Question
What is the highest common factor of (x³ - x² - x -
15) and (x³ - 3x² - 3x + 9)?Solution
x³ - x² - x - 15 = x³ - 3x² + 2x² - 6x + 5x - 15 = x²(x - 3) + 2x(x - 3) + 5(x - 3) = (x - 3)(x² + 2x + 5) x³ - 3x² - 3x + 9 = x²(x - 3) - 3(x - 3) = (x - 3)(x² - 3) ∴ HCF = (x - 3)
Two dice are rolled together. Find the probability that the sum of the numbers on the two dice is less than 4.
A box contains only three colors of balls- red, green and blue. What is the minimum number of balls that should be picked from the box to ensure that at...
A coin is tossed successively three times. Find the probability of getting exactly one tail or two tails?
- A bag contains x pink balls, (x + 2) blue balls and (x + 7) green balls. If probability of getting a blue ball is 1/9 more than that of getting a pink ball...
A bag contains 20 white and some black balls. If the probability of drawing a black ball from the bag is 1.3 times that of drawing a white ball, ...
Two cards are drawn from a pack of 52 cards. The probability that 1 is Ace and 1 is Queen is?
A box contains 5 blue jellies, some red jelly and rest yellow jelly. The probability of picking a red ball at random is 3/10, while the probability of p...
- A 6-digit number is formed using the digits 1, 2, 3, 4, 5 and 6. If each digit can be used only once, then find the probability that the number formed will...
A container has 'p' orange balls and 15 purple balls. If the probability of getting an orange ball is 2/5, then find the probability of getting differen...
A bag contains x white balls, (x + 4) black balls and (x + 8) yellow balls. If probability of getting a black ball is 1/12 more than that of getting a w...
Relevant for Exams:
