BCS012 Solved Assignment 202122
BCS012 Solved Assignment 202122
Subject Name  Basic Mathematics 
Assignment Code  BCS012 
Session  20212022 (July – January) 
File Type  
Number of Pages  24 
Price  Rs. 40 
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Basic Mathematics (BCS012) 20212022 (JulyJanuary)
Note: This assignment has 20 questions of 80 marks (each question carries equal marks). Answer all the questions. Rest 20 marks are for viva voce. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation.
Question 1:
Use the principle of mathematical induction to show that for every natural number n.
Question 2:
Find the sum of all integers between 100 and 1000 which are divisible by 9.
Question 3:
Reduce the matrix A (given below) to normal form and hence find its rank.
Question 4:
Show that n(n+1) (2n+1) is a multiple of 6 for every natural number n.
Question 5:
Find the sum of an infinite G.P. whose first term is 28 and fourth term is 4/49.
BCS012 Solved Assignment 202122
Question 6:
Check the continuity of the function f(x) at x = 0 :
Question 7:
If , show that
Question 8:
If the midpoints of the consecutive sides of a quadrilateral are joined, then show (by using vectors) that they form a parallelogram.
Question 9:
Solve the equation 2x^{3} – 15x^{2 }+ 37x – 30 = 0, given that the roots of the equation are in A.P.
Question 10:
A young child is flying a kite which is at height of 50 m. The wind is carrying the kite horizontally away from the child at a speed of 6.5 m/s. How fast must the kite string be let out when the string is 130m ?
BCS012 Solved Assignment 202122
IGNOU BCA 1st Sem Solved Assignment 202122
Question 11:
Using first derivative test, find the local maxima and minima of the function f(x) = x^{3} – 12 .
Question 12:
Evaluate the integral
Question 13:
Find the scalar component of projection of the vector on the vector .
Question 14:
If 1, ω, ω^{2} are cube roots unity, show that (2 − ω)(2 − ω^{2})(2 − ω^{10})(2 − ω^{11}) = 49.
Question 15:
Find the length of the curve from (0, 3) to (2, 4).
BCS012 Solved Assignment 202122
IGNOU BCA 1st Sem Solved Assignment 202122
Question 16:
Evaluate the determinant given below, where ω is a cube root of unity.
Question 17:
Using determinant, find the area of the triangle whose vertices are , (– 3, 5), (3, – 6) and (7, 2).
Question 18:
Solve the following system of linear equations using Cramer’s rule:
x + y = 0; y + z = 1; z + x = 3
BCS012 Solved Assignment 202122
Question 19:
If and (A + B)^{2} = A^{2} + B^{2} , Find a and b.
Question 20:
Use De Moivre’s theorem to find (√3 + i)^{3} .
IGNOU BCA 1st Sem Solved Assignment 202122
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