Ask & Answer: India's Largest Education Community

Fortune.com lists OK State in USA Master's in Business Analytics and Data Science programme at No. 2 in 2025 in Best Master's in Data Science for 2025 rankings. Over the past four years, nearly 100% of this course's graduates have received full-time placement within 6 months of graduation. This is a STEM-based program. Students of this course get hands-on training with software and tools such as Azure, Data Bricks, GCP, Python, Snowflake, etc.

46. Given, ax + by2 = cos y.

Differentiating w r t ‘x’ we get,

$\frac{d}{dx}\left(ax+b{y}^2\right)=\frac{dx}{dx}cosy$

= a + b 2y = - sin y $\frac{dy}{dx}$ + sin y $\frac{dy}{dx}$ = -a

= $\frac{dy}{dx}=\frac{-9}{2by+siny}.$

= 2by $\frac{dy}{dx}$

Yes, there are several government MBA colleges in Gujarat where students can study in affordable tuition fees. Some of these colleges are listed below with their course fees:

Source: Official site and may vary.

Disclaimer: This info. is taken from the official website and may differ.

45. Given, 2x + 3y = sin y.

Differentiating w r t x. we get,

$\frac{d}{dx}(2x+3y)=\frac{d}{dx}siny$

$\Rightarrow 2+3\frac{dy}{dx}=cosy\frac{dy}{dx}$

=cos y $\frac{dy}{dx}-3\frac{dy}{dx}=2$

$\Rightarrow \frac{dy}{dx}(cosy-3)=2$

= $\frac{dy}{dx}=\frac{2}{cosy-3}$

44. Kindly go through the solution

To get a seat at MNLU Mumbai, candidate must have the rank as per the category and the course they want admission into. The MNLU Mumbai CLAT Cutoff 2026 for round 1 was released for admission to BA LLB (Hons) and LLM course. Students can find the category and course-wise MNLU Mumbai Cutoff 2026 in the table below: 

No, there is no upper age limit to apply for admission in BBA at St Anne's Degree College for Women, generally, students applying for BBA are in the age range of 17-25 but students older than that are not barred from applying for BBA admission in the institution.

The only criteria for St Anne's Degree College for Women BBA admission are a valid score in Class 12 and a minimum aggregate of 35% in Class 12 board exams. Candidates wanting to apply for St Anne's Degree College for Women BBA should make sure they fulfil the eligibility criteria before applying.

The courses offered at Somaiya School of Civilisation Studies are BA and MA. Candidates are requried to participate in the enhtrance-based admission process to secure a seat. BA is offered at the UG level as a four year course with a specialisation in Liberal Arts. Candidates get to participate in internships in the third and fourth year of the programme. MA is offered with a specialisation in Liberal Arts as well. 
 

43. The given f x ⁿ is

f(x) = 0 < $\left|x\right|$ < 3

At x = 1

L×H×L× = $\underset{h\to 0^{-}}{lim}\frac{f(1+h)-f\left(0\right)}{h}$

$=\underset{h\to 0^{-}}{lim}\frac{[1+h]-[1]}{h}$

$\underset{h\to \sigma }{lim}\frac{0-1}{h}$ $\left\{\begin{array}{ccc}\hfill ?h<0\hfill & \hfill ,1+h<1-1\hfill & \hfill So, [1+h]=0\hfill \end{array}\right\}$

$=\underset{h\to 0}{lim}\frac{-1}{h}=\infty$

Hence lines does not exist

Qf is not differentiable at x = 1

At x = 2

L×H×L = $\underset{h\to 0^{-}}{lim}\frac{f(2+h)-f(2)}{h}$ $\left\{\begin{array}{ccc}\hfill ?h<0\hfill & \hfill 2+h<2\hfill & \hfill 30,[2+h]=1\hfill \end{array}\right\}$

$=\underset{h\to 0^{-}}{lim}\frac{[2+h]-[2].}{h}$

$=\underset{h\to 0^{-}}{lim}\frac{1-2}{h}=\underset{h\to 0^{-}}{lim}\frac{-1}{h}$

Hence, limit does not exist.

Qf is not differentiable at x = 2

42. The given f x v is

f(x) = |x- 1|, x ε R

For a differentiable f x v f at x = c,

$\underset{h\to 0^{-}}{lim}\frac{f(c+h)-f(c)}{h}$ and $\underset{h\to 0^{+}}{lim}\frac{f(c+h)-f(c)}{h}$ are finite & equal.

So, at x = 1. f(1) = |1 - 1| = 0.

Now,

L×H×L× = $\underset{h\to 0^{-}}{lim}\frac{f(1+h-f(1)}{h}$

= $\underset{h\to 0^{-}}{lim}\frac{|1+h-1|-0.}{h}=\underset{h\to 0^{-}}{lim}-\frac{h}{h}$ $\left\{\begin{array}{l}\therefore h<0\\ \left|h\right|=-h\end{array}\right\}$

$=\underset{h\to {\sigma }^{-}}{lim}(-1)$

R×H×L = $\underset{h\to 0^{+}}{lim}\frac{f(1+h)-f(1)}{h}$ = - 1.

$=\underset{h\to 0^{+}}{lim}\frac{(1+h-1)-0}{h}=\underset{h\to 0^{+}}{lim}\frac{h}{h}=\underset{h\to 0^{+}}{lim}1$ $\left\{\begin{array}{cc}\hfill ?f_{n}h>0\hfill & \hfill \left|h\right|=h\hfill \end{array}\right\}$

= 1

Hence, L×H×S ¹ R×H×L×

So, f is not differentiable at x = 2.

41. L.H.S. = cos 4x.

= cos 2 (2x)

= 1 – 2 Sin² (2x) [ cos 2x = 1 – 2 Sin²x]

= 1 – 2 [2 sin xcosx]² [ sin 2x = 2 sin xcos x]

= 1 – 2 [4 sin²xcos²x]

= 1 – 8 sin²xcos²x

= R.H.S.

Candidates applying for St Anne's Degree College for Women BBA must appear for their Class 12 exam in their respective stream. The institute does not consider any other entrance exam for admission.

After clearing the exam, Candidates do not have to sit for further rounds of admission, as only the merit score of Class 12 is considered.

To get an MBA seat at Sambalpur University, students must follow the below-mentioned steps:

1. Visit the official website of SAMS.

2. After submitting the application, students are required to participate in the counselling process. This counselling process is conducted by the Higher Education Department of Odisha.

4. Students who are offered a seat must report to the allocated institute for verification of documents.

5. Lastly, pay the admission fee as prescribed by the university to confirm the seat.

40. $$L.H.S. = tan 4x

We know that,

$tan2=\frac{2tan}{1-ta{n}^2}.$ , we can write

$L.H.S=tan2(2x)=\frac{2tan2x}{1-ta{n}^{2}2x.}$

$=\frac{2\left(\frac{2tanx}{1-ta{n}^{2}x}\right)}{1-{\left(\frac{2tanx}{1-ta{n}^{2}x}\right)}^2}$

$=\frac{\frac{4tanx}{\left(1-ta{n}^{2}x\right)}}{\frac{{\left(1-ta{n}^{2}x\right)}^2-4ta{n}^{2}x}{{\left(1-ta{n}^{2}x\right)}^2}}$

$=\frac{4tanx\times \left(1-ta{n}^{2}x\right)}{1+ta{n}^{4}x-2ta{n}^{2}x-4ta{n}^{2}x}$

$=\frac{4tanx\left(1-ta{n}^{2}x\right)}{1-6ta{n}^{2}x+ta{n}^{4}x}$

= R.H.S.

Sambalpur University offers a good number of seats for MBA admissions. As per official sources, the university has 288 seats available for the MBA programme. These seats are further distributed among various colleges affiliated with the university.

Note: Students must note that the above-mentioned is as per official sources. However, it is subject to change at the discretion of concerned authorities.