IPMAT 2020 Question Paper IPM Indore Quantitative Ability. Solve questions from IPMAT 2020 Question Paper from IPM Indore and check the solutions to get adequate practice. The best way to ace IPMAT is by solving IPMAT Question Paper. To solve other IPMAT Sample papers, go here: **IPM Sample Paper**

Question 23 : A 2 × 2 matrix is filled with four distinct integers randomly chosen from the set {1,2,3,4,5,6} Then the probability that the matrix generated in such a way is singular is

- \\frac{2}{45})
- \\frac{1}{45})
- \\frac{4}{15})
- \\frac{1}{15})

\\frac{2}{45})

Valid until 1st Dec

Online Batches Available Now!

A matrix is singular if and only if the determinant of the matrix is 0.

In a 2 × 2 matrix,

\\left|\begin{array}{cc}a & c \\d & b\end{array}\right| \\) = ab - cd = 0

Or ab = cd

If one of a,b,c or d is 5, then ab ≠ cd, because in the set {1,2,3,4,5,6} there is only one multiple of 5.

So, we just have the set {1,2,3,4,6} to deal with and out of these we'll have select 4 integers.

We can't pick either 3 or 6. We'll have to pick them both.

That is 3 and 6 have to stay on either side of the equation ab = cd

So, the equation now becomes, 3b = 6d

Clearly, b > d

{b, d} ⊂ {1, 2, 4}

If b = 4, d = 2

If b = 2, d = 1

So, only two such combinations exist.

{a, b, c, d} = {1, 2, 3, 6} or {a, b, c, d} = {4, 2, 3, 6}

We can select four numbers from the six in ^{6}C_{4} = 15 ways

After selecting the 4 integers, we can arrange them in order in 4! ways.

So, the total number of matrices that can be constructed = 15 × 4!

Once we select {a, b, c, d} = {1, 2, 3, 6} or {a, b, c, d} = {4, 2, 3, 6},

To construct a singular matrix, for example, 2 & 3 should be on the same diagonal. Similarly, 4 & 3 too in case of {a, b, c, d} = {4, 2, 3, 6}.

Only one-third of the arrangments yeild a singular matrix and the others dont.

But the probabilty of getting a singular matrix = \\frac{2 × 4! ÷ 3}{15 × 4!}) = \\frac{2}{45})

The question is **" A 2 × 2 matrix is filled with four distinct integers randomly chosen from the set {1,2,3,4,5,6} Then the probability that the matrix generated in such a way is singular is " **

Choicve A is the correct answer.

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484 / 94459 38484

**WhatsApp:** WhatsApp Now

**Email: **info@2iim.com