IGNOU MTE 3 SOLVED ASSIGNMENT

MTE 3: Mathematical Methods

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Title Name	IGNOU MTE 3 SOLVED ASSIGNMENT
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	BACHELOR DEGREE PROGRAMMES
Course Code	BSC
Course Name	Bachelor in Science
Subject Code	MTE 3
Subject Name	Mathematical Methods
Year	2026
Session	-
Language	English Medium
Assignment Code	MTE 3/Assignment-1/2026
Product Description	Assignment of BSC (Bachelor in Science) 2026. Latest MTE 03 2026 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU BEGC-131 (BAG) 2025-26 Assignment is for January 2026 Session: 30th September, 2026 (for December 2025 Term End Exam). Semester Wise January 2025 Session: 30th March, 2026 (for June 2026 Term End Exam). July 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).
Format	Ready-to-Print PDF (.soft copy)

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MTE 3 2025 - English

Assignment

(To be done after studying all the blocks)

Course Code: MTE-03

Assignment Code: MTE-03/TMA/2025

Maximum Marks: 100

1. Which of the following statements are true or false? Give a short proof or a counter - example in support of your answer.

i) The mean of a binomial distribution, when n=6 and P(X=4) = P(X=2) is 3/2.

ii) Mean deviation is minimum about median.

iii) The domain of , 6x³ - 7Y³ + 4xy, where it is continuous is − ∞ < x < ∞ 0, < y < ∞,

iv) $int_{1}^{2}frac{1}{x^{4}}dx=frac{7}{23}.$

v)The CDF of any distribution satisfies $F(-infty)=0,quad F(infty)=1.$ and non-decreasing.

2.Find $lim_{x ightarrow 2}frac{x^{2}+6}{x-1}$

b) Differentiate sin xw.r.t. tanx.

3.a) For a given data, the mean and S.D. of 100 observations were obtained are 40 and 5.1 respectively. Later it was found that an observation was wrongly written as 50 instead of 40. Find the true mean and S.D.

b) If the p.d.f. of xis $f(x)=2x^{k},quad 0<x<1$ and zero elsewhere. Find kand S.D. of x.

4. Given x+y=6 find the least value of x² + y².

5.a) Evaluate $intfrac{(sin^{-1}x)^{2}}{sqrt{1-x^{2}}}dx.$

b) Find the equation of the plane through the intersection of the planes $x+2y+3z=4$ and $4x+3y+2z+1=0$ and passing through the origin.

6.a) How many times the combination of 4 heads and 3 tails will appear when 7 coins are tossed 1000 times?

b) The position vectors of four points A, B, C and D are $2hat{i}+4hat{k},quad 5hat{i}+3sqrt{3}hat{j}+4hat{k},$ $-2sqrt{3}hat{i}+hat{k},2hat{i}+hat{k}$ respectively. Show that AB is parallel to CD and CD $=frac{2}{3}AB.$

7.a) Solve (1-sin x tan y) dx + (cos x sec" y)dy=0.

b) Find the estimated value of y = 70 given the following data:

$ar{x}=67,quadar{y}=65,quadsigma_{x}=3.5,quadsigma_{y}=2.5,quad r=0.8$

8. For $f(x)= heta e^{- heta x},quad xge 0,quad heta>0,$ find the E(x) and V(x).

9. Calculate the correlation coefficient between X and Y for the following data:

$egin{array}{|c|c|}hline X&Y\hline 1&9\2&8\3&10\4&12\5&11\6&13\7&14\8&16\9&15\hlineend{array}$

a) Verify Euler's theorem for:

$f(x,y)=ax^{2}+2hxy+by^{2}$

b) The first and last term of a series are 4 and 76 respectively. The sum is given to be 1920. Find the number of terms in the series.

MTE 3 2026 - English

Assignment
(To be done after studying all the blocks)

Course Code: MTE-03
Assignment Code: MTE-03/TMA/2026
Maximum Marks: 100

1. Which of the following statements are true or false? Give a short proof or a counter-example in support of your answer.
i) The mean of a binomial distribution, when $n=6$ and $P(X=4) = P(X=2)$ is $\frac{3}{2}$ .

ii) Mean deviation is minimum about median.

iii) The domain of 6x³ - 7y³ + 4xy, where it is continuous is $-\infty < x < \infty, 0 < y < \infty$ .

iv) $\int_{1}^{2} \frac{1}{x^4} dx = \frac{7}{23}$ .

v) The CDF of any distribution satisfies $F(-\infty) = 0, F(\infty) = 1$ and non-decreasing.

2. a) Find $\lim_{x \to 2} \frac{x^2 + 6}{x - 1}$ .

b) Differentiate $\sin x$ w.r.t. $\tan x$ .

3. a) For a given data, the mean and S.D. of 100 observations were obtained are 40 and 5.1 respectively. Later it was found that an observation was wrongly written as 50 instead of 40. Find the true mean and S.D.

b) If the p.d.f. of x is $f(x) = 2x^k, 0 < x < 1$ and zero elsewhere. Find k and S.D. of x.

4. Given $x + y = 6$ , find the least value of x² + y².

5. a) Evaluate $\int \frac{(\sin^{-1} x)^2}{\sqrt{1 - x^2}} dx$ .

b) Find the equation of the plane through the intersection of the planes $x + 2y + 3z = 4$ and

$4x + 3y + 2z + 1 = 0$ and passing through the origin.

6. a) How many times the combination of 4 heads and 3 tails will appear when 7 coins are tossed 1000 times?

b) The position vectors of four points A, B, C and D are $2\hat{i} + 4\hat{k}$ , $5\hat{i} + 3\sqrt{3}\hat{j} + 4\hat{k}$ , $-2\sqrt{3}\hat{i} + \hat{k}$ , $2\hat{i} + \hat{k}$ respectively. Show that AB is parallel to CD and $CD = \frac{2}{3}AB$ .

7. a) Solve $(1 - \sin x \tan y)dx + (\cos x \sec^2 y)dy = 0$ .

b) Find the estimated value of $y = 70$ given the following data:

$\bar{x} = 67, \bar{y} = 65, \sigma_x = 3.5, \sigma_y = 2.5, r = 0.8$

8. For $f(x) = \theta e^{-\theta x}, x \geq 0, \theta > 0$ , find the E(x) and V(x).

9. Calculate the correlation coefficient between X and Y for the following data:

X	Y
1	9
2	8
3	10
4	12
5	11
6	13
7	14
8	16
9	15

10. a) Verify Euler’s theorem for:

$f(x, y) = ax^2 + 2hxy + by^2$

b) The first and last term of a series are 4 and 76 respectively. The sum is given to be 1920. Find the number of terms in the series.

MTE 3 2025 - Hindi

सत्रीय कार्य

(सभी ब्लॉकों का अध्ययन करने के बाद किया जाना है)

पाठ्यक्रम कोड: MTE-03

सत्रीय कार्य कोड: MTE-03/TMA/2025

अधिकतम अंक: 100

1. निम्नलिखित में से कौन-से कथन सत्य और कौन-से कथन असत्य हैं? अपने उत्तर के पक्ष संक्षिप्त उपपत्ति या प्रति-उदाहरण दीजिए :

i) n = 6 और P(X = 4) = P(X = 2) वाले द्विपद बंटन का माध्य 3/2 है।

ii) मध्याहृता मध्यिका के परितः न्यूनतम होता है।

iii) 6x³ -7y³ + 4xy का वह प्रांत, जहाँ यह सतत् है, - ∞ <x<∞,0<y<∞ है।

iv) $int_{1}^{2}frac{1}{x^{4}}dx=frac{7}{23}.$

v) F(x) का CDF F(-∞) = 0, F(x) = 1, x का एक अहासमान फलन, द्वारा परिभाषित है।

a) $lim_{x ightarrow 2}frac{x^2+6}{x-1}$ ज्ञात कीजिए।

b) sin x का tan x के सापेक्ष अवकलन ज्ञात कीजिए।

3. a) एक दिये गये आँकड़े के लिए 100 प्रेक्षणों का माध्य और S.D. क्रमशः 40 और 5.1 हैं। बाद में यह पाया गया कि एक प्रेक्षण गलती से 40 के बजाय 50 लिखा गया। सही माध्य और S.D ज्ञात कीजिए।

b) यदि x का p.d.f., f(x) = 2x^k,0<x<1 है, तो k का मान और x का S.D. ज्ञात कीजिए।

4. यदि x+y = 6 है, तो x² + y² का न्यूनतम मान ज्ञात कीजिए।

a) $intfrac{(sin^{-1}x)^2}{sqrt{1-x^2}}dx$ का मान ज्ञात कीजिए।

b) उस समतल की समीकरण ज्ञात कीजिए जो समतलों x+2y+3z = 4 और 4x+3y+2z+1=0 के प्रतिच्छेदन बिंदु से तथा मूल बिंदु से गुजरता है।

a) जब 7 सिक्कों को 1000 बार उछाला जाता है, तो 4 चित और 3 पट कितनी बार आयेंगे?

b) चार बिंदुओं A, B, C और D के स्थिति सदिश क्रमशः 2 + 4k, 5i+3√3j+4k, - 2√3+ और 2i+k हैं। हैं। दर्शाइए कि AB, CD के समांतर है तथा CD =2/3 AB है।

a) हल कीजिए: (1-sin x tan y)dx+(cos x sec² y)dy = 0.

b) निम्नलिखित आँकड़ों से y = 70 का मान आकलित कीजिए :

$overline{x}=67,overline{y}=65,sigma_x=3.5,sigma_y=2.5,r=0.8$

8. Image ignouassignments-ignouacademy-com-ignou-mte-3-solved-assignment-html-p-assignment-93270 के लिए E(x) और V(x) ज्ञात कीजिए।

9. निम्नलिखित आँकड़ों से X और Y के बीच सहसंबंध गुणांक ज्ञात कीजिए :

10.

a) f(x, y) = ax² + 2hxy+by² के लिए आइलर प्रमेय सत्यापित कीजिए।

b) एक श्रेणी का पहला और आखरी पद क्रमशः 4 और 76 हैं। श्रेणी का योगफल 1920 है। श्रेणी के पदों की संख्या ज्ञात कीजिए।

MTE 3 2026 - Hindi

सत्रीय कार्य

(सभी ब्लॉकों का अध्ययन करने के बाद किया जाना है)

पाठ्यक्रम कोड: MTE-03

सत्रीय कार्य कोड : MTE-03/TMA/2026
अधिकतम अंक: 100

1. निम्नलिखित में से कौन-से कथन सत्य और कौन-से कथन असत्य हैं? अपने उत्तर के पक्ष संक्षिप्त उपपत्ति या प्रति-उदाहरण दीजिए :
i) $n = 6$ और $P(X = 4) = P(X = 2)$ वाले द्विपद बंटन का माध्य $\frac{3}{2}$ है।

ii) माध्य विचलन माध्यिका के परितः न्यूनतम होता है।

iii) 6x³ - 7y³ + 4xy का वह प्रांत, जहाँ यह सतत् है, $-\infty < x < \infty, 0 < y < \infty$ है।

iv) $\int_{1}^{2} \frac{1}{x^4} dx = \frac{7}{23}$ .

v) F(x) का CDF $F(-\infty) = 0, F(\infty) = 1, x$ का एक अहासमान फलन, द्वारा परिभाषित है।

2. a) $\lim_{x \to 2} \frac{x^2 + 6}{x - 1}$ ज्ञात कीजिए।

b) $\sin x$ का $\tan x$ के सापेक्ष अवकलन ज्ञात कीजिए।

3. a) एक दिये गये आँकड़े के लिए 100 प्रेक्षणों का माध्य और S.D. क्रमशः 40 और 5.1 हैं। बाद में यह पाया गया कि एक प्रेक्षण गलती से 40 के बजाय 50 लिखा गया। सही माध्य और S.D ज्ञात कीजिए।

b) यदि x का p.d.f., $f(x) = 2x^k, 0 < x < 1$ है, तो k का मान और x का S.D. ज्ञात कीजिए।

4. यदि $x + y = 6$ है, तो x² + y² का न्यूनतम मान ज्ञात कीजिए।

5. a) $\int \frac{(\sin^{-1}x)^2}{\sqrt{1 - x^2}} dx$ का मान ज्ञात कीजिए।

b) उस समतल की समीकरण ज्ञात कीजिए जो समतलों $x + 2y + 3z = 4$ और $4x + 3y + 2z + 1 = 0$ के प्रतिच्छेदन बिंदु से तथा मूल बिंदु से गुजरता है।

6. a) जब 7 सिक्कों को 1000 बार उछाला जाता है, तो 4 चित और 3 पट कितनी बार आयेंगे?

b) चार बिंदुओं A, B, C और D के स्थिति सदिश क्रमशः $2\hat{i} + 4\hat{k}$ , $5\hat{i} + 3\sqrt{3}\hat{j} + 4\hat{k}$ , $-2\sqrt{3}\hat{i} + \hat{k}$ और $2\hat{i} + \hat{k}$ हैं। दर्शाइए कि AB, CD के समांतर है तथा $CD = \frac{2}{3}AB$ है।

7. a) हल कीजिए : $(1 - \sin x \tan y)dx + (\cos x \sec^2 y)dy = 0$ .

b) निम्नलिखित आँकड़ों से $y = 70$ का मान आकलित कीजिए :

यहाँ आठवीं छवि में दिए गए पाठ का लिखित रूप है:

$$\bar{x} = 67, \bar{y} = 65, \sigma_x = 3.5, \sigma_y = 2.5, r = 0.8$ $

8. $f(x) = \theta e^{-\theta x}, x \geq 0, \theta > 0$ , के लिए E(x) और V(x) ज्ञात कीजिए।

9. निम्नलिखित आंकड़ों से X और Y के बीच सहसंबंध गुणांक ज्ञात कीजिए :

X	Y
1	9
2	8
3	10
4	12
5	11
6	13
7	14
8	16
9	15

10. a) $f(x, y) = ax^2 + 2hxy + by^2$ के लिए आइलर प्रमेय सत्यापित कीजिए।

b) एक श्रेणी का पहला और आखिरी पद क्रमशः 4 और 76 हैं। श्रेणी का योगफल 1920 है। श्रेणी के पदों की संख्या ज्ञात कीजिए।

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