116875
The function \(f(x)=\tan \pi x-x+[x]\) has period
1 1
2 \(\pi\)
3 \(2 \pi\)
4 None of these
Explanation:
D Given function is \(f(x)=\tan \pi x-x+[x]\) Since, \([\mathrm{x}]\) is not periodic function. \(\therefore \mathrm{f}(\mathrm{x})\) is a non-periodic function.
CG PET- 2018
Sets, Relation and Function
116856
\(A\) is a set having 6 distinct elements. The number of distinct functions from \(A\) to \(A\) which are not bijections is
1 \(6 !-6\)
2 \(6^6-6\)
3 \(6^6-6\) !
4 6 !
Explanation:
C Given, \(\mathrm{A}\) is a set having 6 distinct elements Then, total number of distinct function from \(A\) to \(A=6\) And the total number of bijections (one-one not) from A to \(\mathrm{A}=6\) ! So, the number of distinct functions from \(A\) to \(A\) which are not bijections is \(6^6-6\) !
Karnataka CET 2018
Sets, Relation and Function
116900
\(\frac{x^4}{x^3-3 x+2}\) is a...............
1 Proper fraction
2 Improper fraction
3 Mixed fraction
4 Not a fraction
Explanation:
B \(\left(\frac{x^4}{x^3-3 x+2}\right)\) is a improper fraction since (degree of numerator \(\geq\) degree of denominator) for a improper fraction.
Shift-I
Sets, Relation and Function
116927
Which of the following is an even function?
1 \(\sqrt{\mathrm{x}}\)
2 \(x^2+\sin ^2 x\)
3 \(\sin ^3 x\)
4 None of these
Explanation:
B Let \(f(x)=x^2+\sin ^2 x\), then \(f(-x)=f(x)\). Therefore, \(f(x)=x^2+\sin ^2 x\) is an even function.
NEET Test Series from KOTA - 10 Papers In MS WORD
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Sets, Relation and Function
116875
The function \(f(x)=\tan \pi x-x+[x]\) has period
1 1
2 \(\pi\)
3 \(2 \pi\)
4 None of these
Explanation:
D Given function is \(f(x)=\tan \pi x-x+[x]\) Since, \([\mathrm{x}]\) is not periodic function. \(\therefore \mathrm{f}(\mathrm{x})\) is a non-periodic function.
CG PET- 2018
Sets, Relation and Function
116856
\(A\) is a set having 6 distinct elements. The number of distinct functions from \(A\) to \(A\) which are not bijections is
1 \(6 !-6\)
2 \(6^6-6\)
3 \(6^6-6\) !
4 6 !
Explanation:
C Given, \(\mathrm{A}\) is a set having 6 distinct elements Then, total number of distinct function from \(A\) to \(A=6\) And the total number of bijections (one-one not) from A to \(\mathrm{A}=6\) ! So, the number of distinct functions from \(A\) to \(A\) which are not bijections is \(6^6-6\) !
Karnataka CET 2018
Sets, Relation and Function
116900
\(\frac{x^4}{x^3-3 x+2}\) is a...............
1 Proper fraction
2 Improper fraction
3 Mixed fraction
4 Not a fraction
Explanation:
B \(\left(\frac{x^4}{x^3-3 x+2}\right)\) is a improper fraction since (degree of numerator \(\geq\) degree of denominator) for a improper fraction.
Shift-I
Sets, Relation and Function
116927
Which of the following is an even function?
1 \(\sqrt{\mathrm{x}}\)
2 \(x^2+\sin ^2 x\)
3 \(\sin ^3 x\)
4 None of these
Explanation:
B Let \(f(x)=x^2+\sin ^2 x\), then \(f(-x)=f(x)\). Therefore, \(f(x)=x^2+\sin ^2 x\) is an even function.
116875
The function \(f(x)=\tan \pi x-x+[x]\) has period
1 1
2 \(\pi\)
3 \(2 \pi\)
4 None of these
Explanation:
D Given function is \(f(x)=\tan \pi x-x+[x]\) Since, \([\mathrm{x}]\) is not periodic function. \(\therefore \mathrm{f}(\mathrm{x})\) is a non-periodic function.
CG PET- 2018
Sets, Relation and Function
116856
\(A\) is a set having 6 distinct elements. The number of distinct functions from \(A\) to \(A\) which are not bijections is
1 \(6 !-6\)
2 \(6^6-6\)
3 \(6^6-6\) !
4 6 !
Explanation:
C Given, \(\mathrm{A}\) is a set having 6 distinct elements Then, total number of distinct function from \(A\) to \(A=6\) And the total number of bijections (one-one not) from A to \(\mathrm{A}=6\) ! So, the number of distinct functions from \(A\) to \(A\) which are not bijections is \(6^6-6\) !
Karnataka CET 2018
Sets, Relation and Function
116900
\(\frac{x^4}{x^3-3 x+2}\) is a...............
1 Proper fraction
2 Improper fraction
3 Mixed fraction
4 Not a fraction
Explanation:
B \(\left(\frac{x^4}{x^3-3 x+2}\right)\) is a improper fraction since (degree of numerator \(\geq\) degree of denominator) for a improper fraction.
Shift-I
Sets, Relation and Function
116927
Which of the following is an even function?
1 \(\sqrt{\mathrm{x}}\)
2 \(x^2+\sin ^2 x\)
3 \(\sin ^3 x\)
4 None of these
Explanation:
B Let \(f(x)=x^2+\sin ^2 x\), then \(f(-x)=f(x)\). Therefore, \(f(x)=x^2+\sin ^2 x\) is an even function.
116875
The function \(f(x)=\tan \pi x-x+[x]\) has period
1 1
2 \(\pi\)
3 \(2 \pi\)
4 None of these
Explanation:
D Given function is \(f(x)=\tan \pi x-x+[x]\) Since, \([\mathrm{x}]\) is not periodic function. \(\therefore \mathrm{f}(\mathrm{x})\) is a non-periodic function.
CG PET- 2018
Sets, Relation and Function
116856
\(A\) is a set having 6 distinct elements. The number of distinct functions from \(A\) to \(A\) which are not bijections is
1 \(6 !-6\)
2 \(6^6-6\)
3 \(6^6-6\) !
4 6 !
Explanation:
C Given, \(\mathrm{A}\) is a set having 6 distinct elements Then, total number of distinct function from \(A\) to \(A=6\) And the total number of bijections (one-one not) from A to \(\mathrm{A}=6\) ! So, the number of distinct functions from \(A\) to \(A\) which are not bijections is \(6^6-6\) !
Karnataka CET 2018
Sets, Relation and Function
116900
\(\frac{x^4}{x^3-3 x+2}\) is a...............
1 Proper fraction
2 Improper fraction
3 Mixed fraction
4 Not a fraction
Explanation:
B \(\left(\frac{x^4}{x^3-3 x+2}\right)\) is a improper fraction since (degree of numerator \(\geq\) degree of denominator) for a improper fraction.
Shift-I
Sets, Relation and Function
116927
Which of the following is an even function?
1 \(\sqrt{\mathrm{x}}\)
2 \(x^2+\sin ^2 x\)
3 \(\sin ^3 x\)
4 None of these
Explanation:
B Let \(f(x)=x^2+\sin ^2 x\), then \(f(-x)=f(x)\). Therefore, \(f(x)=x^2+\sin ^2 x\) is an even function.
