Question:
If $f(x)= 3\sqrt{(x-2)}+\sqrt{4-x }$ If minimum value = α Maximum value = β find $α2 + β2 $.
If $f(x)= 3\sqrt{(x-2)}+\sqrt{4-x }$ If minimum value = α Maximum value = β find $α2 + β2 $.
Updated On: Nov 3, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 22
Solution and Explanation
The correct answer is 22.
Was this answer helpful?
1
6
Top Questions on Relations and functions
Let $R$ be a relation defined on the set $\{1,2,3,4\times\{1,2,3,4\}$ by \[ R=\{((a,b),(c,d)) : 2a+3b=3c+4d\} \] Then the number of elements in $R$ is
- JEE Main - 2026
- Mathematics
- Relations and functions
- Consider a set \( S = \{a, b, c, d\} \). Then the number of reflexive as well as symmetric relations from \( S \to S \) is:
- JEE Main - 2026
- Mathematics
- Relations and functions
- Let \( A = \{-2,-1,0,1,2,3,4\} \) and \( R \) be a relation such that \[ R=\{(x,y): 2x+y \le -2,\ x\in A,\ y\in A\}. \] Let
\( l \) = number of elements in \( R \),
\( m \) = minimum number of elements to be added to \( R \) to make it reflexive,
\( n \) = minimum number of elements to be added to \( R \) to make it symmetric. Then \( (l+m+n) \) is:- JEE Main - 2026
- Mathematics
- Relations and functions
Let \(M = \{1, 2, 3, ....., 16\}\), if a relation R defined on set M such that R = \((x, y) : 4y = 5x – 3, x, y (\in) M\). How many elements should be added to R to make it symmetric.
- JEE Main - 2026
- Mathematics
- Relations and functions
- If set $A$ has 3 elements and set $B$ has 4 elements, then the number of injective mappings from $A$ to $B$ is
- IPU CET - 2025
- Mathematics
- Relations and functions
View More Questions
Questions Asked in JEE Main exam
Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.- JEE Main - 2026
- Complex Numbers and Quadratic Equations
- The work functions of two metals ($M_A$ and $M_B$) are in the 1 : 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated electrons of $M_A$ : $M_B$ is in the ratio of 2.642 : 1. The work functions (in eV) of $M_A$ and $M_B$ are respectively.
- JEE Main - 2026
- Dual nature of matter
- 10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from \( P_1 \) to \( P_2 \) is \( \alpha \) Joule \((P_1 = 21.7 \text{ Pa}, P_2 = 30 \text{ Pa}, C_v = 21 \text{ J/K mol}, R = 8.3 \text{ J/mol K})\). The value of \( \alpha \) is ________.
- JEE Main - 2026
- Thermodynamics
- The system of linear equations
$x + y + z = 6$
$2x + 5y + az = 36$
$x + 2y + 3z = b$
has- JEE Main - 2026
- Matrices and Determinants
- The displacement of a particle executing simple harmonic motion with time period \(T\) is expressed as \[ x(t)=A\sin\omega t, \] where \(A\) is the amplitude of oscillation. If the maximum value of the potential energy of the oscillator is found at \[ t=\frac{T}{2\beta}, \] then the value of \(\beta\) is ________.
- JEE Main - 2026
- Waves and Oscillations
View More Questions