A monochromatic wave propagates along a waveguide in z direction. These points of constant phase travel in constant phase travel at a phase velocity Vp is given by?

Two monochromatic waves having frequencies $$\omega $$ and $$\omega + \Delta \omega \left( {\Delta \omega \ll \omega } \right)$$ and corresponding wavelengths $$\lambda $$ and $$\lambda - \Delta \lambda \left( {\Delta \lambda \ll \lambda } \right)$$ of same polarization, travelling along X-axis are superimposed on each other. The phase velocity and group velocity of the resultant wave are respectively given by

A

$$\frac{{\omega \lambda }}{{2\pi }},\,\frac{{\Delta \omega {\lambda ^2}}}{{2\pi \Delta \lambda }}$$

B

$$\omega \lambda ,\,\frac{{\Delta \omega {\lambda ^2}}}{{\Delta \lambda }}$$

C

$$\frac{{\omega \Delta \lambda }}{{2\pi }},\,\frac{{\Delta \omega \Delta \lambda }}{{2\pi }}$$

D

$$\omega \Delta \lambda ,\,\omega \Delta \lambda $$

What happens when the shock wave propagates in the opposite direction with the same magnitude as wave velocity?

A

Velocity increases

B

Velocity decreases

C

Appears stationary

D

Becomes sonic

Velocity of a man is 25 units in the positive X direction and 75 units in negative Y direction starting from the origin. Velocity of a woman is 25 units in the positive Y direction and 75 units in the negative X direction starting from the origin. What is the relative velocity of the man with respect to the woman?

A

100î – 100&jcirc;

B

100î + 100&jcirc;

C

-100î – 100&jcirc;

D

0î + 0&jcirc;

Velocity of a dog is 15 units in the positive X direction and 3 units in positive Y direction starting from the origin. Velocity of a pig is 7 units in the positive Y direction and 17 units in the positive X direction starting from the origin. What is the relative velocity of the dog with respect to the pig?

A

-2î – 4&jcirc;

B

-3î – 2&jcirc;

C

-4î – 2&jcirc;

D

7î + 4&jcirc;

Measurements were made of the monochromatic absorptivity and monochromatic hemispherical irradiation incident on an opaque surface, and the variation of these parameters with wavelength may be approximated by the result shown below. Determine the total hemispherical absorptivity

A

0.557

B

0.667

C

0.777

D

0.887

A finite wave train, of an unspecified nature, propagates along the positive X-axis with a constant speed v and without any change of shape. The differential equation among the four listed below, whose solution it must be, is

A

$$\left( {\frac{{{\partial ^2}}}{{\partial {x^2}}} - \frac{1}{{{v^2}}}\frac{{{\partial ^2}}}{{\partial {t^2}}}} \right)\psi \left( {x,\,t} \right) = 0$$

B

$$\left( {{\nabla ^2} - \frac{1}{{{v^2}}}\frac{{{\partial ^2}}}{{\partial {t^2}}}} \right)\psi \left( {\overrightarrow r ,\,t} \right) = 0$$

C

$$\left( { - \frac{h}{{2m}}\frac{{{\partial ^2}}}{{\partial {x^2}}} - ih\frac{\partial }{{\partial t}}} \right)\psi \left( {x,\,t} \right) = 0$$

D

$$\left( {{\nabla ^2} + a\frac{\partial }{{\partial t}}} \right)\psi \left( {\overrightarrow r ,\,t} \right) = 0$$

Suppose on performing reduced error pruning, we collapsed a node and observed an improvement in the prediction accuracy on the validation set. Which among the following statements are possible in light of the performance improvement observed? (a) The collapsed node helped overcome the effect of one or more noise affected data points in the training set (b) The validation set had one or more noise affected data points in the region corresponding to the collapsed node (c) The validation set did not have any data points along at least one of the collapsed branches (d) The validation set did have data points adversely affected by the collapsed node

A

a and b

B

a and d

C

b, c and d

D

all of the above

In the following items, each passage consists of six sentences. The first and the sixth sentence are given in the beginning as S1 and S6. The middle four sentences in each have been removed and jumbled up. These are labeled P, Q, R and S. You are required to find out the proper sequence of the four sentences and mark your response accordingly on the Answer Sheet. S1 :Why do the English travel?
S6:For here, in cosmopolitan England, one is always exposed to the danger of meeting all sorts of peculiar aliens.
P:Besides, they are taught that travel broadens the mind.
Q:They do so mainly because their neighbor does this and they have caught the bug from him.
R:Although they have now discovered the sad truth that whatever travel may do to the mind, it certainly broadens other parts of the body.
S:But, and perhaps mainly, they travel to avoid foreigners. The proper sequence should be

A

R S Q P

B

P R S Q

C

S Q P R

D

Q P R S

The guided phase constant of a TEM wave in a waveguide with a phase constant of 2.8 units is

A

2.8

B

1.4

C

0

D

Infinity

I travel 20 miles towards north and then travel 25 miles eastward. I then travel 40 miles rightwards, then travel 30 miles towards left and then travels 12 miles to the left and finally 20 miles northwards. How far am i pproximately from my original destination and in what direction ?

A

20 miles towards south

B

13 miles towards south-west

C

12 miles towards east

D

13 miles towards north-east