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According to unofficial sources, the acceptance rate of Ohio University stands at 85% approximately, showing that the addmissions at the university is fairly competitive and students have a decent level of chace of getting accepted if they meet the admission requirements and submit all the documents during the application process as per the programme of choice. As per the recent data, the university received over 25,000 applications, out of which, around 4,517 were enrolled.

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhat:tan{1}^{0}tan{2}^{0}tan{3}^0\dots tan89^0\\ =tan{1}^{0}tan{2}^{0}tan{3}^0\dots tan45^0.tan{\left(90-44\right)}^0.tan{\left(90-43\right)}^0\dots tan{\left(90-1\right)}^0\\ =tan{1}^{0}cot{1}^0.tan{2}^{0}cot{2}^0.tan{3}^{0}cot{3}^0\dots tan89^0.cot89^0\\ =1.1.1.1\dots 1.1=1\\ Hence,thecorrectoptionis\left(b\right).\end{array}$

The Ohio University tuition fees for international students varies depending on the level of study and the course chosen by the applicant. The tuition fees for undergraduate programs lie in the range INR 20.44 L - 21.24 L and that of postgraduate programs lie in the range INR 13.84 L - 29.94 L. Students can check the Ohio University tuition fees for some popular programs from the table below:

This is an Objective Type Questions as classified in NCERT Exempar

Sol:

$\begin{array}{l}sin\theta =-\frac{1}{5}iscorrect.?-1\le sin\theta \le 1\\ So\left(a\right)iscorrect.\\ cos\theta =1iscorrect.?cos{0}^0=1\\ So\left(b\right)iscorrect.\\ sec\theta =\frac{1}{2}\Rightarrow cos\theta =2isnotcorrect.?-1\le cos\theta \le 1\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

$\begin{array}{l}sin\theta =-\frac{1}{5}iscorrect.?-1\le sin\theta \le 1\\ So\left(a\right)iscorrect.\\ cos\theta =1iscorrect.?cos{0}^0=1\\ So\left(b\right)iscorrect.\\ sec\theta =\frac{1}{2}\Rightarrow cos\theta =2isnotcorrect.?-1\le cos\theta \le 1\\ Hence,thecorrectoptionis\left(c\right).\end{array}$

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

            $\begin{array}{l}Weknowthat\\ tan\left(\theta +?\right)=\frac{tan\theta +tan?}{1-tan\theta tan?}=\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}\times \frac{1}{3}}=\frac{\frac{5}{6}}{\frac{5}{6}}=1\\ \Rightarrow tan\left(\theta +?\right)=tan\frac{\pi }{4}\\ \therefore \theta +?=\frac{\pi }{4}.\\ Hence,thecorrectoptionis\left(d\right).\end{array}$

This is a Long Answer Type Questions as classified in NCERT Exemplar
Sol:

$\begin{array}{l}LetP\left(n\right):Numberofsubsetsofasetcontainingndistinctelementsis{2}^n,foralln\in N.\\ Step1:ItisclearthatP\left(1\right)istrueforn=1.Numberofsubsets=2^1=2.Whichistrue.\\ Step2:P\left(k\right)isassumedtobetrueforn=k.Sincethenumberofsubsets=2^k.\\ Step3:P\left(k+1\right)=2^{k+1}\\ Weknowifonenumber\left(i.e.,element\right)isaddedtotheelementsofagivenset,thenumber\\ ofsubsetsbecomedouble.\\ \therefore Numberofsubsetsofasethaving\left(k+1\right)distinctelements=2\times 2^k=2^{k+1}whichistrueforP\left(k+1\right).\\ Hence,P\left(k+1\right)istruewheneverP\left(k\right)istrue.\end{array}$

Ohio University offers over 203 programs that are available to international students. Some of teh areas of study and programs are more popular among students than the others. Below is the list of top programs at Ohio University:

• Biological Sciences
• Nursing
• Psychology
• Business
• Marketing
• Exercise Physiology
• Finance
• Media Arts and Studies

This is a Long Answer Type Questions as classified in NCERT Exemplar
Sol:

$\begin{array}{l}LetP\left(n\right):\frac{1}{n+1}+\frac{1}{n+2}+\dots +\frac{1}{2n}>\frac{13}{24},\forall n\in N.\\ Step1:P\left(2\right):\frac{1}{2+1}+\frac{1}{2+2}>\frac{13}{24}\Rightarrow \frac{1}{3}+\frac{1}{4}>\frac{13}{24}\\ \Rightarrow \frac{7}{12}>\frac{13}{24}\Rightarrow \frac{14}{24}>\frac{13}{24}whichistrueforP\left(2\right).\\ Step2:P\left(k\right):\frac{1}{k+1}+\frac{1}{k+2}+\dots +\frac{1}{2k}>\frac{13}{24}.LetitbetrueforP\left(k\right)\\ Step3:P\left(k+1\right):\frac{1}{k+1}+\frac{1}{k+2}+\dots +\frac{1}{2k}+\frac{1}{2\left(k+1\right)}>\frac{13}{24}\\ Since\frac{1}{k+1}+\frac{1}{k+2}+\dots +\frac{1}{2k}>\frac{13}{24}\\ So,\frac{1}{k+1}+\frac{1}{k+2}+\dots +\frac{1}{2k}+\frac{1}{2\left(k+1\right)}>\frac{13}{24}\\ WhichistrueforP\left(k+1\right).\\ Hence,P\left(k+1\right)istruewheneverP\left(k\right)istrue.\end{array}$

This is a Long Answer Type Questions as classified in NCERT Exemplar
Sol:

$\begin{array}{l}LetP\left(n\right):\frac{n^5}{5}+\frac{n^3}{3}+\frac{7n}{15},\forall n\in N.\\ Step1:P\left(1\right):\frac{1^5}{5}+\frac{1^3}{3}+\frac{7.1}{15}=\frac{3+5+7}{15}=\frac{15}{15}=1whichistrueforP\left(1\right).\\ Step2:P\left(k\right):\frac{k^5}{5}+\frac{k^3}{3}+\frac{7k}{15}.LetitbetrueforP\left(k\right).Andlet\frac{k^5}{5}+\frac{k^3}{3}+\frac{7k}{15}=\lambda \\ Step3:P\left(k+1\right):\frac{{\left(k+1\right)}^5}{5}+\frac{{\left(k+1\right)}^3}{3}+\frac{7\left(k+1\right)}{15}\\ =\frac{1}{5}\left[k^5+5k^4+10k^3+10k^2+5k+1\right]+\frac{1}{3}\left[k^3+3k^2+3k+1\right]+\frac{7k}{15}+\frac{7}{15}\\ =\left(\frac{k^5}{5}+\frac{k^3}{3}+\frac{7k}{15}\right)+\left(k^4+2k^3+3k^2+5k\right)+\frac{1}{5}+\frac{1}{3}+\frac{7}{15}\\ =\lambda +k^4+2k^3+3k^2+2k+1\left[FromStep2\right]\\ =positiveintegers=naturalnumber\\ WhichistrueforP\left(k+1\right).\\ Hence,P\left(k+1\right)istruewheneverP\left(k\right)istrue.\end{array}$

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Giventhat:A=\left\{a,b\right\},B=\left\{x,y\right\}\\ \therefore A\times B=\left\{\left(a,x\right),\left(a,y\right),\left(b,x\right),\left(b,y\right)\right\}\\ Hence,thestatementis\text{'}True\text{'}.\end{array}$

As per the Tezpur University JEE Main cutoff 2025, the Round 3 seat allotment results are finally published by Tezpur University. Considering the Tezpur University cutoff 2025 for the Round 3 seat allotment results, the BTech in CSE at Tezpur University has the increasing cutoffs over the years. In the JEE Main 2025 Round 3 seat allotment results, the required closing rank to get into the institute for BTech in CSE for the General AI category stood at 60217. Also, it has the lowest cutoff among all courses, making it highly competitive and solidifying its position as the most sought-after branch at the institute.