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79. Given, Men having grey hair $=5\mathrm{\%}$

Women having grey hair $=0.25\mathrm{\%}$

Total people with grey hair $=(5+0.25)\mathrm{\%}$ $=5.25\mathrm{\%}$

Probability that the selected person’s hair is of male $=\frac{5}{5.25}=\frac{1}{1.05}=\frac{100}{105}=\frac{20}{21}$

With a general category rank of 449, you stand a strong chance of securing admission in IIT Jodhpur, and are very likely or highly likely for IIT Dharwad, IIT Dhanbad, and potentially IIT Roorkee, depending on seat availability and later counseling rounds.

 The approximate subject-wise weightage in GPAT is as follows:

• Pharmacology – 25–30 questions

• Pharmaceutics – 20–25 questions

• Pharmaceutical Chemistry – 15–20 questions

• Pharmacognosy – 10–15 questions

Other subjects (Biochemistry, Microbiology, etc.) – 10–15 questions
This distribution may vary slightly year to year, but the core subjects consistently have the highest weightage.

78. i. Here, Sample space of given condition,

$S=\{(B,B),(B,G),(G,B),(G,G)\}$

Let, $E:$ denotes the event both children are male

$F:$ denotes the event at least one of the children is a male

$\therefore E\cap F=\{(B,B)\}$

$\Rightarrow P(E\cap F)=\frac{1}{4}$

Here, $P(E)=\frac{1}{4}$ and $P(F)=\frac{3}{4}$

$\Rightarrow P(E/F)=\frac{P(E\cap F)}{P(F)}=\frac{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}=\frac{1}{3}$

ii. Let, $A:$ event that both children are female

$B:$ event that elder child is female

$A=\{G,G\}$ $P(A)=\frac{1}{4}$

$B=\{(G,G),(G,B)\}$ $P(B)=\frac{2}{4}=\frac{1}{2}$

$A\cap B=\{(G,G)\}$ $P(A\cap B)=\frac{1}{4}$

$P(A/B)=\frac{P(A\cap B)}{P(B)}$

$=\frac{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=\frac{1}{4}\times 2=\frac{1}{2}$

Applicants of an Singapore student visa can expect to incur around SGD 120 (INR 8.6 K),  in the form of visa application fee.

This includes a processing fee, an issuance fee, & an multiple-entry visa fee. The table below gives a detailed breakdown of the Singapore student visa cost for Indian students:

A total of 779 students participated and 657 students were placed during IIT Dhanbad placements 2025.

$$77. $A$ is a subset of $B$

$\Rightarrow A\cap B=A$

$\therefore P(A\cap B)=P(B\cap A)=P(A)$

$=P(B/A)=\frac{P(B\cap A)}{P(A)}=1$

$A\cap B\ne 0$

$(A\cap B)=0$

$\Rightarrow P(B/A)=\frac{P(B\cap A)}{P(A)}=0$

The branch-wise placement rate recorded during IIT Dhanbad BTech placement 2025 is presented below:

According to media reports, 4 Computer Science and Engineering students received salary package of 80 LPA during the phase 1 placement drive 2026. In 2025, highest package offered was INR 122 LPA.

Placements ranging between INR 1.8 Lacs to INR 3.25 Lacs per annum, but these figures are not exclusive to the Nutrition and Dietetics students and cover all departments collectively.

As per the available information related to the MCNUJC, Bhopal BCom programme, the selection of candidates is based on the scores obtained in the last qualifying exam. It is essential for candidates to meet the requisite eligibility criteria before applying for the programme. To be considered for the programme, candidates must have completed their Class 12 in the relevant stream from a recognised board. This merit-based selection ensures that only eligible candidates are shortlisted for the programme.

The key highlights of IIT Dhanbad placements 2025 are presented below:

The overall average package recorded during IIT Dhanbad placments 2025 was INR 17.49 LPA. In BTech, BTech Double Major and BTech+MTech courses, average package recorded was 19.68 LPA, 30.81 LPA and 22.17 LPA. 

In MTech, MBA and MSc, average salary received was 10.87 LPA, 10.48 LPA and 7.46 LPA.

Yes, the BCom programmes are available at MCNUJC with a course duration of three to four years. The selection of candidates is based on merit. Interested candidates can refer to the following table for more information related to the MCNUJC Bhopal BCom programme:

NOTE: The above-mentioned seat intake is taken from the official website. It is still subject to change and, hence, is indicative.

Khwaja Moinuddin Chishti Language University hasn't released any placement data for its BBA course. However, as per the recent placements data, a total of 200 students and 70 FoET students were placed during Khwaja Moinuddin Chishti Language University placements 2023. Apart from this, many top companies such as Microsoft, Tech Mahindra, and Genpact among others visited the campus during the recent placement drive.