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When two subjects in a sentence are joined by 'and', usually the plural verb is used to make the sentence gramatically correct. However, if both nouns refer to a single idea,  singular verb is used.

Examples:

• My brother and I are going on a trip.
• Fish and chips is a popular dish in the UK.

$ta{n}^{-1}\left(\frac{2\times \frac{3}{5}}{1-\frac{9}{25}}\right)+si{n}^{-1}\frac{5}{13}\Rightarrow ta{n}^{-1}\frac{15}{8}+ta{n}^{-1}\frac{5}{12}=ta{n}^{-1}\frac{\frac{15}{8}+\frac{5}{12}}{1-\frac{15}{8}\frac{5}{12}}=ta{n}^{-1}\frac{220}{21}$

$\therefore tan\left(ta{n}^{-1}\frac{220}{21}\right)=\frac{220}{21}$

Students planning to pursue the BTech programme at MSRUAS can access the complete fee structure, including tuition, registration, and other charges, on the institute's official website. It is recommended to refer to the latest updates provided by MSRUAS, as the fee details are subject to change.

As stated in the given passage “Brian Swann suggests an additional explanation: tribal poetry is oral, whereas Europeans arrived in the New World with a deeply ingrained belief in the primacy of the written word.” These lines make option A the best choice.

Seat matrix depends on many factors such as availability and number of applicants in this session. AAE Bangalore offers BBA (General) and BBA (Aviation Management). The seats in BBA Aviation Management is 60. To get a seat in AAE Bangalore BBA programmes, students need to follow the admission process without fail. Students are also advised to abide by deadlines.

The tuition fee for the BTech programme at MSRUAS is INR 7.2 Lacs - INR 21 Lakh. In addition, students must pay a one-time registration fee, a security deposit, and other essential charges. These fees are sourced from the official MSRUAS website or the sanctioning body but are subject to change, so students should verify before applying.

$P_B^O=$ vapour pressure of benzene at 20°C = 70 torr

$P_M^O$ = vapour pressure of toluene at 20°C = 20 torr

Mixture is equimolar, X_B = 0.5 and X_M = 0.5

Total vapour pressure (P_T) = 70 × 0.5 + 20 × 0.5 = 45 torr

Mole fraction of benzene in vapour phase $\left(x_B^{\text{'}}\right)=\frac{P_B^O{X}_B}{P_T}=\left(\frac{70\times 0.5}{45}\right)torr$

= 0.777 = 77.7 × 10^-2 torr

Ans. = 78 (the nearest integer)

$\left|\begin{array}{ccc}\hfill 3\hfill & \hfill -1\hfill & \hfill 4\hfill \\ \hfill 1\hfill & \hfill 2\hfill & \hfill -3\hfill \\ \hfill 6\hfill & \hfill 5\hfill & \hfill k\hfill \end{array}\right|=0\Rightarrow k=-5$

The PGIMER  BSc nursing result will be published on the official website, pgimer.edu.in. Candidates can also check the result by providing their login ID to download the scorecard when issued by PGIMER. 

Kindly consider the following figure

The PGIMER BSc Result 2025 will be declared on August 9, 2025 in online mode on the official website, pgimer.edu.in. 

Hence, electronic configuration of CO²⁺ is $\left[Ar\right]3d^{7}4s^0$ . In complex ${\left[Co{\left(CN\right)}_6\right]}^{4-},$ given ligand CN^- is $\therefore$ strong hence, after pairing in d-subshell, total number of unpaired electron =

spin magnetic moment = $\sqrt[]{1\left(1+2\right)}=\sqrt[]{3}=1.73BM$ $=1.73BM\approx 2.0BM$  

Equation of plane ${\perp }^r$ to line $\frac{x-3}{2}=\frac{x-1}{1}=\frac{x-2}{1}$ and passes through the point

(2, 3, -1) is 2(x – 2) + 1(y – 3) + 1 (z + 1) = 0

=> 2x + y + z – 6 = 0         .(i)

Hence point (1, 2, 2) satisfies equation (i)

$z=\frac{1}{1-cos\theta +2isin\theta }=\frac{1-cos\theta -2isin\theta }{{\left(1-cos\theta \right)}^2-{\left(2isin\theta \right)}^2}=\frac{2si{n}^2\frac{\theta }{2}-2isin\theta }{{\left(1-cos\theta \right)}^2+4si{n}^2\theta }$      

$\therefore Re\left(z\right)=\frac{2si{n}^2\frac{\theta }{2}}{4si{n}^2\frac{\theta }{2}\left(si{n}^2\frac{\theta }{2}+4co{s}^2\frac{\theta }{2}\right)}=\frac{1}{2\left(1+3co{s}^2\frac{\theta }{2}\right)}=\frac{1}{5}\Rightarrow co{s}^2\frac{\theta }{2}=\frac{1}{2}$   

$\Rightarrow \theta =\frac{\pi }{2}\therefore {\displaystyle {\int }_0^{\frac{\pi }{2}}sinxdx=1}$

For Ni²⁺, crystal field CFSE magnitude shows the magnitude of absorbed light. Following are the energy absorbed order

  ${\left[NiC{l}_4\right]}^{2-}<{\left[Ni\left(H_{2}O\right)\right]}^{2+}<{\left[Ni{\left(CN\right)}_4\right]}^{2-}$

Hence order of colour of compounds are.

${\left[NiC{l}_4\right]}^{2-}>{\left[Ni{\left(H_{2}O\right)}_6\right]}^{2+}>{\left[Ni{\left(CN\right)}_4\right]}^{2-}$

NFSC BTech admissions are based on JEE (Mains) Paper-I, and the percentile scores of the candidate in the respective Board of Education will be called in a proportionate ratio decided by the competent authority based on the CRL Rank provided by NTA in the JEE (Mains) 2025. 

Candidates seeking admission to the National Fire Service College must fulfil the college's eligibility criteria. For the BTech course, applicants must have completed Class 12 with a 50% aggregate with Physics and Mathematics/English as compulsory subjects. The selection process for all courses is based on JEE (Main) 2025 Paper-I.