Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More
Bengali
English
Hindi
Marathi

Question

Download Solution PDF

ম্যাট্রিক্স A-তে x সারি এবং (x + 5) কলাম এবং ম্যাট্রিক্স B-এ y সারি এবং (11 - y) কলাম রয়েছে। যদি AB এবং BA উভয় ম্যাট্রিক্স বেরিয়ে যায়, তাহলে x এবং y এর মান কত হবে?

This question was previously asked in
NIMCET 2016 Official Paper
Download PDF Attempt Online
View all NIMCET Papers >
  1. 8, 3
  2. 3, 5
  3. 3, 8
  4. 8, 5

Answer (Detailed Solution Below)

Option 3 : 3, 8
Free Tests
View all Free tests >
Free
NIMCET 2020 Official Paper
10.7 K Users
120 Questions 480 Marks 120 Mins
Start Now

Detailed Solution

Download Solution PDF

ধারণা:

A হল mxn এর একটি ম্যাট্রিক্স এবং B হল ক্রম pxq এর একটি ম্যাট্রিক্স

যেখানে m হল সারির সংখ্যা এবং n হল A ম্যাট্রিক্সের কলামের সংখ্যা

একইভাবে p হল সারির সংখ্যা এবং q হল B ম্যাট্রিক্সের কলামের সংখ্যা

ম্যাট্রিক্স গুণনের অস্তিত্বের জন্য: প্রথম ম্যাট্রিক্সের কলামের N সংখ্যা দ্বিতীয় ম্যাট্রিক্সের সংখ্যা সারির সমান

তাই ম্যাট্রিক্স গুণের জন্য AB , n = p

সুতরাং ম্যাট্রিক্স গুণের জন্য BA, q = m

গণনা:

প্রদত্ত:

ম্যাট্রিক্স A

সারির সংখ্যা (m) = x

কলামের সংখ্যা (n) = x + 5

ম্যাট্রিক্স B

সারির সংখ্যা (p) = y

কলামের সংখ্যা (q) = 11 - y

AB এবং BA উভয়ই বিদ্যমান

n = p ⇒ x + 5 = y ....(1)

m = q ⇒11 - y = x ....(2)

1 এর মধ্যে 2 থেকে y এর মান বসিয়ে পাই,

11-(x + 5) = x

11 - 5 - x = x

6 = 2 x

\(\therefore \) x = 3

1 থেকে x = 3 এর মান বসিয়ে পাই,

y = 8

\( \therefore\) x = 3 এবং y = 8

Download Solution PDF
Latest NIMCET Updates

Last updated on Jun 12, 2025

->The NIMCET 2025 provisional answer key is out now. Candidates can log in to the official website to check their responses and submit objections, if any till June 13, 2025.

-> NIMCET exam was conducted on June 8, 2025.

-> NIMCET 2025 admit card was out on June 3, 2025.

-> NIMCET 2025 results will be declared on June 27, 2025. Candidates are advised to keep their login details ready to check their scrores as soon as the result is out.

-> Check NIMCET 2025 previous year papers to know the exam pattern and improve your preparation.

More Operations on Matrices Questions

Q1.Find the additive inverse of matrix A = \(\left[\begin{array}{cc}2 & 1 \\ −3 & 0\end{array}\right]\)
Q2.The number of all possible matrices of order 2 × 2 with each entry 0 or 1 is:
Q3.On using elementary row operation R1 → R1 – 3R2 in the following matrix equation: \(\left[\begin{array}{ll}4 & 2 \\ 3 & 3\end{array}\right] = \left[\begin{array}{ll}1 & 2 \\ 0 & 3\end{array}\right]\left[\begin{array}{ll}2 & 0 \\ 1 & 1\end{array}\right]\), we have :
Q4.On using elementary column operations C2 → C2 – 2C1 in the following matrix equation \(\left[\begin{array}{cc}1 & −3 \\ 2 & 4\end{array}\right] = \left[\begin{array}{cc}1 & −1 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}3 & 1 \\ 2 & 4\end{array}\right]\), we have :
Q5.For any two matrices A and B, we have
Q6.If A = \(\left[\begin{array}{ccc}2 & −1 & 3 \\ −4 & 5 & 1\end{array}\right]\) and B = \(\left[\begin{array}{cc}2 & 3 \\ 4 & −2 \\ 1 & 5\end{array}\right]\), then
Q7.If A and B are square matrices of the same order, then (A + B) (A – B) is equal to
Q8.If A = \(\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \cos \theta & \sin \theta \\ 0 & \sin \theta & −\cos \theta\end{array}\right)\), then which of the following are correct? 1. A + adj A is a null matrix 2. A−1 + adj A is a null matrix 3. A − A−1 is a null matrix Select the correct answer using the code given below :
Q9.Let A and B be non-singular matrices of the same order such that AB = A and BA = B. Which of the following statements is/are correct ? 1. A2 = A 2. AB2 = A2B Select the correct answer using the code given below:
Q10.Consider the following statements in respect of square matrices A and B of same order : 1. If AB is a null matrix, then at least one of A and B is a null matrix. 2. If AB is an identity matrix, then BA = AB. Which of the above statements is/are correct?

More Matrices Questions

Q1.Let α be a root of the equation x2 + x+ 1= 0 and the matrix A = \(\frac{1}{\sqrt{3}}\left[\begin{array}{ccc} 1 & 1 & 1 \\ 1 & \alpha & \alpha^2 \\ 1 & \alpha^2 & \alpha^4 \end{array}\right]\) then the matrix A31 is equal to
Q2.ধরা যাক A এবং B দুটি 3 x 3 বাস্তব ম্যাট্রিক্স এমন যে A একটি প্রতিসম ম্যাট্রিক্স এবং B একটি বিপ্রতিসম ম্যাট্রিক্স। তাহলে (A2B2 − B2A2)X = O রৈখিক সমীকরণের নিয়ম, যেখানে X অজ্ঞাত চলকের 3 x 1 স্তম্ভ ম্যাট্রিক্স এবং O একটি 3 x 1 শূন্য ম্যাট্রিক্স, এর সমাধান হবে:
Q3.Let α ∈ (0, α) and \(A = \begin{bmatrix} 1 & 2 & \alpha \\\ 1 & 0 & 1 \\\ 0 & 1 & 2 \end{bmatrix}\). If det(adj(2A - AT). adj(A - 2AT)) = 28, then (det(A))2 is equal to: 
Q4.For a 3 × 3 matrix A = [aij], whose element aij is given by aij = \(\rm \sqrt{i^2+3j}\) then what is element a31?
Q5.Let \(A=\left(\begin{array}{cc} α & 1 \\ 0 & -1 \end{array}\right)\) and \(B=\left(\begin{array}{ll} 4 & 1 \\ 0 & 1 \end{array}\right)\), such that A2 = B, then the value of α is:
Q6.The number of solutions of the matrix equation \(A^2=\left[\begin{array}{ll}1 & 1 \\ 2 & 3\end{array}\right]\) is:
Q7.If \(A=\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]\) and A + A' = I, then the value of α is
Q8.If the matrix \(\left[\begin{array}{lll}5 & 8 & 6 \\ 3 & 2 & 4 \\ 1 & 7 & 9\end{array}\right]\) is expressed in the form A + B, where A is symmetric and B is skew-symmetric, then the value of B is
Q9.Find the additive inverse of matrix A = \(\left[\begin{array}{cc}2 & 1 \\ −3 & 0\end{array}\right]\)
Q10.Let l ≥ 1 be a positive integer. What is the dimension of the ℝ-vector space of all polynomials in two variables over R having a total degree of at most l?
Suggested Test Series
View All >
NIMCET Previous Year Papers Mock Test
8 Total Tests with 1 Free Tests
Start Free Test
Suggested Exams
Exam-Logo
NIMCET
Exam-Logo
Army Technical Agniveer
Exam-Logo
NDA

NIMCET Important Links

More Mathematics Questions

Q1.log10 10000 = _______?
Q2.Consider a system equation \(2x+y-z=0\), \(4x - py + 4z = 4\) and \(x-y+z=q\) where \(p, q \in I\) and \(p, q \in [1, 10]\), then identify the correct statement(s).   List-I List-II (I) Number of ordered pairs \((p, q)\) for which system of equation has unique solution is (P) 1 (II) Number of ordered pairs \((p, q)\) for which system of equation has no solution is (Q) 9 (III) Number of ordered pairs \((p, q)\) for which system of equation has infinite solution is (R) 91 (IV) Number of ordered pairs \((p, q)\) for which system of equation has atleast one solution is (S) 90
Q3.Match List I with List II:   List - I List - II (I) The number of solutions of the equation\((1 - \cos 2x)(\cos 2x + \cot^2 x) = 0\) where \(0 \le x \le 2\pi\) is (P) 4 (II) \(\tan 81^\circ - \tan 63^\circ - \tan 27^\circ + \tan 9^\circ\) equals (Q) 3 (III) The number of solutions of (x, y), which satisfy |y| = sin x and y = cos-1(cos x), where -2π ≤ x ≤ 2π is (R) 2 (IV) For the equation \(\cos^{-1}x + \cos^{-1}2x + \pi = 0\), the number of real solutions is (S) 1     (T) 0  
Q4.If Σn = 36, find n
Q5.If log 2 = 0.2614, log 3 = 0.3521, log 6 = ?
Q6.The growth model for a population is Nt = N0ert where Nt is the population at time t, N0 is the initial population and r is the per capita growth rate. How long does it take for the population numbers to double?
Q7.Suppose that the growth rate of the number of individuals (N) in a population in an environment with a carrying capacity K is modelled as \(\frac{d N}{d t}=r N \frac{K-N}{K}\) where r is the per capita growth rate and t is time; r and K are positive constants. At which of the following values of N will the population growth rate be the maximum?
Q8.The shadow of a vertical pole, formed due to a nearby lamp which is at a height of 12 m, measures 4 m. If the lamp is moved horizontally 2 m further away from the pole, the length of the shadow measures 8 m. What is the height (in m) of the pole?
Q9.A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Out of these 16 number of cards, two cards are drawn at random. Find the probability that at least one of them is an ace :
Q10.If the equations 2x2 + kx - 5 = 0 and x2 - 3x - 4 = 0 have one root common, then find the value of k.
Important Exams
Super Coaching
Exams
Test Series
Previous Year Papers
Objective Questions
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
[email protected]
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Our Apps
Follow us on
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Get Free Access Now
Hot Links： teen patti sequence teen patti master purana teen patti go