Properties of Functions and Graphs
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Sets, Relation and Function

116880 If \(f(x)=\frac{x}{x-1}\) then \(\frac{f(a)}{f(a+1)}\) is equal to

1 \(\mathrm{f}\left(\mathrm{a}^2\right)\)
2 \(\mathrm{f}\left(\frac{1}{\mathrm{a}}\right)\)
3 \(\mathrm{f}(-\mathrm{a})\)
4 \(\mathrm{f}\left[\frac{-\mathrm{a}}{\mathrm{a}-1}\right]\)
AMU-2002
Sets, Relation and Function

116881 Consider a function \(\mathrm{f}: \mathrm{N} \rightarrow \mathrm{R}\), satisfying \(f(1)+2 f(2)+3 f(3)+\ldots . .+x f(x)=x(x+1) f(x): x\) \(\geq 2\) with \(\mathrm{f}(1)=1\). Then \(\frac{1}{\mathrm{f}(2022)}+\frac{1}{\mathrm{f}(2028)}\) is equal to

1 8400
2 8100
3 8200
4 8000
Shift-II
Sets, Relation and Function

116882 The remainder when \((2021)^{2023}\) is divided by 7 is :

1 1
2 2
3 5
4 6
Shift-I
Sets, Relation and Function

116883 The absolute minimum value, of the function \(f(x)=\left|\mathbf{x}^2-\mathbf{x}+\mathbf{1}\right|+\left[\mathbf{x}^2-\mathbf{x}+\mathbf{1}\right]\), where \([\mathbf{t}]\) denotes the greatest integer function, in the interval \([-1,2]\), is

1 \(\frac{3}{2}\)
2 \(\frac{1}{4}\)
3 \(\frac{5}{4}\)
4 \(\frac{3}{4}\)
Shift-II
Sets, Relation and Function

116884 The total number of functions, \(f:\{1,2,3,4\}-\) \(\{1,2,3,4,5,6\}\) such that \(f(1)+f(2)=f(3)\), is equal to:

1 60
2 90
3 108
4 126
Shift-I
NEET DIGITAL LIBRARY
Sets, Relation and Function

116880 If \(f(x)=\frac{x}{x-1}\) then \(\frac{f(a)}{f(a+1)}\) is equal to

1 \(\mathrm{f}\left(\mathrm{a}^2\right)\)
2 \(\mathrm{f}\left(\frac{1}{\mathrm{a}}\right)\)
3 \(\mathrm{f}(-\mathrm{a})\)
4 \(\mathrm{f}\left[\frac{-\mathrm{a}}{\mathrm{a}-1}\right]\)
AMU-2002
Sets, Relation and Function

116881 Consider a function \(\mathrm{f}: \mathrm{N} \rightarrow \mathrm{R}\), satisfying \(f(1)+2 f(2)+3 f(3)+\ldots . .+x f(x)=x(x+1) f(x): x\) \(\geq 2\) with \(\mathrm{f}(1)=1\). Then \(\frac{1}{\mathrm{f}(2022)}+\frac{1}{\mathrm{f}(2028)}\) is equal to

1 8400
2 8100
3 8200
4 8000
Shift-II
Sets, Relation and Function

116882 The remainder when \((2021)^{2023}\) is divided by 7 is :

1 1
2 2
3 5
4 6
Shift-I
Sets, Relation and Function

116883 The absolute minimum value, of the function \(f(x)=\left|\mathbf{x}^2-\mathbf{x}+\mathbf{1}\right|+\left[\mathbf{x}^2-\mathbf{x}+\mathbf{1}\right]\), where \([\mathbf{t}]\) denotes the greatest integer function, in the interval \([-1,2]\), is

1 \(\frac{3}{2}\)
2 \(\frac{1}{4}\)
3 \(\frac{5}{4}\)
4 \(\frac{3}{4}\)
Shift-II
Sets, Relation and Function

116884 The total number of functions, \(f:\{1,2,3,4\}-\) \(\{1,2,3,4,5,6\}\) such that \(f(1)+f(2)=f(3)\), is equal to:

1 60
2 90
3 108
4 126
Shift-I
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Sets, Relation and Function

116880 If \(f(x)=\frac{x}{x-1}\) then \(\frac{f(a)}{f(a+1)}\) is equal to

1 \(\mathrm{f}\left(\mathrm{a}^2\right)\)
2 \(\mathrm{f}\left(\frac{1}{\mathrm{a}}\right)\)
3 \(\mathrm{f}(-\mathrm{a})\)
4 \(\mathrm{f}\left[\frac{-\mathrm{a}}{\mathrm{a}-1}\right]\)
AMU-2002
Sets, Relation and Function

116881 Consider a function \(\mathrm{f}: \mathrm{N} \rightarrow \mathrm{R}\), satisfying \(f(1)+2 f(2)+3 f(3)+\ldots . .+x f(x)=x(x+1) f(x): x\) \(\geq 2\) with \(\mathrm{f}(1)=1\). Then \(\frac{1}{\mathrm{f}(2022)}+\frac{1}{\mathrm{f}(2028)}\) is equal to

1 8400
2 8100
3 8200
4 8000
Shift-II
Sets, Relation and Function

116882 The remainder when \((2021)^{2023}\) is divided by 7 is :

1 1
2 2
3 5
4 6
Shift-I
Sets, Relation and Function

116883 The absolute minimum value, of the function \(f(x)=\left|\mathbf{x}^2-\mathbf{x}+\mathbf{1}\right|+\left[\mathbf{x}^2-\mathbf{x}+\mathbf{1}\right]\), where \([\mathbf{t}]\) denotes the greatest integer function, in the interval \([-1,2]\), is

1 \(\frac{3}{2}\)
2 \(\frac{1}{4}\)
3 \(\frac{5}{4}\)
4 \(\frac{3}{4}\)
Shift-II
Sets, Relation and Function

116884 The total number of functions, \(f:\{1,2,3,4\}-\) \(\{1,2,3,4,5,6\}\) such that \(f(1)+f(2)=f(3)\), is equal to:

1 60
2 90
3 108
4 126
Shift-I
For More Updates join with Us
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Sets, Relation and Function

116880 If \(f(x)=\frac{x}{x-1}\) then \(\frac{f(a)}{f(a+1)}\) is equal to

1 \(\mathrm{f}\left(\mathrm{a}^2\right)\)
2 \(\mathrm{f}\left(\frac{1}{\mathrm{a}}\right)\)
3 \(\mathrm{f}(-\mathrm{a})\)
4 \(\mathrm{f}\left[\frac{-\mathrm{a}}{\mathrm{a}-1}\right]\)
AMU-2002
Sets, Relation and Function

116881 Consider a function \(\mathrm{f}: \mathrm{N} \rightarrow \mathrm{R}\), satisfying \(f(1)+2 f(2)+3 f(3)+\ldots . .+x f(x)=x(x+1) f(x): x\) \(\geq 2\) with \(\mathrm{f}(1)=1\). Then \(\frac{1}{\mathrm{f}(2022)}+\frac{1}{\mathrm{f}(2028)}\) is equal to

1 8400
2 8100
3 8200
4 8000
Shift-II
Sets, Relation and Function

116882 The remainder when \((2021)^{2023}\) is divided by 7 is :

1 1
2 2
3 5
4 6
Shift-I
Sets, Relation and Function

116883 The absolute minimum value, of the function \(f(x)=\left|\mathbf{x}^2-\mathbf{x}+\mathbf{1}\right|+\left[\mathbf{x}^2-\mathbf{x}+\mathbf{1}\right]\), where \([\mathbf{t}]\) denotes the greatest integer function, in the interval \([-1,2]\), is

1 \(\frac{3}{2}\)
2 \(\frac{1}{4}\)
3 \(\frac{5}{4}\)
4 \(\frac{3}{4}\)
Shift-II
Sets, Relation and Function

116884 The total number of functions, \(f:\{1,2,3,4\}-\) \(\{1,2,3,4,5,6\}\) such that \(f(1)+f(2)=f(3)\), is equal to:

1 60
2 90
3 108
4 126
Shift-I
NEET DIGITAL LIBRARY
Sets, Relation and Function

116880 If \(f(x)=\frac{x}{x-1}\) then \(\frac{f(a)}{f(a+1)}\) is equal to

1 \(\mathrm{f}\left(\mathrm{a}^2\right)\)
2 \(\mathrm{f}\left(\frac{1}{\mathrm{a}}\right)\)
3 \(\mathrm{f}(-\mathrm{a})\)
4 \(\mathrm{f}\left[\frac{-\mathrm{a}}{\mathrm{a}-1}\right]\)
AMU-2002
Sets, Relation and Function

116881 Consider a function \(\mathrm{f}: \mathrm{N} \rightarrow \mathrm{R}\), satisfying \(f(1)+2 f(2)+3 f(3)+\ldots . .+x f(x)=x(x+1) f(x): x\) \(\geq 2\) with \(\mathrm{f}(1)=1\). Then \(\frac{1}{\mathrm{f}(2022)}+\frac{1}{\mathrm{f}(2028)}\) is equal to

1 8400
2 8100
3 8200
4 8000
Shift-II
Sets, Relation and Function

116882 The remainder when \((2021)^{2023}\) is divided by 7 is :

1 1
2 2
3 5
4 6
Shift-I
Sets, Relation and Function

116883 The absolute minimum value, of the function \(f(x)=\left|\mathbf{x}^2-\mathbf{x}+\mathbf{1}\right|+\left[\mathbf{x}^2-\mathbf{x}+\mathbf{1}\right]\), where \([\mathbf{t}]\) denotes the greatest integer function, in the interval \([-1,2]\), is

1 \(\frac{3}{2}\)
2 \(\frac{1}{4}\)
3 \(\frac{5}{4}\)
4 \(\frac{3}{4}\)
Shift-II
Sets, Relation and Function

116884 The total number of functions, \(f:\{1,2,3,4\}-\) \(\{1,2,3,4,5,6\}\) such that \(f(1)+f(2)=f(3)\), is equal to:

1 60
2 90
3 108
4 126
Shift-I