Description
BCS012 Basic Mathematics Solved Assignment For IGNOU BCA 1st Semester
Assignment Code: BCA(1)012/Assignment/201819
Last Date For Submission: 15th October, 2018 (For July, 2018 Session)
15th April, 2019 (For January, 2019 Session)
All Questions are Solved in this Assignment Solution



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+2^{2}+…+2^{n}=2^{n+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 d^{2}ydx^{2}=2lnx−3/x^{3}

If the midpoints 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 vector
a = 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}= A^{2}+ B^{2}, 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).


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