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(a):Let, s be the speed of stream.

So, 8 + s = 2 (8 – s)

s = 8/3 mph

(a):Let G be (X, Y) then $X=\frac{\left\{3+5+(-3)\right\}}{3}=\frac{5}{3}$ $\frac{}{}\frac{}{}$

$Y=\frac{(7+5+2)}{3}=\frac{14}{3}$

$\Rightarrow Gis \left(\frac{5}{3},\frac{14}{3}\right)$

Yes, FIEM does offer a BTech course for the duration of four years, divided into eight semesters. Moreover, the college also offers lateral entries to the BTech course. To get admission into the BTech course, applicants must complete their Class 12 with a minimum aggregate of 45%. Additionally, for the selection process, the college accepts valid scores of WBJEE/JEE Mains. 

IIIT Lucknow MBA fees is INR 2.7 lakh and total fees may include other components. This amount is taken from the official sources and may change. For more info you can check the website.

9B + 3 + 5G + 4 = 200  9B + 5G = 193

The positive integer solutions are (B, G) = (2, 35) (7, 25) (12, 17) (17, 8)

Only one of the (B, G) gives G > B and 9B + 3 > 100, i.e. (B, G) = (12, 17)

17 – 12 = 5

Candidates seeking admission to various programme can enrol for admission with Class 12 marks. The college offers various courses such as BCA, BSc, MBA, etc. Candidates must complete Class 12 as the basic eligibility criteria for UG courses and graduation for PG courses.

(c) :As per the problem:

Average score of 20 candidate = 25 marks

Total score of 20 candidate = 500 marks

Let the score of the topper be x. Then,

$\frac{(500-x)}{19}=23$

500 – x = 437

x = 500 – 437 = 63 marks

Admission to the BCom programme at Prestige Institute of Management and Research (Deemed to be University), Indore is merit-based. Candidates are selected based on their performance in the Class 12 examination. No entrance exam is required, making it essential for applicants to secure strong academic scores in their qualifying exams to improve their chances.

To be eligible for the BCom course at Prestige Institute of Management and Research (Deemed to be University), Indore, candidates must have passed Class 12 in any stream from a recognised board with at least 50% aggregate marks. Admission is granted strictly based on merit in the Class 12 examination.

9B + 3 + 5G + 4 = 200  9B + 5G = 193

The positive integer solutions are (B, G) = (2, 35) (7, 25) (12, 17) (17, 8)

Only one of the (B, G) gives G > B and 9B + 3 > 100, i.e. (B, G) = (12, 17)

12 * 9 – 17 * 5 = 23

f (3n) – f (3n– 3) = n

n = 1

f (3) – f (0) = 1

f (0) = 0

n = 2

$\begin{array}{l}f\left(6\right)–f\left(3\right)=2\\ ?\text{?}??\end{array}$

f (3n) – f (3) = 2 + 3 + 4+…………….+ n

f (3n) = 1 + 2 + 3 +…………….+ n

= $n\frac{\left(n+1\right)}{2}$

$?$ f (1312) – f (3 × 311)

$\frac{3^{11}}{2}\left(3^{11}+1\right)=\frac{3^{22}+3^{11}}{2}$

Hence, remainder $\left[\frac{\frac{3^{22}+3^{11}}{2}}{10}\right]$ = 8

BCom programme at Prestige Institute of Management and Research (Deemed to be University), Indore has a standard duration of three years. However, under the New Education Policy (NEP), students have the option to extend their studies to four years to earn a BCom (Hons) degree, offering deeper specialisation and enhanced career prospects.

$1-log10_{10}5=\frac{1}{3}\left[log10_{10}\frac{x\times 5^{1/3}}{2}\right]$

3 [log101010 – log10105] = $log10_{10}\frac{x\times 5^{1/3}}{2}$

log101023 = $log10_{10}\frac{x\times 5^{1/3}}{2}$

23 = $\frac{x\times 5^{1/3}}{2}$

x = $\frac{2^4}{5^{1/3}}$

Hence, m + 3n = $4+3\times \frac{1}{3}$ = 5

Let the interest rate be r percent interest earned from 1.2 Lacs at the end of year

= 1,200,000 * r /100

= 1200r

From 1.8 lakh, = 8/12 * 1, 80,000 * 2r/100

= 2400r

Total interest = 3600r = 54000

r = 15 percent

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No. Since kinetic energy is a scalar quantity, it only depends on speed of the body and not the direction. So if the direction of the body is changed but the speed remains unchanged, there won't be any effect on the kinetic energy. However, if changing the direction also changes the speed of the body, then kinetic energy of the body will also change.

If you look closely at the formula of kinetic energy (1/2*m*v^2), the velocity is squared which automatically gives a positive integer. And mass of the body can never be a negative value, which leads to the result being a positive integer.