GATE Electronics & Communication Engineering Mathematics Paper-3

Test Preparation on GATE Electronics & Communication Engineering Mathematics Paper-3

1.

Starting from x = 1, one step of Newton –
Raphson method in solving the equation
x³ +3x 7=0 gives the next value (x₁) as

1x₁=0.5
2x₁=1.406
3x₁ = 1.5
4x₁=2

2.

With a 1 unit change in b, what is the change in x in the solution of the system of equation x+y=2, 1.01x+0.99y=b?

1Zero
22 units
350 units
4100 units

3.

1P-1 Q-4 R-3 S-2
2P-1 Q-4 R-2 S-3
3P-1 Q-3 R-2 S-4
4P-4 Q-1 R-2 S-3

4.

Equation of the line normal to function

1y=3x-5
2y=3x+5
33y=x+15
43y=x-15

5.

10.00000
21.0000
30.00500
40.00025

6.

Torque exerted on a flywheel over a cycle
is listed in the table. Flywheel energy (in
J per unit cycle) using impson’s rule is

1542
2992.7
31444
41986

7.

11.000
21.098
31.111
41.120

8.

1P – 2 , Q – 1, R – 3
2P – 3, Q – 2 , R – 1
3P – 1, Q – 2 , R – 3
4P – 3, Q – 1 , R – 2

9.

Using the trapezoidal rule, and dividing
the interval of integration into three equal
sub intervals, the definite integral

11.10 to 1.12
21.12 to 1.14
31.14 to 1.16
41.10 to 1.11

10.

11.74 to 1.76
21.74 to 1.75
31.76 to 1.78
41.76 to 1.77

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