The plane passing through the twinning axis and separating the region of twinning from undeformed part is called ___ planes.

Match the following (a) Separating Salt and Camphor (i) Winnowing (b) Separating Salt and water (ii) Decantation (c) Separating husk from the grain (iii) Evaporation (d) Separating soil from water (iv) Sublimation

A

(a) - (iv), (b) - (iii), (c) - (i), (d) - (ii)

B

(a) - (ii), (b) - (iii), (c) - (i), (d) - (iv)

C

(a) - (iv), (b) - (iii), (c) - (ii), (d) - (i)

D

(a) - (iii), (b) - (iv), (c) - (ii), (d) - (i)

According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $$I$$P) is given by (where, A = Area of the section, $$I$$G = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)

A

$$I{\text{P}} = I{\text{G}} + {\text{A}}{{\text{h}}^2}$$

B

$$I{\text{P}} = I{\text{G}} - {\text{A}}{{\text{h}}^2}$$

C

$$I{\text{P}} = \frac{{I{\text{G}}}}{{{\text{A}}{{\text{h}}^2}}}$$

D

$$I{\text{P}} = \frac{{{\text{A}}{{\text{h}}^2}}}{{I{\text{G}}}}$$

According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $${I_{\text{P}}}$$) is given by (where, A = Area of the section, $${I_{\text{G}}}$$ = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)

A

$${I_{\text{P}}} = {I_{\text{G}}} + {\text{A}}{{\text{h}}^2}$$

B

$${I_{\text{P}}} = {I_{\text{G}}} - {\text{A}}{{\text{h}}^2}$$

C

$${I_{\text{P}}} = \frac{{{I_{\text{G}}}}}{{{\text{A}}{{\text{h}}^2}}}$$

D

$${I_{\text{P}}} = \frac{{{\text{A}}{{\text{h}}^2}}}{{{I_{\text{G}}}}}$$

Consider the following statement: A ray of light passing through the optical centre of a convex lens emerges without any deviation after refraction. A ray of light passing through the first principal focus of a convex lens emerges parallel to the principal axis after refraction. A ray of light passing through the optical centre of a convex lens emerges parallel to the principal axis after refraction. Which one of the following statements INCORRECT?

A

Only 1

B

Only 2

C

Only 3

D

All 1, 2 and 3

Consider a two-sided discrete-time signal (neither left sided, nor right sided). The region of convergence (ROC) of the z-transform of the sequence is: 1) All region of z-plane outside a unit circle (in z-plane) 2) All region of z-plane inside a unit circle (in z-plane) 3) Ring in z-plane Which of the above is/are correct?

A

1 only

B

2 only

C

3 only

D

1 and 3

Three consecutive absorption lines at 64.275 cm^-1, 77.130 cm^-12 and 89.985 cm^-1 have been observed in a microwave spectrum for a linear rigid diatomic molecule. The moments of inertia $${I_A}$$ and $${I_B}$$ are ($${I_A}$$ is with respect to the bond axis passing through the centre of mass and $${I_B}$$ is with respect to an axis passing through the centre of mass and perpendicular to bond axis)

A

both equal to $$\frac{{{\hbar ^2}}}{{12.855\,hc}}$$ g-cm²

B

zero and $$\frac{{{\hbar ^2}}}{{12.855\,hc}}$$ g-cm²

C

both equal to $$\frac{{{\hbar ^2}}}{{6.427\,hc}}$$ g-cm²

D

zero and $$\frac{{{\hbar ^2}}}{{6.427\,hc}}$$ g-cm²

Twinning is not associated with specific crystallographic direction; it only depends on the direction of mechanical force. There is no preferred orientation of twinning in crystal.

A

True

B

False

Consider the following statements: A ray parallel to the principal axis incident on a concave mirror after reflection passes through the focus. A ray passing through the center of curvature of a concave mirror after reflection is reflected back along the same path. A ray passing through the center of curvature of a concave mirror after reflection passes through the focus. Which of the following statement is INCORRECT?

A

Only 2

B

Both 1 and 2

C

Only 3

D

All 1, 2, and 3

A rectangle is having base b and height h. The ratio of the moment of inertia when axis is passing through its base to moment of inertia of when axis passing through center of gravity and parallel to base is ___________

A

3

B

4

C

12

D

9

A triangle is having base b and height h. The ratio of the moment of inertia when axis is passing through its base to moment of inertia of when axis passing through centroid and parallel to base is ______

A

3

B

6

C

12

D

9

The plane passing through the twinning axis and separating the region of twinning from undeformed part is called ___ planes.

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