1
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
Let M be a real 4 $$ \times $$ 4 matrix. Consider the following statements :

S1: M has 4 linearly independent eigenvectors.

S2: M has 4 distinct eigenvalues.

S3: M is non-singular (invertible).

Which one among the following is TRUE?
A
S1 implies S2
B
S2 implies S1
C
S1 implies S3
D
S3 implies S2
2
GATE ECE 2018
Numerical
+2
-0
The position of a particle y(t) is described by the differential equation :

$${{{d^2}y} \over {d{t^2}}} = - {{dy} \over {dt}} - {{5y} \over 4}$$.

The initial conditions are y(0) = 1 and $${\left. {{{dy} \over {dt}}} \right|_{t = 0}}$$ = 0.

The position (accurate to two decimal places) of the particle at t = $$\pi $$ is _______.
Your input ____
3
GATE ECE 2018
Numerical
+2
-0
Let r = x2 + y - z and z3 - xy + yz + y3 = 1. Assume that x and y are independent variables. At (x, y, z) = (2, -1, 1), the value (correct to two decimal places) of $${{\partial r} \over {\partial x}}$$ is ________________.
Your input ____
4
GATE ECE 2018
MCQ (Single Correct Answer)
+2
-0.67
A curve passes through the point ($$x$$ = 1, $$y$$ = 0) and satisfies the differential equation

$${{dy} \over {dx}} = {{{x^2} + {y^2}} \over {2y}} + {y \over x}$$. The equation that describes the curve is
A
$$\ln \left( {1 + {{{y^2}} \over {{x^2}}}} \right) = x - 1$$
B
$${1 \over 2}\ln \left( {1 + {{{y^2}} \over {{x^2}}}} \right) = x - 1$$
C
$${1 \over 2}\ln \left( {1 + {y \over x}} \right) = x - 1$$
D
$$\ln \left( {1 + {y \over x}} \right) = x - 1$$
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