Each question is followed by two statements I and II 1 If the question can be answered by any one of...........

Math and Mental Ability Data Sufficiency

Each question is followed by two statements, I and II.

1.If the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.

2.If the question can be answered by using either statement alone.

3.If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

4.If the question cannot be answered even by using both statements together.

There is a circle with centre C at the origin and radius r cm. Two tangents are drawn from an external point D at a distance d cm from the centre. What are the angles between each tangent and X - axis?

I. The coordinates of D are given.

II.The X-axis bisects one of the tangents.

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Explanation:

Correct option 1: 1

Statement I: The coordinates of D are given.

If we know coordinates of D(x,y), we already know the location of the external point with respect to the circle centered at the origin (0,0).
Equation of circle: x²+y²=r²
Equations of tangents from point D to circle can be determined.
From those tangent equations, we can calculate slopes → angles with X-axis.
So, Statement I alone is sufficient.

?Statement II: The X-axis bisects one of the tangents.

If the X-axis bisects one tangent, then the tangent is symmetric with respect to the X-axis.
But without knowing where DDD is or radius rrr, we cannot uniquely determine the angle of tangents with the X-axis. Multiple configurations are possible.
So, Statement II alone is not sufficient.

?Correct option : statement I alsone is sufficient.

?(Because Statement I alone is sufficient, Statement II alone is not).