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BCS-012 Solved Assignment 2021-22

BCS-012 Solved Assignment 2021-22

Subject Name Basic Mathematics
Assignment Code BCS-012
Session 2021-2022 (July – January)
File Type PDF
Number of Pages 24
Price Rs. 40

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Basic Mathematics (BCS-012) 2021-2022 (July-January)

Note: This assignment has 20 questions of 80 marks (each question carries equal marks). Answer all the questions. Rest 20 marks are for viva voce. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation.

Question 1:

Use the principle of mathematical induction to show that  \small 2+2^{2}+...+2^{n}=2^{n+1}-2  for every natural number n.

Question 2:

Find the sum of all integers between 100 and 1000 which are divisible by 9.

Question 3:

Reduce the matrix A (given below) to normal form and hence find its rank.

\small A=\begin{bmatrix} 5 &3 &8 \\0 &1 &1 \\0 &1 &1 \end{bmatrix}

Question 4:

Show that  n(n+1) (2n+1)  is a multiple of  6  for every natural number  n.

Question 5:

Find the sum of an infinite G.P. whose first term is 28 and fourth term is  4/49.

BCS-012 Solved Assignment 2021-22

Question 6:

Check the continuity of the function  f(x)  at  x = 0 :

\small f\left ( x \right )=\left\{\begin{matrix} \frac{\left | x \right |}{x}, &x\neq 0 \\0, &x=0 \end{matrix}\right.

Question 7:

If \small y=\frac{lnx}{x} , show that  \small \frac{d^{2}y}{dx^{2}}=\frac{2\, lnx-3}{x^{3}}.

Question 8:

If the mid-points of the consecutive sides of a quadrilateral are joined, then show (by using vectors) that they form a parallelogram.

Question 9:

Solve the equation 2x3 – 15x2  +  37x  –  30  = 0,  given that the roots of the equation are in A.P.

Question 10:

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 ?

BCS-012 Solved Assignment 2021-22

IGNOU BCA 1st Sem Solved Assignment 2021-22

Question 11:

Using first derivative test,  find the local maxima and minima of the function f(x) = x3 – 12 .

Question 12:

Evaluate the integral  \small I=\int \frac{x^{2}}{\left ( x+1 \right )^{3}}\: dx

Question 13:

Find the scalar component of projection of the vector \small \vec{a}=2\hat{i}+3\hat{j}+5\hat{k}  on the vector   \small \vec{b}=2\hat{i}-2\hat{j}-\hat{k} .

Question 14:

If  1, ω,  ω2 are cube roots unity,  show that   (2 − ω)(2 − ω2)(2 − ω10)(2 − ω11) = 49.

Question 15:

Find the length of the curve   \small y=3+\frac{x}{2}   from  (0, 3)  to  (2, 4).

BCS-012 Solved Assignment 2021-22

IGNOU BCA 1st Sem Solved Assignment 2021-22

Question 16:

Evaluate the determinant given below, where ω is a cube root of unity.

\small \begin{vmatrix} 1 &\omega &\omega ^{2} \\\omega &\omega ^{2} &1 \\\omega ^{2} &1 &\omega \end{vmatrix}

Question 17:

Using determinant, find the area of the triangle whose vertices are ,  (– 3,  5), (3, – 6)  and  (7, 2).

Question 18:

Solve the following system of linear equations using Cramer’s rule:

x + y = 0; y + z = 1; z + x = 3

BCS-012 Solved Assignment 2021-22

Question 19:

If \small A=\begin{bmatrix} 1 &-2 \\2 &-1 \end{bmatrix},B=\begin{bmatrix} a &1 \\b &-1 \end{bmatrix}   and  (A + B)2 = A2 + B2 ,  Find  a  and  b.

Question 20:

Use De Moivre’s theorem to find  (√3 + i)3 .

IGNOU BCA 1st Sem Solved Assignment 2021-22

BCS-012 Assignment Question PDF Download

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