CUET · MATHS · PYQ PAPER 2023

The equation of motion of a missile is x = 3t, y = -4t, z = t where time 't' is in seconds and the distance is measured in kilometres.
If the position of rocket at a certain instant of time is (5, -8, 10), then what will be the height of the rocket from the ground? (Ground is considered as xy plane)

A 10 km
B 11 km
C 12 km
D 20 km

Verified Solution

Answer & Solution

Correct Answer

(A) 10 km

Step-by-step Solution

Detailed explanation

\( \text{Height} = z \)-coordinate \( \text{Position} = (5, -8, 10) \) \( \text{Height} = 10 \text{ km} \)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List I with List II with regard to degree of the Differential Equation.

List - I	List - II
(A) \(\frac{d^3 y}{d x^3}+\sin y=0\)	(I) 4
(B) \(\left(\frac{d y}{d x}\right)^4+\cos \left(\frac{d y}{d x}\right)-1=0\)	(II) 1
(C) \(\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^4=0\)	(III) Not defined
(D) \(\left(\frac{d^2 y}{d x^2}\right)^5+2\left(\frac{d^3 y}{d x^3}\right)^4+7=0\)	(IV) 2

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The equation of motion of a missile is x = 3t, y = -4t, z = t where time 't' is in seconds and the distance is measured in kilometres.If the position of rocket at a certain instant of time is (5, -8, 10), then what will be the height of the rocket from the ground? (Ground is considered as xy plane)

Step-by-step Solution