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The RK University 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 RK University placements 2025:

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

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=\{\begin{array}{cc}\hfill x^2+3x+p,\hfill & \hfill x\le 1\hfill \\ \hfill qx+2,\hfill & \hfill x>1\hfill \end{array}atx=1.\\ L.H.L.f\text{'}\left(c\right)=\underset{x\to 1^{-}}{lim}\frac{f\left(x\right)-f\left(c\right)}{x-c}\\ f\text{'}\left(1\right)=\underset{x\to 1^{-}}{lim}\frac{f\left(x\right)-f\left(1\right)}{x-1}\\ =\underset{x\to 1^{-}}{lim}\frac{\left(x^2+3x+p\right)-\left(1+3+p\right)}{x-1}\\ =\underset{h\to 0}{lim}\frac{\left[{\left(1-h\right)}^2+3\left(1-h\right)+p\right]-\left(1+3+p\right)}{1-h-1}\\ =\underset{h\to 0}{lim}\frac{\left[1+h^2-2h+3-3h+p\right]-\left(4+p\right)}{-h}\\ =\underset{h\to 0}{lim}\frac{\left[h^2-5h+4+p\right]-\left[4+p\right]}{-h}\\ =\underset{h\to 0}{lim}\frac{h^2-5h+4+p-4-p}{-h}\\ =\underset{h\to 0}{lim}\frac{h^2-5h}{-h}=\underset{h\to 0}{lim}\frac{h\left[h-5\right]}{-h}=5\\ R.H.L.f\text{'}\left(1\right)=\underset{x\to 1^{+}}{lim}\frac{f\left(x\right)-f\left(1\right)}{x-1}\\ =\underset{x\to 1^{+}}{lim}\frac{\left(qx+2\right)-\left(1+3+p\right)}{x-1}\\ =\underset{h\to 0}{lim}\frac{\left[q\left(1+h\right)+2\right]-\left[4+p\right]}{1+h-1}\\ =\underset{h\to 0}{lim}\frac{q+qh+2-4-p}{h}=\underset{h\to 0}{lim}\frac{q+qh-2-p}{h}\\ Forexistingthelimit\\ q-2-p=0\Rightarrow q-p=0\dots \left(1\right)\\ \underset{h\to 0}{\Rightarrow lim}\frac{qh-0}{h}=q\\ IfL.H.L.f\text{'}\left(1\right)=R.H.L.f\text{'}\left(1\right)thenq=5.\\ Nowp\end{array}$

The UK 12th result is very important in student's life. Check the points below where the UK 12th result will be mandatory.

• For higher education
• For entrance tests
• For career

ISMS Pune offers various courses at the PG level. The selection criteria are entrance based as per course requirement. The application process at ISMS Pune is conducted online. To secure a seat at ISMS Pune, students can check the following steps presented below:

1. Visit the official website and complete the online application process. 
2. Candidates can also apply online for various courses.
3. Ensure eligibility and selection criteria for all programme.
4. The selection criteria is merit or entrance-based.
5. Upon selected, pay the specified fee to confirm and secure your seat.

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

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=\left|sinx+cosx\right|atx=\pi \\ Putg\left(x\right)=sinx+cosxandh\left(x\right)=\left|x\right|\\ \therefore h\left[g\left(x\right)\right]=h\left(sinx+cosx\right)=\left|sinx+cosx\right|\\ Now,g\left(x\right)=sinx+cosxisacontinuousfunctionsincesinxandcosxaretwocontinuous\\ functionsatx=\pi .\\ Weknowthateverymodulusfunctionisacontinuousfunctioneverywhere.\\ Hence,f\left(x\right)=\left|sinx+cosx\right|isacontinuousfunctionatx=\pi .\end{array}$

Do 1–2 full mock tests at home with timer. If your scores are close to your target band, you are doing good. If not, check what part is weak and give more time there.

BA curriculum at Faculty of Liberal Arts, MIT WPU includes a blend of core subjects, general and open electives, skill enhancement courses, and peace studies. Topics range from British Literature and Biopsychology to Political Theory, Human Rights, and Yoga.

A total of 33,042 applications have been rejected or found invalid during the initial screening process for the Bihar Police Constable recruitment. 

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

Sol:

$\begin{array}{l}Wehavef\left(x\right)=\frac{1}{t^2+t-2}\\ \Rightarrow f\left(t\right)=\frac{1}{{\left(\frac{1}{x-1}\right)}^2+\frac{1}{x-1}-2}\left[Puttingt=\frac{1}{x-1}\right]\\ =\frac{1}{\frac{1+x-1-2{\left(x-1\right)}^2}{{\left(x-1\right)}^2}}=\frac{{\left(x-1\right)}^2}{x-2x^2-2+4x}\\ =\frac{{\left(x-1\right)}^2}{-2x^2+5x-2}=\frac{{\left(x-1\right)}^2}{-\left(2x^2-5x+2\right)}\\ =\frac{{\left(x-1\right)}^2}{-\left[2x^2-4x-x+2\right]}=\frac{{\left(x-1\right)}^2}{-\left[2x\left(x-2\right)-1\left(x-2\right)\right]}\\ =\frac{{\left(x-1\right)}^2}{-\left(x-2\right)\left(2x-1\right)}=\frac{{\left(x-1\right)}^2}{\left(2-x\right)\left(2x-1\right)}\\ So,iff\left(t\right)isdiscontinuous,then2-x=0\therefore x=2\\ and2x-1=0\therefore x=\frac{1}{2}\\ Hence,therequiredofdiscontinuityare2and\frac{1}{2}.\end{array}$

While preparing the cutoff for the ANA Group of Institutions BTech course, the authorities will consider examination and admission-related factors. The listed factors will be checked and considered by the authorities while determining the cutoff of ANA Group of Institutions- previous years' cutoff trends, difficulty level of exam, total number of qualified candidates, total number of candidates applying for a specific course, number of seats available for particular BTech specialisation, etc. After checking all of these factors, the authorities will prepare the cutoff based on CUET/ JEE Mains scores for BTech. 

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

Sol:

$\begin{array}{l}f\left(x\right)=\frac{1}{x+2}\\ f\left[f\left(x\right)\right]=\frac{1}{f\left(x\right)+2}=\frac{1}{\frac{1}{x+2}+2}=\frac{1}{\frac{1+2x+4}{x+2}}=\frac{x+2}{2x+5}\\ \therefore f\left[f\left(x\right)\right]=\frac{x+2}{2x+5}\\ Thisfunctionwillnotbedefinedandcontinuouswhere2x+5=0\\ \Rightarrow x=\frac{-5}{2}.\\ Hence,x=\frac{-5}{2}isthepointofdiscontinuity.\end{array}$

Central Selection Board of Constable (CSBC) released rejection list for ongoing recruitment process under Advertisement No. 01/2025 for post of Bihar Police Constable. The notice released provides insights into number and reasons behind rejection of Bihar Police Constable 2025 applications, reflecting screening challenges and applicant behaviour during this large-scale recruitment drive.

ANA Group of Institutions offers five specialisations in the BTech course, namely, Computer Science Engineering with Data Science & AI, Civil Engineering,  Electronics and Communication Engineering, Mechanical Engineering, and Electrical Engineering. The total number of seats offered in these specialisation is 300. To get a seat in the BTech course, candidates are required to complete the basic eligibility criteria first, which state applicants must complete their Class 12 from the PCM stream with an aggregate of 50% (45% for reserved categories). 

Yes, if you use them well. You can use Shiksha Free IELTS Classes, IDP website, and free apps. YouTube also has lots of free IELTS practice videos. Just be regular.