CBSE 10th Maths Question Paper 2023

A number ends with zero if its prime factorization contains at least one pair of 2 and 5. In option (B), (2 * 5)^n = 10^n, which always ends in zero for any natural number n. Options A (6^n), C (12^n), and D (15^n) do not contain the necessary pair of 2 and 5 to produce a trailing zero.

Total number of outcomes = Number of prizes + Number of blanks = 5 + 20 = 25. Number of favorable outcomes (getting a prize) = 5. Probability = Favorable outcomes / Total outcomes = 5 / 25 = 1 / 5. Wait, the provided options list 1/4 as (A). Let's re-calculate: The probability is 5 / (5+20) = 5/25 = 1/5. Given the options provided, there is a discrepancy. However, based on mathematical calculation, 1/5 is correct. If compelled to choose from options, check if the question implies 5 prizes out of 20 total, but standard interpretation is 1/5. If 1/5 is not A, B, C, or D exactly as intended, 1/5 is the calculated answer.

Given the equations: (1) 2x + 3y = 15 and (2) 3x + 2y = 25. Adding the two equations: (2x + 3x) + (3y + 2y) = 15 + 25, which gives 5x + 5y = 40. Dividing by 5, we get x + y = 8. Thus, choice (b) is correct.

Assuming the figure implies similar triangles (often ΔAPB ~ ΔDPC where A=C and angles at P are vertically opposite), the ratio of corresponding sides is equal. AB/CD = AP/CP. Given 6/CD = 12/4. 6/CD = 3. Therefore, CD = 6 / 3 = 2 cm. Re-evaluating: If the triangle setup is ΔAPB and ΔDPC, AP/CP = BP/DP = AB/CD. 12/4 = 6/CD => 3 = 6/CD => CD = 2. Option (A) is 2 cm.

The polynomial is p(x) = 2x^2 + 0x - 17. The sum of zeroes for a quadratic ax^2 + bx + c is given by -b/a. Here, b = 0 and a = 2. Thus, the sum of zeroes is -0/2 = 0.