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.

5. 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.

6. 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.

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