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The branch-wise placement percentage recorded during MBA placements 2025 is mentioned below:

The average package received during IIT Dhanbad MBA placements 2025 was INR 10.48 LPA.

No, you cannot do BAMS with 12th in PCM and BPharma in graduation.

Yes, MBA placements at IIT Dhanbad are good. The  key highlights of MBA placements 2025 at IIT Dhanbad are presented below:

86. Let the man toss the coin n times. The n tosses are n Bernoulli trials.

Probability (p) of getting a head at the toss of a coin is 1/2.

∴ p = 1/2 ⇒ q = 1/2

$\therefore P\left(X=x\right)={\mathrm{nC}}_x$
$p^{n-x}{q}^x={\mathrm{nC}}_x$
${\left(\frac{1}{2}\right)}^{n-x}{\left(\frac{1}{2}\right)}^x={\mathrm{nC}}_x$
${\left(\frac{1}{2}\right)}^n$

It is given that,

P (getting at least one head) > 90/100

P (x ≥ 1) > 0.9

⇒ 1 − P (x = 0) > 0.9

$1-{\mathrm{nC}}_0$
$.\frac{1}{2^n}>0.9\\ {\mathrm{nC}}_0$
$\begin{array}{l}.\frac{1}{2^n}<0.1\\ \frac{1}{2^n}<0.1\\ 2^n>\frac{1}{0.1}\\ 2^n>10......(1)\end{array}$

The minimum value of n that satisfies the given inequality is 4.

Thus, the man should toss the coin 4 or more than 4 times.

85. The probability of success is twice the probability of failure.

Let the probability of failure be x.

∴ Probability of success = 2x

$\begin{array}{l}x+2x=1\\ \Rightarrow 3x=1\\ \Rightarrow x=\frac{1}{3}\\ \therefore 2x=\frac{2}{3}\end{array}$

Let $p=\frac{1}{3}$ and $q=\frac{2}{3}$

Let X be the random variable that represents the number of successes in six trials.

By binomial distribution, we obtain

$P\left(X=x\right)={\mathrm{nC}}_x$
$p^{n-x}{q}^x$

Probability of at least 4 successes $=P\left(X\ge 4\right)$

$=P\left(X=4\right)+P\left(X=5\right)+P\left(X=6\right)\\ ={\mathrm{6C}}_4$
$\mathrm{}{\left(\frac{2}{3}\right)}^4{\left(\frac{1}{3}\right)}^2+{\mathrm{6C}}_5$
$\mathrm{}{\left(\frac{2}{3}\right)}^5\left(\frac{1}{3}\right)+{\mathrm{6C}}_6$
$\begin{array}{l}\mathrm{}{\left(\frac{2}{3}\right)}^6\\ =\frac{15{\left(2\right)}^4}{3^6}+\frac{6{\left(2\right)}^5}{3^6}+\frac{{\left(2\right)}^6}{3^6}\\ =\frac{{\left(2\right)}^4}{{\left(3\right)}^6}\left[15+12+4\right]\\ =\frac{31\times 2^4}{{\left(3\right)}^6}\\ =\frac{31}{9}{\left(\frac{2}{3}\right)}^4\end{array}$

The placement rate recorded during IIT Dhanbad MTech placements 2025 was 70.78%. In Integrated MTech, placement percentage recorded was 90.54%.

84. A leap year has 366 days which means 52 complete weeks and 2 days. If any one of these two days in a Tuesday, then the year will have 53 Tuesdays.

Number of total days in a week = 7

Number of favourable days = 2

Therefore, P (the year will have 53 Tuesday) = 2/7

The median package received during IIT Dhanbad placements 2025 for MTech and Integrated MTech programs was INR 8.75 LPA and 26.25 LPA.

The tuition fee for the BCom programmes at MCNUJC, Bhopal, is INR 1 lakh. However, apart from this tuition fee, it may also include various fee elements, such as admission fees, security charges, miscellaneous fees, and other one-time charges. These fees are paid only once at the time of admission. It must be noted that the above-mentioned fees are taken from the official website. They are still subject to change and, hence, are indicative.

83. The probability of getting a six in a throw of die is 1/6 and not getting a six is 5/6.

Let p = 1/6 and q = 5/6

The probability that the 2 sixes come in the first five throws of the die is

${\mathrm{5C}}_2$
$\mathrm{}{\left(\frac{1}{6}\right)}^2{\left(\frac{5}{6}\right)}^3=\frac{10\times {\left(5\right)}^3}{{\left(6\right)}^5}$

∴ Probability that third six comes in the sixth throw =

$\begin{array}{l}=\frac{10\times {\left(5\right)}^3}{{\left(6\right)}^5}\times \frac{1}{6}\\ =\frac{10\times 125}{{\left(6\right)}^6}\\ =\frac{10\times 125}{46656}\\ =\frac{625}{23328}\end{array}$

Yes, IIT Dhanbad is worth in terms of MTech placements. The key highlights of IIT Dhanbad MTech placement 2025 are presented below:

IIT Dhanbad MTech placement highlights 2025 are mentioned below:

82. Let p and q respectively be the probabilities that the player will clear and knock down the hurdle.

$\begin{array}{l}\therefore P=\frac{5}{6}\\ \Rightarrow q=1-p=1-\frac{5}{6}=\frac{1}{6}\end{array}$

Let X be the random variable that represents the number of times the player will knock down the hurdle.

Therefore, by binomial distribution, we obtain

$P\left(X=x\right)={\mathrm{nC}}_x$
$p^{n-x}{q}^x$

P (player knocking down less than 2 hurdles) $=P\left(X<2\right)$

$=P\left(X=0\right)+P\left(X=1\right)\\ ={\mathrm{10C}}_0$

$\mathrm{}{\left(q\right)}^0{\left(p\right)}^{10}+{\mathrm{10C}}_1$
$\begin{array}{l}\mathrm{}\left(q\right){\left(p\right)}^9\\ ={\left(\frac{5}{6}\right)}^{10}+10.\frac{1}{6}.{\left(\frac{5}{6}\right)}^9\\ ={\left(\frac{5}{6}\right)}^9\left[\frac{5}{6}+\frac{10}{6}\right]\\ =\frac{5}{2}{\left(\frac{5}{6}\right)}^9\\ =\frac{{\left(5\right)}^{10}}{2\times {\left(6\right)}^9}\end{array}$

The National University of Singapore tuition fees range between INR 11 L and INR 1 Cr for undergraduate courses, and between INR 11 L and INR 91 L for postgraduate students. Students can check the National University of Singapore for popular programs below:

80. It is given that $90\mathrm{\%}$ of people are right handed.

$p=P$ (right handed) $=90\mathrm{\%}=\frac{90}{100}=\frac{9}{10}$ and $q=P$ (left handed) $=1-\frac{9}{10}=\frac{1}{10}$

Using Binomial distribution,

Probability more than $6$ people are right handed is given by

$=\sum _{r=7}^{10}{\mathrm{10c}}_r$

${\displaystyle \mathrm{}{p}^r{q}^{n-r}}$

$=\sum _{r=7}^{10}{\mathrm{10c}}_r$

${\displaystyle \mathrm{}{\left(\frac{9}{10}\right)}^r{\left(\frac{1}{10}\right)}^{10-r}}$

Hence, probability of having at most $6$ right handed people:

$=1-P$ (more than $6$ people are right handed)

$=1-\sum _{r=7}^{10}{\mathrm{10c}}_r$

${\displaystyle \mathrm{}{\left(\frac{9}{10}\right)}^r{\left(\frac{1}{10}\right)}^{10-r}}$

Yes, candidates can join MCNUJC, Bhopal for BCom without appearing for any entrance exam. As per the admission criteria, the university shortlists candidates based on the scores obtained in the previous qualifying exam. Therefore, candidates are not required to appear for any entrance examination. However, it is necessary for applicants to review the eligibility criteria before applying for the desired course specialisation.