IGNOU MTE 3 SOLVED ASSIGNMENT HINDI

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IGNOU MTE 3 SOLVED ASSIGNMENT HINDI

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Rs. 41

IGNOU MTE 3 SOLVED ASSIGNMENT HINDI

~~Rs. 80~~
Rs. 41

Last Date of Submission of IGNOU MTE-03 (BSC) 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 MTE 3 SOLVED ASSIGNMENT HINDI
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-03/Assignmentt-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 MTE-03 (BSC) 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.

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।

Ques 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।

Ques 3.

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।

Ques 4.

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।

Ques 5.

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

Ques 6.

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

Ques 7.

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।

Ques 8.

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

Ques 9.

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।

Ques 10.

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

Ques 11.

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$ $

Ques 12.

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

Ques 13.

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

Ques 14.

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

Ques 15.

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

Ques 16.

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

Ques 17.

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.

Ques 18.

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

Ques 19.

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

Ques 20.

) 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.

Ques 21.

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

Ques 22.

) 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.

Ques 23.

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 $CD = \frac{2}{3}AB$ .

Ques 24.

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

Ques 25.

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

Ques 26.

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

Ques 27.

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.

Ques 28.

Ques 29.

a) $\lim_{x \to 2} \frac{x^2 + 6}{x - 1}$ ज्ञात कीजिए।
b) $\sin x$ का $\tan x$ के सापेक्ष अवकलन ज्ञात कीजिए।

Ques 30.

Ques 31.

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।

Ques 32.

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

Ques 33.

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

Ques 34.

Ques 35.

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

Ques 36.

Ques 37.

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

Ques 38.

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$ $

Ques 39.

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

Ques 40.

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

Ques 41.

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

Ques 42.

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

Ques 43.

Ques 44.

Ques 45.

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

Ques 46.

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

Ques 47.

Ques 48.

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

Ques 49.

) 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.

Ques 50.

Ques 51.

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

Ques 52.

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

Ques 53.

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

Ques 54.

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.

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Course Name	Bachelor in Science
Course Code	BSC
Programm	BACHELOR DEGREE PROGRAMMES Courses
Language	English

IGNOU MTE 3 Solved Assignment

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IGNOU MTE 3 SOLVED ASSIGNMENT HINDI

IGNOU MTE 3 SOLVED ASSIGNMENT HINDI

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