Question
Find the least 4-digit number which, when divided by 9,
12, and 15, leaves a remainder of 4 in each case.Solution
Prime factorization of 9 = 3²
Prime factorization of 12 = 2² × 3
Prime factorization of 15 = 3 × 5 LCM of (9, 12, and 15) = 2² × 3² × 5 = 180 Least 4-digit number divisible by 180 = 1,080 So, required number = 1080 + 4 = 1,084 Hence, option A.
More No. System Questions
I. 8x2 - 2x – 15 = 0
II. 12y2 - 17y – 40 = 0
I. 3x2 - 14x + 15 = 0
II. 15y2 - 34 y + 15 = 0
I. x²= 961
II. y= √961
I. 20y² - 13y + 2 = 0
II. 6x² - 25x + 14 = 0
- What should be the value of t in the equation x² + tx + 64 = 0 so that it has two equal real roots?
I. 2y2 + 31y + 99 = 0
II. 4x2 + 8x – 45 = 0
I. 2x² - 9x + 10 = 0
II. 3y² + 11y + 6 = 0
I. 6x² - 23x + 7 = 0
II. 6y² - 29y + 9 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 34x + 285 = 0
Equation 2: y² - 26y + 165 = 0
I. 3p2 - 11p + 10 = 0
II. 42q2 + q -1 = 0
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