Success TrackerSuccess Tracker
Log inSign up

GATE CE 2024 Set 1 — Question 48

Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.
NAT+2 / -0HardFirst-Order Linear EquationsOrdinary Differential EquationsEngineering MathematicsApplications of ODEs

Engineering Mathematics → Ordinary Differential Equations → Applications of ODEs

Last updated

Question

A 2 m×2 m2\text{ m} \times 2\text{ m} tank of 3 m3\text{ m} height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At t=0t = 0, an inflow of a salt solution of concentration 5 g/m35\text{ g/m}^3 at the rate of 2 litre/s2\text{ litre/s} and an outflow of the well stirred mixture at the rate of 1 litre/s1\text{ litre/s} are initiated. This process can be modelled using the following differential equation:dmdt+m6000+t=0.01\frac{dm}{dt} + \frac{m}{6000 + t} = 0.01where mm is the mass (grams) of the salt at time tt (seconds). The mass of the salt (in grams) in the tank at 75%75\% of its capacity is _____________ (rounded off to 2 decimal places).
Your answer

Enter a number. Decimals, negative values and scientific notation are accepted.

The solution stays hidden until you check.

Continue learning with Success Tracker

A step still unclear? Work through it with support

Use Success Tracker to ask about the reasoning, then try another GATE CE question to check your understanding.

AI-powered practice· Unlimited practice on eligible plans
PYQs with solutions
Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
Practice that adapts
Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
AI doubt support
Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.

Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.

Start with a free accountView plans and allowances

This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.

More questions on Ordinary Differential Equations

2026 Set 1 Q3At how many points will the curves y=x2y = x^2 and y=−x2−2x−1y = -x^2 - 2x - 1 intersect in the real (x,y)(x, y)…2026 Set 1 Q11Matrix PP is given as P=[101010101]P = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix}…2026 Set 2 Q11Matrix AA has the eigenvalues 1, 2, and 3. The Trace of A2A^2 is2026 Set 1 Q12Given:…2026 Set 2 Q12A fifth-degree polynomial in xx is defined for x>0x > 0. All coefficients of the polynomial are…