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Department of Library and Information Science (SVU Mumbai) offers a full-time MLISc course. Candidates seeking admission to the course must apply through the common admission portal on the official SVU website. While applying, they must compulsorily pay an application fee of INR 250. It can be paid through the online payment gateway available on the website. The application fee is non-refundable. It must be noted that the mentioned application fee is sourced from the official website. It is still subject to change and hence, is indicative.

We have,

$=\left[\begin{array}{cc}\hfill 3(1+2k)+(-4k)\times 1\hfill & \hfill -4(1+2k)+(-4k)(-1)\hfill \\ \hfill 3k+1\times (1-2k)\hfill & \hfill -4\times k+(1-2k)(-1)\hfill \end{array}\right]$

$=\left[\begin{array}{cc}\hfill 3+6k-4k\hfill & \hfill -4-8k+4k\hfill \\ \hfill 3k+1-2k\hfill & \hfill -4k+2k-1\hfill \end{array}\right]=\left[\begin{array}{cc}\hfill 3+2k\hfill & \hfill -4-4k\hfill \\ \hfill 1+k\hfill & \hfill -1-2k\hfill \end{array}\right]$

$=\left[\begin{array}{cc}\hfill 1+2+2k\hfill & \hfill -4(1+k)\hfill \\ \hfill 1+k\hfill & \hfill 1-2-2x\hfill \end{array}\right]$

$=\left[\begin{array}{cc}\hfill 1+2\left(1+k\right)\hfill & \hfill -4(1+k)\hfill \\ \hfill 1+k\hfill & \hfill 1-2(1+k)\hfill \end{array}\right]$

The results also holds for n = k + 1. Hence, An $=\left[\begin{array}{cc}\hfill 1+2n\hfill & \hfill -4n\hfill \\ \hfill n\hfill & \hfill 1-2n\hfill \end{array}\right]$

Holds for all natural number n.

This is a multiple choice type question as classified in NCERT Exemplar

Correct option (ii)

On adding water to cement it gets harder over a period of time. This is known as setting of cement. Gypsum is added to the cement to slow the setting time of cement which occurs in the presence of water.

We have,

(E) P (n) : If A = $[$
$\begin{array}{l}\mathrm{}\\ \\ \end{array}<math><mfenced\; open="["\; close="]"\; separators="|"><mrow><mrow><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd></mtr></mtable></mrow></mrow></mfenced></math>$ ]. then Aⁿ = $\left[\begin{array}{l}{3}^{n-1}{3}^{n-1}{3}^{n-1}\\ 3^{n-1}{3}^{n-1}{3}^{n-1}\\ 3^{n-1}{3}^{n-1}{3}^{n-1}\end{array}\right]$ n ? N.

P (1) : A¹= $\left[\begin{array}{l}{3}^{1-1}{3}^{1-1}{3}^{1-1}\\ 3^{1-1}{3}^{1-1}{3}^{1-1}\\ 3^{1-1}{3}^{1-1}{3}^{1-1}\end{array}\right]$ = $\left[\begin{array}{l}{3}^0{3}^0{3}^0\\ 3^0{3}^0{3}^0\\ 3^0{3}^0{3}^0\end{array}\right]$ =$[$
$\begin{array}{l}\mathrm{}\\ \\ \end{array}<math><mfenced\; open="["\; close="]"\; separators="|"><mrow><mrow><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd></mtr></mtable></mrow></mrow></mfenced></math>$ ]

So, the result holds true for n = 1.

Let the result be for n = k. So,

P (k): A^u= $\left[\begin{array}{l}{3}^{k-1}{3}^{k-1}{3}^{k-1}\\ 3^{k-1}{3}^{k-1}{3}^{k-1}\\ 3^{k-1}{3}^{k-1}{3}^{k-1}\end{array}\right]$

Then P (k+1): A^{k + 1} = A^k. A = $\left[\begin{array}{l}{3}^{k-1}{3}^{k-1}{3}^{k-1}\\ 3^{k-1}{3}^{k-1}{3}^{k-1}\\ 3^{k-1}{3}^{k-1}{3}^{k-1}\end{array}\right]$ $[$
$\begin{array}{l}\mathrm{}\\ \\ \end{array}<math><mfenced\; open="["\; close="]"\; separators="|"><mrow><mrow><mtable><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd><mtd><mrow><mn>1</mn></mrow></mtd></mtr></mtable></mrow></mrow></mfenced></math>$ ]

= $\left[\begin{array}{ccc}\hfill 3^{k-1}+3^{k-1}+3^{k-1}\hfill & \hfill 3^{k-1}+3^{k-1}+3^{k-1}\hfill & \hfill 3^{k-1}+3^{k-1}+3^{k-1}\hfill \\ \hfill 3^{k-1}+3^{k-1}+3^{k-1}\hfill & \hfill 3^{k-1}+3^{k-1}+3^{k-1}\hfill & \hfill 3^{k-1}+3^{k-1}+3^{k-1}\hfill \\ \hfill 3^{k-1}+3^{k-1}+3^{k-1}\hfill & \hfill 3^{k-1}+3^{k-1}+3^{k-1}\hfill & \hfill 3^{k-1}+3^{k-1}+3^{k-1}\hfill \end{array}\right]$

= A^{k + 1} = $\left[\begin{array}{l}{3}^{\left(k+1\right)-1}{3}^{\left(k+1\right)-1}{3}^{\left(k+1\right)-1}\\ 3^{\left(k+1\right)-1}{3}^{\left(k+1\right)-1}{3}^{\left(k+1\right)-1}\\ 3^{\left(k+1\right)-1}{3}^{\left(k+1\right)-1}{3}^{\left(k+1\right)-1}\end{array}\right]$

The result holds for n = k + 1. Hence,

Aⁿ = $\left[\begin{array}{l}{3}^{n-1}{3}^{n-1}{3}^{n-1}\\ 3^{n-1}{3}^{n-1}{3}^{n-1}\\ 3^{n-1}{3}^{n-1}{3}^{n-1}\end{array}\right]$ holds for all natural number.

This is a multiple choice type question as classified in NCERT Exemplar

Correct option (i)

The alkali metals dissolve in liquid ammonia and give a blue solution, which is conductive in nature. A solution of sodium in liquid ammonia at −30^? C conducts electricity. The ammoniated electrons are responsible for the blue color of the solution as they absorb energy in the visible region of light and impart blue color to the solution.

The Ira A Fulton acceptance rate stands at 90%, which makes it selective but only to a limited extent. The Minnesota College of Science on the other hand, has an acceptance rate of 77%, which suggests the institute is fairly selective & shows a preference towards picking students with a solid academic background.

It can be inferred that Ira A Fulton is comparitively easier to secure admissions at than Minnesota College of Science, however, students are advised to maintain a solid academic background & satisfy these respective school's eligibility criteria to boost their chances of admissions.

To be eligible for the MSCAS BSc Electronics and Communication Science course, students must have passed the higher secondary examination with Mathematics, Physics, or Computer Science as a subject. Alternatively, students holding a Diploma in ECE, EEE, E&I, CSE, or Mechanical Engineering are also eligible to apply.

Matrices A and B will be inverse of each other if.

(E) AB = BA = I.

Here option D is correct.

The Placement Office conducts campus and off-campus interviews, organises industry-institute interaction meets, personality development programmes, industrial visits, and guest lectures. It also aims to establish an Entrepreneurship Development Center, facilitate corporate dialogues for MOUs, and organise alumni meets to support student career growth and networking opportunities.

This is a multiple choice type question as classified in NCERT Exemplar

Correct option (i)

Sodium carbonate is prepared by Solvay's process. In this process, ammonia is recovered when ammonium chloride reacts with calcium hydroxide. On reacting NH₄Cl with Ca (OH)₂ calcium chloride is obtained as a by-product. The reaction is given below.

2NH₄Cl+Ca (OH)₂→2NH₃+CaCl₂+H₂O

Maya Somaiya School of Music and Performing Arts MPA admissions are merit-based. The institute does not conduct any entrance exam for admission to MPA courses. Students are evaluated based on their past academic record. Other than this, students' performance in the audition test is also taken into consideration.

Admission to the BSc programme at Mohamed Sathak College of Arts and Science is primarily merit-based. Candidates are selected based on their academic performance in qualifying examinations, such as their higher secondary or equivalent results. The college may also consider reservation policies and eligibility criteria as per regulations. Generally, there is no separate entrance exam for BSc admissions, making the process straightforward and accessible for eligible students.

BSc graduates from MSCAS have diverse career options in the private and government sectors across various specialisations. For example, BSc Microbiology graduates can work as Industrial Microbiologists or Biomedical Scientists (INR 3–6 LPA), while BSc graduates may become Forest Range Officers (INR 4–9 LPA). Salary ranges vary by field and role, with government jobs often offering higher pay and stability.

This is a multiple choice type question as classified in NCERT Exemplar

Correct option (i)

Be (OH)₂ is amphoteric. It reacts with both acids and bases. It reacts with acid to form beryllium chloride and it reacts with base to form beryllate ion which is soluble in sodium hydroxide. The reaction is shown below.

Be (OH)₂+2OH⁻→ [Be (OH)₄]²⁻

Be (OH)₂+2HCl→BeCl₂+2H₂O

Let A = $\left[\begin{array}{ccc}\hfill 2\hfill & \hfill 0\hfill & \hfill -1\hfill \\ \hfill 5\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 3\hfill \end{array}\right]$

$\Rightarrow \left[\begin{array}{ccc}\hfill 1\hfill & \hfill 1\hfill & \hfill 2\hfill \\ \hfill 2\hfill & \hfill 0\hfill & \hfill -1\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 3\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill -2\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]$ A.

$\Rightarrow \left[\begin{array}{ccc}\hfill 1\hfill & \hfill 1\hfill & \hfill 2\hfill \\ \hfill 2-2(1)\hfill & \hfill 0-2(1)\hfill & \hfill -1-2(2)\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 3\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill -2\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 1-2(-2)\hfill & \hfill 0-2(1)\hfill & \hfill 0-2\left(0\right)\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]$ A. (R2      R2  ----> 2R1)

$\Rightarrow \left[\begin{array}{ccc}\hfill 1\hfill & \hfill 1\hfill & \hfill 2\hfill \\ \hfill 0\hfill & \hfill -2\hfill & \hfill -5\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 3\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill -2\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 5\hfill & \hfill -2\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]$ A.

$\Rightarrow \left[\begin{array}{ccc}\hfill 1\hfill & \hfill 1\hfill & \hfill 2\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 3\hfill \\ \hfill 0\hfill & \hfill -2\hfill & \hfill -5\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill -2\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \\ \hfill 5\hfill & \hfill -2\hfill & \hfill 0\hfill \end{array}\right]$ A. (R2  <-->R3)

$\Rightarrow \left[\begin{array}{ccc}\hfill 1\hfill & \hfill 1\hfill & \hfill 2\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 3\hfill \\ \hfill 0+2(0)\hfill & \hfill -2+2(1)\hfill & \hfill -5+2(3)\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill -2\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \\ \hfill 5+2(0)\hfill & \hfill -2+2(0)\hfill & \hfill 0+2(1)\hfill \end{array}\right]$ A. (R3 ->R3 + 2R2)

$\Rightarrow \left[\begin{array}{ccc}\hfill 1\hfill & \hfill 1\hfill & \hfill 2\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 3\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill -2\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \\ \hfill 5\hfill & \hfill -2\hfill & \hfill 2\hfill \end{array}\right]$ A.

$\Rightarrow \left[\begin{array}{ccc}\hfill 1-2(0)\hfill & \hfill 1-2(0)\hfill & \hfill 2-2(1)\hfill \\ \hfill 0-3(0)\hfill & \hfill 1-3(0)\hfill & \hfill 3-3(1)\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill -2-2(5)\hfill & \hfill 1-2(-2)\hfill & \hfill 0-2(2)\hfill \\ \hfill 0-3(5)\hfill & \hfill 0-3(-2)\hfill & \hfill 1-3(2)\hfill \\ \hfill 5\hfill & \hfill -2\hfill & \hfill 2\hfill \end{array}\right]$ A. $\left(\begin{array}{ll}{R}_1\to R_1-2R_3\hfill & R_2\to R_2-3R_3\hfill \end{array}\right)$

$\Rightarrow \left[\begin{array}{ccc}\hfill 1\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill -12\hfill & \hfill 5\hfill & \hfill -4\hfill \\ \hfill -15\hfill & \hfill 6\hfill & \hfill -5\hfill \\ \hfill 5\hfill & \hfill -2\hfill & \hfill 2\hfill \end{array}\right]$ A.

$\Rightarrow \left[\begin{array}{ccc}\hfill 1-0\hfill & \hfill 1-1\hfill & \hfill 0-0\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill -12-(+15)\hfill & \hfill 5-6\hfill & \hfill -4-(-5)\hfill \\ \hfill -15\hfill & \hfill 6\hfill & \hfill -5\hfill \\ \hfill 5\hfill & \hfill -2\hfill & \hfill 2\hfill \end{array}\right]$ A. (R1 --->R1 - R2).

$\Rightarrow \left[\begin{array}{ccc}\hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill 3\hfill & \hfill -1\hfill & \hfill 1\hfill \\ \hfill -15\hfill & \hfill 6\hfill & \hfill -5\hfill \\ \hfill 5\hfill & \hfill -2\hfill & \hfill 2\hfill \end{array}\right]$ A.

∴ A1 = $\left[\begin{array}{ccc}\hfill 3\hfill & \hfill -1\hfill & \hfill 1\hfill \\ \hfill -15\hfill & \hfill 6\hfill & \hfill -5\hfill \\ \hfill 5\hfill & \hfill -2\hfill & \hfill 2\hfill \end{array}\right]$

Students in the BSc programme at Mohamed Sathak College of Arts and Science study a range of core subjects such as Nutritional Biochemistry and its practical, Cell Biology with practical sessions, Biomolecules, and Biochemical Techniques. They also learn Clinical Biochemistry, Enzymes, Intermediary Metabolism, Molecular Biology, and Human Physiology, gaining both theoretical knowledge and hands-on laboratory experience.