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BCA Mathematics-II Question Paper with Solution Notes Pdf

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Section A: Mathematics-II Very Short Question Solutions

Q1. Define sets and Universal sets with example. 

Sol. Set : It is a well-defined collection of objects. The objects of a set are called the elements or members of that set and their membership is defined by certain conditions. 

For example; 

• 1. The collection of all the letters of English alphabet a, b, c, d, … 
• 2. The collection of all natural numbers denoted by N.  
• 3. The collection of vowels in English alphabet.  

Universal Set : When we are given a particular set and we consider different subsets of the given set, this given set is called universal set. It is denoted by U.  

• 1. The universal set is the set of real numbers R, while considering the set of natural numbers, whole numbers, integers and rational numbers.
• 2. The set of alphabets is the universal set from which the letters of any word may be chosen to form a set. 
• 3. In geometry, we discuss set of lines, triangles and circles, then universal set is the plane, in which the lines, triangles and circles lie. 

Q2. Define equivalence Relation and show that the relation S ={(a, b) :a ≥ b} on the set R of real no is an equivalence relation.  

Sol.  A relation R on a set E is said to be an equivalence relation, if it is :

• (a) reflexive
• (b) symmetric, and
• (c) transitive.

Check for Reflexive: 

It is given that R = {(a, b) : a ≥ b} 

It is clear that (a, a) ∈R as a = a 

Therefore, R is reflexive. 

Check for Symmetric:

If a ≥ b, then b ≥ a. 

This statement is true only for the case a=b. 

Therefore, R is symmetric. 

Check for Transitivity: 

Now let (a, b) (b, c) ∈R

Then a ≥ b and b ≥ c 

⇒ (a, c) ∈R 

Therefore, R is a transitive.

Hence, R is reflexive, transitive and symmetric. So, R is an equivalence relation. 

Q3. Show that the inclusion relation ⊆ is a partial ordering on the power set of a set S. 

Sol. Since A ⊆ A for any subset A ⊆ S, we conclude that this relation is reflexive. 

Taking into account that A ⊆ B and B ⊆ A imply A = B, we conclude that the relation is antisymmetric. 

Since A ⊆ B and B ⊆ C imply A ⊆ C,it follows that this relation is transitive. 

Consequently the inclusion relation is a partial ordering on the power set of a set S.  Ans. 

Q4. If z = e xy2 , x = t cost, y = t sint compute dz/dt at t = 𝜋/2.

Sol. Given  z = e xy2  

Q5. If cos α, cos β, and cos γ are the direction cosines of a straight line then prove that sin 2 α + sin 2 β + sin 2 γ = 2.

Sol. Since cosα, cosβ, cosγ are the direction cosines of the given line, therefore

Section B: Mathematics-II Short Question Solutions

Q6. Show that Dual of a complemented lattice is complemented. 

Sol. Let(L, R) be a complemented lattice with 0 and 1 as least and greatest elements. Let (L, R(bar)) be the dual of(L, R) Then 1 and 0 are least and greatest elements of (L, R(bar)). 

Let a 𝛜 L be any element.

Q7. Find the equations of the straight line drawn through the origin which will intersect both the lines. 

Sol. We need to find the equation of line which intersects the lines

and passes through (0, 0, 0). 

Equation of line passing through two points (x 1 ,y 1 , z 1 ) and (x 2 , y 2 , z 2 ), 

We use (x 1 ,y 1 , z 1 ) = (0, 0, 0) 

Now, if point (x 2 , y 2 , z 2 ) lies on (L 1 ) 

⇒ x = p + 1,  y = 4p – 3,   z = 3p + 5

So,  (x 2 , y 2 , z 2 ) = (p + 1, 4p – 3, 3p + 5)  

Thus, the equation of lines will be

Now, if the point (x 2 , y 2 , z 2 ) lies on (L 2 )  

⇒ x = 2q + 4,  y = 3q – 3,  z = 4q + 14 

So,  (x 2 , y 2 , z 2 ) = (2q + 4, 3q – 3, 4q + 14) 

Then the equation of line will be 

Since, the eqs. (iii) and (iv) represents the same line, so the direction ratios of lines are proportional. 

Comparing eqs. (v) and (vi), 

8qk + 16k – 4 = 3qk – 3k + 3 

5qk + 19k = 7 

Comparing eqs. (vi) and (vii), 

9qk – 9k + 9= 16qk + 56k – 20 

7qk + 65 k = 29  

k(7q + 65) = 29  

From eqs. (vii) and (ix), 

7 (7q + 65) = (5q + 19) 29 

49q + 455 = 145 q + 551 

96 q = -96 

Now, putting the value of q in eq. (iv), 

Q8. Show that f(x, y, z) =(x + y + z) – 3(x + y + 2)- 24xyz + a 3 has maxima at (-1, – 1, -1).  

Sol. f(x, y,  z) = (x + y + z) 3 – 3(x + y + z)- 24 xyz + a 3  

Differentiation offw.rtx,y and z, 

3(x + y + z) 2 – 3- 24yz = 0

3(x + y + z) 2 = 3 + 24yz  

(x + y + z)=1 + 8yz                                               …(iv)

and 3(x + y + z) 2 – 3 – 24xz = 0

3(x + y + z) = 3 + 24xz 

(x + y + z) 2 = 1 + 8xz                                            …(v)

and 3(x + y +z) 2 – 3 – 24xy = 0

3(x + y + z) 2 = 3 + 24xy  

(x + y + z) = 3 + 24xy 

(x + y + z) = 1 + 8xy                                             …(vi)

From eqs. (iv), (v) and (vi)  

1 + 8yz = 1 + 8xz = 1 + 8xy

⇒ x = y = z putting in eq. (iv) 

(x + x + x) = 1 + 8xx 

(3x) 2 = 1 + 8x 2  

9x 2 = 1 + 8x²  ⇒   x 2 = 1  

⇒ (x, y, z) = ± (1, 1, 1) 

At point (-1, -1, -1), 

A = – 18, B = – 18, C = – 18 

F = 6, G = 6, H = 6 

(1) A = – 18 < 0  

Hence f is maximum at (- 1, – 1,- 1). 

Section C: Mathematics-II Detailed Question Solutions

Q9. Let the function f : R → R and g : R → R be defined by f(x) = 2x, g(x) = x 2 + 2 ∀x ∈R. 

(a) Check the function f and g for being. 

(i) One-to-One (ii) Onto  

Sol. (1) Given that                     f(x) = 2x 

Checkf is one-one: Let x 1 , x 2 ∈R  

Now,    f(x) = f(x)  

⇒         2x 1 = 2x 2   

⇒         x 1 = x 2   

Therefore, f is one-one

Check g is one-one: Given that g (x) = x 2 + 2 

Let        x 1 , x 2 ∈R 

Now,     g(x 1 ) = g(x 2 ) 

⇒          x 1 2 +2 = x 2 2 + 2  

⇒          x 2 1 = x 2 2   

⇒         x 2 1 – x 2 2 = 0

⇒        (x 1 – x 2 ) (x 1 + x 2 ) = 0 

⇒        x 1 = ± x 2  

Therefore, g(x 1 ) = g(x 2 ) does not implies that x 1 = x 2  

Therefore, g is not one- one.  

Eg.    g(-1) = 1 + 2 = 3    

         g(1) = 1 + 2 = 3  

g(- 1) = g(1) 

but – 1 ≠ 1.

(ii) Check f is onto: 

Let C ∈ R,    f(x) = 2x 

⇒                 f(x) = C

⇒                 2x= C

which implies that C is the image of C/2.

∴ f is onto. 

Check g is onto:        g(x) = x 2 + 2  

Let g(x) = C, such that C ∈ R

Note that Cis a real number, it can be negative also.

Putting            C = – 2  

which is not possible as root of negative number is not real. 

Hence x is not real.  

So, y is not onto. 

(b) Find the formula defining the function fog and gof and obtain the values of (fog) (2) and (gof) (1). 

Sol. Composition of function: 

Let f: A → B and y : B → C be two real valued functions. Then the composition of f and g denoted by gof, such that gof: A → C is defined by 

(gof) (x) =g (f(x))

This is also known as function of a function or resultant of a function.

Similarly,                 (fog) (x) =f(g(x))  

Since we have        f(x) = 2x and g(x) = x 2 + 2 

Now,                       fog(x) =f(g(x)) = f(x 2 + 2) = 2(x 2 + 2) 

                               fog (x) = 2(x 2 + 2)  

                               fog (2) = 2(2 2 + 2) = 2(4 + 2) = 12  

and                         gof (x) = g(f (x)) = g(2x) = (2x) 2 + 2 = 4x 2 + 2  

                               gof (x) = 4x 2 +2 

                               gof (1) = 4(1) 2 + 2 = 4 + 2 = 6.  

Q10. (a) If (L, < ) is a lattice and a, b, c and d ∈ L then. 

  (i) a ≤ b, c ≤ d ⇒ a ∧ c ≤ b ∧ d 

(ii) a ∧ (b v c) ≥ (a ∧ b) v (a ∧ c) 

Sol. (i) Since a ∧ c ≤ a and a ∧ c ≤ c,  

therefore, again by transitivity  

a ∧ c ≤ b and a ∧ c ≤ d (∵ a ≤ b, and c ≤ d).

⇒ a ∧ c is a lower bound of b and d. 

But since b ∧ d is the g.l.b of b and d, 

therefore, we have a ∧ c ≤ b ∧ d.  

(ii) We know that  

because a ∧ (b v c) is the greatest lower bound of {a, b v c} 

(b) Show that dual of a lattice is a lattice. 

Sol.  Let (L, R) be a given lattice and let (L, R(bar)) be its dual, where R(bar) is defined as x R(bar)y if yRx. Then, it can be shown easily that (L, R(bar)) is a poset.  

Let x v y = sup {x, y} in (L, R). Then we have x R(x v y) and y R (x v y) 

(x v y) R(bar)x and (x v y) R(bar)y  

= x v y is a lower bound of {x, y} in (L, R(bar))  

Now, we will show that x v y is the greatest lower bound of {x, y} in (L, R(bar)). 

Let z be any lower bound of (x, y) in (L, R(bar)), then z R(bar)x and z R(bar)y.  

⇒ x R z and y R z 

⇒ z is an upper bound of {x, y} in (L, R) 

⇒ (x v y) Rz as x v y = sup {x, y} in (L, R) 

⇒ z R(x v y) 

⇒ x v y is the greatest lower bound of (x, y) in (L, R(bar)). 

Similarly, it can be shown that x ∧ y is the least upper bound in (L, R(bar)). 

Therefore (L, R(bar)) is a lattice. 

11. (a) Show that f(x, y, z – 2x) = 0, satisfies under suitable conditions, the equation 

What are these conditions. 

Sol. Let u = xy, V = 2 – 2x, then, 

12. (a) Find the equations of the plane parallel to the plane 2x – 3y – 5z + 1 = 0 and distant 5 units from the point (- 1, 3, 1).  

Sol. A plane parallel to the plane 2x – 3y – 5z + 1 =0  

can be written as   

2x – 3y – 5z + 𝛌 = 0

where 𝛌 is a scalar quantity. 

Now distance of plane (in eq. (i)) from the point (- 1,3, 1)  

Substituting the values of 𝛌 in eq. (i),

Hence, these are the equations of required planes. 

(b) Find the equation of the sphere which touches the sphere x 2 + y 2 + z 2 + 2x – 6y + 1 = 0  at (1, 2, -2) and passes through the point (1, – 1, 0). 

Sol. x 2 + y 2 + z 2 + 2x – 6y + 1 = 0

Equation of tangent plane to the sphere at (1, 2, – 2) 

S 1 : xx 1 + yy 1 + zz 1 + u(x + x 1 ) + w(y + y 1 ) + v(z 2 + z 1 ) + d = 0

S : x 2 + y 2 + z 2 + 2ux + 2wy + 2vz + d = 0 

2u = 2,     2w = -6,      2v = 0 

u = 1,         w = -3,        v = 0 

S 1 = 1x + 2y – 2z + 1 (x + 1) + (-3) (y + 2) + 0 + 1 = 0 

S 1 = 2x + 2y – 2z +1 – 6 – 3y + 1 = 0 

= 2x – y – 2z – 4 = 0 

Equation of sphere = S + 𝜋 S 1 = 0

             = (x 2 + y 2 + z 2 + 2x – 6y + 1) + 𝜋 (2x – y – 2z + 4) = 0 

Passing through (1, -1),  

⇒ (1 +1+0 + 2 +6 + 1) + 𝜋(2 +1-0+4) = 0  

⇒ 11 + 7𝜋 = 0 

Equation of sphere 

13. (b) Evaluate the following integrals by first converting to Polar coordinates.  

Sol. The given double integral  

From the limits of integration it is obvious that the region of integration R is bounded by 

i.e. the region of integration is the area AOBCA of the circle x 2 + y 2 – 1 = 0 bounded by the lines x = -1 and x = 1. 

Putting x = r cos 𝛉,y = r sin 𝛉 the corresponding pol¡r equation of the circle is r 2 (cos 2 𝛉 + sin 2 𝛉) = 1. 

Now,    r 2 = 1  ⇒ r = 1

Thus, r varies from r = 0 to r = 1 and 𝛉 varies from 𝛉 = 0° to 𝛉 = 𝜋. Also the polar equivalent of dx dy is rd𝛉dr.

Hence, the transformation to polar coordinates, 

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Bca tu college list of in valley, kathmandu college of technology, mathematics one notes bca first semester bca tu.

BCA First Semester Mathematics One Notes Unitwise.These all are shared for Students only for Study Purposes, AND Also we are Providing Yearly Question papers, MCQ, Lab Reports, and related Mathematics I study Materials. It may be helpful for you.

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Mathematics I (One)

• Unit One  Set Theory and Real & Complex Number
• Unit Two  Relation, Functions, and Graphs
• Unit Three Sequence and series
• Unit Four Matrices and Determinants
• Unit five Analytical Geometry
• unit six Permutation and combination

all chapters-wise Exercise Solution

2019 year question paper solution 

2020 year question paper Solution

2021 year Mathematics I MCQ answer sheet

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2018,2019,2020,2021 year all subject MCQ and yearly question paper 

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Mathematiccs One MatLab Labreports

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IGNOUHelp.in

A Leading Portal for IGNOU Students

IGNOU BCA Assignment 2023-2024 (July – January)

IGNOU BCA Assignments 2024 - IGNOU BCA Assignment Question Paper has been uploaded by the university for its current session 2024. The students of the BCA program can now download the Assignment Questions from this page. Candidates have to compulsory download and submit these assignments with the solutions to the university to get permission for attending the Term End Exam of the IGNOU BCA Program.

We also inform all BCA students that the assignment questions for each of the courses of the IGNOU BCA program are available for download from here. You have to prepare each of BCA assignment separately so that IGNOU Evaluators can easily understand and identify the course code of each subject.

• IGNOU BCA Syllabus
• IGNOU BCA Study Material

List of IGNOU BCA Assignment 2024

• Download IGNOU BCA Assignments 2024

Each of the Assignment questions will have different marks and the same will be printed on each question. Candidates should write the solutions to all questions according to the instructions given in the IGNOU BCA Assignment Question Paper . The BCA students have to submit the Assignments for each course to IGNOU Study Centre in which they get registered. The candidates have to submit it before the due date to appear in Term End Exam conducted by IGNOU.

IGNOU BCA Assignment Submission Last Date for 2024

Here is the Last Date for Submission of the IGNOU BCA Assignment to appear in the Upcoming Term End Exam June 2024 or December 2024 .

Where to Submit IGNOU BCA Assignments?

If you have completely solved your assignment then you have to submit your IGNOU BCA Assignments to the coordinator of the study centre which is allotted to you at the time of admission. Don’t forget to get a receipt for the submission of BCA Assignments.

After preparing the solution for your BCA Assignment, you have to submit IGNOU Assignments to the coordinator of the study centre which was allotted to you at the time of taking admission. Moreover, Don't forget to get a receipt for the submission of BCA Assignments.

Related Posts:

• IGNOU MSCENV Assignment 2023-2024 (January - July)
• IGNOU MBA Assignment 2023-2024 (July - January)
• IGNOU BA Assignment 2023-2024 (July - January)
• IGNOU MAH Assignment 2023-2024 (July – January)
• IGNOU MPS Assignment 2023-2024 (July - January)
• IGNOU MPA Assignment 2023-2024 (July - January)

36 thoughts on “IGNOU BCA Assignment 2023-2024 (July – January)”

How to complete assignments if we do not have received books till now. When will be the induction meeting?

I didn’t get any communication yet regarding study materials for the 2018 January batch, then how may I submit the assignment? When will be the induction meeting? does admission is not completed?

The same situation is with my daughter, who is a student of BCA 2018 July batch.

sir you have to manage assignments by yourself by the way classes had started but books are not delivered even by now

Is This assignment is also for Dec 2019 session?

assignments of English & Business Organisation is not received through post. Pl, Send as quickly as possible.

I got Admission for BCA course on December 2017 but i have no idea what to do next, i went to my centre so many times but they are unhelpful. please some one help me.

U can go pcti pitampura this is a good study center

BCA FEG-02 and ECO-01 Assignments are not in there

did you find the FEG-02 and ECO-01 Assignments? I’m still searching for it. Plz share if you have found

Same here. Cannot find FEG and ECO assignment question paper. Only 3 apart from this are available. The contact number of iGnou in Bangalore seems to be dead even though I tried calling mulitple numbers many times. Their inbox is full. There is no way to contact them and get this clarified. What to do?

Go for BCOM (ECO 01) BA & BDP (FEG 02)

Yes i have found it..

Mujhe assignment banane me aapka help chahiye kis tarah se banaya jata hai .

how can we complete assignments when we have not received study material yet.

july 2018 bca assignment last due date ?

tell about the fresh admission assignment

Till I did not get any study materials from ignou. Than how will I do practice of exam. And I never get classes for study ignou center ..

In bca 1st year assignment. We have given the assignment of BCSL-013. But we are told to solve those questions on different softwares like PowerPoint, Outlook, Spreadsheet, Word.

But what I am not getting is that how to submit these assignments?

Because everywhere it is told that we have to submit handwritten assignments.

Somebody help. Please.

the first semester , two subject assigenment are left sir kindly provide all assigment on the website sir.

Sir I’m the student of BCA 4th semester, I have not submitted any assignment of all previous semester. What should i do? Which session I will choose to complete my assignment .2018-19, 2019-20,

When is the submission date for FY BCA, August 31 Admission date ?

Please help me which session I should select 2020-21 or 2021-22 to write assignment, (MHD 2nd year 2020 April I re-registered)

i try to communicate with ignou help center i didn’t get any admission confirmation mail and i am unable to log in with my enrollment no. what should i do now i have mailed to ignou but every time they ignored my problem also any of your help no. is not working ..

Have you uploaded assignments for bca programmes for 1st semester for the session 2021-22? Kindly share the link!

I need that too

jinka new start hai unki assigment kb tk aay ge

please give the communications to students for assignments and admissions and proper dates , with out proper communication and details , how can we submit the assignments , we need some type of proper structure like 1 admission 2 books/soft copy 3 assignments 4 exams few people are there who didn’t know there is assignments for their course and how to do it please help the students confusions

sir ma july 2021 session bca me admission liya hu… 2021 july session ka assignment kon sa hai ….????/ ignou website me kab tak update hoga

I enrolled myself for the course of BCA on 2021-10-20. I have no idea or received no communication as to when will the exams take place and from where do I download the assignment material. Please help !

please give the communication to for assignment and books & soft copy and how to do it please help us ….

This assignment are old 2021-2022 batch jan to june 2022 please provide new assignment 2022-2023 batch.

Here is a big problem of communication and I am not getting anything clearly. I just enrolled in bca course 2 days ago and now last date for assignment submission is 30 sept, but no such kind of assignment is available for 22-23 batch

how to submit lab assignment

what is the last date submission of assignment for june session BCA

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Solved question paper for MATHS Dec-2018 (BCA 1st)

Maths (bridge course)

Previous year question paper with solutions for maths (bridge course) dec-2018.

Our website provides solved previous year question paper for Maths (bridge course) Dec-2018. Doing preparation from the previous year question paper helps you to get good marks in exams. From our MATHS question paper bank, students can download solved previous year question paper. The solutions to these previous year question paper are very easy to understand.

These Questions are downloaded from www.brpaper.com You can also download previous years question papers of 10th and 12th (PSEB & CBSE), B-Tech, Diploma, BBA, BCA, MBA, MCA, M-Tech, PGDCA, B-Com, BSc-IT, MSC-IT.

Question paper 1.

• Write briefly:

No of elements of A=3.

(c) Define an ant is ymmertic relation by giving suitable example .

Antisymmetric  Relatio n :A binary relation on a set x is antisymmetric

If there is no fair of distinct  elts of X each of which is related by R to the other ,

Or equivalent ly,

Is anti cymmetric on the set

Contrapositive of

(g) Define a multi graph.

(h) Define a simple path and cycle in  a graph.

Simple path : An open walk in which every vertex is distinct is know as simple path

Cycle : A closed walk in which no vertex ( except the initial and terminal vertex) appears more than once.

2. IF A and B are any two sets, then prove that  

3. Prove the following by the principle of  mathematical induction

Basic we prove the result for n=1.

 Assumption : We assume the result is true for n=k.

4. (a) Define the following graphs by taking suitable examples .

• Eulerian graph.

 A graph which contains either Euler path or Euler

Circuit is called Eulerian Graph.

ii. Hamiltonian graph

 A Graph Which contains either Hamiltonian circuit a Hamiltonian graph

(b) find the minimum n of colors required to paint the following graph

5. Find the inverse of the following matric

Determine whether or not each of the above relations on A is:

(i) Reflexive      (ii)  symmetric;  (iii) transitive;

i. the only T is reflexive

       S is not sym .

7. (a) Determine which of the following are Eulerian or Hamilton or both?

This graph contains vertices of add degree.

(b) In a group of 50 person 14 drink tea but not coffee and 30 drink tea fond:

(i) How many drink tea and coffee both? (ii) How manu drink coffee but not tea ? 

The graph is Euler Graph

In this graph, neither Hamiltonian circuit exists nor the Hamiltonian path

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