Bcs012 june 2021 solved question paper
Hello Students !!
In this video lecture we will Solve IGNOU BCS040 December 2021 Question Paper.
1. (a) If A = 2 – 1 1 – 2
; B = b – 1 a 1
and (A + B)2 = A2 + B2, find a and b.
(b) If the first term of an AP is 22, the common difference is – 4, and the sum to n terms is 64, find n.
(c) Find the angle between the lines
(d) If , are roots of x2 – 2kx + k2 – 1 = 0, and 2 + 2 = 10, find k.
(e) If y = 1 + ln (x + , prove that (x2 + 1)
(f) Find the points of discontinuity of the following function :
f(x) =
(g) Solve the inequality
|x – 3| 5 7
(h) Evaluate the integral
2. (a) Use the principle of mathematical induction to show that 2 + 22 + ... + 2n = 2n+1 – 2 for each natural number n.
(b) Using determinant, find the area of the triangle whose vertices are (1, 2); (– 2, 3) and (– 3, – 4).
(c) Draw the graph of the solution set for the
following inequalities : 2x + y 8, x + 2y 8 and x + y 6 5
(d) Use De Moivre’s theorem to find (i + 3 ) 3
3. (a) Find the absolute maximum and minimum of the following function : f(x) = x 2 x3 on [– 1, 1]
(b) Reduce the matrix A = normal form and hence find its rank.
(c) If
(d) Find the length of function y = 3 – 2x from (0, 3) to (2, – 1) using integration
4. (a) Find the quadratic equation with real coefficients and with the following pair of roots :
m – n m n
(b) If x = a + b, y = a + b 2 , z = a 2 + b (where is a cube root of unity and 1), show that xyz = a3 + b3
(c) Solve the following system of linear equations using Cramer’s rule :
x + y = 0; y + z = 1; z + x = 3
(d) If y = ln , find dx/dy
5. (a) A software development company took the designing and development job of a website. The designing job fetches the company 2,000 per hour and development job fetches them 1,500 per hour. The company can devote at most 20 hours per day for designing and atmost 15 hours for development of website. If total hours available for a day is at most 30, find the maximum revenue the software company can get per day.
(b) Evaluate x 3 – 2x dx
(c) Find the vector and Cartesian equations of the line passing through the points (– 2, 0, 3) and (3, 5, – 2).