Question:
If \( H \) is the harmonic mean between \( P \) and \( Q \), then the value of
\[
\frac{H}{P} + \frac{H}{Q}
\]
is
If \( H \) is the harmonic mean between \( P \) and \( Q \), then the value of
\[
\frac{H}{P} + \frac{H}{Q}
\]
is
Show Hint
The harmonic mean is related to the arithmetic mean and the geometric mean. Use the formula \( H = \frac{2PQ}{P + Q} \) for solving related problems.
Updated On: Jan 6, 2026
- \( \frac{PQ}{P + Q} \)
- \( \frac{P + Q}{PQ} \)
- \( \frac{1}{2} \)
- \( 2 \)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Formula for harmonic mean.
The harmonic mean is given by \( H = \frac{2PQ}{P + Q} \). Using this formula, we can simplify the expression \( \frac{H}{P} + \frac{H}{Q} \).
Step 2: Conclusion.
Thus, the correct answer is option (B).
Final Answer: \[ \boxed{\text{(B) } \frac{P + Q}{PQ}} \]
Was this answer helpful?
0
0
Top VITEEE Mathematics Questions
- The product of all values of $(\cos \alpha + i \sin \alpha)^{3/5}$ is equal to
- A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of 0.02 cm/s. The rate of increase of its volume when the radius is 10 cm is ___________$\pi$ cm/s
- The interval in which the function $f\left(x\right) = \frac{4x^{2}+1}{x}$ is decreasing is :
- If the normal to the curve $y = f(x)$ at $(3,4)$ makes an angle $\frac{3 \pi}{4}$ with the positive x-axis, then $f'(3)$ is equal to
- The principal value of $sin^{-1} \left(sin \frac{5\pi}{3}\right)$ is
View More Questions
Top VITEEE Sequences and Series Questions
- Series of 6, 9_ ,12, 24
- The middle term in the expansion of \[ (10x + x^{10})^{10} \] {is:}
- The fourth, seventh, and tenth terms of a G.P. are \( p, q, r \) respectively, then:
- If \[ \frac{1}{q + r}, \quad \frac{1}{r + p}, \quad \frac{1}{p + q} \] {are in A.P., then:}
- The sum of the first n terms of the series $$ 1^2 + 2 \cdot 2^2 + 3^2 + 2 \cdot 4^2 + 5^2 + 2 \cdot 6^2 + \cdots $$ is $$ \frac{n(n + 1)^2}{2} \quad \text{when n is even. When n is odd the sum is} $$
View More Questions
Top VITEEE Questions
- A motor of power $P_0$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe $n$ times, the power of the motor is increased to $P_1$. The ratio of $P_1 $ to $P_0$ is
- A $30\,V-90\,W$ lamp is operated on a $120\,V$ DC line. A resistor is connected in series with the lamp in order to glow it properly. The value of resistance is
- Which of the following is not a characteristic of transition elements ?
- Most crystals show good cleavage because their atoms, ions or molecules are
- Which of the following sets consists only of essential amino acids ?
View More Questions