2D Cartesian system Practice Questions - NDA Mathematics Question Bank

Question 1 of 5 NDA MCQ

What is the maximum numberof points ofintersection of 5 circles?

Detailed Explanation

Solution

Option (c) is correct.

Explanation:

The maximum number of intersection points between two circles is 2. Thus, for \( n \) circles, the maximum number of intersection points \( P \) can be calculated using the formula:

\[ P = n(n-1) \]

where \( n \) is the total number of circles. The factor of 2 is included due to the two intersection points per circle pair. Therefore, we rewrite:

\[ P = 2 \cdot \frac{n(n-1)}{2} \]

For \( n = 5 \):

\[ P = 2 \cdot \frac{5(5-1)}{2} = 2 \cdot \frac{5 \cdot 4}{2} = 5 \cdot 4 = 20 \]

Thus, the maximum number of intersection points of 5 circles is 20.

📌 Hints / Properties Used:

Maximum intersections between two circles = 2
General formula for circles' intersections = \( P = 2 \cdot \frac{n(n-1)}{2} \)

📊 Visual Diagram Suggestion:

A diagram illustrating five overlapping circles with highlighted intersection points demonstrating a total of 20 intersections would clarify the solution visually.

📖 Factual Verification & Reference:

Verified against standard combinatorial geometry principles.

Question 2 of 5 NDA MCQ

For the following two (02) items:

Suppose S is the sphere with the smallest radius that passes through the points A(1, 0, 0), B(0, 1, 0) and C(0, 0, 1). On

which one of the following planes does the centre of S lie?

Detailed Explanation

Question 3 of 5 NDA MCQ

For the following two (02) items: Suppose S is the sphere with the smallest radius that passes through the points A(1, 0, 0), B(0, 1, 0) and C(0, 0, 1).

What is the radius of S?

Detailed Explanation

Question 4 of 5 NDA MCQ

For the following two (02) items:

A plane P is parallel to the line having direction ratios ⟨1, 3, 2⟩ and contains the line of intersection of the planes 6x + 4y - 5z = 2 and x - 2y + 3z = 0.

What is the equation of the plane P?

Detailed Explanation

Question 5 of 5 NDA MCQ

For the following two (02) items:

A plane P is parallel to the line having direction ra- tios ⟨1, 3, 2⟩ and contains the line of intersection of the planes 6x + 4y - 5z = 2 and x - 2y + 3z = 0.

Which of the following are the direction ratios of the line of intersection of the given planes?

Detailed Explanation

2D Cartesian system

Solution

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