NEET Test Series from KOTA - 10 Papers In MS WORD
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Sets, Relation and Function
116877
How many integral points are there within the graph of \(|\mathbf{x}|+|\mathbf{y}|\lt 3\) ?
1 13
2 15
3 21
4 24
Explanation:
A From question, Integral points are \((-2,0),(-1,0),(0,0),(1,0),(2,0),(0,1),(0,2)\) \((0,-1),(0,-2),(1,1),(-1,1),(1,-1),(-1,1)\) So, total integral points are 13 .
SCRA-2015
Sets, Relation and Function
116894
If \(f(x)=\frac{x-1}{x+1}\), then \(f(2 x)\) is
116899
If \(f: Z \rightarrow Z\) is defined by \(f(x)=x^9-11 x^8-2 x^7\) \(+22 x^6+x^4-12 x^3+11 x^2+x-3 \forall x \in Z\), then \(\mathbf{f ( 1 1 )}=\)
1 7
2 8
3 6
4 9
Explanation:
B Given, If, \(f: Z \rightarrow Z\) is defined by \(f(x)=x^9-11 x^8-2 x^7+\) \(22 x^6+x^4-12 x^3+11 x^2+x-3 \forall x \in Z\) Then, \(f(11)=11^9-11(11)^8-2(11)^7+22(11)^6+(11)^4-\) \(12(11)^3+11(11)^2+11-3\) \(f(11)=8\)
Shift-II
Sets, Relation and Function
116903
If \(f: R \rightarrow R\) is defined by \(f(x)=7+\cos (5 x+3)\) for \(x \in R\), then the period of \(f\) is
1 \(2 \pi\)
2 \(\pi\)
3 \(\frac{\pi}{5}\)
4 \(\frac{2 \pi}{5}\)
Explanation:
D Given, \(f: R \rightarrow R\) is defined by \(f(x)=7+\cos (5 x+3)\) for \(x \in R\) Then, if adding a constant term to a function shifts the graph above but does not change the period of the function. \(\therefore\) The period of the function is same as that of the period of function \(\cos (5 x+3)\). Since, the period of \(\cos (x)\) is \(2 \pi\) and the period of \(\cos (\mathrm{nx})\) would be \(\frac{2 \pi}{\mathrm{n}}\). So, the period of \(f(x)\) is \(\frac{2 \pi}{5}\).
116877
How many integral points are there within the graph of \(|\mathbf{x}|+|\mathbf{y}|\lt 3\) ?
1 13
2 15
3 21
4 24
Explanation:
A From question, Integral points are \((-2,0),(-1,0),(0,0),(1,0),(2,0),(0,1),(0,2)\) \((0,-1),(0,-2),(1,1),(-1,1),(1,-1),(-1,1)\) So, total integral points are 13 .
SCRA-2015
Sets, Relation and Function
116894
If \(f(x)=\frac{x-1}{x+1}\), then \(f(2 x)\) is
116899
If \(f: Z \rightarrow Z\) is defined by \(f(x)=x^9-11 x^8-2 x^7\) \(+22 x^6+x^4-12 x^3+11 x^2+x-3 \forall x \in Z\), then \(\mathbf{f ( 1 1 )}=\)
1 7
2 8
3 6
4 9
Explanation:
B Given, If, \(f: Z \rightarrow Z\) is defined by \(f(x)=x^9-11 x^8-2 x^7+\) \(22 x^6+x^4-12 x^3+11 x^2+x-3 \forall x \in Z\) Then, \(f(11)=11^9-11(11)^8-2(11)^7+22(11)^6+(11)^4-\) \(12(11)^3+11(11)^2+11-3\) \(f(11)=8\)
Shift-II
Sets, Relation and Function
116903
If \(f: R \rightarrow R\) is defined by \(f(x)=7+\cos (5 x+3)\) for \(x \in R\), then the period of \(f\) is
1 \(2 \pi\)
2 \(\pi\)
3 \(\frac{\pi}{5}\)
4 \(\frac{2 \pi}{5}\)
Explanation:
D Given, \(f: R \rightarrow R\) is defined by \(f(x)=7+\cos (5 x+3)\) for \(x \in R\) Then, if adding a constant term to a function shifts the graph above but does not change the period of the function. \(\therefore\) The period of the function is same as that of the period of function \(\cos (5 x+3)\). Since, the period of \(\cos (x)\) is \(2 \pi\) and the period of \(\cos (\mathrm{nx})\) would be \(\frac{2 \pi}{\mathrm{n}}\). So, the period of \(f(x)\) is \(\frac{2 \pi}{5}\).
116877
How many integral points are there within the graph of \(|\mathbf{x}|+|\mathbf{y}|\lt 3\) ?
1 13
2 15
3 21
4 24
Explanation:
A From question, Integral points are \((-2,0),(-1,0),(0,0),(1,0),(2,0),(0,1),(0,2)\) \((0,-1),(0,-2),(1,1),(-1,1),(1,-1),(-1,1)\) So, total integral points are 13 .
SCRA-2015
Sets, Relation and Function
116894
If \(f(x)=\frac{x-1}{x+1}\), then \(f(2 x)\) is
116899
If \(f: Z \rightarrow Z\) is defined by \(f(x)=x^9-11 x^8-2 x^7\) \(+22 x^6+x^4-12 x^3+11 x^2+x-3 \forall x \in Z\), then \(\mathbf{f ( 1 1 )}=\)
1 7
2 8
3 6
4 9
Explanation:
B Given, If, \(f: Z \rightarrow Z\) is defined by \(f(x)=x^9-11 x^8-2 x^7+\) \(22 x^6+x^4-12 x^3+11 x^2+x-3 \forall x \in Z\) Then, \(f(11)=11^9-11(11)^8-2(11)^7+22(11)^6+(11)^4-\) \(12(11)^3+11(11)^2+11-3\) \(f(11)=8\)
Shift-II
Sets, Relation and Function
116903
If \(f: R \rightarrow R\) is defined by \(f(x)=7+\cos (5 x+3)\) for \(x \in R\), then the period of \(f\) is
1 \(2 \pi\)
2 \(\pi\)
3 \(\frac{\pi}{5}\)
4 \(\frac{2 \pi}{5}\)
Explanation:
D Given, \(f: R \rightarrow R\) is defined by \(f(x)=7+\cos (5 x+3)\) for \(x \in R\) Then, if adding a constant term to a function shifts the graph above but does not change the period of the function. \(\therefore\) The period of the function is same as that of the period of function \(\cos (5 x+3)\). Since, the period of \(\cos (x)\) is \(2 \pi\) and the period of \(\cos (\mathrm{nx})\) would be \(\frac{2 \pi}{\mathrm{n}}\). So, the period of \(f(x)\) is \(\frac{2 \pi}{5}\).
116877
How many integral points are there within the graph of \(|\mathbf{x}|+|\mathbf{y}|\lt 3\) ?
1 13
2 15
3 21
4 24
Explanation:
A From question, Integral points are \((-2,0),(-1,0),(0,0),(1,0),(2,0),(0,1),(0,2)\) \((0,-1),(0,-2),(1,1),(-1,1),(1,-1),(-1,1)\) So, total integral points are 13 .
SCRA-2015
Sets, Relation and Function
116894
If \(f(x)=\frac{x-1}{x+1}\), then \(f(2 x)\) is
116899
If \(f: Z \rightarrow Z\) is defined by \(f(x)=x^9-11 x^8-2 x^7\) \(+22 x^6+x^4-12 x^3+11 x^2+x-3 \forall x \in Z\), then \(\mathbf{f ( 1 1 )}=\)
1 7
2 8
3 6
4 9
Explanation:
B Given, If, \(f: Z \rightarrow Z\) is defined by \(f(x)=x^9-11 x^8-2 x^7+\) \(22 x^6+x^4-12 x^3+11 x^2+x-3 \forall x \in Z\) Then, \(f(11)=11^9-11(11)^8-2(11)^7+22(11)^6+(11)^4-\) \(12(11)^3+11(11)^2+11-3\) \(f(11)=8\)
Shift-II
Sets, Relation and Function
116903
If \(f: R \rightarrow R\) is defined by \(f(x)=7+\cos (5 x+3)\) for \(x \in R\), then the period of \(f\) is
1 \(2 \pi\)
2 \(\pi\)
3 \(\frac{\pi}{5}\)
4 \(\frac{2 \pi}{5}\)
Explanation:
D Given, \(f: R \rightarrow R\) is defined by \(f(x)=7+\cos (5 x+3)\) for \(x \in R\) Then, if adding a constant term to a function shifts the graph above but does not change the period of the function. \(\therefore\) The period of the function is same as that of the period of function \(\cos (5 x+3)\). Since, the period of \(\cos (x)\) is \(2 \pi\) and the period of \(\cos (\mathrm{nx})\) would be \(\frac{2 \pi}{\mathrm{n}}\). So, the period of \(f(x)\) is \(\frac{2 \pi}{5}\).
