jee-advanced 2005 Q14

jee-advanced · India · screening Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification

14. $f ( x ) = \left\{ \begin{array} { l } x , \quad \text { if } x \text { is rational } \\ 0 , \quad \text { if } x \text { is irrational } \end{array} \right.$ and
$$g ( x ) = \left\{ \begin{array} { l } 0 , \quad \text { if } x \text { is rational } \\ x , \quad \text { if } x \text { is irrational. } \end{array} \text { Then } \mathrm { f } - \mathrm { g } \right. \text { is: }$$
(a) one-one and into
(b) neither one-one nor onto
(c) many one and onto
(d) one-one and onto

The tangent to the curve $y = x ^ { 2 } + 6$ at the point $P ( 1,7 )$ touches the circle $x ^ { 2 } + y ^ { 2 } + 16 x + 12 y + c = 0$ at a point $Q$. Then the coordinates of $Q$ are

14. $f ( x ) = \left\{ \begin{array} { l } x , \quad \text { if } x \text { is rational } \\ 0 , \quad \text { if } x \text { is irrational } \end{array} \right.$ and

$$g ( x ) = \left\{ \begin{array} { l } 
0 , \quad \text { if } x \text { is rational } \\
x , \quad \text { if } x \text { is irrational. }
\end{array} \text { Then } \mathrm { f } - \mathrm { g } \right. \text { is: }$$

(a) one-one and into\\
(b) neither one-one nor onto\\
(c) many one and onto\\
(d) one-one and onto\\

Paper Questions

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