The domain of the function
\(f(x) = sin^-1 [2x^2-3]+log2(log_{\frac{1}{2}}(x^2-5x+5))\)
where [t] is the greatest integer function, is
\(f(x) = sin^-1 [2x^2-3]+log2(log_{\frac{1}{2}}(x^2-5x+5))\)
where [t] is the greatest integer function, is
- \((-\sqrt\frac{5}{2},\frac{5-√5}{2})\)
- \((\frac{5-√5}{2},\frac{5+√5}{2})\)
- \((1,\frac{5-√5}{2})\)
- \((1,\frac{5+√5}{2})\)
The Correct Option is C
Solution and Explanation
The correct answer is(C): \((1,\frac{5-√5}{2})\)
![The domain of the function \(f(x) = sin^-1 [2x^2-3]+log2(log_{\frac{1}{2}}(x^2-5x+5))\) where [t] is the greatest integer function, is](https://images.collegedunia.com/public/qa/images/content/2024_01_31/image_e6c230b61706702850578.png)
Taking intersection
\(x ∈(1,\frac{5-√5}{2})\)
Top Questions on range
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Questions Asked in JEE Main exam
A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field \( B \) exists into the page. The bar starts to move from the vertex at time \( t = 0 \) with a constant velocity. If the induced EMF is \( E \propto t^n \), then the value of \( n \) is _____.
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- Magnetic Field
- Concentrated nitric acid is labelled as 75%by mass. The volume in mL of the solution which contains 30 g of nitric acid is: Given: Density of nitric acid solution is 1.25 g/mL.
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- Solutions
- A physical quantity \( Q \) is related to four observables \( a \), \( b \), \( c \), and \( d \) as follows: \[ Q = \frac{a b^4}{c d^2} \] Where:
- \( a = (60 \pm 3) \, \text{Pa} \),
- \( b = (20 \pm 0.1) \, \text{m} \),
- \( c = (40 \pm 0.2) \, \text{N·s/m}^2 \),
- \( d = (50 \pm 0.1) \, \text{m} \).
Then the percentage error in \( Q \) is:- JEE Main - 2025
- Error analysis
- Let circle $C$ be the image of
$$ x^2 + y^2 - 2x + 4y - 4 = 0 $$
in the line
$$ 2x - 3y + 5 = 0 $$
and $A$ be the point on $C$ such that $OA$ is parallel to the x-axis and $A$ lies on the right-hand side of the centre $O$ of $C$.
If $B(\alpha, \beta)$, with $\beta < 4$, lies on $C$ such that the length of the arc $AB$ is $\frac{1}{6}$ of the perimeter of $C$, then $\beta - \sqrt{3}\alpha$ is equal to: - Assume a living cell with 0.9%(\(w/w\)) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data up to first decimal place only) The cell will:
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- osmosis
Concepts Used:
Range
The range in statistics for a provided data set is the difference between the highest and lowest values. For instance, if the provided data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.
Thus, the range could also be described as the difference between the highest observation and lowest observation. The acquired result is called the range of observation. The range in statistics states the spread of observations.
