IGNOU BEY 18 SOLVED ASSIGNMENT

Included:

BEY 18 2025 - English

Assignment -4

(To be done after studying the course material)

Course Code: BEY-018

Course Title: Linear Algebra and Calculus

Assignment Code: BEY-018/TMA/2025

Maximum Marks: 100

Last Date of Submission: May 31, 2025 (For June TEE), September 30, 2025 (For December TEE)

Note:

1. All questions are compulsory. Marks for the questions are shown within the brackets on the right side.

Q.1 a) If A, B are symmetric matrices of the same order, then what will be the type of matrix (AB-BA)? Give reasons in support of your answer.

b) If the matrix A is both symmetric and skew-symmetric, then determine A.

c) If A is a square matrix, such that A² =A, then find (I + A)³ - 7A.

d) 

Q.2  a) , and  find vector  such that and

b)

Show that area of a parallelogram whose diagonals are given by and  is Also find the area of the parallelogram whose diagonals are  and 

Q.3 a) Find a vector of magnitude 6, which is perpendicular to both the vectors  and

b) Find the angle between the vectors and .

c) If , show that   x  =  x  =  x .

d) If A,B,C,D are the points with position vectors , respectively. Find the projection of  along .

e) Using vectors, find the area of the triangle ABC with vertices A(1,2,3), B(2, -1, 4) and C(4,5,-1).

Q.4 a) Prove that

b) Prove that

   is independent of a, b, c.

Q.5 a) Show that the conical tent of given capacity will require the least amount of canvas if its height is √2 times its base radius.

b) An open storage bin with square base and vertical sides is to be constructed from a given amount of material. Determine its dimensions if its volume is to be maximum neglecting the thickness of material and waste in constructing it.

c) Find the height of a right cylinder with greatest lateral surface area that may be inscribed in a given sphere of radius R.

d) Given a point on the axis of the parabola y² = 2px at a distance a from the vertex, find the abscissa of the point of the curve closest to it.

e)Can Rolle's theorem be applied to each of the following functions? Find 'c' in case it can be applied.

i. f(x) = sin² x on the interval [0, π].

ii. f (x) = x² + 4 on [-2, 2].

iii. f(x) = sinx + cos x on  

iv. f(x) = x³- 2x on [0, 1].

Q.6 a) Explain why Lagrange's mean value theorem is not applicable to the following functions in the respective intervals: f(x) = 13x +11, x∈ [1,3].

b) Verify means values theorem for the function f(x) = 4x³-4x in the interval [a,b], where a=0, and b=3.

c) Find 'c' of Cauchy's mean value theorem for the function f(x) = 2.ln(x) and g(x) = x²-1 in the interval [2,3].

Q.7 Find the first order partial derivatives

a)

b)

c) Find  and  for the function x² sin(y³)+xe^3z-cos(z²)=3y-6z+8 

Q.8 a) Find the orthogonal trajectories of the family of circles x² + (y - c)² = c², where c is a parameter.

b) In a certain isolated population p (t) the rate of population growth  is equal to , where k and ɛ are both positive constants. If p (0) = 1, then find the limiting population as t→ ∞.

Q.9 a) Use the method of Laplace transforms to find the solution of the initial value problem y" + 9y = 6 cos 3t, y(0) = 2, y'(0) = 0

b) Determine the solution of the undamped (forced vibrations) system mü + Ku = F_o cos wt, u(0) = 0, u(0) = 1 When, w ≠  

Q.10 a) Reduce the equation

xy" + y' + xy = 0, x > 0

into Bessel's equation and hence write its general solution in terms of Bessel's functions.

b) Prove that

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Course Name	Bachelor of Science (Applied Science-Energy)
Course Code	BSCAEY
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Language	English

 

 

 

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