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The institute has not released its course wise data yet. However, NIRF Report for 2025 is out. According to the NIRF report 220 PG 2-year students were placed during Manonmaniam Sundaranar University placements. Refer to the table below to know more:

Note: The data provided above is taken from NIRF report 2024

It is mandatory to have 75% attendance to get the JKBOSE class 12 admit card for the examinations. However, you may submit a medical certificate in case you couldn't attend school due to illness or due to any other medical condition to get a waiver.

59. Let y = $\frac{e^x}{sinx}$

$\therefore \frac{dy}{dx}=\frac{sinx\frac{d{e}^x}{dx}-e^x\frac{d}{dx}sinx}{si{n}^{2}x}$

$=\frac{sinx{e}^x-e^{x}cosx}{si{n}^{2}x}$

$=e^x\frac{(sinx-cosx)}{si{n}^{-2}x.}$

For BA LLB (Hons) course, the CLAT 2026 Round 1 closing rank was 284 for NLU Kolkata and 310, for NLU Jodhpur. Based on these ranks, NLU Jodhpur is relatively easier for admissions when compared to NLU Kolkata. However, students can also compare the colleges based on other parameters, including tuition fees and NIRF ranking, to know which NLU would be a better choice. 

58. Kindly go through the solution

PGDAV College placement is known for its excellent placement record. In 2024, the highest package stood at INR 23 LPA. Check out the tabulated data given below to know more about PGDAV College placement in 2022:

Note- The college has not released the placement report for season 2023 as of yet. 

57. Kindly go through the solution

12. Let z = -i

Then $\overline{z}$ = i

And |z|² = (-1)² = 1

So, multiplicative inverse of –i is given by

z^-1 = $\frac{\overline{z}}{\left|z\right|}$ = $\frac{i}{1}$ = I = 0 + i1

56. Kindly go through the solution

11. Let Z = 4 – 3i

Then $\overline{z}$ = 4 + 3i

And, z|² = 4²+ (-3)²= 16 + 9 = 25

Hence, z^-1 = $\frac{\overline{z}}{{\left|z\right|}^2}$ = $\frac{4+3i}{25}$ = $\frac{4}{25}$ + $i\frac{3}{25}$

55. Kindly go through the solution

NLU Kolkata accepts the CLAT entrance exam for admission to its BA LLB (Hons) and BSc LLB (Hons) courses at the UG and LLM course at the PG level. NLU Kolkata CLAT cutoff 2026 for Round 1 was 284 for B.A. LL.B. (Hons.) and 550 for the BSc. LLB. (Hons.) in Criminology and Forensic in the General AI category. 

Similary, for the LLM course, the clat round 1 closing rank was 429.

Illinois Institute of Technology has 4 campuses. Main campus is Mies Campus which is in Bronzeville, Chicago and spans across 120 acres. The other campuses include Conviser Law Center, located in West Loop, Daniel F. and Ada L. Rice Campus, located in East Loop, Road Wheaton, and lastly Moffett Campus, located in  Bedford Park.

The Gandhigram Rural Institute has not released its course wise placement report yet. Once out it will be updated on this page. Meanwhile, students can have a look at the total number of PG 2-year students and the number of students placed during The Gandhigram Rural Institute placements:

10.${\left(-2-\frac{1}{3}i\right)}^3$

= ${\left[-\left(2+\frac{1}{3i}\right)\right]}^3$

= ${\left(-1\right)}^3\left[{\left(2+\frac{1}{3}i\right)}^3\right]$

= $(-8)\left[8+\frac{i^3}{27}+3.2.\frac{1}{3}i\left(2+\frac{i}{3}\right)\right]$ [since, (a + b)³ = a³ + b³ + 3ab(a + b)]

= (–1) $\left[8-\frac{i}{27}+(2i\times 2)+\left(2i\times \frac{i}{3}\right)\right]$ [since, i³ = i².i = –i and i² = –1]

= (–1) $\left[8-\frac{i}{27}+4i+\frac{2i^2}{3}\right]$

= (–1) $\left[8-\frac{2}{3}+i\left(4-\frac{1}{27}\right)\right]$

= $-\frac{22}{3}$ $–\frac{i107}{27}$