# CBSE Class 10 Maths Sample Question Paper | 2019

###### 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. 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

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. 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

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. 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. 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. 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. 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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