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6X + 5Y = 218 . (1)

5X - 3Y = 24 . (2)

Solve to get X = 18, Y = 22.

$\frac{T}{T\text{'}}=\frac{2\pi \sqrt[]{\frac{\mathcal{l}}{g}}}{2\pi \sqrt[]{\frac{\mathcal{l}}{\frac{16}{g}}}}$

$\Rightarrow \frac{T}{T\text{'}}=\frac{1}{\left(\frac{1}{4}\right)}=4$

$\Rightarrow T\text{'}=\frac{T}{4}$

Candidates can expect the following topics to be covered under the BBA course at Techno Main Salt Lake:-

• Management
• Accounting
• Finance
• Marketing
• Entrepreneurship, etc. 

  $S_{10}=530\Rightarrow 5\left[2a+9d\right]=530$

2a + 9d = 106 . (i)

$S_5=140\Rightarrow \frac{5}{2}\left[2a+4d\right]=140$              

a + 2d = 28 . (ii)

Solving (i) & (ii) a = 88 d = 10

$\therefore S_{20}-S_6=14a+175d=1862$            

There is an entrance test for GEMS B School, Bangalore admission. The institute conducts the GEMS Online Admission Test, on the basis of which applicants are shortlisted. Students are required to appear for the exam as part of the evaluation process as this test is conducted to assess the candidates' aptitude, analytical skills, and knowledge relevant to the management programmes offered by the GEMS B-School Bangalore.

If X in m be the length of train, then $\frac{}{}$ $\frac{(X+116)}{Y}=10,$ $\frac{(X+236)}{Y}=16$ $\frac{}{}$

(Y = speed of train in m/s) Solve to get X = 84, Y = 20

Let x be the required percent.

Using the successive percentage change rule, we have

150 + x + $\frac{150x}{100}$ $\frac{}{}$ = 0

$\frac{}{}$ $\frac{250x}{100}$  = – 150

x = – 60%

so 60%

Primus B School offers Bachelor of Commerce or BCom for 3 years in regular mode. The 3 year BCom course is split into 6 semesters and is offered along with the specialisation in Accounting, Banking and Insurance, Finance, Marketing, Human Resources, and IT. Admission to the respective course is offered on the basis of merit and would require candidates to secure a minimum aggregate in Class 12. 

$\overrightarrow{a}=\alpha \overrightarrow{b}+\beta \overrightarrow{c}=\left(2\alpha +\beta \right)i+\left(\alpha -\beta \right)J+\left(\alpha +\beta \right)k$

is perpendicular to   $\overrightarrow{d}=3\widehat{i}+2\widehat{j}+6\widehat{k}$

$\Rightarrow 3\left(2\alpha +\beta \right)+2\left(\alpha +\beta \right)+6\left(\alpha +\beta \right)=0$              

->14a + 7b = 0 Þ b = -2a .(i)

$\Rightarrow \overrightarrow{a}=3\alpha j-\alpha k$

$\left|\overrightarrow{a}\right|=\sqrt[]{9{\alpha }^2+{\alpha }^2}=\sqrt[]{10}\Rightarrow \left|\alpha \right|=1\Rightarrow \alpha \pm 1,for\alpha =1,\overrightarrow{a}=3\widehat{j}-\widehat{k}$       

for $\alpha =-1,\overrightarrow{a}=-3\widehat{j}+\widehat{k}$  

$\overrightarrow{d}\times \overrightarrow{a}=\pm \left|\begin{array}{ccc}\hfill i\hfill & \hfill j\hfill & \hfill k\hfill \\ \hfill 3\hfill & \hfill 2\hfill & \hfill 6\hfill \\ \hfill 0\hfill & \hfill 3\hfill & \hfill -1\hfill \end{array}\right|$

$=\pm 42$              

W = mgh

$=80\times 9.8\times \left(\frac{80}{100}\right)$

$=627.2J$

$\begin{array}{l}\Rightarrow w_f+w_g=0\\ \Rightarrow w_f=-627.2J\end{array}$  

When comparing MBA programmes, candidates should consider tuition fees, faculty quality, infrastructure, hospital facilities, and placement opportunities. UIM, Karnavati University stands out for its low fees, high ratings, and strong academic reputation. However, students should also assess location convenience, patient exposure in hospitals, and extracurricular opportunities before making a final decision. 

Required time t =

$\frac{1760}{2\pi r}=\frac{1760}{\left[2\times \left(\frac{22}{7}\right)\times \frac{3.5}{2}\right]}=160min.$

The important CAT 2025 dates for admission to the MBA programme at UIM, Karnavati University are as follows: Registration runs from 1 Aug '25 to 13 Sep '25, admit card download is available from 5 Nov '25 to 30 Nov '25, and the exam will be held on 30 Nov '25. Results are expected in Dec '25.

 Admission to the MBA programme at UIM, Karnavati University is strictly entrance-based. Candidates must appear for either the CAT or CMAT exam and achieve a valid score. Only those who meet the required performance standards are shortlisted for counseling, after which document verification and fee payment secure their seat in the programme.

$E=\frac{hc}{\lambda }=\frac{1242eV-nm}{621nm}=2eV$

minimum 2eV is required to emit.

Those wishing to join the BBA course offered at GEMS B School, Bangalore need to first ensure that they meet the course-specific admission criteria as specified by the institute. Eligible students can then follow the steps mentioned below to complete GEMS B School, Bangalore BBA admission process:

Step 1: Appear for the online admission test conducted by GEMS B School and secure a minimum of 50% aggregate.

Step 2: Provide necessary documents for the document verification process. 

Step 3: Pay the course fee and secure a seat. 

CAT exam is not compulsory for the MBA programme at UIM, Karnavati University, but candidates must qualify in either the CAT or CMAT. A valid score in one of these exams is mandatory for selection, as it serves as the primary criterion for shortlisting applicants for counseling and final admission.

  $f\left(x\right)=[\begin{array}{l}-\frac{4}{3}{x}^3+2x^2+3x,x>0\\ 3x{e}^x,x\le 0\end{array}$

  $f\text{'}\left(x\right)>0forx<0e^x\left(x+1\right)>0\Rightarrow X>-1\Rightarrow x\in \left(-1,0\right)$            

for  x > 0  $-4x^2+4x+3>0$   

$\Rightarrow x\in \left(0,\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)$  

Again    at  x = 0  f’(0) = 3 > 0

$\therefore f\left(x\right)isincreasingin\left(-1,\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)$