If \(p, q\) and \(r\) are in AP, then what is \(p^3+3pr(p+r)+r^3\) equal to?
\(8q^3\)
Since \(p^3+3pr(p+r)+r^3 = (p+r)^3\) (using \((p+r)^3 = p^3+r^3+3pr(p+r)\)), and \(p,q,r\) in AP gives \(p+r=2q\), the expression equals \((2q)^3 = 8q^3\).
The mean of 12 observations is 75. If two observation are discarded, then the mean of the remaining observations is 65. What is the mean of the discarded observations?
The arithmetic mean of 1, 8, 27, 64, … up to n terms is given by
Let a, b, c be in AP and k ≠ 0 be a real number. Which of the following are correct?
1. ka, kb, kc are in AP
2. k - a, k - b, k - c are in AP
3. \(\frac{a}{k},\frac{b}{k},\frac{c}{k}\) are in AP
Select the correct answer using the code given below:How many two-digit numbers are divisible by 4?
If the sum of m terms of an AP is n and the sum of n terms is m, then the sum of (m + n) terms is
What is a1 + a5 - a10 - a15 - a20 - a25 + a30 + a34 equal to ?
What is \(\displaystyle \sum_{n=1}^{34} a_n\) equal to ?
The mean of 12 observations is 75. If two observation are discarded, then the mean of the remaining observations is 65. What is the mean of the discarded observations?
Calculate the value of x if the arithmetic mean of the following data is zero-
| Numbers | Frequency |
| x + 3 | 3 |
| x - 7 | 7 |
| x - 4 | 11 |
The arithmetic mean of 1, 8, 27, 64, … up to n terms is given by
Let a, b, c be in AP and k ≠ 0 be a real number. Which of the following are correct?
1. ka, kb, kc are in AP
2. k - a, k - b, k - c are in AP
3. \(\frac{a}{k},\frac{b}{k},\frac{c}{k}\) are in AP
Select the correct answer using the code given below:How many two-digit numbers are divisible by 4?