Question:
Let \(x, y > 0\). If \(x^3y^2 = 2^{15}\), then the least value of \(3x + 2y\) is
Let \(x, y > 0\). If \(x^3y^2 = 2^{15}\), then the least value of \(3x + 2y\) is
Updated On: Sep 24, 2024
- 30
- 32
- 36
- 40
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
\(x, y > 0\) and \(x^3y^2 = 2^{15}\)
Now,
\(3x+2y = (x+x+x)+(y+y)\)
So, by A.M G.M inequality
\(\frac{3x+2y}{5} \geq 5\sqrt{x^3.y^2}\)
\(∴ \; 3x+2y \geq 55\sqrt{2^{15}}\)
\(≥40\)
\(∴ \) Least value of \(3x + 4y = 40\)
Therefore, the correct option is (D): \(40\)
Was this answer helpful?
0
0
Top Questions on Random Variables
- A force $F =\left(5+3 y^2\right)$ acts on a particle in the $y$-direction, where $F$ is in newton and $y$ is in meter The work done by the force during a displacement from $y=2 m$ to $y=5 m$ is___$J$
- JEE Main - 2023
- Physics
- Random Variables
- Let \(X\) be a random variable having binomial distribution \(B(7, p)\). If \(P(X = 3) = 5P(X = 4)\), then the sum of the mean and the variance of \(X\) is:
- JEE Main - 2022
- Mathematics
- Random Variables
- Let \(x * y\) = \(x^2 + y^3\) and \((x * 1) * 1\) = \(x * (1 * 1)\). Then a value of \(2 sin^{-1}\bigg(\frac{x^4+x^2-2}{x^4+x^2+2}\bigg)\) is
- JEE Main - 2022
- Mathematics
- Random Variables
- A random variable \(X\) has the following probability distribution :
x 0 1 2 3 4 P(x) k 2k 4k 6k 8k The value of \(P(1 < X < 4 | x ≤ 2)\) is equal to
- JEE Main - 2022
- Mathematics
- Random Variables
- Coin is tossed till heads is obtained what is expectation of no. of coin tosses
- VITEEE - 2022
- Mathematics
- Random Variables
Questions Asked in JEE Main exam
- Let \[ \vec{a} = 2\hat{i} + \alpha \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} + \hat{k}, \quad \vec{c} = \beta \hat{j} - \hat{k}, \] where \( \alpha \) and \( \beta \) are integers and \( \alpha \beta = -6 \). Let the values of the ordered pair \( (\alpha, \beta) \) for which the area of the parallelogram of diagonals \( \vec{a} + \vec{b} \) and \( \vec{b} + \vec{c} \) is \( \frac{\sqrt{21}}{2} \), be \( (\alpha_1, \beta_1) \) and \( (\alpha_2, \beta_2) \). Then \( \alpha_1^2 + \beta_1^2 - \alpha_2 \beta_2 \) is equal to:
- JEE Main - 2024
- Vectors
- The molecular formula of second homologue in the homologous series of monocarboxylic acid is
- JEE Main - 2024
- Aldehydes, Ketones and Carboxylic Acids
- Given below are two statements: Statement I: $\text{PF}_5$ and $\text{BrF}_5$ both exhibit $\text{sp}^3\text{d}$ hybridisation.Statement II: Both $\text{SF}_6$ and $[\text{Co}(\text{NH}_3)_6]^{3+}$ exhibit $\text{sp}^3\text{d}^2$ hybridisation. In the light of the above statements,choose the correct answer from the options given below:
- JEE Main - 2024
- Hybridisation
- Consider the system of linear equations \( x + y + z = 4\mu \), \( x + 2y + 2\lambda z = 10\mu \), \( x + 3y + 4\lambda^2 z = \mu^2 + 15 \), where \( \lambda, \mu \in \mathbb{R} \). Which one of the following statements is NOT correct?
- JEE Main - 2024
- Linear Algebra
- If the constant term in the expansion of \((1 + 2x - 3x^3) \left(\frac{3}{2}x^2 - \frac{1}{3x}\right)^9\) is \( p \), then \( 108p \) is equal to _________.
- JEE Main - 2024
- Algebra
View More Questions
Concepts Used:
Random Variable
A random variable is a variable whose value is unknown or a function that assigns values to each of an experiment's results. Random variables are often deputed by letters and can be classified as discrete, which are variables that have particular values, or continuous, which are variables that can have any values within a continuous range.
Random variables are often used in econometric or regression analysis to ascertain statistical relationships among one another.
Types of Random Variable
There are two types of random variables, such as:
- Discrete Random Variable - A discrete random variable can take only a finite number of unique values such as 0, 1, 2, 3, 4, … and so on. The probability distribution of a random variable has a list of probabilities differentiated with each of its possible values known as the probability mass function.
- Continuous Random Variable - An arithmetically valued variable is said to be continuous if, in any unit of measurement, whenever it can take on the values a and b. If the random variable X can presume an infinite and uncountable set of values, it is said to be a continuous random variable. When X takes any value in a given interval (a, b), it is also known to be a continuous random variable in that interval.