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Devc Question Bank

The document is a question bank for a course on Differential Equations and Vector Calculus, organized into five units. Each unit contains a series of questions categorized by Bloom's taxonomy levels, ranging from application to creation. The questions cover various topics including solving differential equations, analyzing functions, and applying theorems in vector calculus.

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57 views2 pages

Devc Question Bank

The document is a question bank for a course on Differential Equations and Vector Calculus, organized into five units. Each unit contains a series of questions categorized by Bloom's taxonomy levels, ranging from application to creation. The questions cover various topics including solving differential equations, analyzing functions, and applying theorems in vector calculus.

Uploaded by

sathishvanaparla2
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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DIFFERENTIAL EQUATIONS &VECTOR CALCULUS(V23112CC22)

QUESTION BANK(LAT)

UNIT- I
S.No Question Blooms
taxonomy
level

1 Solve the differential equation


(𝑥𝑦𝑠𝑖𝑛𝑥𝑦+𝑐𝑜𝑠𝑥𝑦)𝑦𝑑𝑥+(𝑥𝑦𝑠𝑖𝑛𝑥𝑦−𝑐𝑜𝑠𝑥𝑦)𝑥𝑑𝑦=0 Apply

2 Remember
If the air is maintained at 15 0C and the temperature of thebody
drops from 70 0 C to 400 C in 10 minutes. What will be its
temperature after 30 minutes

3
If 30% of radioactive substance disappears in 10 Apply
days then how long will it take for 90% of it to
disappear?

4
Solve the differential equation Apply

𝑑𝑦
+𝑦𝑡𝑎𝑛𝑥=𝑦 2 𝑠𝑒𝑐𝑥
𝑑𝑥

UNIT -2
5 Understand
Solve (𝐷 3 − 6𝐷 2 + 11𝐷 − 6)𝑦 = 𝑒 −2𝑥 + 𝑒 −3𝑥

6 Understand
Solve (𝐷 3 − 3𝐷 2 + 4𝐷 − 2)𝑦 = 𝑒 𝑥 + 𝑐𝑜𝑠𝑥 + 𝑥
7 Analyze
Test whether the functions excosx,and exsinx are linearly
independent or not
8 𝑑2 𝑦 Apply
Apply the method of variation of parameters to solve 𝑑𝑥 2 +
𝑦 = 𝑐𝑜𝑠𝑒𝑐𝑥
Unit-3

9 Form the partial differential equation by eliminating the arbitrary Create


𝑥2 𝑦2 𝑧2
constants a,b,c from + +
𝑎2 𝑏2
=1
𝑐2
10 Form the differential equation by eliminating the arbitrary Create
function f from xyz = f(x2 +y2 +z2 )
11 Solve the partial differential equations x2(y-z)p +y2(z-x)q=z2(x-y) Apply

12 Solve (mz-ny)p +(nx –lz)q =ly-mx Apply

Unit-4

13 Find the directional derivative of 2xy + z2 at (1, 1, 3) in the Understand


direction of i+2j+3k.

14 Prove that (𝑔𝑟𝑎𝑑 𝑟m)=𝑚(𝑚+1)𝑟𝑚−2 . Understand

15 Find the work done by F= (2x-y-z)i + (x+y-z)j + (3x-2y-5z)k Understand


along a curve ‘C’ in the xy-plane given by x2+𝑦2=4

16 Evaluate the line integral ∫[(𝑥 2+𝑥𝑦)𝑑𝑥+(𝑥2+𝑦2)𝑑𝑦]𝑐 where c is Evaluate


the square formed by the lines 𝑥±1

Unit-5

17 If 𝐹̅=4𝑥𝑧𝑖−y2 𝑗̅+𝑦𝑧𝑘̅ evaluate ∫𝐹̅.𝑛 𝑑𝑠 𝑆 where 𝑆 is the surface of Apply


the cube bounded by 𝑥=0,=𝑎,𝑦=0,𝑦=𝑎,𝑧=0,𝑧=𝑎.

18 Verify Green’s theorem in plane for ∮(3x2−8y2)𝑑𝑥+(4𝑦−6𝑥𝑦) Apply


𝑑𝑦 where 𝐶 is the region bounded by 𝑦=√𝑥 and 𝑦= x2

19 Verify Stokes theorem for Apply


𝐹̅=(𝑦−𝑧+2)𝑖+(𝑦𝑧+4)𝑗̅−𝑥𝑧𝑘̅ where 𝑆 is the
surface of the cube 𝑥=0,𝑦=0,𝑧=0,𝑥=2,𝑦=2,𝑧=2
above the 𝑥𝑦−plane.
20 Evaluate the line integral∫𝑐 [ (𝑥 2 + 𝑥𝑦)𝑑𝑥 + (𝑥 2 + Evaluate
𝑦 2 )𝑑𝑦] 𝑤ℎ𝑒𝑟𝑒 𝑐 is the square formed by the lines x = 1and y =
1.

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