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Yes, a law degree from NUS Law School is deemed acceptable by Indian authorities. NUS Law graduates are free to practice in India pending successful completion of the country's All India Bar Examination. 
 
The exam is conducted twice a year by the Bar Council of India in an open book format across 50 Indian cities & 140 exam centres.

When you apply for admission in any university with your DET score, the admission committee needs no verification. As Duolingo itself share the scorecard of your test directly to the university through its secure portal. This is to ensure authenticity and prevent tampering.

Yes, you can send your certified Duolingo English Test score report to as many universities as you wish. It is free of charge.

If you have not started your Duolingo English Test only then you can request for fee refund. Log in to your DET account and raise the refund request withtin 21 days of purchaging the test. Remember, after the DET test is started or the 21 days window passes, you can not ask for refund.

Yes, the National University of Singapore is ranked among the top 10 institutions in Singapore & Asia for its law programs by several prominent international ranking bodies. According to the data that is available on the institute's official website, the institute is ranked #1 in Asia and #8 in the world by QS World Rankings of 2025, solidifying its status as a global leader in higher education. 

${\left(2x^3+\frac{3}{x^k}\right)}^{12}$

gen term = 

${=}^{12}{C}_r{2}^{12-r}.3^r.x^{36-3r-rk}$  

For constant term

36 – 3r – rk = 0

$\Rightarrow k=\frac{36-3r}{r}$  

for r = 1, 2, 4   

Possible values of k = 3, 1

$\overrightarrow{a}=2\widehat{i}+\widehat{j}+3\widehat{k}$

$\begin{array}{l}\overrightarrow{b}=3\widehat{i}+3\widehat{j}+\widehat{k}\\ \overrightarrow{c}=c_1\widehat{i}+c_2\widehat{j}+c_3\widehat{k}\end{array}$

$Coplnanar\Rightarrow \left|\begin{array}{ccc}\hfill 2\hfill & \hfill 1\hfill & \hfill 3\hfill \\ \hfill 3\hfill & \hfill 3\hfill & \hfill 1\hfill \\ \hfill c_1\hfill & \hfill c_2\hfill & \hfill c_3\hfill \end{array}\right|=0$

$\begin{array}{l}\Rightarrow -8c_1+7c_2+12c_3=0........(i)\\ \overrightarrow{a}.\overrightarrow{c}=5\Rightarrow 2c_1+c_2+3c_3=5........(ii)\\ \overrightarrow{b}.\overrightarrow{c}=0\Rightarrow 3c_1+3c_2+c_3=0........(iii)\end{array}$

Solving (i), (ii), (iii)

$C_1=\frac{10}{122},c_2=\frac{-85}{122},c_3=\frac{225}{122}$

$\therefore 122\left(c_1+c_2+c_3\right)=150$

$e^{4x}+4e^{3x}-58e^{2x}+4e^x+1=0$

$\left(e^{2x}+\frac{1}{e^{2x}}\right)+4\left(e^x+\frac{1}{e^x}\right)-58=0$

$\Rightarrow {\left(e^x+\frac{1}{e^x}+2\right)}^2=64$

$e^x=\frac{6\pm \sqrt[]{32}}{2}=3\pm 2\sqrt[]{2}$

A = {1, 2, 3, ….50}

R₁ = (2, 1), (2, 2), (2, 4)…. (2, 32)

(3, 1) (3, 3) (3, 9) (3, 27)

(13, 1) (13, 13)   etc.

R₂ = { (2, 1), (2, 2), (3, 1), (3, 3), (5, 1), (5, 5), (7, 1), (7, 7), (1, 1), (11, 11)…}

$\therefore R_1-R_2$  contains only 9 elements.

Candidates appearing for their final year exam can apply for FPM at Jaipuria Institute of Management, Jaipur. If selected, such aspirants are provisionally admitted provided they complete all the requirements in obtaining their master's degree before September 30 of the year of admission. The admission of such aspirants remains provisional until they produce the marksheet proving their eligibility criteria. The deadline to submit the final year marksheet is December 31.

kindly consider the following Image 

Jaipuria Institute of Management conducts JFPMAT or Jaipuria Fellow Programme in Management Aptitude Test to shortlist candidates for FPM programme. The institute tests the knowledge of the candidates in the domain of Business and Management, General Awareness, Research Methodology, General and  Teaching Aptitude. Once the test results are out, selected candidates have to further pass the personal interview round for final admission.