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11 months ago

National Institute of Pharmaceutical Education and Research, Hyderabad National Institute of Pharmaceutical Education and Research S.A.S. Nagar

What is the tuition fee for the MBA programme at NIPER Hyderabad?

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Himanshu Singh

Contributor-Level 10

The tuition fee for the MBA programme at NIPER Hyderabad is INR 4.1 lakh. In addition to tuition, the total cost includes other components like application fees, security deposit, hostel accommodation, and mess charges. Students are encouraged to check the official website for any updates, as the fee structure is subject to change.

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11 months ago

University Of The West Of England Study Abroad

Where do most UWE students live?

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Akash Gaur

Contributor-Level 10

Most UWE students are known to reside as part of the university maintained housing facilities across its campuses: Frenchay, City Campus & the Glenside campus.

Some students also opt to reside as part of off-campus facilities across City Centre, Redland & Clifton that are located at close distance to the university campus & offer an environment that is ideal for students, since many students enrolled in UK university are known to reside in these areas.

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11 months ago

National Institute of Pharmaceutical Education and Research, Hyderabad National Institute of Pharmaceutical Education and Research S.A.S. Nagar

What are the eligibility criteria for the MBA at NIPER Hyderabad?

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Himanshu Singh

Contributor-Level 10

To be eligible for the MBA programme at NIPER Hyderabad, candidates must hold a Bachelor's degree in Pharmacy or an equivalent discipline with at least 60% marks. Relaxations are provided for SC, ST, and PH categories. Additionally, applicants must qualify the NIPER JEE entrance exam and possess a valid GPAT or TGICET score.

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11 months ago

National Institute of Pharmaceutical Education and Research, Hyderabad National Institute of Pharmaceutical Education and Research S.A.S. Nagar

What is the duration of the MBA programme at NIPER Hyderabad?

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Himanshu Singh

Contributor-Level 10

MBA programme at NIPER Hyderabad is a two-year postgraduate course divided into four semesters. It is specifically designed to provide in-depth knowledge and training in pharmaceutical management. The curriculum blends academic learning with industry insights, preparing students for leadership roles in the pharmaceutical and healthcare sectors.

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11 months ago

Limits and Derivatives Maths

44. Find the derivative of the following functions from first principle:

(i) x (ii) (x)1 (iii) sin(x + 1) (iv) cos $(x - \frac{π}{8})$

Find the derivative of the following functions (it is to be understood that a, b, c, d,

p, q, r and s are fixed non-zero constants and m and n are integers):

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alok kumar singh

Contributor-Level 10

44.

= \underset{h \to 0}{l i m} \frac{- x - h + x}{h}

= \underset{h \to 0}{l i m} \frac{- h}{h}

= \underset{h \to 0}{l i m} - 1

= - 1.

(ii) Given, f(x) = (-x)^-¹

by first principle,

f(x) $\underset{h \to 0}{l i m} \frac{[-] {(x + h)}^{- 1} - {(- x)}^{- 1}}{h}$

(iii) Given, f(x) = sin(x + 1)

By first principle,

f’(x) = $\underset{h \to 0}{l i m} \frac{f (x + h) - f (x)}{h}$

$= \underset{h \to 0}{l i m} \frac{s i n (x + h + 1) - s i n (x + 1)}{h}$

$= \underset{h \to 0}{l i m} \frac{2}{h} \cdot c o s (\frac{x + h + 1 + x + 1}{2}) \cdot s i n (\frac{x + h + 1 - (x + 1)}{2})$

$= \underset{h \to 0}{l i m} \frac{2}{h} c o s (\frac{2 x + 2 + h}{2}) s i n (\frac{h}{2}) .$

$= \underset{h \to 0}{l i m} c o s (\frac{2 x + 2 + h}{2}) \underset{h \to 0}{l i m} \frac{s i n \frac{h}{2}}{\frac{h}{2}}$

$= c o s (\frac{2 x + 2 + 0}{2}) \times 1 .$

= cos (x + 1)

(iv) Given, f(x) = cos $(x - \frac{π}{8})$

By first principle,

f(x) = $\underset{h \to 0}{l i m} \frac{f (x + h) - f (x)}{h}$

$= \underset{h \to 0}{l i m} \frac{c o s (x + h - \frac{π}{8}) - c o s (x - \frac{π}{8})}{h}$

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11 months ago

Jaipur National University Colleges in Rajasthan

Is there any increasing ranking trend of BBA courses at Jaipur National University?

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Chanchal Gaurav

Contributor-Level 10

When it comes to BBA Course, Jaipur National University was at 69th position in 2023 and 2024 according to Outlook. Moreover, the course has backed the rank of 95 and 103 by India Today in the years 2023 & 2024, but as per the ranking of India Today, the ranking slipped from the 95 to 103 in the year 2024 showing a declining trend.

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11 months ago

Exam Odisha 12th Board Result

Please provide the latest information on results for Odisha CHSE.

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11 months ago

43. Find the derivative of the following functions:

(i) sin x cos x (ii) $s e c x$ (iii) 5 sec x + 4 cosx

(iv) $c o s e c x$ (v) 3cot x + 5 cosec x

(vi) $5 s i n x - 6 c o s x + 7$ (vii) $2 t a n x - 7 s e c x$

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alok kumar singh

Contributor-Level 10

. (i) f(x)=sin x cos x

So, $f^{?} (x) = \underset{h ? 0}{l i m} \frac{f (x + h) ? f (x)}{h}$

$= \underset{h ? 0}{l i m} \frac{s i n (x + h) c o s (x + h) ? s i n x c o s x}{h}$

$= \underset{h ? 0}{l i m} \frac{1}{2 h} * [2 s i n (x + h) c o s (x + h) ? 2 s i n x c o s x]$

$= \underset{h ? 0}{l i m} \frac{1}{2 h} [s i n 2 (x + h) ? s i n 2 x]$

$= \underset{h ? 0}{l i m} \frac{1}{2 h} [2 c o s \frac{2 (x + h) + 2 x}{2} s i n \frac{2 (x + h) ? 2 x}{2}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [c o s (2 x + h) s i n h]$

$= \underset{h ? 0}{l i m} c o s (2 x + h) * \underset{h ? 0}{l i m} \frac{s i n h}{h}$

$= c o s (2 x + 0)$

$= c o s 2 x$

$(ii) f (x) = s e c x$

So, $f^{?} (x) = \underset{h ? 0}{l i m} \frac{f (x + h) ? f (x)}{h}$

$= \underset{h ? 0}{l i m} \frac{1}{h} [s e c (x + h) ? s e c x]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{1}{c o s (x + h)} ? \frac{1}{c o s x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{c o s x ? c o s (x + h)}{c o s (x + h) c o s x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{? 2 s i n (\frac{x + x + h}{2}) s i n (\frac{x ? (x + h)}{2})}{c o s (x + h) c o s x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [? \frac{2 s i n (\frac{2 x + h}{2}) s i n (? h / 2)}{c o s (x + h) c o s x}]$

$= \underset{h ? 0}{l i m} \frac{(? 1 s i n (\frac{2 x + h}{2})}{c o s (x + h) c o s x} * \underset{h ? 0}{l i m} (? 1) \frac{s i n h / 2}{h / 2}$

$= \frac{s i n x}{c o s x ? c o s x} * 1$

$= t a n x ? s e c x .$

(iii) Given f(x)=5 sec x+4 cosx.

So, $f^{?} (x) = \underset{h ? 0}{l i m} \frac{f (x + h) ? f (x)}{h}$

$\begin{array}{l} = \underset{h ? 0}{l i m} \frac{5 s e c (x + h) + 4 c o s (x + h) ? [5 s e c x + 4 c o s x]}{h} . \end{array}$

$= \underset{h ? 0}{l i m} \frac{5}{h} [s e c (x + h) ? s e c x] + \underset{h ? 0}{l i m} \frac{4}{h} [c o s (x + h) ? c o s x]$

$= \underset{h ? 0}{l i m} \frac{5}{h} [\frac{1}{c o s (x + h)} ? \frac{1}{c o s x}] + \underset{h ? 0}{l i m} \frac{4}{h} [? 2 s i n (\frac{x + h + x}{2}) s i n (\frac{x + h ? x}{2})]$

$= \underset{h ? 0}{l i m} \frac{5}{h} [\frac{c o s x ? c o s (x + h)}{c o s (x + h) (c o s x)}] + \underset{h ? 0}{l i m} \frac{4}{h} [? 2 s i n (\frac{2 x + h}{2}) s i n \frac{h}{2}]$

$= \underset{h ? 0}{l i m} \frac{5}{h} [? \frac{2 s i n (\frac{2 x + h}{2}) s i n (? h / 2)}{c o s (x + h) c o s x}] ? 4 \underset{h ? 0}{l i m} s i n (\frac{2 x + h}{2}) \underset{h ? 0}{l i m} \frac{s i n h / 2}{h / 2}$

$= \frac{s i n (\frac{2 x + 0}{2})}{c o s (x + 0) c o s x} * 1 ? 4 s i n (\frac{2 x}{2})$

$= 5 \frac{s i n x}{c o s x} ? \frac{1}{c o s x} ? 4 s i n x$

$= 5 t a n x ? s e c x ? 4 s i n x$

$(iv) Given f (x) = c o s e c x$

$f^{?} (x) = \underset{h ? 0}{l i m} \frac{f (x + h) ? f (x)}{h}$

$= \underset{h ? 0}{l i m} \frac{1}{h} [c o s e c (x + h) ? c o s e c x]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{1}{s i n (x + h)} ? \frac{1}{s i n x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{s i n x ? s i n (x + h)}{s i n (x + h) s i n x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{2 c o s (\frac{x + x + h}{2}) s i n (\frac{x ? (x + h)}{2})]}{s i n (x + h) s i n x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{2 c o s (\frac{x + x + h}{2}) s i n (\frac{x ? (x + h)}{2})}{s i n (x + h) s i n x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{2 c o s (\frac{2 x + h}{2}) s i n (? h / 2)]}{s i n (x + h) s i n x}]$

$= \underset{h ? 0}{l i m} \frac{c o s (\frac{2 x + h}{2})}{s i n (x + h) s i n x} * \frac{(? 1) s i n (2)}{h / 2})$

$= \frac{c o s (\frac{2 x + 0}{2})}{s i n (x + 0) s i n x} * (? 1)$

$= ? \frac{c o s x}{s i n x} * \frac{1}{s i n x}$

$= ? c o t x ? c o s e c x$

(v) Given,f(x)=3 cot x+5cosecx.

So, $f^{?} (x) = \underset{h ? 0}{l i m} \frac{f (x + h) ? f (x)}{h}$ $= \frac{2}{c o s (x + 0) c o s x} * 1 + 7 s i n (\frac{2 x + 0}{2}) * (? 1)$

$= \underset{h ? 0}{l i m} 3 c o t (x + h) + 5 c o s e c (x + h) ? [3 c o t x + 5 c o s x)$

$_{h ? 0} \frac{3}{h} [c o t (x + h) ? c o t x] + \underset{h ? 0}{l i m}$

$= ? \frac{5}{h} [c o s e c (x + h) ? c o s e c x]$

$= \underset{h ? 0}{l i m} \frac{3}{h} [\frac{c o s (x + h)}{s i n (x + h)} ? \frac{c o s x}{s i n x}] + \underset{h ? 0}{l i m} \frac{5}{h} [\frac{1}{s i n (x + h)} ? \frac{1}{s i n x}]$

$= \underset{h ? 0}{l i m} \frac{3}{h} [\frac{c o s (x + h) s i n x ? c o s x s i n (x + h)}{s i n (x + h) s i n x}] + \underset{h ? 0}{l i m} \frac{5}{h} [\frac{s i n x ? s i n (x + h)}{s i n (x + h) s i n x}]$

$= \underset{h ? 0}{l i m} \frac{3}{h} [\frac{s i n (x ? (x + h))}{s i n (x + h) s i n x} + \underset{h ? 0}{l i m} \frac{5}{h} [\frac{2 c o s (\frac{x + x + h}{2}) s i n (\frac{x ? (x + h)}{2})}{s i n (x + h) s i n x}$

$= \underset{h ? 0}{l i m} \frac{3}{s i n (x + h) s i n x} * \underset{h ? 0}{l i m} (? 1) \frac{s i n h}{h} + \underset{h ? 0}{l i m} \frac{5}{h} [\frac{2 c o s (\frac{2 x + h}{2}) s i n (? h / 2)}{s i n (x + h) s i n x}$

$= \frac{3}{s i n x ? s i n x} * (? 1) + 5 l i m$

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New Question 11 months ago

B.Sc. Gokul Global University

Is Gokul Global University good for the BSc course?

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Anushka Bidhi Contributor-Level 10

The BSc course is offered to the students at Gokul Global University with a variety of specialisations to choose from. Students are most likely to find their interest of specialisation. The fee structure of the BSc course is yet again in the affordable range as compared to many other universities. Ultimately, the decision of choosing the university has to be taken by the students as per their requirement.

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New Question 11 months ago

Limits and Derivatives Maths

43. Find the derivative of the following functions: (i) sin x cos x

(ii) $s e c x$ (iii) 5 sec x + 4 cosx

(iv) $c o s e c x$ (v) 3cot x + 5 cosec x

(vi) $5 s i n x - 6 c o s x + 7$ (vii) $2 t a n x - 7 s e c x$

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alok kumar singh

Contributor-Level 10

(i) f(x)=sin x cos x