Home
Test SeriesNEW!
New AppNEW!
About Us

Virat Batch 2027
Champion Batch 2028
Divine JEE 1-on-1

Contact Us
Knowledge Check

Let M be any 3 x 3 matrix with entries from the set 0 1... | null (Mathematics) | DivineJEE

Home
Test SeriesNEW!
New AppNEW!
About Us

Virat Batch 2027
Champion Batch 2028
Divine JEE 1-on-1

Contact Us
Knowledge Check

Mathematics

Exam

Mathematics

Let M be any 3

\times

3 matrix with entries from the set {0, 1, 2}. The maximum number of such matrices, for which the sum of diagonal elements of M^TM is seven, is ________.

Correct Answer:

540

Explanation

\left[ {\matrix{ a & b & c \cr d & e & f \cr g & h & i \cr } } \right]\left[ {\matrix{ a & d & g \cr b & e & h \cr c & f & i \cr } } \right]

{a^2} + {b^2} + {c^2} + {d^2} + {e^2} + {f^2} + {g^2} + {h^2} + {i^2} = 7

Case I : Seven (1's) and two (0's)

Number of such matrices =

{}^9{C_2} = 36

Case II : One (2) and three (1's) and five (0's)

Number of such matrices =

{{9!} \over {5!3!}} = 504

\therefore

Total = 540

Select an option to instantly check whether it is correct or wrong.

Picture of the author

Related Questions

The minimum number of elements that must be added to the relation R = {(a,b),(b,c),(b,d)} on the set { a,b,c,d} so that it is an equivalence relation is

For integers n and r let n r nCr ifn ge r ge 0 0 otherwise

The integral int_0^1 \frac{1}{7^{\left[\frac{1}{x}\right]}} {dx}, where [.] denotes the greatest integer function is equal to

The area of the region enclosed by the parabolas y=4x-x^2 and 3y=(x-4)^2 is equal to

Let the relations R_{1} and R_{2} on the set X = { 1,2,3,...,20} be given by R_{1} = {(x,y):2x - 3y = 2} and R_{2} = {(x,y) : - 5x + 4y = 0}. If M and N be the minimum number of elements required to be added in R_{1} and R_{2}, respectively, in order to make the relations symmetric, then M + N equals

For (2 leq r leq n,binom{n}{r} + 2binom{n}{r - 1} + binom{n}{r - 2} =)

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated, is

Area of the region (x,y):x^2+(y-2)^2≤4,x^2≥2y is

Let R be the set of real numbers. end{enumerate} Statement-1: A = {(x,y) in R X R:y - x is an integer } is an equivalence . relation on R. Statement-2: B = {(x,y) in R X R:x = alpha y for some rational number } is . an equivalence relation on R.

In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspaper is

Download Divine JEE App

Learn on the go with our mobile app. Access courses, live classes, and study materials anytime, anywhere.

Divine JEE App Preview

Empowering students to achieve their IIT dreams through personalized learning and expert guidance.

Quick Links

About Us
Courses
Contact Us
Knowledge Check
Blogs

Exam Categories

JEE Main
JEE Advanced
NEET
BITS Pilani

Contact Info

contact.divinejee@gmail.com
+91 9137402346
2nd floor, C, 10, Mahant Swami Marg, nr. Pratap Stadium, Chitrakoot, Jaipur, Rajasthan 302021

Copyright © 2026 Divine JEE. All Rights Reserved.

Divine JEE