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The Gandhi Engineering College had 81 M.Tech students placed in 2024. The median salary for M.Tech placements at Gandhi Engineering College in 2024 was INR 5.2 LPA. These stats are collated from the NIRF data released for the Engineering branch. Check out the table for reference:

A total of 52 BDS students were placed in 2025. Refer to the table below to know more:

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Lety=ta{n}^{-1}\left(secx+tanx\right)\\ Differentiatingbothsidesw.r.t.x\\ \frac{dy}{dx}=\frac{d}{dx}\left[ta{n}^{-1}\left(secx+tanx\right)\right]\\ =\frac{1}{1+{\left(secx+tanx\right)}^2}.\frac{d}{dx}\left(secx+tanx\right)\\ =\frac{1}{1+se{c}^{2}x+ta{n}^{2}x+2secxtanx}.\left(secxtanx+se{c}^{2}x\right)\\ =\frac{1}{\left(1+ta{n}^{2}x\right)+se{c}^{2}x+2secxtanx}.secx\left(tanx+secx\right)\\ =\frac{1}{se{c}^{2}x+se{c}^{2}x+2secxtanx}.secx\left(tanx+secx\right)\\ =\frac{1}{2se{c}^{2}x+2secxtanx}.secx\left(tanx+secx\right)\\ =\frac{1}{2secx\left(secx+tanx\right)}.secx\left(tanx+secx\right)=\frac{1}{2}\\ Hence,\frac{dy}{dx}=\frac{1}{2}\end{array}$

This is a multiple choice answer as classified in NCERT Exemplar

(d) When the earth is the closest to the sun, speed of the earth is maximum, hence KE is maximum. When the earth is the farthest from the sun speed is minimum hence, KE is minimum but never zero and negative.

This variation is correctly represented by option d

The median salary for BTech placements at Gandhi Engineering College in 2024 was INR 5.3 LPA. These stats are collated from the NIRF data released for the Engineering branch. Check out the table for reference:

The average package offered at King George Medical College BDS placements is not out yet. However, the median package for BDS stood at INR 9 LPA. The table below presents the same:

The Gandhi Engineering College had 665 BTech students placed in 2024. The median salary for BTech placements at Gandhi Engineering College in 2024 was INR 5.3 LPA. These stats are collated from the NIRF data released for the Engineering branch. Check out the table for reference:

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

Are BDS placements good at King George Medical College?

The key highlights recorded during King George Medical College BDS Placements are given in the data tabulated below:

This is a multiple choice answer as classified in NCERT Exemplar

(b) Power =constant

P+dw/dt=fds/dt

Fds=fdscos0

P=fds/dt=constant

Fv=constant

[MLT^-2] [LT^-1]= constant

[L²T^-3]= constant

L $\propto T$ ^3/2

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This is a multiple choice answer as classified in NCERT Exemplar

(b) v=ax^3/2

m=0.5kg, a= 5m/s²

a= dv/dt= vdv/dt= ax^3/2d/dx (ax^3/2)

= ax^3/2a $\times \frac{3}{2}\times$ x^1/2= 3/2a²x²

Force = ma= m $\frac{3}{2}$ a²x²

Work done = ${\int }_0^{2}fdx={\int }_0^3\frac{3}{2}m{a}^2{x}^2$ dx

= $\frac{3}{2}$ ma² (x³/3)₀²

= $\frac{1}{2}m{a}^2\times 8=\frac{1}{2}\times \left(0.5\right)\times 25\times 8$ =50J

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

The institution has not released the overall average package. The median package offered at King George Medical College placement in 2024 are tabulated below:

The institution has not released the course-wise placement packages as of yet. Meanwhile the NIRF report has been released. Check out the table below to know more:

NOTE: The above data is obtained from the NIRF report 2025.

The average salary package for placements at King George Medical College has not yet been disclosed. However, the median salary package has been published. Please refer to the table below for the median packages recorded in recent years.

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Lety={\left(x+1\right)}^2{\left(x+2\right)}^3{\left(x+3\right)}^4\\ Takinglogonbothsides,\\ logy=log\left[{\left(x+1\right)}^2.{\left(x+2\right)}^3.{\left(x+3\right)}^4\right]\\ \Rightarrow logy=log{\left(x+1\right)}^2+log{\left(x+2\right)}^3+log{\left(x+3\right)}^4\left[?logxy=logx+logy\right]\\ \Rightarrow logy=2log\left(x+1\right)+3log\left(x+2\right)+4log\left(x+3\right)\left[?log{x}^y=ylogx\right]\\ Differentiatingbothsidesw.r.t.x\\ \frac{1}{y}.\frac{dy}{dx}=2.\frac{d}{dx}log\left(x+1\right)+3.\frac{d}{dx}log\left(x+2\right)+4.\frac{d}{dx}log\left(x+3\right)\\ \frac{1}{y}.\frac{dy}{dx}=2.\frac{1}{x+1}+3.\frac{1}{x+2}+4.\frac{1}{x+3}\\ \frac{dy}{dx}=y\left[\frac{2}{x+1}+\frac{3}{x+2}+\frac{4}{x+3}\right]\\ ={\left(x+1\right)}^2{\left(x+2\right)}^3{\left(x+3\right)}^4\left[\frac{2}{x+1}+\frac{3}{x+2}+\frac{4}{x+3}\right]\\ ={\left(x+1\right)}^2{\left(x+2\right)}^3{\left(x+3\right)}^4\left[\frac{2\left(x+2\right)\left(x+3\right)+3\left(x+1\right)\left(x+3\right)+4\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}\right]\\ =\left(x+1\right){\left(x+2\right)}^2{\left(x+3\right)}^3\left[2x^2+10x+12+3x^2+12x+9+4x^2+12x+8\right]\\ =\left(x+1\right){\left(x+2\right)}^2{\left(x+3\right)}^3\left[9x^2+34x+29\right]\\ Hence,\frac{dy}{dx}=\left(x+1\right){\left(x+2\right)}^2{\left(x+3\right)}^3\left[9x^2+34x+29\right]\end{array}$

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• Mastercard
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