Properties of Functions and Graphs
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Sets, Relation and Function

116942 Let \(R\) be the set of all real number.
Statement I: The function
\(\mathbf{f}:\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow \mathbf{R}\) defined by \(f(x)=\sec x+\tan\) \(x\) is a one-one function.
Statement II: The function \(\mathrm{f:}[0, \infty) \rightarrow R\) defined by \(f(x)=x^2\) is a one -one function.
Which of the above statement is (are) true?

1 Statement I is true, but Statement II is false
2 Statement II is true, but Statement I is false
3 Both Statement I and Statement II are true
4 Both Statement I and Statement II are false
Shift-II
Sets, Relation and Function

116943 The number of functions f from \(\{1,2,3, \ldots . .20\}\) onto \(\{1,2,3, \ldots . .20\}\) such that \(f(k)\) is a multiple of 3 , whenever \(k\) is a multiple of 4 , is

1 \((15) ! \times 6\) !
2 \(5^6 \times 15\)
3 \(5 ! \times 6\) !
4 \(6^5 \times(15)\) !
JEE Main 11.01.2019 Shift - II
Sets, Relation and Function

116985 If \(\log _2\left[\log _3\left\{\log _4\left(\log _5 x\right)\right\}\right]=0\), then the value of \(x\) is

1 \(5^{24}\)
2 1
3 \(2^{25}\)
4 \(5^{64}\)
J and K CET-2003
Sets, Relation and Function

116945 The number of integral values of \(x\) satisfying \(\mathbf{9 x}-\mathbf{2}\lt (\mathrm{x}+2)^2\lt \mathbf{1 2 x}-\mathbf{3}\) is

1 not finite
2 3
3 4
4 5
Shift-I
NEET DIGITAL LIBRARY
Sets, Relation and Function

116942 Let \(R\) be the set of all real number.
Statement I: The function
\(\mathbf{f}:\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow \mathbf{R}\) defined by \(f(x)=\sec x+\tan\) \(x\) is a one-one function.
Statement II: The function \(\mathrm{f:}[0, \infty) \rightarrow R\) defined by \(f(x)=x^2\) is a one -one function.
Which of the above statement is (are) true?

1 Statement I is true, but Statement II is false
2 Statement II is true, but Statement I is false
3 Both Statement I and Statement II are true
4 Both Statement I and Statement II are false
Shift-II
Sets, Relation and Function

116943 The number of functions f from \(\{1,2,3, \ldots . .20\}\) onto \(\{1,2,3, \ldots . .20\}\) such that \(f(k)\) is a multiple of 3 , whenever \(k\) is a multiple of 4 , is

1 \((15) ! \times 6\) !
2 \(5^6 \times 15\)
3 \(5 ! \times 6\) !
4 \(6^5 \times(15)\) !
JEE Main 11.01.2019 Shift - II
Sets, Relation and Function

116985 If \(\log _2\left[\log _3\left\{\log _4\left(\log _5 x\right)\right\}\right]=0\), then the value of \(x\) is

1 \(5^{24}\)
2 1
3 \(2^{25}\)
4 \(5^{64}\)
J and K CET-2003
Sets, Relation and Function

116945 The number of integral values of \(x\) satisfying \(\mathbf{9 x}-\mathbf{2}\lt (\mathrm{x}+2)^2\lt \mathbf{1 2 x}-\mathbf{3}\) is

1 not finite
2 3
3 4
4 5
Shift-I
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Sets, Relation and Function

116942 Let \(R\) be the set of all real number.
Statement I: The function
\(\mathbf{f}:\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow \mathbf{R}\) defined by \(f(x)=\sec x+\tan\) \(x\) is a one-one function.
Statement II: The function \(\mathrm{f:}[0, \infty) \rightarrow R\) defined by \(f(x)=x^2\) is a one -one function.
Which of the above statement is (are) true?

1 Statement I is true, but Statement II is false
2 Statement II is true, but Statement I is false
3 Both Statement I and Statement II are true
4 Both Statement I and Statement II are false
Shift-II
Sets, Relation and Function

116943 The number of functions f from \(\{1,2,3, \ldots . .20\}\) onto \(\{1,2,3, \ldots . .20\}\) such that \(f(k)\) is a multiple of 3 , whenever \(k\) is a multiple of 4 , is

1 \((15) ! \times 6\) !
2 \(5^6 \times 15\)
3 \(5 ! \times 6\) !
4 \(6^5 \times(15)\) !
JEE Main 11.01.2019 Shift - II
Sets, Relation and Function

116985 If \(\log _2\left[\log _3\left\{\log _4\left(\log _5 x\right)\right\}\right]=0\), then the value of \(x\) is

1 \(5^{24}\)
2 1
3 \(2^{25}\)
4 \(5^{64}\)
J and K CET-2003
Sets, Relation and Function

116945 The number of integral values of \(x\) satisfying \(\mathbf{9 x}-\mathbf{2}\lt (\mathrm{x}+2)^2\lt \mathbf{1 2 x}-\mathbf{3}\) is

1 not finite
2 3
3 4
4 5
Shift-I
For More Updates join with Us
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Sets, Relation and Function

116942 Let \(R\) be the set of all real number.
Statement I: The function
\(\mathbf{f}:\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow \mathbf{R}\) defined by \(f(x)=\sec x+\tan\) \(x\) is a one-one function.
Statement II: The function \(\mathrm{f:}[0, \infty) \rightarrow R\) defined by \(f(x)=x^2\) is a one -one function.
Which of the above statement is (are) true?

1 Statement I is true, but Statement II is false
2 Statement II is true, but Statement I is false
3 Both Statement I and Statement II are true
4 Both Statement I and Statement II are false
Shift-II
Sets, Relation and Function

116943 The number of functions f from \(\{1,2,3, \ldots . .20\}\) onto \(\{1,2,3, \ldots . .20\}\) such that \(f(k)\) is a multiple of 3 , whenever \(k\) is a multiple of 4 , is

1 \((15) ! \times 6\) !
2 \(5^6 \times 15\)
3 \(5 ! \times 6\) !
4 \(6^5 \times(15)\) !
JEE Main 11.01.2019 Shift - II
Sets, Relation and Function

116985 If \(\log _2\left[\log _3\left\{\log _4\left(\log _5 x\right)\right\}\right]=0\), then the value of \(x\) is

1 \(5^{24}\)
2 1
3 \(2^{25}\)
4 \(5^{64}\)
J and K CET-2003
Sets, Relation and Function

116945 The number of integral values of \(x\) satisfying \(\mathbf{9 x}-\mathbf{2}\lt (\mathrm{x}+2)^2\lt \mathbf{1 2 x}-\mathbf{3}\) is

1 not finite
2 3
3 4
4 5
Shift-I