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Sewa Community College B.Tech

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This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e g i v e n p l a n e a r e \vec{r} . (2 \hat{i} - 3 \hat{j} + \hat{k}) = 1 a n d \vec{r} . (\hat{i} - \hat{j}) = 4 \\ H e r e, \vec{b_{1}} = 2 \hat{i} - 3 \hat{j} + \hat{k} a n d \vec{n_{2}} = \hat{i} - \hat{j} \\ S o, c o s θ = \frac{\vec{b_{1}} \vec{n_{2}}}{| \vec{b_{1}} | | \vec{n_{2}} |} \\ \Rightarrow c o s θ = \frac{(2 \hat{i} - 3 \hat{j} + \hat{k}) . (\hat{i} - \hat{j})}{\sqrt[]{4 + 9 + 1} \sqrt[]{1 + 1}} = \frac{2 + 3}{\sqrt[]{14} \sqrt[]{2}} = \frac{5}{\sqrt[]{28}} \\ ∴ θ = c o s^{- 1} (\frac{5}{\sqrt[]{28}}) w h i c h i s f a l s e . \\ H e n c e, t h e g i v e n s t a t e m e n t i s F a l s e . \end{array}$

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9 months ago

How can I take admission to Sewa Community College Thane BTech?

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Can I get into a college for UG courses with 400/1000 marks in CUET?

Contributor-Level 10

Candidates aspiring to take admission to BTech courses offered by Sewa Community College Thane must have completed Class 12 or a Diploma in a relevant subject. Those who satisfy this condition can apply for their preferred course by visiting the institute's official website.

After applying, the students whose applications are approved are required to pay the fees stated by the college. Once the fee payment is done, the college carries out the enrolment process of the student with the associated college.

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9 months ago

CUET Bachelors

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9 months ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

The angle between the line $\vec{r} = (5 \hat{i} + 3 \hat{j} + 7 \hat{k})$ + $λ (2 \hat{i} - \hat{j} + \hat{k})$ and the plane $\vec{r} = \hat{3 i} - 4 \hat{j} - 4 \hat{k}$ + 5 = 0 is $s i n^{- 1} (5 / 2 \sqrt 91)$ . .

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Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

Contributor-Level 10

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} E q u a t i o n o f l i n e i s \vec{r} = (5 \hat{i} - \hat{j} - 4 \hat{k}) + λ (2 \hat{i} - \hat{j} + \hat{k}) a n d t h e \\ e q u a t i o n o f p l a n e i s \vec{r} . (3 \hat{i} - 4 \hat{j} - \hat{k}) + 5 = 0 \\ H e r e, \vec{b_{1}} = 2 \hat{i} - \hat{j} + \hat{k} a n d \vec{n_{2}} = 3 \hat{i} - 4 \hat{j} - \hat{k} \\ ∴ s i n θ = \frac{\vec{b_{1}} \vec{n_{2}}}{| \vec{b_{1}} | | \vec{n_{2}} |} \\ \Rightarrow s i n θ = \frac{(2 \hat{i} - \hat{j} + \hat{k}) . (3 \hat{i} - 4 \hat{j} - \hat{k})}{\sqrt[]{4 + 4 + 1} \sqrt[]{9 + 16 + 1}} = \frac{6 + 4 - 1}{\sqrt[]{6} \sqrt[]{26}} = \frac{9}{\sqrt[]{6} \sqrt[]{26}} \\ \Rightarrow s i n θ = \frac{9}{2 \sqrt[]{39}} w h i c h i s f a l s e . \\ H e n c e, t h e g i v e n s t a t e m e n t i s F a l s e . \end{array}$

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9 months ago

The intercepts made by the plane $2 x - 3 y + 5 z + 4 = 0$ on the coordinate axis are $- 2, \frac{4}{3}, - \frac{4}{5}$ .

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Contributor-Level 10

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} E q u a t i o n o f t h e p l a n e i s 2 x - 3 y + 5 z + 4 = 0 \\ \Rightarrow 2 x - 3 y + 5 z = - 4 \\ \Rightarrow \frac{2}{- 4} x - \frac{3}{- 4} y + \frac{5}{- 4} z = 1 \\ \Rightarrow \frac{x}{- 2} - \frac{y}{4 / 3} + \frac{z}{- 4 / 5} = 1 \\ S o, t h e r e q u i r e d intercepts a r e - 2, \frac{4}{3} a n d \frac{- 4}{5} \\ H e n c e, t h e g i v e n s t a t e m e n t i s T r u e . \end{array}$

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9 months ago

Are there any government job opportunities after completing BTech from Sewa Community College Thane?

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Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

Contributor-Level 10

Yes, after doing a BTech course from Sewa Community College Thane, students can apply for jobs in the government sector. BTech graduates can seek out job opportunities in reputed government organisations, such as Indian Railways, ONGC, BHEL, ISRO, and others. Students who possess no prior experience are generally recruited for entry-level positions such as Research Assistant, Jr. Developer, Software Engineer, Quality Analyst, and such. Students can expect to start with a salary ranging from INR 4 to 6 LPA.

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9 months ago

The unit vector normal to the plane $x + 2 y + 3 z - 6 = 0$ is $1 / \sqrt 14 \hat{i} + 2 / \sqrt 14 \hat{j} + 3 / \sqrt 14 \hat{k} .$

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Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

Contributor-Level 10

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} G i v e n p l a n e i s x + 2 y + 3 z - 6 = 0 \\ V e c t o r n o r m a l t o t h e p l a n e \vec{n} = \hat{i} + 2 \hat{j} + 3 \hat{k} \\ ∴ \hat{n} = \frac{\vec{n}}{| \vec{n} |} = \frac{\hat{i} + 2 \hat{j} + 3 \hat{k}}{\sqrt[]{{(1)}^{2} + {(2)}^{2} + {(3)}^{2}}} = \frac{1}{\sqrt[]{14}} \hat{i} + \frac{2}{\sqrt[]{14}} \hat{j} + \frac{3}{\sqrt[]{14}} \hat{k} \\ H e n c e, t h e g i v e n s t a t e m e n t i s T r u e . \end{array}$

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9 months ago

The cartesian equation of the plane $\hat{\vec{r}} \cdot \hat{i} + \hat{j} + \hat{k} = 2$ is __________.

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Contributor-Level 10

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} G i v e n e q u a t i o n \vec{r} . (\hat{i} + \hat{j} - \hat{k}) = 2 \\ \Rightarrow (x \hat{i} + y \hat{j} + z \hat{k}) . (\hat{i} + \hat{j} - \hat{k}) = 2 \\ \Rightarrow x + y - z = 2 \\ H e n c e, t h e C a r t e s i a n e q u a t i o n o f t h e p l a n e i s x + y - z = 2 \end{array}$

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9 months ago

Does Sewa Community College Thane offer shcolarships to BTech students?

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Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

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Yes, Sewa Community College Thane does offer scholarships to students officially enrolled in any of the BTech courses offered. These scholarships work as a means for the college to reward meritorious students. Moreover, the institute offers these scholarships to students who have secured high scores in the qualifying examination and have a good academic record.

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9 months ago

The vector equation of the line through the points (3, 4, –7) and (1, –1, 6) is __________.

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University of Luxembourg Study Abroad

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This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} G i v e n points a r e (3, 4, - 7) a n d (1, - 1, 6) \\ H e r e, \vec{a} = 3 \hat{i} + 4 \hat{j} - 7 \hat{k} a n d \vec{b} = \hat{i} - \hat{j} + 6 \hat{k} \\ E q u a t i o n o f t h e l i n e i s \vec{r} = \vec{a} + λ (\vec{b} - \vec{a}) \\ \Rightarrow \vec{r} = (3 \hat{i} + 4 \hat{j} - 7 \hat{k}) + λ [(\hat{i} - \hat{j} + 6 \hat{k}) - (3 \hat{i} + 4 \hat{j} - 7 \hat{k})] \\ \Rightarrow \vec{r} = (3 \hat{i} + 4 \hat{j} - 7 \hat{k}) + λ (- 2 \hat{i} + - 5 \hat{j} + 13 \hat{k}) \\ \Rightarrow (x \hat{i} + y \hat{j} + z \hat{k}) = (3 \hat{i} + 4 \hat{j} - 7 \hat{k}) + λ (- 2 \hat{i} + - 5 \hat{j} + 13 \hat{k}) \\ \Rightarrow (x - 3) \hat{i} + (y - 4) \hat{j} + (z + 7) \hat{k} = λ (- 2 \hat{i} + - 5 \hat{j} + 13 \hat{k}) \\ H e n c e, t h e v e c t o r e q u a t i o n o f t h e l i n e i s \\ (x - 3) \hat{i} + (y - 4) \hat{j} + (z + 7) \hat{k} = λ (- 2 \hat{i} + - 5 \hat{j} + 13 \hat{k}) \end{array}$

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9 months ago

Does the University of Luxembourg offer Engineering courses?

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9 months ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

The vector equation of the line $\frac{x - 5}{3} = \frac{y + 4}{7} = \frac{z - 6}{2}$ is __________.

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Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

Contributor-Level 10

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e g i v e n e q u a t i o n i s \\ \frac{x - 5}{3} = \frac{y + 4}{7} = \frac{z - 6}{2} \\ H e r e, \vec{a} = (5 \hat{i} - 4 \hat{j} + 6 \hat{k}) a n d \vec{b} = (3 \hat{i} + 7 \hat{j} + 2 \hat{k}) \\ E q u a t i o n o f t h e l i n e i s \vec{r} = \vec{a} + \vec{b} λ \\ H e n c e, t h e v e c t o r e q u a t i o n o f t h e g i v e n l i n e i s \\ \vec{r} = (5 \hat{i} - 4 \hat{j} + 6 \hat{k}) + λ (3 \hat{i} + 7 \hat{j} + 2 \hat{k}) \end{array}$

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9 months ago

The direction cosines of the vector $(2 \hat{i} + 2 \hat{j} - \hat{k})$ are __________.

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Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

Contributor-Level 10

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} L e t \vec{a} = 2 \hat{i} + 2 \hat{j} - \hat{k} \\ d i r e c t i o n r a t i o s o f \vec{a} a r e 2, 2, - 1 \\ ∴ t h e d i r e c t i o n cosines a r e \frac{2}{\sqrt[]{4 + 4 + 1}}, \frac{2}{\sqrt[]{4 + 4 + 1}}, \frac{- 1}{\sqrt[]{4 + 4 + 1}} \\ \Rightarrow \frac{2}{3}, \frac{2}{3}, \frac{- 1}{3} \\ H e n c e, t h e d i r e c t i o n cosines o f t h e g i v e n v e c t o r a r e \frac{2}{3}, \frac{2}{3}, \frac{- 1}{3} . \end{array}$

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9 months ago

A plane passes through the points (2, 0, 0), (0, 3, 0), and (0, 0, 4). The equation of the plane is __________.

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Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

Contributor-Level 10

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l} G i v e n points a r e (2, 0, 0), (0, 3, 0) a n d (0, 0, 4) . \\ S o, t h e intercepts c u t s b y t h e p l a n e o n t h e a x e s a r e 2, 3, 4 \\ E q u a t i o n o f t h e p l a n e (intercept f o r m) i s \\ \frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1 \Rightarrow \frac{x}{2} + \frac{y}{3} + \frac{z}{4} = 1 \\ H e n c e, t h e e q u a t i o n o f t h e p l a n e i s \frac{x}{2} + \frac{y}{3} + \frac{z}{4} = 1 \end{array}$

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9 months ago

The plane $2 x - 3 y + 6 z - 11 = 0$ makes an angle $s i n^{- 1} (α)$ with the x-axis. The value of $α$ is equal to:

(A) $\frac{\sqrt[]{3}}{2}$

(B) $\frac{\sqrt[]{2}}{3}$

(C) $\frac{2}{7}$

(D) $\frac{3}{7}$

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Contributor-Level 10

This is a Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} D i r e c t i o n r a t i o s o f t h e n o r m a l t o t h e p l a n e 2 x - 3 y + 6 z - 11 = 0 a r e 2, - 3, 6 \\ D i r e c t i o n r a t i o s o f x - a x i s a r e 1, 0, 0 \\ ∴ a n g l e b e t w e e n p l a n e a n d t h e l i n e i s \\ ∴ s i n θ = \frac{2 (1) - 3 (0) + 6 (0)}{\sqrt[]{{(2)}^{2} + {(- 3)}^{2} + {(6)}^{2}} . \sqrt[]{{(1)}^{2} + {(0)}^{2} + {(0)}^{2}}} \\ \Rightarrow s i n θ = \frac{2}{\sqrt[]{4 + 9 + 36}} = \frac{2}{7} \\ H e n c e, t h e c o r r e c t o p t i o n i s (c) . \end{array}$

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9 months ago

Is fee an important factor while comparing the Sewa Community College Thane BTech course with other similar institutes?

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Contributor-Level 10

Yes, fees is one of the significant factors that students can take into account when comparing the BTech course offered by Sewa Community College Thane with other similar colleges. Drawing a comparison based on fees helps students calculate the affordability of a programme. The lower the fees, the greater the affordability. As per official sources, the total fees to pursue an BTech at the university range is INR 60,000.

Note: The above-mentioned fee is as per the official sources. However, it is indicative and subject to change.

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9 months ago

Does Sewa Community College Thane provide placement support to BTech students?

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Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

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Yes, at Sewa Community College Thane, students who are officially pursuing a BTech course are provided placement support. As per the official website of the college, 100% job placement assistance is offered to the students enrolled in this programme. Moreover, it is important to note that the college may have a placement policy that students may be required to adhere to.

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9 months ago

The locus represented by $x y + y z = 0$ is:

(A) A pair of perpendicular lines

(B) A pair of parallel lines

(C) A pair of parallel planes

(D) A pair of perpendicular planes

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Contributor-Level 10

This is a Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} G i v e n t h a t x y + y z = 0 \\ y . (x + z) = 0 \\ y = 0 o r x + z = 0 \\ H e r e, y = 0 i s o n e p l a n e a n d x + z = 0 i s a n o t h e r p l a n e . S o, i t i s a p a i r o f p e r p e n d i c u l a r p l a n e s . \\ H e n c e, t h e c o r r e c t o p t i o n i s (d) . \end{array}$

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9 months ago

What documents are required while reporting for BTech admissions at Sewa Community College Thane?

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Exemplar Solution Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

Contributor-Level 10

Document verification is an important part of the Sewa Community College Thane BTech admissions process. In this process, the students who are offered final admissions must report to the college along with the documents listed below:

Class 10 marksheet
Class 12 marksheet
Migration certificate
School leaving certificate/transfer certificate
Category certificate (if applicable)
Income certificate (applicable for candidates seeking admission via EWS category)

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9 months ago

The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, –1), C(4, 5, 0) and D(2, 6, 2), is equal to:

(A) 9 sq. units

(B) 18 sq. units

(C) 27 sq. units

(D) 81 sq. units

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