BCS-012 Solved Assignment 2026-27 in English | Bachelor of Computer Applications

BCS-012 Solved Assignment 2026-27 in English is designed for Bachelor of Computer Applications students studying BCS-012: Basic Mathematics. The assignment covers important mathematical concepts including matrices, mathematical induction, arithmetic and geometric progressions, complex numbers, quadratic equations, inequalities, differentiation, integration, vectors and linear programming.

The uploaded assignment is for the 2026-27 session and carries a maximum of 100 marks. It contains 20 questions of 80 marks, with the remaining 20 marks allocated to viva voce.

BCS-012 Basic Mathematics Course Information

IGNOU lists BCS-012 as Basic Mathematics within the Bachelor of Computer Applications programme, and the current assignment listing includes BCS-012 for both BCA_NEW and BCA_NEWOL for the July 2026 and January 2027 sessions.

BCS-012 Solved Assignment 2026-27 Overview

The BCS-012 Solved Assignment 2026-27 in English covers a broad range of mathematical topics required in the Basic Mathematics course. Matrix operations and the matrix inverse method form an important part of the assignment. Mathematical induction, A.P., G.P. and divisibility-based calculations are also included.

Complex-number concepts appear through cube roots of unity and De Moivre’s theorem. Quadratic equations are covered through relationships between roots and the formation of equations with transformed roots.

The assignment also includes inequality solving, logarithmic differentiation, second-order derivatives, increasing and decreasing functions, and local maximum and minimum problems. Integration is represented through indefinite integration and curve-length calculations.

Vector projection and linear programming complete the question set. As a result, the assignment provides coverage across algebra, calculus, vectors and optimisation.

The official BCA programme structure identifies BCS-012 as a 4-credit Semester 1 course, while the programme guide describes its objective as developing mathematical understanding useful for further computer-science-oriented study.

BCS-012 Basic Mathematics Assignment Questions

Course Code: BCS-012
Course Title: Basic Mathematics
Assignment Code: BCA_NEW/BCAOL(I)012/Assign/2026-27
Maximum Marks: 100

Question 1

If A=[3 −1; 2 1]A = [3\ -1;\ 2\ 1], show that A2−4A+5I2=0A^2 – 4A + 5I_2 = 0. Also find A4A^4.

Question 2

Solve the following system of equations using the matrix inverse method:

3x+4y+7z=143x + 4y + 7z = 14 2x−y+3z=42x-y+3z=4 2x+2y−3z=02x+2y-3z=0

Question 3

Use the principle of mathematical induction to prove that:

11×2+12×3+⋯+1n(n+1)=nn+1\frac{1}{1\times2}+\frac{1}{2\times3}+\cdots+ \frac{1}{n(n+1)}=\frac{n}{n+1}

Question 4

If the pthp^{th} term of an A.P. is qq and the qthq^{th} term of the same A.P. is pp, find its rthr^{th} term.

Question 5

How many terms of the G.P.

3, 3, 33,…\sqrt3,\ 3,\ 3\sqrt3,\ldots

add up to 39?

Question 6

Find the sum of all integers between 100 and 1000 that are divisible by 7.

Question 7

If 1,ω,ω21,\omega,\omega^2 are the cube roots of unity, show that:

(2−ω)(2−ω2)(2−ω19)(2−ω23)=49(2-\omega)(2-\omega^2)(2-\omega^{19})(2-\omega^{23})=49

Question 8

Use De Moivre’s theorem to find the value of:

(3+i)3(\sqrt3+i)^3

Question 9

If α\alpha and β\beta are the roots of

x2−3ax+a2=0x^2-3ax+a^2=0

find the value of aa when:

α2+β2=74\alpha^2+\beta^2=\frac74

Question 10

If α\alpha and β\beta are the roots of

2×2−3x−5=02x^2-3x-5=0

form the quadratic equation whose roots are α2\alpha^2 and β2\beta^2.

Question 11

Solve the equation:

x3−13×2+15x+189=0x^3-13x^2+15x+189=0

given that one root exceeds another by 2.

Question 12

Solve the inequality and graph its solution:

2x−1>5\frac{2}{x-1}>5

Question 13

If

y=log⁡[1+x−1−x1+x+1−x],y=\log\left[ \frac{\sqrt{1+x}-\sqrt{1-x}} {\sqrt{1+x}+\sqrt{1-x}} \right],

find:

dydx\frac{dy}{dx}

Question 14

If

y=aemx+be−mx,y=ae^{mx}+be^{-mx},

prove that:

d2ydx2=m2y\frac{d^2y}{dx^2}=m^2y

Question 15

Determine the intervals in which

f(x)=x4−8×3+22×2−24x+21f(x)=x^4-8x^3+22x^2-24x+21

is increasing and decreasing.

Question 16

Find the points of local maximum and local minimum of:

f(x)=x3−6×2+9x+2014f(x)=x^3-6x^2+9x+2014

Question 17

Evaluate:

∫x25x−3 dx\int x^2\sqrt{5x-3}\,dx

Question 18

Using integration, find the length of the curve

y=3−xy=3-x

from (−1,4)(-1,4) to (3,0)(3,0).

Question 19

Find the scalar component of projection of the vector

a=2i^+3j^+5k^a=2\hat{i}+3\hat{j}+5\hat{k}

on the vector

b=2i^−2j^+k^.b=2\hat{i}-2\hat{j}+\hat{k}.

Question 20

A tailor needs at least 40 large buttons and 60 small buttons. A box contains 6 large and 2 small buttons, and a card contains 2 large and 4 small buttons. If the cost of a box is $3 and the cost of a card is $2, formulate and solve the problem as a linear programming problem to minimize expenditure.

What Does This BCS-012 Solved Assignment PDF Include?

The BCS-012 Solved Assignment 2026-27 in English provides coverage of the complete 20-question assignment supplied for the 2026-27 session.

Key Features

• BCS-012 Basic Mathematics coverage
• 2026-27 assignment
• English Medium
• Complete 20-question coverage
• Structured reference answers
• Matrix and algebra problems
• Mathematical induction
• A.P. and G.P.
• Complex numbers
• Quadratic equations
• Inequalities
• Differentiation
• Integration
• Vector projection
• Linear programming
• Digital PDF format
• Instant download
• Mobile and desktop friendly
• Useful for academic reference

The assignment itself states that all questions should be answered and that illustrations and diagrams may be used where appropriate.

Who Can Use the BCS-012 Assignment?

The BCS-012 assignment is intended for students enrolled in the Bachelor of Computer Applications programme who are completing the Basic Mathematics course for the applicable 2026-27 session.

It can be used as an academic reference while preparing responses to questions involving matrices, progressions, complex numbers, calculus, vectors and linear programming. The official IGNOU programme page places BCS-012 in the BCA curriculum as a Semester 1, 4-credit theory course.

Students should match their course code, session and medium with the assignment details before using the material.

How to Get This BCS-012 PDF

Step 1: Add the Product

Select the BCS-012 solved assignment product and add it to the cart.

Step 2: Complete Payment

Complete the website checkout process using the available payment option.

Step 3: Get Instant Access

After successful payment, access to the digital product will be provided.

Step 4: Download the PDF

Download the BCS-012 assignment PDF to your device.

Step 5: Start Preparing

Use the material as a structured reference while preparing your assignment responses.

Helpful Resources

• Mother Publication Home: https://motherpublication.co.in/
• IGNOU Updates: https://motherpublication.co.in/blog/
• Handwritten Assignment Hard Copy: https://motherpublication.co.in/handwritten-hardcopy/
• Official IGNOU Assignment Questions: IGNOU Assignment Questions
• Solved Guess Papers: https://mothernotes.in/

Frequently Asked Questions

1. What is BCS-012?

BCS-012 is Basic Mathematics, a 4-credit theory course in the Bachelor of Computer Applications programme.

2. What is the BCS-012 assignment code?

The uploaded 2026-27 assignment gives the assignment code as BCA_NEW/BCAOL(I)012/Assign/2026-27.

3. What is the course title?

The course title is Basic Mathematics.

4. Which programme includes BCS-012?

BCS-012 is included in the Bachelor of Computer Applications programme. IGNOU currently lists the new BCA programmes as BCA_NEW and BCA_NEWOL.

5. Which session does this assignment cover?

The assignment covers the 2026-27 session, with submission dates specified for July 2026 and January 2027 sessions.

6. Is the BCS-012 PDF available in English?

Yes. The supplied product is for English Medium.

7. How many marks does the assignment carry?

The assignment has a maximum of 100 marks. The question section carries 80 marks and the remaining 20 marks are for viva voce.

8. How many questions are included?

There are 20 questions in the assignment.

9. What format will I receive?

The product is provided as a digital PDF.

10. Can I get a handwritten assignment hard copy?

Handwritten assignment hard-copy information is available through the dedicated resource page: Handwritten Assignment Hard Copy

Disclaimer

Mother Publication independently prepares this material for educational and reference purposes. Students should understand the content and prepare their assignments appropriately. Mother Publication is not affiliated with, endorsed by, or officially associated with IGNOU.

PRODUCT TAGS

BCS-012, BCS 012, BCS012, BCS-12, BCS 12, BCS12, BCS-012 solved assignment 2026-27, BCS 012 solved assignment 2026-27, BCS012 solved assignment 2027, BCS-12 assignment 2027, BCS 12 assignment 2027, BCS12 assignment 2027, BCS-012 solved assignment 2027, BCS-012 Basic Mathematics, BCS 012 Basic Mathematics, BCS012 Basic Mathematics, Basic Mathematics assignment 2026-27, Basic Mathematics solved assignment, Basic Mathematics PDF, BCS-012 assignment PDF, BCS 012 assignment PDF, BCS012 assignment PDF, BCA BCS-012, BCA Basic Mathematics, BCA solved assignment 2026-27, BCA assignment PDF 2026-27, Bachelor of Computer Applications assignment, BCS-012 English Medium, BCS 012 English Medium, BCS012 English Medium, BCS-012 2026-27, BCS 012 2026 27, BCS012 2027, BCS-012 solved assignment 2027, Basic Mathematics solved PDF, BCS-012 assignment questions, BCS-012 2026-27 PDF