The contour on the x - y plane, where the partial derivative of x2 + y2 with respect to y is equal to the partial derivative of 6y + 4x with respectto x, is

If u (x, y, z, t) = f(x + iβy - vt) + g(x - iβy - vt), where f and g are arbitrary and twice differentiable functions, is a solution of the wave equation $$\frac{{\partial {u^2}}}{{\partial {x^2}}} = \frac{{{\partial ^2}u}}{{\partial {y^2}}} = \frac{1}{{{c^2}}}\frac{{{\partial ^2}u}}{{\partial {t^2}}}$$ then β is

A

$${\left( {1 - \frac{v}{c}} \right)^{\frac{1}{2}}}$$

B

$$\left( {1 - \frac{v}{c}} \right)$$

C

$${\left( {1 - \frac{{{v^2}}}{{{c^2}}}} \right)^{\frac{1}{2}}}$$

D

$$\left( {1 - \frac{{{v^2}}}{{{c^2}}}} \right)$$

The values of the integral $$\frac{1}{{2\pi {\text{j}}}}\oint\limits_{\text{c}} {\frac{{{{\text{e}}^{\text{z}}}}}{{{\text{z}} - 2}}{\text{dz}}} $$ along a closed contour c in anti-clockwise direction for
i. the point z₀ = 2 inside the contour c, and
ii. the point z₀ = 2 outside the contour c, respectively, are

A

i. 2.72, ii. 0

B

i. 7.39, ii. 0

C

i. 0, ii. 2.72

D

i. 0, ii. 7.39

Which principle specifies the relationship between enclosure of poles & zeros by s-plane contour and the encirclement of origin by q(s) plane contour?

A

Argument

B

Agreement

C

Assessment

D

Assortment

Which of the following partial derivative is equal to $${\left( {\frac{{\partial S}}{{\partial P}}} \right)_T}?$$

A

$$ - {\left( {\frac{{\partial V}}{{\partial T}}} \right)_P}$$

B

$$ - {\left( {\frac{{\partial S}}{{\partial V}}} \right)_T}$$

C

$${\left( {\frac{{\partial V}}{{\partial T}}} \right)_S}$$

D

$$ - {\left( {\frac{{\partial S}}{{\partial V}}} \right)_T}$$

A line of 12 cm length is perpendicular to profile plane and the least distance from this line to profile plane is 6 cm. This is at a distance of 4 cm from the vertical plane and 5 cm from the horizontal plane. What is distance from the point on line far away from the profile plane to profile plane?

A

12 cm

B

9 cm

C

18 cm

D

6 cm

A line of length 10 cm at first lied on the horizontal plane parallel to vertical plane and then keeping one of its ends fixed turned 30 degrees with respect to vertical plane and then turned 45 degrees with respect to horizontal plane. What is the length of line in top view?

A

5 cm

B

7.07 cm

C

3.53 cm

D

10 cm

A line of length 10 cm at first lied on the horizontal plane parallel to vertical plane and then keeping one of its ends fixed turned 30 degrees with respect to vertical plane and then turned 45 degrees with respect to horizontal plane. What is the length of line in front view?

A

8.66 cm

B

7.07 cm

C

3.53 cm

D

6.12 cm

A line of length 15 cm at first lied on the vertical plane parallel to horizontal plane and then keeping one of its ends fixed turned 30 degrees with respect to horizontal plane and then turned 50 degrees with respect to vertical plane. What is the length of the line in top view?

A

9.6 cm

B

7.5 cm

C

12.99 cm

D

11.49 cm

A line of length 15 cm at first lied on the vertical plane parallel to horizontal plane and then keeping one of its ends fixed turned 30 degrees with respect to horizontal plane and then turned 50 degrees with respect to vertical plane. What is the length of the line in front view?

A

9.6 cm

B

12.99 cm

C

7.5 cm

D

11.49 cm

A line of length 15 cm at first lied on the profile plane parallel to horizontal plane and then keeping one of its ends fixed turned 30 degrees with respect to horizontal plane and then turned 50 degrees with respect to profile plane. What is the length of the line in top view?

A

9.6 cm

B

12.99 cm

C

7.5 cm

D

11.49 cm

The contour on the x - y plane, where the partial derivative of x² + y² with respect to y is equal to the partial derivative of 6y + 4x with respectto x, is

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