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This is a multiple choice answer as classified in NCERT Exemplar

(b) When two bodies of equal masses collides elastically, their velocities are interchanged.

When ball 1 collides with ball 2 then velocity of ball1, v₁ becomes zero and velocity of ball 2, v₂ becomes v.

V₁=0, V₂=v

When ball 2 collides will ball 3 v₂ =0, v₃=v

Yes, Gandhi Engineering College has an impressive placement record. The table below provides the placement data for the past three years as per the NIRF Report 2025:

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

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The Gandhi Engineering College provides good placements to its graduating students. Check out the table below to know the key highlights of the Gandhi Engineering College placements in 2024:

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

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

Sol:

$\begin{array}{l}Lety=si{n}^{m}xco{s}^{n}x\\ Differentiatingbothsidesw.r.t.x\\ \frac{dy}{dx}=\frac{d}{dx}\left(si{n}^{m}xco{s}^{n}x\right)\\ =si{n}^{m}x.\frac{d}{dx}\left(co{s}^{n}x\right)+co{s}^{n}x.\frac{d}{dx}\left(si{n}^{m}x\right)\\ =si{n}^{m}x.n.co{s}^{n-1}x\frac{d}{dx}\left(cosx\right)+co{s}^{n}x.m.si{n}^{m-1}x\frac{d}{dx}\left(sinx\right)\\ =n.si{n}^{m}x.co{s}^{n-1}x.\left(-sinx\right)+m.co{s}^{n}x.si{n}^{m-1}x.cosx\\ =-n.si{n}^{m+1}x.co{s}^{n-1}x+m.co{s}^{n+1}x.si{n}^{m-1}x\\ =si{n}^{m}x.co{s}^{n}x\left[-n\frac{sinx}{cosx}+m.\frac{cosx}{sinx}\right]\\ Hence,\frac{dy}{dx}=si{n}^{m}x.co{s}^{n}x\left[-ntanx+m.cotx\right]\end{array}$

This is a multiple choice answer as classified in NCERT Exemplar

(b) Total energy is E=KE+PE……………1

When particle is at x =x_m i.e at extreme position, returns back. Hence at x=x_m and x=0 KE=0

From eqn1

E= PE+0 = PE= V (x_m)=1/2kx_m²

Tritya Institute of Event Management is one of the top leading event management institute. TIEM offers a comprehensive and innovative curriculum designed to equip students with the necessary skills and knowledge for a successful career in event management. The institute is recognised by the UGG and ISO 9001:2015 and accredited by NAAC A+ Grade, IAO, IAF, MMS, and EGAC. The institute has a strong placement cell and collaborates with top recruiting companies to provide students with excellent internship and job opportunities. 

Some the top recruiters for Gandhi Engineering College placement are listed below:

This is a multiple choice answer as classified in NCERT Exemplar

(c) From conservation of mechanical energy

$\frac{1}{2}m{v}^2=mgh$

V= $\sqrt[]{2gh}$

Hence speed is same for both stones .

a₁=acceleration along inclined plane = gsin $\theta$ ₁

Similarly for stone a₂=gsin $\theta$ ₂ as $\theta$ ₂> $\theta$ ₁, hence a₂>a₁

According to QS World University Rankings 2025, the university is ranked at #171 whereas in 2024 it was ranked at #154. This ranking is based on different criteria such as number of international students enrolled, number of faculty, placement etc. On comparing the ranks, it has been observed that there is a decline in ranking criteria, resulting in increase in ranking. 

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

Sol:

$\begin{array}{l}Lety={\left(sinx\right)}^{cosx}\\ Takinglogonbothsides,\\ logy=log{\left(sinx\right)}^{cosx}\\ logy=cosx.log\left(sinx\right)\\ Differentiatingbothsidesw.r.t.x\\ \frac{1}{y}.\frac{dy}{dx}=\frac{d}{dx}cosx.log\left(sinx\right)\\ \Rightarrow \frac{1}{y}.\frac{dy}{dx}=cosx.\frac{d}{dx}log\left(sinx\right)+log\left(sinx\right).\frac{d}{dx}cosx\\ \Rightarrow \frac{1}{y}.\frac{dy}{dx}=cosx.\frac{1}{sinx}.\frac{d}{dx}\left(sinx\right)+log\left(sinx\right).\left(-sinx\right)\\ \Rightarrow \frac{1}{y}.\frac{dy}{dx}=cotx.cosx-sinx.log\left(sinx\right)\\ \frac{dy}{dx}=y\left[cotx.cosx-sinx.log\left(sinx\right)\right]\\ Hence,\frac{dy}{dx}={\left(sinx\right)}^{cosx}\left[\frac{co{s}^{2}x}{sinx}-sinx.log\left(sinx\right)\right]\end{array}$

The average salary package for placements at Gandhi Engineering 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:

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

King George Medical College provides good placements to its graduating students. Check out the table below to know the key highlights of the King George Medical College placement packages 2024:

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

In order to enroll for course admission at Amity Business School candidates must complete graduation. The selection criteria for course admission is entrance-based. The application mode is online. For admission to the various programmes, aspirants need to apply at the official website. Candidates have to fill up all the details carefully, such as name, mobile number, name of the state, etc. 

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

Sol:

DYPCOE Akurdi offers M.Tech in Computer Engineering for 2 years with an annual intake of 13 students. The Institute offers admission to the respective course on the basis of 50% aggregate in graduation along with valid scores in accepted exams such as GATE, MHTCET MTech. The Institute offers the respective course with a total tuition fees worth INR 1.66 Lakh. 

This is a multiple choice answer as classified in NCERT Exemplar

(c) when we are considering the two bodies as system the total external force on the system will be zero . hence total linear momentum of the system remains conserved.

The King George Medical College placement report for 2024 is not out yet. However the NIRF report for 2025 has been released.Check out the tabulated data given below to know more about King George Medical College placement 2024:

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