COMEDK · Maths · 36. Probability
A determinant of the second order is made with elements 0 and 1 . What is the probability that the determinant made is non-negative?
- A \(\dfrac{7}{16}\)
- B \(\dfrac{3}{16}\)
- C \(\dfrac{13}{16}\)
- D \(\dfrac{11}{16}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{13}{16}\)
Step-by-step Solution
Detailed explanation
A second order determinant is given by \(\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc\). Each element \(a, b, c, d\) can take values from the set \(\{0, 1\}\). Since there are 4 positions and each position has 2 choices, the total number of possible determinants is…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Consider an experiment \(E\) in which a box contains 10 identical tickets numbered 1 to 10 and 2 tickets are drawn at random from the box. What is the probability that both the tickets have even number on them?COMEDK 2014 Medium
- \(\lim _\limits{x \rightarrow 0} \dfrac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a(a+x)}}\) equals toCOMEDK 2024 Medium
- Matrix \(A = \begin{bmatrix} 1 & 1 & 2 \\ 1 & -2 & 2 \\ 1 & 0 & -1 \end{bmatrix}\),
Given \(M_{22}\) and \(A_{32}\) are the minor and cofactor of the adjoint matrix of A respectively then the value of the expression \(M_{22} + A_{32} - |adj\ A|\) is:COMEDK 2026 Hard - The number of positive divisors of 4896 isCOMEDK 2012 Easy
- Given that \(z\) is a real number and \(z=\dfrac{\lambda+4 i}{1+\lambda i}\) where \(\lambda \in R\), then the possible value of \(\lambda\) isCOMEDK 2025 Medium
- Quadrilateral PQRS is inscribed inside a rectangle of dimensions \(10 \mathrm{~cm} \times 8 \mathrm{~cm}\). The value of ' \(x\) ', if the area of the quadrilateral is minimum is
COMEDK 2025 Medium
More PYQs from COMEDK
- Bohr's radius of 2 nd orbit of \(\mathrm{Be}^{3+}\) is equal to that ofCOMEDK 2023 Medium
- If \(\vec{a}\) and \(\vec{b}\) are two vectors such that \(\vec{a} \cdot \vec{b}=|\vec{a} \times \vec{b}|\) then the angle between \(\vec{a}\) and \(\vec{b}\) isCOMEDK 2025 Easy
- The molar heat capacity in a process of a diatomic gas if it does a work of \(\frac{Q}{4}\), when a heat of \(Q\) is supplied to it isCOMEDK 2024 Hard
- For an ideal gas undergoing an isothermal change, there isCOMEDK 2026 Easy
- If two positive numbers are in the ratio \(3+2 \sqrt{2}: 3-2 \sqrt{2}\), then the ratio between their A.M (arithmetic mean) and G.M (geometric mean) isCOMEDK 2024 Medium
- Inverse of the matrix \(\left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right]\) isCOMEDK 2013 Easy