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 4 : Suppose \\left|\begin{array}{ccc}a & a^{2} & a^{3}-1 \\b & b^{2} & b^{3}-1 \\ c & c^{2} & c^{3}-1\end{array}\right| \\) = 0 where a, b and c are distinct real numbers. If a= 3, then the value of a b c is

Try upto 40 hours for free

Learn from the best!

Limited Seats Available - Register Now!

\\left|\begin{array}{ccc}a & a^{2} & a^{3}-1 \\b & b^{2} & b^{3}-1 \\ c & c^{2} & c^{3}-1\end{array}\right| \\) = 0

Performing the following row operations

R_{3} = R_{3} - R_{2}

R_{2} = R_{2} - R_{1}

we get,

\\left|\begin{array}{ccc}a & a^{2} & a^{3}-1 \\b-a & b^{2}-a^{2} & b^{3}-a^{3} \\ c-a & c^{2}-b^{2} & c^{3}-c^{3}\end{array}\right| \\) = 0

\\left|\begin{array}{ccc}a & a^{2} & a^{3}-1 \\b-a & [b-a][b+a] & [b-a][b^{2}+ab+a^{2}] \\ c-a & [c+a][c-a] & [c-a][c^{2}+cb+b^{2}]\end{array}\right| \\) = 0

(b-a)(c-b)\\left|\begin{array}{ccc}a & a^{2} & a^{3}-1 \\1 & b+a & b^{2}+ab+a^{2} \\ 1 & c+a & c^{2}+cb+b^{2}\end{array}\right| \\) = 0

Perform R_{2} = R_{2} - R_{3}

(b-a)(c-b)\\left|\begin{array}{ccc}a & a^{2} & a^{3}-1 \\0 & a-c & ab+a^{2}-c^{2}-cb \\ 1 & c+a & c^{2}+cb+b^{2}\end{array}\right| \\) = 0

(b-a)(c-b)\\left|\begin{array}{ccc}a & a^{2} & a^{3}-1 \\0 & a-c & [a-c][a+b+c] \\ 1 & c+a & c^{2}+cb+b^{2}\end{array}\right| \\) = 0

(b-a)(c-b)(a-c)\\left|\begin{array}{ccc}a & a^{2} & a^{3}-1 \\0 & 1 & a+b+c \\ 1 & c+a & c^{2}+cb+b^{2}\end{array}\right| \\) = 0

Solving which we get (b-a)(c-b)(a-c)(abc - 1) = 0

Since a, b, c are distinct, only (abc-1) = 0

abc - 1 = 0

abc = 1

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

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

**WhatsApp:** WhatsApp Now

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