Instructions

Let 𝑆 be the circle in the 𝑥𝑦-plane defined by the equation $$x^{2}+y^{2}=4$$
(There are two questions based on PARAGRAPH “X”, the question given below is one of them)

Question 51

Question 52

# Let 𝑃 be a point on the circle 𝑆 with both coordinates being positive. Let the tangent to 𝑆 at 𝑃 intersect the coordinate axes at the points 𝑀 and 𝑁. Then, the mid-point of the line segment 𝑀𝑁 must lie on the curve

Instructions

There are five students $$𝑆_{1}, 𝑆_{2}, 𝑆_{3}, 𝑆_{4} and 𝑆_{5}$$ in a music class and for them there are five seats $$𝑅_{1}, 𝑅_{2}, 𝑅_{3}, 𝑅_{4} and 𝑅_{5}$$ arranged in a row, where initially the seat $$𝑅_{𝑖}$$ is allotted to the student $$𝑆_{𝑖}$$, 𝑖 = 1, 2, 3, 4, 5. But, on the examination day, the five
students are randomly allotted the five seats

Question 53

Question 54

OR