IGNOU BMTC 131 SOLVED ASSIGNMENT

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IGNOU BMTC 131 SOLVED ASSIGNMENT

~~Rs. 80~~
Rs. 41

IGNOU BMTC 131 SOLVED ASSIGNMENT

~~Rs. 80~~
Rs. 41

Last Date of Submission of IGNOU BMTC-131 (BSCG) 2026 Assignment is for January 2026 Session: 30th September, 2026 (for December 2026 Term End Exam).
Semester Wise
January 2026 Session: 30th March, 2026 (for June 2026 Term End Exam).
July 2026 Session: 30th September, 2026 (for December 2026 Term End Exam).

Title Name	IGNOU BMTC 131 SOLVED ASSIGNMENT
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	BACHELOR DEGREE PROGRAMMES
Course Code	BSCG
Course Name	Bachelor of Science
Subject Code	BMTC 131
Subject Name	Calculus
Year	2026
Session
Language	English Medium
Assignment Code	BMTC-131/Assignmentt-1//2026
Product Description	Assignment of BSCG (Bachelor of Science) 2026. Latest BMTC 131 2026 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU BMTC-131 (BSCG) 2026 Assignment is for January 2026 Session: 30th September, 2026 (for December 2026 Term End Exam). Semester Wise January 2026 Session: 30th March, 2026 (for June 2026 Term End Exam). July 2026 Session: 30th September, 2026 (for December 2026 Term End Exam).

~~Rs. 80~~
Rs. 41

Questions Included in this Help Book

Ques 1.

. Which of the following statements are true or false? Give reasons for your answer in the form of a short proof or a counter-example, whichever is appropriate. $\quad (10)$

Ques 2.

The set $\{x \in \mathbf{R} : x^2 - 3x + 2 = 0\}$ is an infinite set.

Ques 3.

The greatest interger function is continuous on $\mathbf{R}$ .

Ques 4.

) $\frac{d}{dx} \left[ \int_{3}^{e^x} \ln t \, dt \right] = x e^x - \ln 3$ .

Ques 5.

Every integrable function is monotonic.

Ques 6.

$a \oplus b = \sqrt{a + b}$ defines a binary operation on $\mathbf{Q}$ , the set of rational numbers.

Ques 7.

Find the domain of the function f given by $f(x) = \sqrt{\frac{2 - x}{x^2 + 1}}$ .

Ques 8.

The set $\mathbf{R}$ of real numbers with the usual addition (+) and usual multiplication $(\cdot)$ is given. Define (*) on $\mathbf{R}$ as:

$$a <em> b = \frac{a + b}{2}, \forall a, b \in \mathbf{R}.$
Is () associative in $\mathbf{R}$ ? Is $(\cdot)$ distributive over (*) in $\mathbf{R}$ ? Check.

Ques 9.

If $|z - 1 + 2i| = 4$ , show that the point z + i describes a circle. Also draw this circle.

Ques 10.

) Express $\frac{x - 1}{x^3 - x^2 - 2x}$ as a sum of partial fractions.

Ques 11.

Find the least value of $a^2 \sec^2 x + b^2 \csc^2 x$ , where a > 0, b > 0.

Ques 12.

Evaluate:

$$\int \frac{x^2 \cot^{-1}(x^3)}{1 + x^6} dx$

Ques 13.

For any two sets S and T, show that:

$$S \cup T = (S - T) \cup (S \cap T) \cup (T - S).$

Depict this situation in the Venn diagram.

Ques 14.

) Let f and g be two functions defined on $\mathbf{R}$ by:

$$f(x) = x^3 - x^2 - 8x + 12$

and $g(x) = \begin{cases} \frac{f(x)}{x + 3}, & \text{when } x \neq -3 \\ \alpha, & \text{when } x = -3 \end{cases}$
i) Find the value of $\alpha$ for which g is continuous at $x = -3$ .
ii) Find all the roots of $f(x) = 0$ .

Ques 15.

Find the area between the curve $y^2(4 - x) = x^3$ and its asymptote parallel to y-axis.

Ques 16.

Find the area between the curve $y^2(4 - x) = x^3$ and its asymptote parallel to y-axis. If the revenue function is given by $\frac{dR}{dx} = 15 + 2x - x^2$ , x being the input, find the maximum revenue. Also find the revenue function R, if the initial revenue is 0.

Ques 17.

Trace the curve $y^2(x + 1) = x^2(3 - x)$ , clearly stating all the properties used for tracing it.

Ques 18.

Find the length of the cycloid $x = \alpha(\theta - \sin \theta), y = \alpha(1 - \cos \theta)$ and show that the line $\theta = \frac{2\pi}{3}$ divides it in the ratio 1 : 3.

Ques 19.

) Find the condition for the curves, $ax^2 + by^2 = 1$ and $a'x^2 + b'y^2 = 1$ intersecting orthogonally.

Ques 20.

If $y = e^{m \sin^{-1} x}$ , then show that $(1 - x^2)y_2 - xy_1 - m^2y = 0$ . Hence using Leibniz's formula, find the value of (1 - x²)y_n+2 - (2n + 1)xy_n+1.

Ques 21.

Find the largest subset of $\mathbf{R}$ on which the function $f : \mathbf{R} \to \mathbf{R}$ defined as:
$$f(x) = \begin{cases} 2x &, x > 5 \\ x + 5 &, 1 \leq x \leq 5 \\ |x| &, x < 1 \end{cases}$
is continuous.

Ques 22.

Solve the equation:

$$x^4 + 15x^3 + 70x^2 + 120x + 64 = 0$

given that its roots are in G.P.

Ques 23.

Evaluate:

$$\lim_{x \to 0} \frac{\tan x - \sin x}{x^3}$

Ques 24.

If $I_{m,n} = \int x^m (\log x)^n dx$ , show that:

$$(m+1)I_{m,n} = x^{m+1}(\log x)^n - n I_{m,n-1}.$
Hence find the value of $\int x^4 (\log x)^3 dx$ .

Ques 25.

Verigy Lagrange's mean value theorem for the function f defined by

$f(x) = 2x^2 - 7x - 10$ over [2, 5].

Ques 26.

. Which of the following statements are true or false? Give reasons for your answer in the form of a short proof or a counter-example, whichever is appropriate. $\quad (10)$

Ques 27.

The set $\{x \in \mathbf{R} : x^2 - 3x + 2 = 0\}$ is an infinite set.

Ques 28.

The greatest interger function is continuous on $\mathbf{R}$ .

Ques 29.

) $\frac{d}{dx} \left[ \int_{3}^{e^x} \ln t \, dt \right] = x e^x - \ln 3$ .

Ques 30.

Every integrable function is monotonic.

Ques 31.

$a \oplus b = \sqrt{a + b}$ defines a binary operation on $\mathbf{Q}$ , the set of rational numbers.

Ques 32.

Find the domain of the function f given by $f(x) = \sqrt{\frac{2 - x}{x^2 + 1}}$ .

Ques 33.

The set $\mathbf{R}$ of real numbers with the usual addition (+) and usual multiplication $(\cdot)$ is given. Define (*) on $\mathbf{R}$ as:

$$a <em> b = \frac{a + b}{2}, \forall a, b \in \mathbf{R}.$
Is () associative in $\mathbf{R}$ ? Is $(\cdot)$ distributive over (*) in $\mathbf{R}$ ? Check.

Ques 34.

If $|z - 1 + 2i| = 4$ , show that the point z + i describes a circle. Also draw this circle.

Ques 35.

) Express $\frac{x - 1}{x^3 - x^2 - 2x}$ as a sum of partial fractions.

Ques 36.

Find the least value of $a^2 \sec^2 x + b^2 \csc^2 x$ , where a > 0, b > 0.

Ques 37.

Evaluate:

$$\int \frac{x^2 \cot^{-1}(x^3)}{1 + x^6} dx$

Ques 38.

For any two sets S and T, show that:

$$S \cup T = (S - T) \cup (S \cap T) \cup (T - S).$

Depict this situation in the Venn diagram.

Ques 39.

) Let f and g be two functions defined on $\mathbf{R}$ by:

$$f(x) = x^3 - x^2 - 8x + 12$

Ques 40.

Find the area between the curve $y^2(4 - x) = x^3$ and its asymptote parallel to y-axis.

Ques 41.

Ques 42.

Trace the curve $y^2(x + 1) = x^2(3 - x)$ , clearly stating all the properties used for tracing it.

Ques 43.

Find the length of the cycloid $x = \alpha(\theta - \sin \theta), y = \alpha(1 - \cos \theta)$ and show that the line $\theta = \frac{2\pi}{3}$ divides it in the ratio 1 : 3.

Ques 44.

) Find the condition for the curves, $ax^2 + by^2 = 1$ and $a'x^2 + b'y^2 = 1$ intersecting orthogonally.

Ques 45.

If $y = e^{m \sin^{-1} x}$ , then show that $(1 - x^2)y_2 - xy_1 - m^2y = 0$ . Hence using Leibniz's formula, find the value of (1 - x²)y_n+2 - (2n + 1)xy_n+1.

Ques 46.

Ques 47.

Solve the equation:

$$x^4 + 15x^3 + 70x^2 + 120x + 64 = 0$

given that its roots are in G.P.

Ques 48.

Evaluate:

$$\lim_{x \to 0} \frac{\tan x - \sin x}{x^3}$

Ques 49.

If $I_{m,n} = \int x^m (\log x)^n dx$ , show that:

$$(m+1)I_{m,n} = x^{m+1}(\log x)^n - n I_{m,n-1}.$
Hence find the value of $\int x^4 (\log x)^3 dx$ .

Ques 50.

Verigy Lagrange's mean value theorem for the function f defined by

$f(x) = 2x^2 - 7x - 10$ over [2, 5].

~~Rs. 80~~
Rs. 41

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Course Name	Bachelor of Science
Course Code	BSCG
Programm	BACHELOR DEGREE PROGRAMMES Courses
Language	English

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IGNOU BMTC 131 SOLVED ASSIGNMENT

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