GATE 2023 Engg. Mathematics Quiz 12

If a force displaces a particle in the x-y plane from (0, 0) to (1, 4) along a curve y = 4x²

Find the work done.

The function f(x) = |x| is

Let f₁(x) = e^x and f₂(x) = e^-x be the two defined in [a, b], then by Cauchy’s MVT

The solution of the differential equation  will represent family of curves

The particular integral of is

Let A be the matrix  with a, C ϵ R and C ≠ 0

Then there is a 2 × 2 matrix P such that PAP^–1 is diagonal

If for the given equations x + 2y – 3y = 1, (K + 2)z = 3, (2K + 1)y + 3 = 2 are inconsistent then the value of K is

The value of there 'C' is the left half of the unit circle, is