BCS-012 Basic Mathematics Solved Assignment For IGNOU BCA 1st Semester
Assignment Code: BCA(1)-012/Assignment/2018-19
Last Date For Submission: 15th October, 2018 (For July, 2018 Session)
Evaluate the determinant given below, where w is a cube root of unity.
1 ? ?2
? ?2 1
?2 1 ?
Using determinant, find the area of the triangle whose vertices are (−3,5), (3,−6) and (7,2).
Use the principle of mathematical induction to show that 2+22+…+2n=2n+1–2 for every natural number n.
Find the sum of all integers between 100 and 1000 which are divisible by 9.
Check the continuity of the function f(x) at x = 0 :
If y=lnx/x, show that d2ydx2=2lnx−3/x3
If the mid-points of the consecutive sides of a quadrilateral are joined, then show (by using vectors) that they form a parallelogram.
Find the scalar component of projection of the vectora = 2i + 3j + 5k on the vector b = 2i–2j–k
- Solve the following system of linear equations using Cramer’s rule:
x + y = 0, y + z = 1, z + x = 3
If A=[1 −2,2 −1], B=[a 1, b −1]and (A + B)2= A2+ B2, Find a and b.
- Reduce the matrix A(given below) to normal form and hence find its rank.
5 3 8
A = 0 1 1
1 -1 0
- Show that n(n+1) (2n+1) is a multiple of 6 for every natural number n.
- Find the sum of an infinite G.P. whose first term is 28 and fourth term is 4/49.
- Use De Moivre’s theorem to find (√3 + ?)3.
- If 1, ?, ?2 are cube roots unity, show that (2-?) (2-?2) (2-?10) (2-?11) = 49.
- Solve the equation 2×3 – 15×2 + 37x – 30 = 0, given that the roots of the equation are in A.P.
- 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 ?
- Using first derivative test, find the local maxima and minima of the function f(?) = ?3–12?.
- Evaluate the integral I= ∫?2/(?+1)3 dx
- Find the length of the curve y = 3 + ?/2 from (0, 3) to (2, 4).