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Admission through JEE Main Paper 2 (B.Arch/B.Planning) depends on both your rank and NATA/JEE score. With a decent rank, you can target SPA Delhi, SPA Bhopal, SPA Vijayawada, and architecture departments of NITs like Trichy, Calicut, and Bhopal. Private options include CEPT Ahmedabad and Sharda University, where cutoffs vary by specialisation and category.

35. Number of balls contain in win $=5$ red

$=5$ black

Let the red ball be drawn in the first attempt

$\therefore$ $P$ (drawing a red ball) $=\frac{5}{10}=\frac{1}{2}$

By question, if added two red balls to the win, then $7$ red balls and $5$ black balls contain.

$P$ (drawing a red ball) $=\frac{7}{12}$

Let a black ball be drawn at first attempt

$\therefore$ $P$ (drawing a black ball) $=\frac{5}{10}=\frac{1}{2}$

If two black balls are added to the win, then $7$ black balls and $5$ red balls contain.

$P$ (drawing a red ball) $=\frac{5}{12}$

Therefore, probability of drawing the second ball as of red colour is

$=\left(\frac{1}{2}\times \frac{7}{12}\right)+\left(\frac{1}{2}\times \frac{5}{12}\right)=\frac{1}{2}\left(\frac{7}{12}+\frac{5}{12}\right)=\frac{1}{2}\times \frac{12}{12}=\frac{1}{2}\times 1=\frac{1}{2}$

According latest data shared by Union Education Minister, no. of Indian students in Russia stood at 31,444 in 2024, increasing for 3rd year in row.

Below are total Indian students in Russia in last few years-

Yes, there are many government Design colleges in Delhi NCR. Some of them are mentioned below along with their tuition fees:

Disclaimer: This information is sourced from the official website/ sanctioning body and may vary.

$$34. $P(A^{\prime }{B}^{\prime })=[1-P(A)][1-P(B)]$

$\Rightarrow P(A^{\prime }\cap B^{\prime })=1-P(A)-P(B)+P(A)P(B)$

$\Rightarrow -[P(A)+P(B)-P(A\cap B)]=-P(A)-P(B)+P(A)(B)$

$\Rightarrow -P(A)-P(B)+P(A\cap B)=-P(A)-P(B)+P(A)P(B)$

$\Rightarrow P(A\cap B)=P(A).P(B)$

Therefore, it shows A and B are independant

Candidates can refer to the following table for important dates of PU UGLAW counselling:

33. The outcome of rolling $2$ dice is $36$ . The only prime number is $2$ .

Let,  $E=$ event of getting an even prime number on each die

$E=\{(2,2)\}$ therefore

$P(E)=\frac{1}{36}$

Therefore, the correct answer is $(D)$ $\frac{1}{36}$

There are a total of 140 seats for the BPharm courses. Candidates are admitted as per the sanctioned intake and performance in the selection rounds. It is within the rights of the university to revise the seat count. The mentioned seat intake is as per the official website/ sanctioning body. It is still subject to changes and hence, is indicative. 

SIES College of Management Studies MAH CET Cutoff 2024 has been released for General AI Quota. The cutoffs were released in terms of percentage. Considering the SIES College of Management Studies cutoff 2024, the CMAT cutoff stood at 80. Other than that, CAT, MAT, and XAT cutoff percentile for the General AI category candidates stood at 25, 80, and 70, respectively.

32. Let,

$P(H)=$ denote the student who read Hindi newspaper

$P(E)=$ denote the student who read English newspaper

Then, $P(H)=60\mathrm{\%}=\frac{6}{10}=\frac{3}{5}$

$P(E)=40\mathrm{\%}=\frac{4}{10}=\frac{2}{5}$

$\mathrm{i.\; P}(H\cap E)=20\mathrm{\%}=\frac{2}{10}=\frac{1}{5}$

$\Rightarrow P(H\cup E{)}^{\prime }=1-[P(H)+P(E)-P(H\cap E)]$

$=1-\left[\frac{3}{5}+\frac{2}{5}-\frac{1}{5}\right]$

$=1-\frac{3+2-1}{5}$

$=1-\frac{4}{5}=\frac{1}{5}$

ii. Probability of randomly chosen student that reads English newspaper, if she reads Hindi newspaper, is given by

$P(E/H)=\frac{P(E\cap H)}{P(H)}=\frac{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}=\frac{1}{3}$

iii. Probability that randomly chosen student reads Hindi newspaper, if she reads English newspaper, is given by

$P(H/E)=\frac{P(H\cap E)}{P(E)}=\frac{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}=\frac{1}{2}$

The provisional merit list for the PU UGLaw 2026 will be published mostly in July. Candidates who qualified the exam will have to fill the admission form separately to participate in the counselling process. 

The PU UGLAW tentative merit list will be published on the official website. Candidates can raise objections regarding tentative merit list on the basis of already filled up information. 

Yes, CBSE renamed the compartment exams as supplementary exams based on the recommendations of NEP 2020. This was done in 2023 to offer opportunities for students to improve their performance in 10th/12th board exams. the objective was to shift the focus from simply passing the exams to enhancing overall performance.

The PU UGLAW Exam Dates have not been announced yet. Along with the notification, the university will also release the PU UGLAW Admission Form details and last deadline.

The aspirants of BPharm at DPSRU have to submit certain documents. These are required for verification purposes. Mentioned below are the documents:

• Class 10 and Class 12 marksheet
• Date of birth certificate
• Provisional certificate from the school last attended
• Proof of gap period after passing Class 12 (if any)
• Character certificate from the school last attended
• Medical certificate from a medical practitioner holding a degree (at least MBBS)
• Scanned photograph and signature
• Caste and income certificates

CBSE will likely conduct the CBSE Class 12 supplementary exams 2026 on July 15, 2026 only for all subjects. The Board released the CBSE 12th date sheet for the supplementary exams in June on the official website- cbse.gov.in. Click on CBSE 12th supplementary date sheet 2026 to check the exam dates.

IPGMER Kolkata accepts the NEET SS entrance exam, followed by the counselling rounds for admission to the DM courses. Institute of Post Graduate Medical Education and Research NEET SS cutoff 2024 has been released wherein the first round closing rank for DM admission ranged between 10 and 271 for the General AI category students. Among all the DM courses, the most and least competitive specialsiations were Pulmonary Medicine and Endocrinology, respectively. Candidates can refer to the table below to check out the IPGMER Kolkata NEET SS cutoff 2024 for all the courses among the students belonging to the General AI quota.