BCS-012 Solved Assignment 2018-19 For IGNOU BCA/MCA

Description

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. 1. 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).