Day 52: CBSE Class 10 Maths

5 questions (11 parts). Try each one first, then open its answer.

Question 1
Probability. This type asked 3 times: 2023, 2024, 2025. This one: 2025
7 $A bag contains red balls and black balls in the ratio 3 : 7. A ball is drawn at random. The probability that ball so drawn is black in colour, is$
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Question 2 (case study, 4 parts)
Probability. This type asked 3 times: 2023, 2024, 2025. This one: 2025
Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by 5, they win by a big margin. If the number is an odd number less than 30, they win by a small margin. And if the number is a prime number between 50 and 74, they lose. Answer the following questions if Rahul draws a card today :
37 (i) $What is the probability that Rahul draws a card with an even number ?$
37 (ii) $What is the probability that Rahul draws a card with an odd number less than 30 ?$
37 (iii) (a) $What is the probability that Rahul draws a card with a prime number between 50 and 74 ?$
37 (iii) (b) $What is the probability that Rahul draws a card with an even number divisible by 5 ?$
Question 3
Quadratic Equations. This type asked 3 times: 2023, 2024, 2025. This one: 2025
3 $Which of the following quadratic equations has real and equal roots ?$
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Question 4
Quadratic Equations. This type asked 3 times: 2022, 2024, 2025. This one: 2025
32 (a) $A 2-digit number is seven times the sum of its digits and two (2) more than 5 times the product of its digits. Find the number.$
Question 5 (case study, 4 parts)
Some Applications of Trigonometry. This type asked 3 times: 2023, 2024, 2025. This one: 2025
Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to the top and found it to be $60^\circ$ . Then, she climbed a nearby observation deck, 40 metres higher than her original position and noticed the angle of elevation to the top of lighthouse to be $45^\circ$ . Based on the above given information, answer the following questions :
38 (i) $If CD is h metres, find the distance BD in terms of ‘h’.$
38 (ii) $Find distance BC in terms of ‘h’.$
38 (iii) (a) $\sqrt{3} = 1{\cdot}73$
38 (iii) (b) $Find distance AE, if AC = 100 m.$

Question 1

Question 2 (case study, 4 parts)

Question 3

Question 4

Question 5 (case study, 4 parts)