Home 2021-2022 BCS-012 Mathematics SOLVED ASSIGNMENT, BCA (For 2021-22 Session)

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# BCS-012 Basic Mathematics

 Title Name BCS-012 Solved Assignment 2021-22 University IGNOU Service Type Solved Assignment (Soft copy/PDF) Course BACHELOR OF COMPUTER APPLICATIONS(BCA) Language ENGLISH Semester BCA(Revised Syllabus)/ASSIGN/SEMESTER-I Session 2021-22 Short Name BCS-012 Assignment Code BCA (1)/012/Assignment/2021-22 Product Assignment of BCA 2021 (IGNOU) Price Rs. 30 Last Date of Submission 31st October 2021 (For July 2021 Session) 15th April 2022 (For January 2022 Session)

Q1: Use the principle of mathematical induction to show that

2 +…+
n
=
n + 1
– for every natural number n.
(4 Marks)
Q2: Find the sum of all integers between 100 and 1000 which are divisible
by .
(4 Marks)
Q3: Reduce the matrix A(given below) to normal form and hence find its
rank.
5 3 8
A = 0 1 1
0 1 1
(4 Marks)
Q4: Show that n(n+1) (2n+1) is a multiple of 6 for every natural number n. (4 Marks)
Q5: Find the sum of an infinite G.P. whose first term is 28 and fourth term
is(4 Marks)
Q6: Check the continuity of the function f(x) at x = 0 :

Q7:(4 Marks)
Q8: If the mid-points of the consecutive sides of a quadrilateral are joined,
then show (by using vectors) that they form a parallelogram.
(4 Marks)
Q9: Solve the equation 2×3
– 15×2
+ 37x – 30 = 0, given that the roots of the
equation are in A.P.
(4 Marks)
Q10: 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.
(4 Marks)
10
How fast must the kite string be let out when the string is 130m ?
Q11: Using first derivative test, find the local maxima and minima of the
function f( ) =3–12 .
(4 Marks)
Q12: Evaluate the integral I=dx (4 Marks)
Q13: Find the scalar component of projection of the vector a = 2i + 3j + 5k
on the vector b = 2i – 2j – k.
(4 Marks)
Q14: If 1, 2 are cube roots unity, show that (2- ) (2-Q15: Find the length of the curve y = 3 +from (0, 3) to (2, 4). (4 Marks)
Q16: Evaluate the determinant given below, where is a cube root of unity.

Q17: Using determinant, find the area of the triangle whose vertices are

(4 Marks)
Q18: Solve the following system of linear equations using Cramer’s rule:
x + y = 0, y + z = 1, z + x = 3
(4 Marks)
Q19:

Q20: Use De Moivre’s theorem to find (
3
. (4 Marks)