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Let A = $\left[\begin{array}{ccc}\hfill a\hfill & \hfill b\hfill & \hfill c\hfill \\ \hfill d\hfill & \hfill e\hfill & \hfill f\hfill \\ \hfill 9\hfill & \hfill h\hfill & \hfill i\hfill \end{array}\right]$  

Now A^TA

trace will be    $a^2+b^2+c^2+d^2+e^2+f^2+9^2+h^2=6$

total ways = 

$\left|f\left(x\right)\right|\le 800\Rightarrow 2n^2-n-1\le 800$  

$\Rightarrow 2n^2-n-801\le 0$                

${\displaystyle \sum _{x\in S}^{}f\left(x\right)={\displaystyle \sum _{}^{}\left(2x^2-x-1\right)}}$                

$=2\left(19^2+18^2+........1^2+0^2+1^2+.....+20^2\right)$                

= 10620

Yes, Calicut University has merit-based admissions for a number of UG and PG courses. UG merit-based admissions use CAP, whereas PG uses PGCAP. Few courses also have entrance exams such as CUCAT, KEAM, or CAT. Always refer to course-specific requirements while applying.

y⁵ – 9xy + 2x = 0

differentiate 5y⁴ – 9x $\frac{dy}{dx}$ - 9y + 2 = 0

$\frac{dy}{dx}=\frac{9y-2}{5y^4-9x}$        

 For horizontal tangent $\frac{dy}{dx}=0\Rightarrow y=\frac{2}{9}$  which does not satisfy the equation so no horizontal

For vertical tangent -> $5y^4-9x=0$  

->m = 0, N = 2

$sin\left(2x^2\right).109_e\left(tan{x}^2\right)dy+4xydx=4\sqrt[]{2}.x.\left(sin{x}^{2}cos\frac{\pi }{4}-cos{x}^{2}sin\frac{\pi }{4}\right)dx$  

$\Rightarrow \mathcal{l}n\left(tan{x}^2\right)dy+\frac{4x}{sin\left(2x^2\right)}ydx=\frac{4x\left(sin{x}^2-cos{x}^2\right)}{sin\left(2x^2\right)}dx$

Integrate

$\Rightarrow y.\mathcal{l}n\left(tan{x}^2\right)=2.\mathcal{l}n\left(\frac{sin{x}^2+cos{x}^2-1}{sin{x}^2+cos{x}^2+1}\right)+C$

$x=\sqrt[]{\frac{\pi }{6}},y=1$  calculate C.

Yes, you can get admission in Calicut University with 60% in Class 12 in most UG courses. In BSc, BA, and BCom, merit-based selection is available through CAP. Satisfying minimum marks makes one eligible but not assured admission. Greater marks provide greater opportunities.

To crack Gurugram University placement interview students can follow the steps given below:

·       Review your resume

·       Practice common interview questions

·       Showcase your strengths

·       Be confident and articulate

The student has to appear in the syllabus prescribed for the year in which he or she plans to appear for the Goa Class 10 exam. Students are advised to go through the syllabus of the Goa SSC board for that academic year. They can check the Goa Class 10 syllabus on the official website of the Goa board. They can also contact their school, for the Goa Class 10 syllabus. 

The placement rate for Gurugram University was 81%. However, Gurugram University provides good placement to its students. The data tabulated below provides Gurugram University placement highlights for 2025:

$e_H=\sqrt[]{1+\frac{64}{49}}=\frac{\sqrt[]{113}}{7}$

$\Rightarrow e_H.e_E=\frac{1}{2}$

$\Rightarrow \frac{113}{49}.\frac{\left(64-a^2\right)}{64}=\frac{1}{4}\Rightarrow a^2-64=\frac{32^2}{113}$

$\mathcal{l}=\frac{2a^2}{b}=2\left(64+\frac{32^2}{113}\right).\frac{1}{8}$

$113\mathcal{l}=1552$

Yes, students can pursue higher studies in another state after passing the Goa SSC exam. They can pursue higher studies or senior secondary studies from a different Board within Goa. Goa SSC 10th Certificate is valid for any senior secondary studies in India. Students have to apply for a migration Certificate if they wish to study in another state. While applying for admission, the students must submit their Migration Certificate issued by the Goa board along with the other requisite documents.

Gurugram University has announced its 2025 placement report. Have a look at the data tabulated below to know more:

The number of students placed during Gurugram University placements has not been released yet. However, some placement details have been released and are provided in the table below:

The placement package recorded at Gurugram University placements 2025 is given in the table below:

While solving the Goa SSC Sample papers and previous year papers, it is important to start familiarising yourself with the structure and pattern of the Goa SSC exam. Go through the entire question paper carefully and understand the type of questions and marks for each question. Ensure you manage the time efficiently while solving the Goa SSC previous year question papers.

Plane through 4ax – y + 5z – 7a = 0 = 2x – 5y – z – 3

is    $x\left(4a+2\lambda \right)+y\left(-1-5\lambda \right)+z\left(5-\lambda \right)=7a+3\lambda$

This plane contains 4, -1, 0

->9a + 1 + 10l = 0          …… (i)

Plane contains the line $\frac{x-4}{1}=\frac{y+1}{-2}=\frac{z}{1}$  

-> $4a+11\lambda +7=0$ ……. (ii)

From (i) & (ii) a = 1,   $\lambda$  =-1

Equation of plane $\pi \equiv x+2y+3z-2=0$  

$\Rightarrow 7P+3-2P+4-12P+9-2=0\Rightarrow P=2$

Gurugram University provides great placements to its students. Check out the table below to know about the Gurugram University placement statistics 2025:

Even though practicing Goa SSC previous year question papers helps in improving your scores, you should not depend only on the  previous year question papers. You should learn the concepts from the prescribed textbooks. Also you should learn to draw diagrams, graphs, properly. 

The placement rate for Gurugram University stood at 81%. The table below states the same:

BBA application fee for Jagannath University, Haryana is INR 500. The amount is non-refundable and has to be paid online while filling the application form. Students can access the registration form on the official website. Abide by the deadline given by the university. Make sure to save transaction receipt for future references.