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).
The HCF and LCM of two numbers are 9 and 360 respectively. If one number is 45, find the other number.
A classic text book question.
Concept: Product of two numbers is equal to the product of the LCM and HCF of the two numbers.
Show that 7 − √5 is irrational, given that √5 is irrational.
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
Find the 20th term from the last term of the AP: 3, 8, 13, .... , 253
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.
If 7 times the 7th term of an A.P is equal to 11 times its 11th term, then find its 18th term.
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}.
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.
Approach: Substitute coordinates of points A and B in the section formula to find the coordinates of point P.
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.
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.
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.
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.
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
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.
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