BCS-12 BCA 2026-27 SOLVED ASSIGNMENT

Description

Course Code : BCS-012
Course Title : Basic Mathematics
Assignment Number : BCA_NEW/BCAOL(I)012/Assign/2026-27
Maximum Marks : 100
Last Date of Submission : 31st October,2026 (For July 2026 Session) : 30th April, 2027 (For January 2027 Session)
Note: This assignment has 20 questions of 80 marks (each question carries equal marks). Answer all the questions. Answer all the questions. Rest 20 marks are for viva voce. You may use illustrations and diagrams to enhance explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation.
Q1: If A = [3 −1; 2 1], show that A² − 4A + 5I₂ = 0. Also find A⁴.
Q2: Solve the following system of equations using the matrix inverse method: 3x + 4y + 7z = 14 2x − y + 3z = 4 2x + 2y − 3z = 0
Q3: Use the principle of mathematical induction to prove that: 1/(1×2) + 1/(2×3) + … + 1/[n(n+1)] = n/(n+1)
Q4: If the pᵗʰ term of an A.P. is q and the qᵗʰ term of the same A.P. is p, find its rᵗʰ term.
Q5: How many terms of the G.P. √3, 3, 3√3, …add up to 39?
Q6: Find the sum of all integers between 100 and 1000 that are divisible by 7.
Q7: If 1, ω, ω² are the cube roots of unity, show that:(2 − ω)(2 − ω²)(2 − ω¹⁹)(2 − ω²³) = 49
Q8: Use De Moivre’s theorem to find the value of (√3 + i)³
Q9: If α and β are the roots of x² − 3ax + a² = 0, find the value of a when α² + β² = 7/4.
Q10: If α and β are the roots of 2x² − 3x − 5 = 0, form the quadratic equation whose roots are α² and β².
Q11: Solve the equation: x³ − 13x² + 15x + 189 = 0, given that one root exceeds another by 2.
Q12: Solve the inequality and graph its solution: 2/(x − 1) > 5 Q13: If y = log[(√(1+x) − √(1−x))/(√(1+x) + √(1−x))], find dy/dx. Q14: If y = aeᵐˣ + be⁻ᵐˣ, prove that: d²y/dx² = m²y Q15: Determine the intervals in which f(x) = x⁴ − 8x³ + 22x² − 24x + 21 is increasing and decreasing. Q16: Find the points of local maximum and local minimum of: f(x) = x³ − 6x² + 9x + 2014
Q17: Evaluate: ∫ x²√(5x − 3) dx
Q18: Using integration, find the length of the curve y = 3 – x from (−1, 4) to (3, 0)
. Q19: Find the scalar component of projection of the vector a = 2î + 3ĵ + 5k ̂ on the vector b = 2î − 2ĵ + k ̂ .
Q20: 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.