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Let $l={\displaystyle \int \frac{2e^x+3e^{-x}}{4e^x+7e^{-x}}}dx={\displaystyle \int \frac{2e^{2x}+3}{4e^{2x}+7}dx}$  

$={\displaystyle \int \frac{2e^{2x}}{4e^{2x}+7}dx+{\displaystyle \int \frac{3e^{-2x}}{4+7e^{-2x}}dx}}$               

Put $4e^{2x}+7=t4+7e^{-2x}=\lambda$  

$8e^{2x}dx=dt-14e^{-2x}dx=d\lambda$              

$=\frac{1}{4}{\displaystyle \int \frac{dt}{t}-\frac{3}{14}{\displaystyle \int \frac{d\lambda }{\lambda }=\frac{1}{4}lnt-\frac{3}{14}ln\lambda +c}}$

$u=\frac{13}{2},v=\frac{1}{2}$              

->so, u + v = 7

The eligibility criteria for admission to the BHM course at Radiance Institute of Management Studies (RIMS), Dehradun requires the candidates to pass Class 12 from a recognised board. They must submit the marksheet and certificate for the same to apply for and confirm admission in Radiance Institute of Management Studies (RIMS), Dehradun.

The relaxation in the upper SBI Clerk age limit provided to SC/ST candidates is five years. This means candidates belonging to this category can apply for the exam till the age of 33 years.

As of 2023 data, there are about 13 top deemed Medical colleges in Maharashtra. Bharati Vidyapeeth University Medical College, Pune, Padmashri Dr.D Y Patil  Medical College, Pimpri, Pune, Rural Medical College, ( Pravara Institute of Medical Sciences, Loni, Krishna Institute of Medical Sciences, Karad, Maharashtra, Padmashri Dr.D Y Patil  Medical College, Navi Mumbai, Maharashtra, Mahatma Gandhi Missions Medical College, Aurangabad. In Maharashtra total 2400 MBBS Seats available in Deemed Medical Colleges.

The relaxation in the upper SBI Clerk age limit 2024 provided to the OBC candidates is three years. Candidates belonging to reserved categories are given relaxation in the upper age limit as per government rule.

Since A (sec θ, 2 tanθ) & B $\left(sec?,2tan?\right)$  lies on 2x² – y² = 2 then

2sec² θ - 4tan^2_θ = 2 or sec² θ - 2 tan² θ = 1

-> $ta{n}^2\theta =0so\theta =0$

Similarly    $?=0but\theta +?=\frac{\pi }{2}$ (given) so not possible

Hence question is not correct

All 3 conditions are false. Because none of them following the selection procedure.

Radiance Institute of Management Studies (RIMS), Dehradun does not accept CUET scores. Admissions in the various courses offered by the institute are merit-based. Candidates are granted admission based on the merit in the last qualifying exam, i.e., Class 8/12 or graduation. Interested candidates must fill out the application form available on the official website of RIMS Dehradun. 

The fee range for the MBA programme at SIOM Nashik ranges between INR 10 lakh-INR 18.1 lakh. This information is sourced from official website/ sanctioning body and is subject to change. The fee covers various academic expenses like tuition fees, laboratory charges, examination fees, library fees, and other relevant charges. Please note that the fee structure is subject to change. Candidates are advised to visit the university's official website for the latest and most accurate information.

Both E and F are selected then W and Y are ruled out respectively. There must be both X and Z.

As per the latest report, the average package offered during VELS Institute of Science, Technology and Advanced Studies placements 2025 was INR 4.5 LPA. The same is tabulated below:

Given variance of boys ${\sigma }_b^2=2\&{\overline{x}}_b=12$ (average marks of boys)

& variance of girls  ${\sigma }_g^2=2\&\mu \to$ average marks of girls

$Now,{\overline{x}}_g=\mu =\frac{50\times 15-12\times 20}{30}=17$           

${\sigma }^2=\frac{20\times 2+30\times 2}{20+30}+\frac{20\times 30}{{\left(20+30\right)}^2}{\left(12-17\right)}^2=8$            

$So,\mu +{\sigma }^2=17+8=25$  

Radiance Institute of Management Studies (RIMS), Dehradun offers various courses to candidates at the UG and PG levels. They are as follows:-

• BHM
• UG Diploma
• Certificate
• PG Diploma
• MHM

If W is selected E and X are rejected. Only senior member rest D, F. If F is selected then Y is ruled out. Only rest member be Z.

Symbiosis International (Deemed University) is one of the best universities present in India and is known for offering great placements to students. Hence, a lot of students compete every year to gain admission to this university. Therefore, getting admission here is difficult but not impossible. If the students want to get admission to various courses at Symbiosis Institute of Operations Management, they must clear the SNAP exam. For this, candidates must go through the SNAP syllabus, keep an eye on SNAP admit card release date, and follow the SNAP preparation guidelines.

Model Institute of Engineering and Technology has a total of 60 seats available for BBA LLB (Hons) programme. The institute offers seats in this course based on scores of candidates in CUET, CLAT or MIET Entrance Test. Those who get selected have to confirm their seat by paying the course fee.

Yes, Radiance Institute of Management Studies (RIMS), Dehradun admissions are open for 2025. Candidates can apply on the official website of the institute by filling out the application form and submitting it by paying the application fee. Additionally, candidates must also ensure fulfilling the eligibility criteria before applying for admission in their preferred course at RIMS Dehradun. 

$x^2+9y^2-4x+3=0,x,y\in R.........\left(i\right)$

$x^2-4x+9y^2+3=0$        

Since $x\in R,D\ge 0i.e.16-4\left(9y^2+3\right)\ge 0$

or $9y^2-1\le 0$

$\Rightarrow y\in \left[-\frac{1}{3},\frac{1}{3}\right]$

$\left(i\right)\Rightarrow 9y^2=-x^2+4x-3$

Since L.H.S. $\ge 0soR.H.S.\ge 0i.e.-x^2+4x-3\ge 0$

or $x^2-4x+3\le 0$

$\left(x-3\right)\left(x-1\right)\le 0$

$\Rightarrow x\in \left[1,3\right]$

Novolac is linear polymer of o-hydroxymethyphenol

According to the given condition, only one of them can be selected – E/W, F/Y, W/X. If X is selected W is rejected and Y is also rejected then 2 senior members must be D, F and 2 Junior will be X, Z.