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

$\begin{array}{l}Thegiven\text{\hspace{0.17em}points}are\left(a,2,1\right)and\left(1,-1,1\right)\\ \therefore \text{\hspace{0.17em}Distance}=\sqrt[]{{\left(a-1\right)}^2+{\left(2+1\right)}^2+{\left(1-1\right)}^2}\\ 5=\sqrt[]{a^2+1-2a+9}\\ Squaringbothsides,wehave\\ 25=a^2+1-2a+9\\ \Rightarrow a^2-2a-15=0\\ \Rightarrow a^2-5a+3a-15=0\\ \Rightarrow a\left(a-5\right)+3\left(a-5\right)=0\\ \Rightarrow \left(a+3\right)\left(a-5\right)=0\\ \therefore a=-3or5\\ Hence,thevalueofthefilleris5or-3.\end{array}$

Once this list is up, candidates could review it and email any discrepancies. Objections to the tentative list could be submitted by email from July 5–7, 2025. For example, if someone's name was missing or category was wrong, they could write in during those dates. University would then verify and correct any valid issues. 

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

$Thegiven\text{\hspace{0.17em}dimensions}$
$\begin{array}{l}are10,13and8\\ Leta=10,b=13andc=8\\ \therefore \text{\hspace{0.17em}Required}length=\sqrt[]{a^2+b^2+c^2}\\ =\sqrt[]{{\left(10\right)}^2+{\left(13\right)}^2+{\left(8\right)}^2}=\sqrt[]{100+169+64}=\sqrt[]{333}\\ Hence,thevalueofthefilleris\sqrt[]{333}.\end{array}$

Mahendra Institute of Management and Technical Studies admission enquiry forms are also available online. Candidates meeting the eligibility criteria can apply for the preferred course. Below are the steps to fill out the form:

Step 1: Visit the official MIMTS website.

Step 2: Fill out the form with basic details such as name, contact number, etc.

Step 3: Complete and submit it. 

CMJ University offers four-year BTech courses in different specialisations. Admission to these courses is entrance-based. The applications are accepted in both online and offline modes. Mentioned below are the available course specialisations:

• Electronics and Communication Engineering
• Computer Science and Engineering
• Automobile
• Information Technology
• Mining, etc.

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

$\begin{array}{l}Theplaneparalleltoyz-planeisperpendiculartox-axis.\\ Hence,thevalueofthefillerisx-axis.\end{array}$

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

$x=arepresentsaplaneparalleltoyz-plane.$

For PU CET (UG) 2026 provisional merit list will publish tentatively in the last week of May. Students are advised to check the website for the updates. 

The PU CET (UG) provisional merit list will be released just before the PU CET (UG) 2026 results. In case of any discrepancy in the results you can contact to the designated authority mentioned on the official website.

Due the absence of inversion and non resonating nature

$A^2=\left(\begin{array}{ll}\mathrm{c}\mathrm{o}\mathrm{s}?2\theta & i\mathrm{s}\mathrm{i}\mathrm{n}?2\theta \\ i\mathrm{s}\mathrm{i}\mathrm{n}?2\theta & \mathrm{c}\mathrm{o}\mathrm{s}?2\theta \end{array}\right)$

Similarly, $A^5=\left(\begin{array}{cc}\mathrm{c}\mathrm{o}\mathrm{s}?5\theta & i\mathrm{s}\mathrm{i}\mathrm{n}?5\theta \\ i\mathrm{s}\mathrm{i}\mathrm{n}?5\theta & \mathrm{c}\mathrm{o}\mathrm{s}?5\theta \end{array}\right)=\left(\begin{array}{ll}a& b\\ c& d\end{array}\right)$

(1) $a^2+b^2={\mathrm{c}\mathrm{o}\mathrm{s}}^2?5\theta -{\mathrm{s}\mathrm{i}\mathrm{n}}^2?5\theta =\mathrm{c}\mathrm{o}\mathrm{s}?10\theta =\mathrm{c}\mathrm{o}\mathrm{s}?{75}^{?}$

(2) $a^2-d^2={\mathrm{c}\mathrm{o}\mathrm{s}}^2?5\theta -{\mathrm{c}\mathrm{o}\mathrm{s}}^2?5\theta =0$

(3) $a^2-b^2={\mathrm{c}\mathrm{o}\mathrm{s}}^2?5\theta +{\mathrm{s}\mathrm{i}\mathrm{n}}^2?5\theta =1$

(4) $a^2-c^2={\mathrm{c}\mathrm{o}\mathrm{s}}^2?5\theta +{\mathrm{s}\mathrm{i}\mathrm{n}}^2?5\theta =1$

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

$\begin{array}{l}yandzcoordinates.\\ Hence,thevalueofthefillerisyandzcoordinates.\end{array}$

Candidates who have passed a master's degree are eligible to apply for PhD programme at DoMS IIT Roorkee. Besides, aspirants must also pass any of the accepted entrance exams for admission. The institute considers scores in GATE, CAT, UGC-JRF, UGC-NET or CSIR JRF for admission. Selected candidates have to further the pass the personal interview round for final admission.

The BSc courses at Garden City University is comprised of both theoretical and practical learning experiences. In each semester, students have to clear at least 3 practical subjects to pass to the next semester. In some BSc courses, the final semester is comprised of upto 6 practical subjects. For more information on which subjects of BSc courses at Garden City University are practical subjects, visitthe official website.

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

$\begin{array}{l}z-coordinates.\\ Hence,thevalueofthefillerisz-coordinates.\end{array}$

Yes, while studying at Stanford University, international students can work part-time. To be eligible for on-campus employment, students must be enrolled full-time. They can only work up to 20 hours or fewer per week when the school is in session. But, during the holidays and vacations, students can work more than 20 hours per week. A few of the Part-time jobs in USA for Indian students are Tour Guide, Campus Tech Support, Teaching Assistant, Barista, Academic Department Assistant, University Book Store Assistant, etc.

$\int {\left(\frac{x}{x\mathrm{s}\mathrm{i}\mathrm{n}?x+\mathrm{c}\mathrm{o}\mathrm{s}?x}\right)}^{2}dx=\int \left(\frac{x}{\mathrm{c}\mathrm{o}\mathrm{s}?x}\right)\cdot \frac{x\mathrm{c}\mathrm{o}\mathrm{s}?xdx}{(x\mathrm{s}\mathrm{i}\mathrm{n}?x+\mathrm{c}\mathrm{o}\mathrm{s}?x{)}^2}$

$\begin{array}{rr}& =\frac{x}{\mathrm{c}\mathrm{o}\mathrm{s}?x}\left(-\frac{1}{x\mathrm{s}\mathrm{i}\mathrm{n}?x+\mathrm{c}\mathrm{o}\mathrm{s}?x}\right)+\int \left(\frac{\mathrm{c}\mathrm{o}\mathrm{s}?x+x\mathrm{s}\mathrm{i}\mathrm{n}?x}{{\mathrm{c}\mathrm{o}\mathrm{s}}^2?x}\right)\left(\frac{1}{x\mathrm{s}\mathrm{i}\mathrm{n}?x+\mathrm{c}\mathrm{o}\mathrm{s}?x}\right)dx\\ & =-\frac{x\mathrm{s}\mathrm{e}\mathrm{c}?x}{x\mathrm{s}\mathrm{i}\mathrm{n}?x+\mathrm{c}\mathrm{o}\mathrm{s}?x}+\int {\mathrm{s}\mathrm{e}\mathrm{c}}^2?xdx\\ & =-\frac{x\mathrm{s}\mathrm{e}\mathrm{c}?x}{x\mathrm{s}\mathrm{i}\mathrm{n}?x+\mathrm{c}\mathrm{o}\mathrm{s}?x}+\mathrm{t}\mathrm{a}\mathrm{n}?x+C\end{array}$

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

$\begin{array}{l}Theequationofz-axisare,x=0andy=0.\\ Hence,thevalueofthefillerisx=0andy=0.\end{array}$

Stanford is located in California. The university is situated on 8,180 acres in the center of San Francisco, Peninsula. It is located 35 miles south of San Francisco and 20 miles north of San Jose. Stanford University is located in the heart of Northern California's “Silicon Valley”.  As of 2025, Stanford has 630 buildings. There is one satellite campus of Stanford namely Redwood City Campus. Its campus size is 35-acres.

Students seeking to join the programmes provided at K.S. Group of Institutions must meet the minimum eligibility requirements set by the institute. For those applying to the undergraduate courses, passing Class 12 or equivalent from a recognised board with the relevant subjects and specified aggregate is neccessary. Similarly, for postgraduate admissions, finishing graduation from a recognised university in a relevant field is compulsory. Find below the general KSGI eligibility criteria: