| Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
| Assertion There is no such point or X-axis which are at a distance c (c < 3) from the point (2, 3) |
| Reason The distance between two points \[\left( {{x}_{1}},\,{{y}_{1}} \right)\] and \[\left( {{x}_{2}},{{y}_{2}} \right)\]is |
| \[\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}\] |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is False.
D) A is false; R is true.
Correct Answer: A
Solution :
| Let a point on X-axis be \[\left( {{x}_{1}},\,0 \right)\], then its distance from the point (2, 3) |
| \[\Rightarrow \,\,\,\sqrt{{{\left( {{x}_{1}}-2 \right)}^{2}}+9}=c\] |
| \[\Rightarrow \,\,{{\left( {{x}_{1}}-2 \right)}^{2}}+9={{c}^{2}}\] |
| \[\Rightarrow \,\,\,{{x}_{1}}-2=\sqrt{{{c}^{2}}-9}\] |
| \[\Rightarrow\] but \[c<3\Rightarrow {{c}^{2}}-9<0\] |
| \[\therefore\]\[{{x}_{1}}\]will be imaginary |
| Hence, both the Assertion are true and Reason is the correct explanation of Assertion. |
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