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L₁ : 3x – 4y + 12 = 0

L₂ : 8x + 6y + 11 = 0

$\left(\alpha ,\beta \right)$ lies on that angle which contain origin

$\therefore$ Equation of angle bisector of that angle which contain origin is

$\frac{3x-4y+12}{5}=\frac{8x+6y+11}{10}$

$\Rightarrow 2x+14y-13=0$

$\left(\alpha ,\beta \right)$ lies on it

$\Rightarrow 2\alpha +14\beta -13=0$ …… (i)

$\Rightarrow 3\alpha -4\beta +7=0$ ……. (ii)

Solving (i) & (ii)

$\alpha =-\frac{23}{25}\&\beta =\frac{53}{50}$

$\therefore \alpha +\beta =\frac{7}{50}$

$\Rightarrow 100\left(\alpha +\beta \right)=14$

From the available data, the tuition fee for MBA at KUK is less than most other institutes that offer MBA courses around Haryana. The MBA tuition fee at KUK is INR 2.04 Lacs while other institute's tuition fee ranges between INR 7 - 10 lakh. This makes KUK a great choice to pursue an MBA course at for most interested candidates.

Kindly consider the following figure

Yes, apart from the tuition fee, students must pay an admission form fee of INR 1,000, an admission fee of INR 5,000, and a registration fee of INR 1,000. Additionally, there is an exam fee of INR 2,000 per semester. These extra charges are mandatory and part of the overall cost of admission.

The tuition fee for the BTech programme at Radha Govind University is INR 2 Lacs in total, which is divided into INR 25,000 per semester. The programme spans eight semesters across four years. Candidates should note that this fee does not include additional charges like registration, exam, and admission fees.

Joining Directorate of Distance and Continuing Education, Utkal University for BA course is generally considered a decent option. Candidates must consider factors like infrastructure, faculty experience, hostel and mess facilities, curriculum, etc. while taking admission. They can apply online or offline for admission at Directorate of Distance and Continuing Education, Utkal University.

$F_R=\left\{\frac{kQ{q}_0}{{\left(a-x\right)}^2}-\frac{kQ{q}_0}{{\left(a+x\right)}^2}\right\}$

$=-kQ{q}_0\left\{\frac{a^2+x^2+2ax-a^2-x^2+2ax}{\left(a^2-x^2\right)}\right\}$

$F_R=-\frac{kQ{q}_0\left(4ax\right)}{{\left(a^2-x^2\right)}^2}$

$T=2\pi \sqrt[]{\frac{a^{3}m}{4kQ{q}_0}=\sqrt[]{\frac{4{\pi }^2{a}^{3}m\times 4\pi {\epsilon }_0}{4Q{q}_0}}}=\sqrt[]{\frac{4{\pi }^3{\epsilon }_{0}m{a}^3}{Q{q}_0}}$

(a) Polluted water has low value of dissolved oxygen, but high value of B.O.D., because chemical and organic matter uses dissolved oxygen to decompose.

(b) Eutrophication is result of excessive growth of weed in water bodies, which consumes dissolved oxygen, thus decreases oxygen.

Admission to Dr. DY Patil Dnyan Prasad University School of Hospitality & Tourism is based on an entrance exam followed by an online PI. The institute offers BBA, Integrated MBA and PhD courses. The exam shall be held in computer-based test mode. Candidates need to pass at least Class 12 or post-graduation for course admission. The institute may conduct an interview.

$l={\displaystyle {\int }_{-3}^{103}\left(\left[sin\left(\pi x\right)\right]+e^{\left[cos\left(2\pi x\right)\right]}\right)}dx$

$\left[sin\pi x\right]$ is periodic with period 2 and

$e^{\left[cos2\pi x\right]}$ is periodic with period 1.

So,

$I=52{\displaystyle {\int }_0^2\left(\left[sin\left(\pi x\right)\right]+e^{\left[cos2\pi x\right]}\right)}dx$

= $\frac{52}{e}$

Linux has replaced UNIX and is dominating the computing field. It is widely used in supercomputers and embedded devices. While Linux has not been able to dominate the desktop space, it is an essential player in this field.

Due to its features, such as flexibility and open-source nature, Linux-based operating systems are now used in various connected devices. Linux is likely to revolutionize emerging technologies, including wearables, the Internet of Things  (IoT), smart home devices, and more.

The duration of BA course at Directorate of Distance and Continuing Education, Utkal University is of three years. The course consists of six semesters. The core subject for this course is Odia, while the medium of instruction in the semester examinations is English/Odia. Candidates must fulfil the eligibility criteria before applying for admission in BA course at Directorate of Distance and Continuing Education, Utkal University.

Cu is least reactive metal and it lies below hydrogen in reactivity series.

Yes, Directorate of Distance and Continuing Education, Utkal University, offers the BA course at the UG level. This is offered for a duration of three years and in distance mode. Candidates must have a valid aggregate in Class 12 or equivalent examination to apply for the course at Directorate of Distance and Continuing Education, Utkal University. 

The duration of Thakur School of Architecture and Planning BArch course is five years. In this duration, students study various theory courses, elective courses and participate in seminars and projects. Students also get to attend seminars, tutorials,  guest lectures, exhibitions, and workshops. Admissions to this course are done based on marks obtained in NATA/JEE Main.

${\left(N{H}_4\right)}_{2}C{r}_2{O}_7\underset{}{\overset{\Delta }{\to }}\boxed{N_2}+C{r}_2{O}_3+4H_{2}O$

$KMn{O}_4+HC\mathcal{l}\to MnC{\mathcal{l}}_2+KC\mathcal{l}+\boxed{C{\mathcal{l}}_2}+H_{2}O$

$A\mathcal{l}+NaOH+H_{2}O\to Na\left[A\mathcal{l}{\left(OH\right)}_4\right]+\boxed{H_2}$

$NaN{O}_3\to NaN{O}_2+\boxed{O_2}$

$P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$

$\Rightarrow \frac{1}{2}=\frac{1}{3}+\frac{1}{5}-P\left(A\cap B\right)$

$P\left(\frac{A}{B\text{'}}\right)+P\left(\frac{B}{A\text{'}}\right)$

$=\frac{P\left(A\right)-P\left(A\cap B\right)}{1-P\left(B\right)}+\frac{P\left(B\right)-P\left(A\cap B\right)}{1-P\left(A\right)}=\frac{5}{8}$

The SSC GD full form is Staff Selection Commission General Duty. The complete exam name is SSC GD Constable recruitment, which is a yearly exam conducted at the national level. The Staff Selection Commission (SSC) and the Union Ministry of Home Affairs hold this exam every year for Constable GD, Rifleman GD and Sepoy posts in the Central Armed Police Forces (CAPFs) and Assam Rifle.