The figure shows three glasses P, Q and R with water and floating ice cube. Glass P has a solid ice cube, glass Q has an ice cube with a small solid steel ball embedded in it and glass R has an ice cube with an air bubble. After the ice cube melts, the level of water in glasses P, Q and R, respectively:
Step 1: Glass P — pure ice cube.
A floating ice cube displaces water equal to its weight. When it melts, it simply becomes the same mass of water. Thus the water level remains the same.
Step 2: Glass Q — ice cube with steel ball.
The steel ball is denser than water. While the ice floats, part of the ball's weight is supported by the ice, causing extra water displacement. After melting, the steel ball sinks and displaces only its own volume, which is less water than before. Hence the water level decreases.
Step 3: Glass R — ice cube with air bubble.
The air bubble makes the ice less dense overall. While floating, the ice displaces water equal to its weight, which is more volume than the water produced after melting (because melting releases water but the bubble disappears). Hence the water level decreases.
Final Answer: (C) remains same, decreases, and decreases

Which of the following statements are true?
A. The same Bernoulli's equation is applicable to all the points in the flow field if the flow is irrotational.
B. The value of "Constant in the Bernoulli's equation" is different for different streamlines if the flow is rotational.
C. When a nozzle is fitted at the end of a long pipeline, the discharge increases.
D. The velocity of flow at the nozzle end is more than that in the case of a pipe without a nozzle, the head in both cases being the same.
Choose the most appropriate answer from the options given below:
Courage : Bravery :: Yearning :
Select the most appropriate option to complete the analogy.
In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of \( P \), \( Q \), and \( R \)?

A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius \( r \) cm as shown in the figure. The side of the dodecagon is \( d \) cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side \( r \) cm, and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are:

The number of patients per shift (X) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is ₹1000(X - 0.2), what is the average amount (in ₹) she has earned per shift in the past 100 shifts?
