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Saturday, 31 October

JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 4 April 2024, Shift 1, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B. NTA dropped this question from the final key; it is left out of every count on this site.

Let A be a square matrix of order 2 such that ∣A∣=2|A|=2 and the sum of its diagonal elements is −3-3. If the points (x,y)(x, y) satisfying A2+xA+yI=OA^2+xA+yI=O lie on a hyperbola, whose transverse axis is parallel to the xx-axis, eccentricity is ee and the length of the latus rectum is ll, then e4+l4e^4+l^4 is equal to ________.

Official answer

Dropped by NTA (marks given to all)

NTA final key: NTA final key: DROP (question dropped).

Chapter
Matrices
Topic
Matrix Multiplication
Idea tested
Cayley-Hamilton Theorem Application

Same idea in other shifts

Asked 10× in all
  1. 2 Apr 2026, Shift 1 · Q4Let A=[121α]A=\begin{bmatrix}1&2\\1&\alpha\end{bmatrix} and B=[33β2]B=\begin{bmatrix}3&3\\\beta&2\end{bmatrix}. If A2−4A+I=OA^2-4A+I=O and B2−5B−6I=OB^2-5B-6I=O,…HardOther
  2. 2 Apr 2025, Shift 2 · Q3Let AA be a 3×33\times3 real matrix such that A2(A−2I)−4(A−I)=OA^2(A-2I) - 4(A-I) = O, where II and OO are the identity and null matrices,…MediumSingle correct
  3. 4 Apr 2024, Shift 2 · Q23Let AA be a 2×22\times2 symmetric matrix such that A[11]=[37]A\begin{bmatrix}1\\1\end{bmatrix}=\begin{bmatrix}3\\7\end{bmatrix} and the…MediumNumerical value
  4. 8 Apr 2024, Shift 1 · Q4Let A=[2a013105b]A=\begin{bmatrix}2&a&0\\1&3&1\\0&5&b\end{bmatrix}. If A3=4A2−A−21IA^3=4A^2-A-21I, where II is the identity matrix of order 3×33\times3, then…MediumSingle correct
  5. 9 Apr 2024, Shift 2 · Q4Let B=[1315]B=\begin{bmatrix}1&3\\1&5\end{bmatrix} and AA be a 2×22\times2 matrix such that AB−1=A−1AB^{-1}=A^{-1}. If BCB−1=ABCB^{-1}=A and…HardSingle correct
  6. 27 Jul 2022, Shift 1 · Q4Let A=(12−2−5)A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix}. Let α,β∈R\alpha, \beta \in \mathbb{R} be such that αA2+βA=2I\alpha A^2 + \beta A = 2I.…MediumSingle correct
  7. 27 Jul 2022, Shift 2 · Q4Let A=(4−2αβ)A = \begin{pmatrix} 4 & -2 \\ \alpha & \beta \end{pmatrix}. If A2+γA+18I=OA^2 + \gamma A + 18I = O, then det (A) is equal to __________.MediumSingle correct
  8. 27 Aug 2021, Shift 1 · Q63If the matrix A=(02K−1)A=\begin{pmatrix}0 & 2\\ K & -1\end{pmatrix} satisfies A(A3+3I)=2IA(A^3+3I)=2I, then the value of KK is :MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.