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Students concerned about financial considerations can avail the benefits of the scholarship schemes provided by Vogue Institute. Given below are the different scholarships at Vogue Institute Bangalore:

1. National Scholarship Portal for Minority Religion
2. Defence Scholarship
3. Merit Scholarship for students scoring above 90% in qualifying examination.
4. National Level Athletes Scholarship

Students at Vogue Institute of Art and Design get access to a vast network of amenities. These include laboratories, activity rooms, library, auditoriums, transportation facilities, well-equipped classrooms, etc. Further, the institute is involved in organizing different workshops, events, fashion shows, among other various programs. Students are sure to get vast technical exposure.

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

Sol:

          $\begin{array}{l}Giventhat:y=\sqrt[]{3}sinx+cosx\dots \left(i\right)\\ \therefore Themaximumdistancefromapointonthegraphofeqn.\left(i\right)fromx-axis\\ =\sqrt[]{{\left(\sqrt[]{3}\right)}^2+{\left(1\right)}^2}=\sqrt[]{3+1}=2.\\ Hence,thevalueofthefilleris2.\end{array}$

Below are some of the prominent Vogue Institute of Art and Design partnerships:

The fee for the various courses at SOU Devibai Narayandas Chhabada Rural Education Society is as follows: 

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

Sol:

$\begin{array}{l}Giventhat:f\left(x\right)=-3cos\sqrt[]{3+x+x^2}\\ Put\sqrt[]{3+x+x^2}=y\\ \therefore f\left(x\right)=-3cosy\\ ?-1\le cosy\le 1\\ 3\ge -3cosy\ge -3\\ \Rightarrow -3\le -3cosy\le 3\\ \Rightarrow -3\le -3cos\sqrt[]{3+x+x^2}\le 3,x>0\\ Hence,thevalueofthefilleris\left[-3,3\right].\end{array}$

The total tuition fee for the BPharm programme at Chandigarh University ranges from INR 8.5 Lacs to INR 11.4 lakh. This amount may include tuition, refundable security deposits, and other components. Students are advised to check the university's official website for the latest fee updates.

The seat intake for the different BTech specialisations at SOU Devibai Narayandas Chhabada Rural Education Society is as follows:

Candidates are required to participate in the admission process and get the final admission offer to get a chance at securing their seat in the programme. 

The Tamil Nadu Public Service Commission released the TNPSC Group 4 admit card 2025 on July 3. The Commission released the admit card on apply.tnpscexams.in. The candidates were required to download their TNPSC Group 4 admit card 2025 in time because they were asked to show their admit card to the examination centre.

Admission to both the regular and lateral entry BPharm programmes at Chandigarh University is based on the candidate's performance in the CUCET (Chandigarh University Common Entrance Test). Meeting the eligibility criteria is also mandatory.

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

Sol:

           $\begin{array}{l}Givenexpressionis\\ 3{\left(sinx-cosx\right)}^4+6{\left(sinx+cosx\right)}^2+4\left(si{n}^{6}x+co{s}^{6}x\right)\\ =3{\left[si{n}^{2}x+co{s}^{2}x-2sinxcosx\right]}^2+6\left[si{n}^{2}x+co{s}^{2}x+2sinxcosx\right]+4\left[{\left(si{n}^{2}x\right)}^3+{\left(co{s}^{2}x\right)}^3\right]\\ =3{\left[1-2sinxcosx\right]}^2+6\left[1+2sinxcosx\right]+4\left[{\left(si{n}^{2}x+co{s}^{2}x\right)}^3-3si{n}^{2}xco{s}^{2}x\left(si{n}^{2}x+co{s}^{2}x\right)\right]\\ =3\left[1+4si{n}^{2}xco{s}^{2}x-4sinxcosx\right]+6\left(1+2sinxcosx\right)+4\left[1-3si{n}^{2}xco{s}^{2}x\right]\\ =3+12si{n}^{2}xco{s}^{2}x-12sinxcosx+6+12sinxcosx+4-12si{n}^{2}xco{s}^{2}x\\ =3+6+4=13\\ Hence,thevalueofthefilleris13.\end{array}$

For BPharm lateral entry admission to Chandigarh University, candidates must hold a Diploma in Pharmacy with at least 50% aggregate marks from an institute affiliated with a university or a state Board of Technical Education, approved by the Pharmacy Council of India (PCI).

To be eligible for BPharm at Chandigarh University, candidates must have passed Class 12 with at least 60% marks, with English, Physics, Chemistry, and Mathematics/Biology as compulsory subjects. Additionally, candidates must be at least 17 years old on or before December 31 of the admission year.

BSc Nursing is indeed a tough course as it involves a rigorous curriculum and hands-on practical training; it can't be compared to other medical fields or courses. MBBS (Bachelor of Medicine, Bachelor of Surgery), B.Pharma (Bachelor of Pharmacy), etc., are also very demanding and need the same dedication.

The BTech specialisations offered by SOU Devibai Narayandas Chhabada Rural Education Society are as follows:

This is a long answer type question as classified in NCERT Exemplar

$\begin{array}{l}Giventhatfor{z}_{1}and{z}_2,arg\left(z_1\right)-arg\left(z_2\right)=0\\ Letusrepresent{z}_{1}and{z}_{2}inpolarform\\ z_1=r_1\left(cos{\theta }_1+isin{\theta }_1\right)and{z}_2=r_2\left(cos{\theta }_2+isin{\theta }_2\right)\\ arg\left(z_1\right)={\theta }_{1}andarg\left(z_2\right)={\theta }_2\\ Sincearg\left(z_1\right)-arg\left(z_2\right)=0\\ \Rightarrow {\theta }_1-{\theta }_2=0\Rightarrow {\theta }_1={\theta }_2\\ Now{z}_1-z_2=r_1\left(cos{\theta }_1-isin{\theta }_1\right)-r_2\left(cos{\theta }_2+isin{\theta }_2\right)\\ =r_{1}cos{\theta }_1-i{r}_{1}sin{\theta }_1-r_{2}cos{\theta }_1+i{r}_{2}sin{\theta }_1\left[?{\theta }_1={\theta }_2\right]\\ =\left(r_{1}cos{\theta }_1-r_{2}cos{\theta }_1\right)+i\left(r_{1}sin{\theta }_1-r_{2}sin{\theta }_1\right)\\ \therefore \left|z_1-z_2\right|=\sqrt[]{{\left(r_{1}cos{\theta }_1-r_{2}cos{\theta }_1\right)}^2+{\left(r_{1}sin{\theta }_1-r_{2}sin{\theta }_1\right)}^2}\\ =\sqrt[]{\left(r_1^{2}co{s}^2{\theta }_1+r_2^{2}co{s}^2{\theta }_1-2r_1{r}_{2}co{s}^2{\theta }_1+r_1^{2}si{n}^2{\theta }_1+r_2^{2}si{n}^2{\theta }_1-2r_1{r}_{2}si{n}^2{\theta }_1\right)}\\ =\sqrt[]{r_1^2\left(co{s}^2{\theta }_1+si{n}^2{\theta }_1\right)+r_2^2\left(co{s}^2{\theta }_1+si{n}^2{\theta }_1\right)-2r_1{r}_2\left(co{s}^2{\theta }_1+si{n}^2{\theta }_1\right)}\\ =\sqrt[]{r_1^2+r_2^2-2r_1{r}_2}=\sqrt[]{{\left(r_1-r_2\right)}^2}=r_1-r_2=\left|z_1\right|-\left|z_2\right|\\ Hence,\left|z_1-z_2\right|=\left|z_1\right|-\left|z_2\right|\end{array}$

This is a long answer type question as classified in NCERT Exemplar

$\begin{array}{l}Wehave\left|z_1\right|=\left|z_2\right|=\dots =\left|z_n\right|=1\\ \Rightarrow {\left|z_1\right|}^2={\left|z_2\right|}^2=\dots ={\left|z_n\right|}^2=1\dots \left(i\right)\\ \Rightarrow z_1{\overline{z}}_1=z_2{\overline{z}}_2=\dots =z_n{\overline{z}}_n=1\left[?z\overline{z}={\left|z\right|}^2\right]\\ \Rightarrow z_1=\frac{1}{{\overline{z}}_1},z_2=\frac{1}{{\overline{z}}_2}=\dots =z_n=\frac{1}{{\overline{z}}_n}\\ L.H.S.\left|z_1+z_2+z_3+\dots +z_n\right|\\ =\left|\frac{z_1{\overline{z}}_1}{{\overline{z}}_1}+\frac{z_2{\overline{z}}_2}{{\overline{z}}_2}+\frac{z_3{\overline{z}}_3}{{\overline{z}}_3}+\dots +\frac{z_n{\overline{z}}_n}{{\overline{z}}_n}\right|\\ =\left|\frac{{\left|z_1\right|}^2}{{\overline{z}}_1}+\frac{{\left|z_2\right|}^2}{{\overline{z}}_2}+\frac{{\left|z_3\right|}^2}{{\overline{z}}_3}+\dots +\frac{{\left|z_n\right|}^2}{{\overline{z}}_n}\right|\left[?z\overline{z}={\left|z\right|}^2\right]\\ =\left|\frac{1}{{\overline{z}}_1}+\frac{1}{{\overline{z}}_2}+\frac{1}{{\overline{z}}_3}+\dots +\frac{1}{{\overline{z}}_n}\right|\left[Using\left(i\right)\right]\\ =\left|\overline{\frac{1}{z_1}+\frac{1}{z_2}+\frac{1}{z_3}+\dots +\frac{1}{z_n}}\right|\left[?{\overline{z}}_1+{\overline{z}}_2=\overline{z_1+z_2}\right]\\ =\left|\frac{1}{z_1}+\frac{1}{z_2}+\frac{1}{z_3}+\dots +\frac{1}{z_n}\right|\left[?\left|z\right|=\left|{\overline{z}}_1\right|\right]\\ L.H.S.-R.H.S.Henceproved.\end{array}$