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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Ten Exemplar Solution

The points A(–2, 1), B(0, 5), C(–1, 2) are collinear.

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Vishal Baghel

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n a r e A (- 2, 1), B (0, 5), C (- 1, 2) \\ A r e a o f Δ A B C = \frac{1}{2} | \begin{matrix} - 2 & 1 & 1 \\ 0 & 5 & 1 \\ - 1 & 2 & 1 \end{matrix} | \\ = \frac{1}{2} | - 2 | \begin{matrix} 5 & 1 \\ 2 & 1 \end{matrix} | - 1 | \begin{matrix} 0 & 1 \\ - 1 & 1 \end{matrix} | + 1 | \begin{matrix} 0 & 5 \\ - 1 & 2 \end{matrix} | | \\ = \frac{1}{2} | - 2 (5 - 2) - 1 (0 + 1) + 1 (0 + 5) | \\ = \frac{1}{2} | - 2 \times 3 - 1 \times 1 + 1 \times 5 | = \frac{1}{2} | - 6 - 1 + 5 | = \frac{1}{2} | - 2 | = 1 s q . u n i t \\ S o, t h e g i v e n a r e n o t c o l l i n e a r . \\ S o, t h e g i v e n s t a t e m e n t i s F a l s e . \end{array}$

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9 months ago

Study Abroad France

What is the France student visa fee for international students?

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Akash Gaur

Contributor-Level 10

International students are required to submit processing fee of EUR 50-99 (INR 5.3 K-INR 10.6 K) based on country of origin.

French student visa fee for EEF procedure countries and territories is EUR 50 (INR 5.3 K), while same for other countries is EUR 99 or INR 10.6 K.

Student visa fee for Indian students is EUR 50 or INR 5.3 K.

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Ten Exemplar Solution

If the vertices of a triangle have integral coordinates, then the triangle cannot be equilateral.

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Vishal Baghel

Contributor-Level 10

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

Sol:

$\begin{array}{l} W e k n o w t h a t i f t h e v e r t i c e s o f t r i a n g l e h a s c o o r d i n a t e s, t h e n t h e t r i a n g l e c a n n o t b e \\ e q u i l a t e r a l . \\ S o, t h e g i v e n s t a t e m e n t i s T r u e . \end{array}$

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Ten Exemplar Solution

Locus of the midpoints of the portion of the line $x s i n θ + y c o s θ = p$ intercepted between the axes is ____.

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Vishal Baghel

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n e q u a t i o n o f t h e l i n e i s \\ x c o s θ + y s i n θ = p \dots (i) \\ L e t C (h, k) b e t h e m i d o f t h e g i v e n l i n e A B w h e r e i t m e e t s t h e t w o a x i s a t \\ A (a, 0) a n d B (0, b) . \\ (a, 0) l i e s o n e q n . (i) t h e n \\ a c o s θ + 0 = p \\ \Rightarrow a = \frac{p}{c o s θ} \dots (i i) \\ B (0, b) a l s o l i e s o n e q n . (i) t h e n \\ 0 + b s i n θ = p \\ \Rightarrow b = \frac{p}{s i n θ} \dots (i i i) \\ C (h, k) i s t h e m i d o f A B \\ ∴ h = \frac{0 + a}{2} \Rightarrow a = 2 h \\ a n d k = \frac{b + 0}{2} \Rightarrow b = 2 k \\ P u t t i n g t h e v a l u e s o f a a n d b i s e q n . (i i) a n d (i i i) w e g e t \\ 2 h = \frac{p}{c o s θ} \Rightarrow c o s θ = \frac{p}{2 h} \dots (i v) \\ a n d 2 k = \frac{p}{s i n θ} \Rightarrow s i n θ = \frac{p}{2 k} \dots (v) \\ S q u a r i n g a n d a d d i n g e q n . (i v) a n d (v) w e g e t \\ c o s^{2} θ + s i n^{2} θ = \frac{p^{2}}{4 h^{2}} + \frac{p^{2}}{4 k^{2}} \\ \Rightarrow 1 = \frac{p^{2}}{4 h^{2}} + \frac{p^{2}}{4 k^{2}} \\ S o, t h e l o c u s o f t h e m i d i s \\ 1 = \frac{p^{2}}{4 x^{2}} + \frac{p^{2}}{4 y^{2}} \\ \Rightarrow 4 x^{2} y^{2} = p^{2} (x^{2} + y^{2}) \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s 4 x^{2} y^{2} = p^{2} (x^{2} + y^{2}) . \end{array}$

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Ten Exemplar Solution

A point moves so that the square of its distance from the point (3, –2) is numerically equal to its distance from the line 5x – 12y = 3. The equation of its locus is ____.

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Vishal Baghel

Contributor-Level 10

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

Sol:

$\begin{array}{l} T h e g i v e n e q u a t i o n o f l i n e i s 5 x - 12 y = 3 a n d t h e g i v e n i s (3, - 2) . \\ L e t (a, b) b e a n y m o v i n g \\ ∴ b e t w e e n (a, b) a n d t h e (3, - 2) = \sqrt[]{{(a - 3)}^{2} + {(b + 2)}^{2}} \\ a n d t h e o f (a, b) f r o m t h e l i n e 5 x - 12 y = 3 \\ = | \frac{5 a - 12 b - 3}{\sqrt[]{25 + 144}} | = | \frac{5 a - 12 b - 3}{13} | \\ A c c o r d i n g t o t h e q u e s t i o n, w e h a v e \\ {[\sqrt[]{{(a - 3)}^{2} + {(b + 2)}^{2}}]}^{2} = | \frac{5 a - 12 b - 3}{13} | \\ T a k i n g n u m e r i c a l v a l u e s, w e h a v e \\ {(a - 3)}^{2} + {(b + 2)}^{2} = \frac{5 a - 12 b - 3}{13} \\ \Rightarrow a^{2} - 6 a + 9 + b^{2} + 4 b + 4 = \frac{5 a - 12 b - 3}{13} \\ \Rightarrow a^{2} + b^{2} - 6 a + 4 b + 13 = \frac{5 a - 12 b - 3}{13} \\ \Rightarrow 13 a^{2} + 13 b^{2} - 78 a + 52 b + 169 = 5 a - 12 b - 3 \\ \Rightarrow 13 a^{2} + 13 b^{2} - 83 a + 64 b + 172 = 0 \\ S o, t h e l o c u s o f t h e i s 13 a^{2} + 13 b^{2} - 83 a + 64 b + 172 = 0 . \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s 13 a^{2} + 13 b^{2} - 83 a + 64 b + 172 = 0 . \end{array}$

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9 months ago

Nightingale Institute of Management Studies Colleges in West Bengal

Is admission to the MBA course at NIMS Institute of Management and Commerce merit-based or entrance-based?

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Himanshu Singh

Contributor-Level 10

Admission to the MBA course at NIMS Institute of Management and Commerce is merit-based. Candidates are selected based on their performance in the last qualifying examination, i.e., their bachelor's degree. No entrance exam is required, making academic performance the primary factor for selection.

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9 months ago

Pharmacy B.pharm

Is lateral entry available for the SRIHER BPharm course?

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Ms Shruti Gupta

Contributor-Level 10

Yes, Diploma holders in Pharmacy are eligible for lateral entry into the second year of the BPharm programme at SRIHER Chennai. The selection criteria for lateral entry students is the same as first year admissions. Lateral Entry students at SRIHER need to only pay the fees for the duration of their lateral entry course.

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Ten Exemplar Solution

The points (3, 4) and (2, –6) are situated on the ____ of the line 3x – 4y – 8 = 0.

0 Follower 3 Views

Vishal Baghel

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n l i n e i s 3 x - 4 y - 8 = 0 \dots (i) \\ a n d g i v e n t h e a r e (3, 4) a n d (2, - 6) . \\ F o r (3, 4), l i n e b e c o m e s = 3 (3) - 4 (4) - 8 \\ = 9 - 16 - 8 = 9 - 24 = - 15 < 0 \\ F o r (2, - 6), l i n e b e c o m e s = 3 (2) - 4 (- 6) - 8 \\ = 6 + 24 - 8 = 30 - 8 = 22 > 0 \\ S o, t h e (3, 4) a n d (2, - 6) a r e s i t u a t e d o n t h e o p p o s i t e s i d e s o f 3 x - 4 y - 8 = 0 . \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s o p p o s i t e . \end{array}$

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9 months ago

St. Joseph's College of Engineering Colleges in Chennai

How many offers were provided at St Joseph's College of Engineering?

0 Follower 2 Views

diksha soni

Contributor-Level 10

As of now, a total of 1,224 offers were provided during St Joseph's College of Engineering. Check the table below to know more about the number of offers provided to students:

Particulars	Placement Statistics (2023)	Placement Statistics (2024)	Placement Statistics (2025)
Average Package	1,848	1,350	1,224

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9 months ago

Nightingale Institute of Management Studies Colleges in Kolkata

What documents are required for MBA admission at NIMS Institute of Management and Commerce?

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Himanshu Singh

Contributor-Level 10

For MBA admission at NIMS Institute of Management and Commerce, applicants must upload essential documents such as Class 10 and 12 mark sheets, bachelor's degree mark sheets, passport-size photographs, and valid ID proof. All documents must be submitted in the correct format to successfully complete the online application process.

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Ten Exemplar Solution

Equations of the lines through the point (3, 2) and making an angle of 45° with the line x – 2y = 3 are ____.

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Vishal Baghel

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n l i n e i s x - 2 y = 3 a n d t h e i s (3, 2) \\ E q u a t i o n o f a l i n e t h r o u g h t h e (3, 2) i s \\ A n g l e b e t w e e n e q n . (i) a n d t h e g i v e n l i n e x - 2 y = 3 w h o s e s l o p e i s \frac{1}{2} \\ ∴ t a n θ = | \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} | \\ \Rightarrow t a n 4 5^{0} = | \frac{m - \frac{1}{2}}{1 + m \times \frac{1}{2}} | \\ \Rightarrow 1 = | \frac{m - \frac{1}{2}}{1 + \frac{m}{2}} | \Rightarrow \frac{m - \frac{1}{2}}{1 + \frac{m}{2}} = \pm 1 \\ T a k i n g (+) s i g n \\ \Rightarrow \frac{m - \frac{1}{2}}{1 + \frac{m}{2}} = 1 \Rightarrow m - \frac{1}{2} = 1 + \frac{m}{2} \\ \Rightarrow m - \frac{m}{2} = 1 + \frac{1}{2} \Rightarrow \frac{m}{2} = \frac{3}{2} \Rightarrow m = 3 \\ T a k i n g (-) s i g n \\ \Rightarrow \frac{m - \frac{1}{2}}{1 + \frac{m}{2}} = - 1 \Rightarrow m - \frac{1}{2} = - 1 - \frac{m}{2} \\ \Rightarrow m + \frac{m}{2} = - 1 + \frac{1}{2} \Rightarrow \frac{3 m}{2} = \frac{1}{2} \Rightarrow m = - \frac{1}{3} \\ S o, t h e r e q u i r e d e q u a t i o n s a r e, \\ W h e n m = 3, \\ y - 2 = 3 (x - 3) \\ \Rightarrow y - 2 = 3 x - 9 \\ \Rightarrow 3 x - y - 7 = 0 \\ W h e n m = - \frac{1}{3}, \\ y - 2 = - \frac{1}{3} (x - 3) \\ \Rightarrow 3 y - 6 = - x + 3 \\ \Rightarrow x + 3 y - 9 = 0 \\ H e n c e, t h e v a l u e o f t h e f i l l e r a r e 3 x - y - 7 = 0 a n d x + 3 y - 9 = 0 . \end{array}$

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9 months ago

St. Joseph's College of Engineering Colleges in Chennai

Does St Joseph's College of Engineering provide 100% placements?

0 Follower 8 Views

diksha soni

Contributor-Level 10

In 2025, St Joseph's College of Engineering recorded a 75% placement rate.However, St Joseph's College of Engineering provides good placement to its students. The data tabulated below provides St Joseph's College of Engineering placement highlights for 2025:

Particulars	Placement Statistics (2025)
the highest package	INR 47 LPA
Average package	INR 6 LPA
No. of Offers	1,224
No. of Companies Visited	312

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Ten Exemplar Solution

The line which cuts off equal intercepts from the axes and passes through the point (1, –2) is ____.

0 Follower 3 Views

Vishal Baghel

Contributor-Level 10

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

Sol:

$\begin{array}{l} I n t e r c e p t f o r m o f t h e l i n e i s \frac{x}{a} + \frac{y}{b} = 1 \dots (i) \\ G i v e n t h a t a = b \\ ∴ \frac{x}{a} + \frac{y}{a} = 1 \Rightarrow x + y = a \dots (i i) \\ I f t h e l i n e (i) p a s s e s t h r o u g h (1, - 2) w e g e t \\ 1 - 2 = a \Rightarrow a = - 1 \\ S o, t h e r e q u i r e d e q u a t i o n i s x + y = - 1 \Rightarrow x + y + 1 = 0 \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s x + y + 1 = 0 . \end{array}$

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9 months ago

Nightingale Institute of Management Studies Colleges in Kolkata

What is the final step of MBA admission at NIMS Institute of Management and Commerce?

0 Follower 2 Views

Himanshu Singh

Contributor-Level 10

The final step of MBA admission at NIMS Institute of Management and Commerce involves confirming your seat by paying the required admission fee of INR 2.8 Lacs - INR 5 Lakh. Candidates who are shortlisted based on merit and listed in the final merit list must complete this payment to secure their admission into the MBA programme.

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9 months ago

St. Joseph's College of Engineering Colleges in India

How are the MBA placements at St Joseph's College of Engineering?

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diksha soni

Contributor-Level 10

Course wise placements for St Joseph's College of Engineering has not been released yet. However, students can refer to the key highlights of the St Joseph's College of Engineering placement statistics given in the table below:

Particulars	Placement Statistics (2025)
the highest package	INR 47 LPA
Average package	INR 6 LPA
No. of Offers	1,224
No. of Companies Visited	312

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Ten Exemplar Solution

If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through ____.

0 Follower 3 Views

Vishal Baghel

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n e q u a t i o n i s a x + b y + c = 0 \dots (i) \\ a, b a n d c a r e i n A . P . \\ ∴ b = \frac{a + c}{2} \\ \Rightarrow a + c = 2 b \\ \Rightarrow a - 2 b + c = 0 \dots (i i) \\ C o m p a r i n g e q n . (i) w i t h e q n . (i i) w e g e t, \\ x = 1, y = - 2 \\ S o, t h e l i n e w i l l p a s s t h r o u g h (1, - 2) \\ H e n c e, t h e v a l u e o f t h e f i l l e r i s (1, - 2) . \end{array}$

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9 months ago

Pharmacy Tamil Nadu

What is the total fee for the BPharm programme at SRIHER Chennai?

0 Follower 2 Views

Ms Shruti Gupta

Contributor-Level 10

BPharm fees at SRIHER is paid annually. Students are required to pay INR 1.25 Lacs in the beginning of each academic year, bringing the total fee to approximately INR 5 Lacs over four years. Additional costs may be applied.

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9 months ago

Which companies generally recruit from ISB&M College of Commerce?

0 Follower 4 Views

Kartik Shekhar

Contributor-Level 10

ISB&M College of Commerce recruiters list include eClerx, Asian Paints, TCS, Wipro, American Express, etc. The placement record is strong.

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9 months ago

St. Joseph's College of Engineering Colleges in Chennai

How are the average packages at St Joseph's College of Engineering?

0 Follower 2 Views

diksha soni

Contributor-Level 10

St Joseph's College of Engineering provides good average packages to its students. Check out the table below which states the average packages recorded during the placement season in the recent years: