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Yes, candidates can apply online on the official website of IIFT Kakinada for admission. Aspirants need to pay an application fee, upload the specified documents and fill out the details to complete the application process. Below are the steps to apply at IIFT Kakinada:

Step 1: Visit the official website of IIFT Kakinada.

Step 2: Click on 'Apply Online' and register with the basic details.

Step 3: Login to fill out the application form and upload the documents.

Step 4: Pay the application fee and submit the form.

53. Let the four numbers is G.P. be a, ar, ar², ar³

Given, $a{r}^2-a=9$

$\Rightarrow$ $a\left(r^2-1\right)=9$ I

And $\Rightarrow$ $ar-a{r}^3=18$

$\Rightarrow$ $ar\left(1-r^2\right)=18$

$\Rightarrow$ $\left(-1\right)ar\left(x^2-1\right)=18$

$\Rightarrow$ $ar\left(x^2-1\right)=-18$ II

Dividing II by I we get,

$\frac{ar\left(r^2-1\right)}{a\left(r^2-1\right)}=\frac{-18}{9}$

r = 2

So, putting r = 2 in I we get ,

$\Rightarrow$ $a\left[{\left(-2\right)}^2-1\right]=9$

$\Rightarrow$ $a\left[4-1\right]=9$

$\Rightarrow$ $a\times 3=9$

$\Rightarrow$ $a\frac{9}{3}$

$\Rightarrow$ a = 3

$\therefore$ The four numbers are 3, 3´(-2), 3´(-2)², 3´(-2)³

$\Rightarrow$ 3, 6, 12, 24

Yes, AURO University admissions are currently open and ongoing for various courses. Interested students can visit the university's official website and apply for the course of choice by completing the admission process. Candidates are advised to apply early to avoid any last minute rush. For more details, students can connect with the admission team of the university.

The product of corresponding terms of the given sequence are

= $a*A+\left(ar\right)*AR+\left(a{r}^2\right)*A{R}^2+......\left(a{r}^{x?1}\right)\left(A{R}^{x?1}\right)$

= $aA+\left(aA\right)+\left(rR\right)+\left(aA\right)$ $......+\left(aA\right){\left(rR\right)}^{x?1}$

So, looking at the sequence forms a G.P.

(above the)

With common ratio = $\frac{\left(aA\right)\left(rR\right)}{\left(aA\right)}=rR$

51. The sum of product of corresponding terms of the given

Sequences = $\left(2\times 128\right)+\left(4\times 32\right)+\left(8\times 8\right)+\left(16\times 2\right)+\left(32\times \frac{1}{2}\right)$

= 256+128+69+32+16

The above is a G.P. of a = 256,  $r=\frac{128}{256}=\frac{1}{2}$< 1 and x = 5

Sum required = $\frac{256\left(1-{\left(\frac{1}{2}\right)}^5\right)}{1-\frac{1}{2}}$

= $\frac{256\left(1-\frac{1}{32}\right)}{\frac{2-1}{2}}$

= $\frac{256\times \left(\frac{32-1}{32}\right)}{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=256\times 2\times \frac{31}{32}=496$

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Yes, aspirants applying for admission also need to take care of the age requirement specified by the institute. Candidates should have been born on or after August 1, 2005 to apply at IIFT Kakinada. There is relaxation in the age requirement for candidates belonging to SC/ ST/ PwD categories. Aspirants belonging to these category should be born on or after August 1, 2000 to apply for admission. 

The Campbellsville University is one of the best universities for higher education in the United States. For Campbellsville admissions, international students must meet the English proficiency requirements as well as the entry requirements. International students can apply for both undergraduate and postgraduate programs via University Official Portal at the university. Campbellsville University takes admissions for international students on rolling basis. As a result, there is no hard deadline. However, international students are advised to apply early to ensure timely processing of admission application.

Yes, there are many private Photography colleges in Pune. SOme of them are mentioned below along with their tuition fees:

Disclaimer: This information is sourced from the official website and may vary.

50. The given sequence, 8, 88, 888, 8888, …., upto xterm is not a G.P. so we can such that it will be changed to a G.P. by the following .

Sum of x terms, s_x = 8+ 88+888+8888 ….upto x term

= $8\left[1+11+111+1111+......\right]$ upto x term

Multiplying the numerator and denumerator by 9 we get,

= $\frac{8}{9}\left[9+99+999+9999+.........\right]$ x terms

= $\frac{8}{9}\left[\left(10-1\right)+\left(10^2-1\right)+\left(10^3-1\right)+\left(10^4-1\right)+.....\right]$ upto x terms

= $\frac{8}{9}$ [(10 + 1010 + 103 +104 …….upto, x terms) (1 +1 + 1 + 1 …… upto, x terms)]

= $\frac{8}{9}\left[\frac{10\left(10^n-1\right)}{10-1}-1\times n\right]$

= $\frac{8}{9}\left[\frac{10\left(10^n-1\right)}{9}-n\right]$

= $\frac{80}{81}\left(10^n-1\right)-\frac{8}{9}n$

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There is no application fee for international students at Campbellsville University which contributes to it being a popular choice amongst international applicants.

Acceptance rate of Campbellsville University is 77% for international students which makes it bit competitive. This shows that out of every 100 students, 77 students secure employment. International students must meet admission requirements at Campbellsville. Students must submit required documents, proof of English proficiency test, competitive exam scores, etc.

The Campbellsville University accepts various English language tests such as IELTS, TOEFL, PTE, Duolingo, and more. International students whose native language is not English are required to submit proof of English Proficiency test at Campbellsville University. Furthermore, Campbellsville University minimum score requirements for the English proficiency test score are given below:

49. Let aand r be the first term and common ration of the G.P.

So,  $a_4=x$

$\Rightarrow$ $a{r}^3=x$ - I

And a₁₀ = y

$\Rightarrow$ $a{r}^9=y$ - II

Also a 16 = z

$a{r}^{15}=z$ - III

So,  $\frac{y}{x}=\frac{a{r}^9}{a{r}^3}=r^{9-3}=r^6$

and $\frac{z}{y}=\frac{a{r}^{15}}{a{r}^9}=r^{15-9}=r^6$

$?\frac{y}{x}=\frac{z}{y}$

$?$ x, y, z are in G.P

Yes,you are eligible to study B.Sc agri as the core subjects are biology and agriculture 

Also, physics is an core subject and you are eligible if you studies physics in +2.

If you have further queries feel free to connect:)

IIFT Kakinada does not offer direct admission. Aspirants have to first apply on the institute's website for admission. Aspirants must hold a valid score in IPMAT for a seat in the institute. Besides, candidates should also meet the eligibility requirements for admission. Once selected, aspirants need to report at the campus for document verification and fee payment.

48. Let a and r be the first term and common ratio.

Then, $\Rightarrow$ $a_1+a_2=-4$

$\Rightarrow$ $a+ar=-4$

$\Rightarrow$ $a\left(1+r\right)=-4$

$\Rightarrow$ a (1+ n) = 4

$\Rightarrow$ $a{r}^4=4a{r}^2$

$\Rightarrow$ r² = 4

$\Rightarrow$ r² =2²

$\Rightarrow$ r = ±2

When r =2

a (1+2)=-4

a 3 = -4

$a=\frac{-4}{3}$

So, the G.P. is a, ar, ar²,…………. $\Rightarrow$ $\frac{-4}{3},\frac{-4}{3}\times 2,\frac{-4}{3}{\left(2\right)}^2...........$

$\Rightarrow$ $\frac{-4}{3},\frac{-8}{3},\frac{-16}{3},.........$

When $r=-2$

$a=\left(1-2\right)=-4$

a = (-) = -4

a = 4

So, the reqd. by G.P. is a, ar, ar²…………. $\Rightarrow$ 4, 4 (-2), 4 (-2)², .

$\Rightarrow$ 4, 8, 16, .

47. Given, a= 729

$a_7=a{r}^6=64$

$\Rightarrow$ 729. r⁶ = 64

$\Rightarrow$ $r^6=\frac{64}{729}$

$\Rightarrow$ $r^6={\left(\frac{2}{3}\right)}^6$

$\Rightarrow$ $r=+\frac{2}{3}$ <1

When $r=\frac{2}{3}$

= $s_7=\frac{a\left(1-r^7\right)}{4-r}=\frac{729\left(1-{\left(\frac{2}{3}\right)}^7\right)}{1-\frac{2}{3}}=\frac{729\left[1-\frac{128}{2187}\right]}{\frac{3-2}{2}}$

= $729\times \frac{3}{1}\times \left[\frac{2187-128}{2187}\right]$

= $729\times \frac{3\times 2059}{2187}$

= 2059

When $r=\frac{2}{3}$

$s_7=\frac{a\left(1-r^7\right)}{1-r}=\frac{729\left[1-{\left(\frac{-2}{3}\right)}^7\right]}{1-\left(\frac{-2}{3}\right)}=\frac{729\left[1+\frac{128}{2187}\right]}{1+\frac{2}{3}}$

= $\frac{729\left[\frac{2187+128}{2187}\right]}{\frac{3+2}{3}}$

= $729\times \frac{3}{5}\times \left[\frac{2315}{2187}\right]$

= 463

(i) Due to inert pair effect Pb²⁺ is more stable than Pb⁴⁺. Whereas Sn⁴⁺ is more stable than Sn²⁺.
(ii) 3Ga⁺ —–> 2Ga + Ga³⁺
This is because Ga³⁺ is more stable than Ga⁺