BCS-012 Basic Mathematics Solved Assignment 2018-19

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)

1. Evaluate the determinant given below, where w is a cube root of unity.
   1 ? ?²
   ? ?² 1
   ?² 1 ?
2. Using determinant, find the area of the triangle whose vertices are (−3,5), (3,−6) and (7,2).
3. Use the principle of mathematical induction to show that 2+2²+…+2ⁿ=2ⁿ⁺¹–2 for every natural number n.
4. Find the sum of all integers between 100 and 1000 which are divisible by 9.
5. Check the continuity of the function f(x) at x = 0 :
6. If y=lnx/x, show that d²ydx²=2lnx−3/x³
7. If the mid-points of the consecutive sides of a quadrilateral are joined, then show (by using vectors) that they form a parallelogram.
8. Find the scalar component of projection of the vector
   a = 2i + 3j + 5k on the vector b = 2i–2j–k
9. Solve the following system of linear equations using Cramer’s rule: x + y = 0, y + z = 1, z + x = 3
10. If A=[1 −2,2 −1], B=[a 1, b −1]and (A + B)²= A²+ B², Find a and b.
11. Reduce the matrix A(given below) to normal form and hence find its rank. 5 3 8 A = 0 1 1 1 -1 0
12. Show that n(n+1) (2n+1) is a multiple of 6 for every natural number n.
13. Find the sum of an infinite G.P. whose first term is 28 and fourth term is 4/49.
14. Use De Moivre’s theorem to find (√3 + ?)³.
15. If 1, ?, ?2 are cube roots unity, show that (2-?) (2-?2) (2-?10) (2-?11) = 49.
16. Solve the equation 2×3 – 15×2 + 37x – 30 = 0, given that the roots of the equation are in A.P.
17. 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 ?
18. Using first derivative test, find the local maxima and minima of the function f(?) = ?3–12?.
19. Evaluate the integral I= ∫?2/(?+1)³ dx
20. Find the length of the curve y = 3 + ?/2 from (0, 3) to (2, 4).