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$x=sin\pi \left(t+\frac{1}{3}\right)$

$v=\frac{dx}{dt}=cos\left[\pi \left(t+\frac{1}{3}\right)\right]\times \pi$

$=cos\left(\pi +\frac{\pi }{3}\right)\times \pi$

$=-cos\frac{\pi }{3}\times \left(\pi \right)$

$=-\frac{\pi }{2}=-1.57m/sec$              

Speed = 157 cm/sec

IIIT Lucknow cutoff 2025 has been released for round 4, on the basis of JEE Main scores. The cutoff was released category-wise for All India quota. The closing ranks among the General All India category candidates was closed between 8890 and 10476. The branch-wise cutoff for IIIT Lucknow for round 4 is given in the table below:

This is an objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhat\underset{x\to 0}{lim}\frac{{\left(1+x\right)}^n-1}{x}\\ =\underset{x\to 0}{lim}\frac{{\left(1+x\right)}^n-{\left(1\right)}^n}{\left(1+x\right)-\left(1\right)}=\underset{1+x\to 1}{lim}\frac{{\left(1+x\right)}^n-{\left(1\right)}^n}{\left(1+x\right)-\left(1\right)}=n{\left(1\right)}^{n-1}=n\left[?\underset{x\to a}{lim}\frac{x^n-a^n}{x-a}=n.a^{n-1}\right]\\ Hence,thecorrectoptionis\left(a\right).\end{array}$

40% of K.E. = $mc\Delta T+mL$  

$0.4\times \frac{1}{2}\times m{v}^2=m\left[125\left(327-127\right)+2.5\times 10^4\right]$                

$\Rightarrow 0.2v^2=\left[250\times 10^2+25\times 10^3\right]$                

$v^2=\frac{2\times 25\times 10^3}{0.2}$                

v = 5 × 100

v = 500 m/sec

Yes, the Staff Selection Commission will release SSC MTS answer key 2025 (tentative) on its official website - ssc.gov.in. The Commission will also ask the candidates to send objections against the incorrect answers. The candidates will be required to provide a reference for their claim.

The candidates will be required to pay the refundable objection fee of INR 50 for each objection. The SSC MTS 2025 exam was conducted from February 4, 2026.

Check out the table below for course-wise the highest package offered during NIT Surat placements 2025:

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Given\underset{x\to 3^{+}}{lim}\frac{x}{\left[x\right]}\\ =\underset{h\to 0}{lim}\frac{\left(3+h\right)}{\left[3+h\right]}=1\\ Hence,thevalueofthefilleris1.\end{array}$

It is good to pursue BTech from SVNIT Surat. BTech placements were good in 2025. The highest package offered was 74 LPA. 82% students placed in 2025 as well.

BTech placement rate recorded during SVNIT Surat placements 2025 was 82%. MTech placement percentage was 61%. Further, 50% MSc students were placed in 2025.

After completing a BSc from Risali Institute of Management, students can pursue careers in fields like hospitality, media, psychology, film production, sound design, and animation, depending on their specialisation. Graduates can also opt for higher studies, freelance opportunities, or explore roles in corporate sectors, research, or creative industries.

The placement packages offered to MTech students during SVNIT Surat placements 2025 are presented in the table below:

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhaty=1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots \\ \frac{dy}{dx}=0+\frac{1}{1!}+\frac{2x}{2!}+\frac{3x^2}{3!}+\dots \\ =1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots =y\\ Hence,thevalueofthefillerisy.\end{array}$

No, Vilnius University does not guarantee on-campus accommodation. Total number of accommodations is limited along with high demand because of which students are advised to submit online application timely so as to avoid any rejections later. Apart from on-campus accommodations, the university has tie ups with private housing providers as well so students can choose off-campus options without any fear.

To get a seat in the BSc programme at Risali Institute of Management, candidates must pass Class 12 from a recognised board and apply online via the official website. Admission is based on merit, and early application improves the chances of securing a seat in the desired specialisation.