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D. Y. Patil College of Engineering and Technology provides good placements to its graduating students. The students are given excellent placement support every year placing them in top companies. Check out the table below to know the key highlights of the D. Y. Patil College of Engineering and Technology placement between 2022-2024:

D. Y. Patil College of Engineering and Technology placement is known for its excellent placement record. Check out the tabulated data given below to know more about D. Y. Patil College of Engineering and Technology placement between 2022-2024:

KMAT Kerala admit card 2026 released on February 16, 2206. KMAT Kerala hall ticket 2026 is available online for registered students. They can download their admit cards by using Application Number and Password.

The R V Institute of Technology and Management placement has been providing excellent placement packages to its students. Check out the table for the overall packages offered during the R V Institute of Technology and Management placement 2023-2025:

Note- The placement season is ongoing for 2025, hence the stats may vary once the final report gets released. 

90. Given, $a\left(\frac{1}{b}+\frac{1}{c}\right),b\left(\frac{1}{c}+\frac{1}{a}\right),c\left(\frac{1}{a}+\frac{1}{b}\right)$ are in A.P.

So, $\frac{a(c+b)}{bc},\frac{b(a+c)}{ac},\frac{c(b+a)}{ab}$ are in A.P.

$\Rightarrow \frac{ac+ab}{bc},\frac{ab+bc}{ac},\frac{bc+ac}{ab}$ are in A.P.

If we add 1 to all each terms of the sequence it will given be an A.P of common difference 1.

So, $\frac{ac+ab}{bc}+1,\frac{ab+bc}{ac}+1,\frac{bc+ac}{ab}+1$ are in A.P.

$\Rightarrow \frac{ac+ab+bc}{bc},\frac{ab+bc+ac}{ac},\frac{Bc+ac+ab}{ab}$ are in A.P.

Dividing add of the sum by ab + bc + ac will conserve.

then A.P so,

$\Rightarrow \frac{1}{bc},\frac{1}{ac},\frac{1}{ab}$ are in A.P.

Similarly multiplying each term by abc we get,

$\Rightarrow \frac{abc}{bc},\frac{abc}{ac},\frac{abc}{ab}$ are in A.P.

a, b, c, are in A.P.

Hence proved

R V Institute of Technology and Management provides excellent placements to its graduating BTech students and it is totally worth it. The highest package of INR 26.35 LPA is offered to its BTech CSE graduates in 2025.Check out the table below to know the key highlights of the R V Institute of Technology and Management placement for BTech in 2023-2024:

A cybersecurity engineer, sometimes referred to as an information security engineer, is an IT professional who works to protect organisations from cyber threats, data breaches, and malicious attacks. Cybersecurity engineers constantly assess the organisation's network security posture, identifying weaknesses and potential entry points for attackers.

SGT University has a total seat intake of 120 for the offered BTech programmes. Out of this, 25% of seats are reserved for students belonging to the state of Haryana. In addition, 10% of those are reserved for SC category candidates within Haryana. This reservation policy is based on Section 35 (3) of the Haryana Private Universities Act, 2006. The mentioned total seat count is as per the official website/ sanctioning body. It is still subject to revision and hence, is indicative.

The BTech course at R V Institute of Technology and Management is considered the best. In 2025, The R V Institute of Technology and Management offered the highest package of INR 26.35 LPA to its BTech CSE graduates. Check out the table below to know the key highlights of R V Institute of Technology and Management BTech placement in 2023-2024: 

R V Institute of Technology and Management provides good placements to its graduating BTech students. Check out the table below to know the R V Institute of Technology and Management placement for BTech in 2023-2024:

The BTech branch-wise the highest packages are out on the official website. Check out the BTech branch-wise the highest package offered at RVITM Bangalore during placements in 2024:

89. Let A and d be the first term & common difference of the A.P.

Then,

$ap=a\to A+(p-1)d=a$ ………I

$a_r=c\to A+(M-1)d=c$ …………III

So, L.H.S. $=(q-1)a+(n-p)b+(q-q)c$

$=(q-r)[A+(p-1)d]+(n-p)[A+(q-1)d]+(p-q)[A+(r-1)d]$

{putting value for I, II, III}

$\Rightarrow Aq+q(p-1)d-Ar-r(p-1)d+Ar+r\left(q-1\right)d-Ap-p\left(q-1\right)d$

$+Ap+p\left(r-1\right)d-Aq-q\left(r-1\right)d$

$\Rightarrow pqd-qd-rpd+rd+rqd-rd-pqd+pd+rpd-pd-rqd+qd$

$=0=$ R.H.S

R V Institute of Technology and Management provides good placements to its BTech graduating students. As of 2025, the highest package offered to BTech CSE stood at INR 26.35 LPA. Check out the table below to know the key highlights of the R V Institute of Technology and Management placement in 2023-2024:

Note- The placement season is ongoing for 2025, hence the stats will be updated once the final report gets published.

88. Let a and r be the first term & common ratio of the G.P.

So, S = a +ar + ar² +……… upto n terms.

$S=\frac{a\left(1-r^n\right)}{1-r}$

and P = a .ar. ar² ar . upton n terms.

$=a^n{r}^{1+2+3+\dots +(n-1)}$

$=a^{n}r\frac{(n-1)(n-1+1)}{2}$

$=a^{n}r\frac{n(n-1)}{2}$

And R = sum of reciprocal of n terms ( $\frac{1}{a}+\frac{1}{a{r}^n}+...........$ upto n terms)

$=\frac{\frac{1}{a}\left[{\left(\frac{1}{r}\right)}^n-1\right]}{\frac{1}{r}-1}$  As r <1

$\frac{1}{r}$ >1

$=\frac{\frac{1}{a}\left[\frac{1}{r^n}-1\right]}{\frac{1-r}{r}}=\frac{1}{a}\left[\frac{1-r^n}{r^n}\right]\times \frac{r}{1-r}$

$=\frac{1-r^n}{a{r}^n}\times \frac{r}{1-r}$

$=\frac{1-r^n}{a(1-r)r^{n-1}}$ …. III

Now, L.H.S. = P² Rⁿ

$={\left[a^{n}r\frac{n\left(n-1\right)}{2}\right]}^2·{\left[\frac{1-x^n}{a(1-n)r^{n-1}}\right]}^n$ { equation II & III}

$=a^{2n}\cdot r^{n(n-1)}\times \frac{{\left[1-r^n\right]}^n}{a^n(1-n){}^n}{r}^{n(n-1)}$

$=a^{2x-n}\times \frac{r^{n(x-1)}}{r^{n(n-1)}}\times \frac{{\left[1-x^n\right]}^n}{{(1-r)}^n}$

$=\frac{a^n{\left[1-r^n\right]}^n}{{(1-r)}^n}$

$={\left[\frac{a\left[1-r^n\right]}{(1-r)}\right]}^n$

$=S^n=$R.H.S { $?$ equation I}

A total 148 BTech students are placed in the R V Institute of Technology and Management placement in 2025 by the leading recruiters that took part in the placement drive. Refer to the table for more clarity:

Note- The placement season is ongoing for 2025, hence the stats may vary once the final report gets released. 

87. Here, $\frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}$

$\Rightarrow (a+bx)(b-cx)=(b+cx)(a-bx)$

$\Rightarrow ab-acx+b^{2}x-bc{x}^2=ab-b^{2}x+acx-bc{x}^2$

$\Rightarrow ab-ab-acx-acx=-b^{2}x-b^{2}x+bc{x}^2-bc{x}^2$

$\Rightarrow -2acx=-2b^{2}x$

$\Rightarrow ac=b^2$

$\Rightarrow \frac{c}{b}=\frac{b}{a}$ …………I

And $\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx}$

$\Rightarrow (b+cx)(c-dx)=(c+dx)(b-cx)$

$\Rightarrow bc-bdx+c^{2}x-cdx=bc-c^{2}x+bdx-cdx$

$\Rightarrow bc-bc+c^{2}x+c^{2}x=bdx+bdx-cdx+cdx$ $$

$\Rightarrow 2c^{2}x=2bdx$

$\Rightarrow c^2=bd$

$\Rightarrow \frac{c}{b}=\frac{d}{c}$ ……………II

From I and II

$\frac{a}{a}=\frac{c}{b}=\frac{d}{c}$

a, b, c and d are in G.P.