GATE 2019
Let X be a square matrix. Consider the following two statements on X:
I. X is invertible
II. Determinant of X is non-zero
Which one of the following is TRUE?
Related Engineering Mathematics PYQs
Consider the first order predicate formula φ: ∀x [ (∀z z|x => ((z = x) ∨ (z = 1))) => ∃w (w > x) ∧ (∀z z|w => ((w = z) ∨ (z = 1)))…
Consider the matrix R = \[\begin{bmatrix}1 & 2 & 4 & 8\\1 & 3 & 9 & 27\\1 & 4 & 16 & 64\\1 & 5 & 25 & 125\end{bmatrix}\]. The abso…
Let T be a full binary tree with 8 leaves. Suppose two leaves a and b are chosen uniformly and independently at random. The expect…
Suppose Y is distributed uniformly in the open interval (1, 6). The probability that the polynomial 3x^2 + 6xY + 3Y + 6 has only r…
Let U = {1, 2, ..., n} and A = {(x, X) | x ∈ X and X ⊆ U}. Consider the following two statements on |A|: I. |A| = n * 2^(n-1) II. …
Let G be an arbitrary group. Consider the following relations on G: R1: ∀a, b ∈ G, a R1 b if and only if ∃g ∈ G such that a = g^(-…
Free account benefits
Turn practice into measurable progress
Public PYQs and reference pages stay free. Sign in when you want GATEverse to remember what you studied and guide what to practise next.
Saved progressKeep answers, mock results and completion history across devices.
Adaptive practiceGet questions matched to your recent accuracy and difficulty level.
Bookmarks and notesBuild a personal revision list and record why a question was difficult.
Performance insightsSee weak subjects, accuracy trends, streaks and exam readiness.