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Correct option is C) peak

Bump maps are grayscale textures you map to objects to create the illusion of surface relief on an otherwise flat object.

Correct option: False

The difference between high pass sharpening and most other methods of sharpening is that high pass sharpening does not actually adjust or change any pixels in your original image. Also, because high pass exists as a separate layer, you can adjust the layer’s Opacity and Blending Modes to control the strength of sharpening over the entire image.

Correct option is B) summit

1. In the Environment section of the camera’s Attribute Editor (View > Camera Attribute Editor), click the Create button to the right of the Image Plane attribute. Maya creates an image plane and connects it to the camera. 

2. Set the Type attribute for the image plane to Texture. 

3. Click the texture button for the Texture attribute. The Create Render Node window appears. 

4.Select the texture you want to use as a background (for example, an Environment Texture). Maya creates the texture and connects it to the image plane.

Displacement maps are grayscale textures you map to objects to create true surface relief (elevations and depressions) on an otherwise flat object.

• Use the Placement attributes to position an image plane relative to the camera. 
• Use the Placement Extras attributes to control which portion of an image file is visible on the image plane.

Correct option is A) jolt

IOR stands for Index of Refraction

Bump maps are grayscale textures you map to objects to create the illusion of surface relief (elevations and depressions) on an otherwise flat object. 

With bump maps, depressions and elevations look real because they don’t alter the geometry of the surface the way Displacement maps do. Bump maps just change the direction of the surface’s normal based on the bump map’s Alpha Gain value. 

Use bump maps to create very shallow reliefs. For example, you can make objects look like they are embossed, have shallow rolling hills, and so on. 

Because bump maps are not true surface relief, they:

• cannot cast or receive shadows 
• cannot be seen if you silhouette the mapped object 
• take less time to render than displacement maps

Correct option: (a) Right

The IOR parameter (Index of Refraction) defines the material's Fresnel reflectivity and is by default the angular function used. Effectively the IOR will define the balance between reflections on surfaces facing the viewer and on surface edges.

There are a lot of items displayed in the Maya user interface which are as follows: 

1. Menu Bar: The Main Menu bar appears at the top of the Maya interface directly below the Maya title bar and displays the chosen menu set. Each menu set corresponds to a module within Maya: Animation, Polygons, Surfaces, Rendering, and Dynamics. Modules are a method for grouping related features and tools. 

2. Status Line: The Status Line, located directly below the Main Menu bar, contains a variety of items, most of which are used while modeling or working with objects within Maya. Many of the Status Line items are represented by a graphical icon. The icons save space in the Maya interface and allow for quick access to tools used most often. 

3. Shelf: The Shelf is located directly below the Status line. The Maya Shelf is useful for storing tools and items that you use frequently or have customized for your own use. You can keep the tools and items you use most frequently in a location that provides handy access. Maya has some of the Shelf items pre-configured for your use.

4. Workspace: The Maya workspace is where you conduct most of your work within Maya. The workspace is the central window where your objects and most editor panels appear.

• The panel is labeled persp at the bottom to indicate that you are viewing the Maya scene from a perspective camera view. 
• The panel has its own menu bar at the top left corner of the panel. These menus allow you to access tools and functions related to that specific panel. 
• The grid is displayed with two heavy lines intersecting at the center of the Maya scene. This central location is called the origin. The origin is the center of Maya’s 3D world, and with all object’s directional values measured from this location.

5. Channel Box: The Channel Box is the primary, fastest, and most streamlined tool for editing object attributes. It lets you quickly change attribute values, set keys on keyable attributes, lock or unlock attributes, and create expressions on attributes. 

6. Quick Layout Buttons: The quick layout buttons display just below the Tool Box and let you switch between useful panel layouts 

7. Toolbox: The Tool Box displays on the left side of the Maya interface by It contains the most commonly-used tools for working in Maya like., Move, Rotate, Scale and Last used tool 

8. Command Line: The command line lets you type single MEL or Python commands without having to open the Script editor. You can switch between MEL and Python mode by clicking the MEL/Python button. The result from the command appears in the output 

9. Time and Range Slider: The Time Slider controls the playback range, keys, and breakdowns within the playback range

To apply a texture to an object, you map the texture to an attribute on the object's material. 

The attribute to which the texture is connected determines how the texture is used and how it affects the final output. 

To map a texture to a material using the Attribute Editor 

1. Select your material in the Hyper shade. 

In the material Attribute Editor, click the map button beside the attribute that you want to connect a texture to. The Create Render Node window appears. 

2. Select a texture from the Create Render Node window. 

If you are selecting a 2D texture, right-click the texture and select a mapping method (Create texture (create normally), Create as projection, Create as stencil). If you do not select a mapping method, the default method (Create texture) is used. 

If you are selecting the File texture, map to the image file by clicking the browse icon beside the Image Name attribute.

The quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, or equivalently, characterizes a resonator's bandwidth relative to its center frequency.

Some surfaces are shinier than others (for example a wet fish has a shinier surface than a dry leaf). By mapping a texture to the Specular attribute of an object’s material, you create a specular map which lets you describe how shine appears on objects (by controlling highlight).Shiny objects reflect light directly; matte objects diffuse light. Specular highlights show the places on the object where the light sources are reflected at consistent angles; reflections on an object show, among other things, light bounced from surrounding objects. 

Specular highlights depend directly on the view (camera), not the position of the light, like diffuse shading does. 

The size of a specular highlight on a surface makes the surface look either flat or shiny. 

Note: Only materials with specular attributes (Anisotropic, Blinn, Phong, and PhongE) have surface highlights. The specular highlight is the white shiny glow on the material.

Mapping a texture to the Specular attribute of an object’s material, you create a specular map which lets you describe how shine appears on objects (by controlling highlight).

Common surface material Specular Shading attributes Some surfaces are shinier than others (for example a wet fish has a shinier surface than a dry leaf). Depending on how shiny a surface is, it reflects light in different ways.

Shiny objects reflect light directly; matte objects diffuse light. Specular highlights show the places on the object where the light sources are reflected at consistent angles; reflections on an object show, among other things, light bounced from surrounding objects.

Specular highlights depend directly on the view (camera), not the position of the light, like diffuse shading does.

The size of a specular highlight on a surface makes the surface look either flat or shiny

Through sexing, biologists and agricultural workers determine the sex of livestock and other animals they work with. 

Concept:

\(\rm \int \frac{1}{x} dx = \log x + c\)

Calculation:

I = \(\rm \int_0^4 \frac{1}{1+ \sqrt x}dx\)

Let 1 + \(\rm \sqrt x\) = t       .... (1)

Differentiating with respect to x, we get

\(\rm \Rightarrow (0+\frac{1}{2\sqrt x})dx = dt\)

\(\rm \Rightarrow dx = {2\sqrt x}dt\)

From equation (1), we get 

\(\rm \sqrt x\) = t - 1

∴ dx = 2(t - 1)dt

Now,

I = \(\rm \int_1^3 \frac{2(t-1)}{t}dt \)

= \(\rm 2\int_1^3 \left(1-\frac{1}{t} \right )dt \)

= \(\rm 2\left[t - \log t \right ]_1^3\)

= 2 [(3 - log 3) - (1 - log 1)]

= 2(2 - log 3)

= 4 - 2log 3

Concept:

Steps to find the equation of the tangent to the curve:

1) Find the first derivative of f(x).

2) Use the point-slope formula to find the equation for the tangent line.

Point-slope is the general form:  

y - y₁=m(x - x₁), Where m = slope of tangent = \(\rm \frac {dy}{dx}\)

Calculation:

Here, y = sin x

\(\rm \frac {dy}{dx}\) = cos x

\(\rm \frac{dy}{dx}|_{x=0}\)= cos 0 = 1

So, Slope = 1

So, Equation of tangent to the curve is (y - 0) = 1(x - 0)

⇒ y = x

⇒ x - y = 0

Hence, option (2) is correct. 

Concept:

Rate of change of 'x' is given by \(\rm \frac {dx}{dt}\)

Circumference of circle = 2πr

Calculation:

Here, \(\rm \frac {dr}{dt}\) = 0.5 cm/sec

Circumference of circle, C = 2πr

Now taking derivatives on both sides, we get 

\(\rm \frac {dC}{dt}\) = 2π \(\rm \frac {dr}{dt}\)

= 2π (0.5)

= π cm/sec

Hence, option (4) is correct. 

Concept:

Rate of change of 'x' is given by \(\rm \frac {dx}{dt}\)

Calculation:

Given that, y = 2x – x² and \(\rm \frac {dx}{dt}\) = 3 units/sec

Then, the slope of the curve, \(\rm \frac {dy}{dx}\) = 2 - 2x = m

⇒\(\rm \frac {dm}{dt}\)  = 0 - 2 × \(\rm \frac {dx}{dt}\)

= -2(3)

= -6 units per second

Hence, the slope of the curve is decreasing at the rate of 6 units per second when x is increasing at the rate of 3 units per second.

Hence, option (2) is correct.

Concept:​

Parametric Form:

If f(x) and g(x) are the functions in x, then 

\(\rm df(x)\over dg(x)\) = \(\rm \frac{df(x)\over dx}{dg(x)\over dx}\) 

Calculation:

Given y = t² + 2t

\(\rm {dy\over dt}\) = 2t + 2

Also x = t³

\(\rm dx\over dt\) = 3t² 

Now \(\rm dy\over dx\) = \(\rm \frac{dy\over dt}{dx\over dt}\) 

\(\rm dy\over dx\) = \(\rm \frac{2t +2}{3t^2}\)

At t = 5,

\(\rm {dy\over dx}\) = \(\rm \frac{2(5) +2}{3(5)^2}\) = \(\rm \frac{12}{75}\) = \(\rm \frac{4}{25}\)

Concept:

Formula:

• cos-1 (cos x) = x
• sin^-1 (sin x) = x
• Slope of the curve = tan θ = \(\rm \frac {dy}{dx}\)

Calculation:

Given: Slope = tan θ

y = sin-1 (cos x)

⇒ y = sin-1 (sin (π/2 -x))

⇒ y = π/2 – x                                        (∵ sin-1 (sin x) = x)

Differentiating both sides with respect to x, we get

\(\rm \frac {dy}{dx}\) = -1

As we know, Slope = \(\rm \frac {dy}{dx}\)

⇒ tan θ  = -1

∴ θ = 3π/4

Concept:

The slope of the line tangent to the curve;

\(\rm {y_2-y_1\over x_2-x_1}=\left(\frac{\mathrm{d} y}{\mathrm{d} x}\right)_{at(x_1, y_1)}\) = m

Where (x1, y1) are the point on which tangent touches the curve and (x2, y2) is any other point on the tangent

Equation of the line with slope m and an on line points (x1, y1) is:

\(\rm (y-y_1) = m(x-x_1)\)

Distance of a point (p, q) from a line ax + by + c = 0:

D = \(\rm \left|{ap+bq+c\over\sqrt{a^2+b^2}}\right|\)

Calculation:

Given curve y2 = 16x

Differentiating w.r.t x on both sides

⇒ \(\rm \frac{\mathrm{d} }{\mathrm{d} x}y^2=\frac{\mathrm{d} }{\mathrm{d} x}16x\)

⇒ 2y \(\rm \frac{\mathrm{d} y}{\mathrm{d} x}\) = 16

The point on which tangent touches the curve is (1, 4)

⇒ \(\rm \frac{\mathrm{d} y}{\mathrm{d} x} = {8\over 4}\) = 2

⇒ Slope of tangent m = 2

Now equation of the tangent: 

\(\rm (y-y_1) = m(x-x_1)\)

⇒ y - 4 = 2(x - 1) 

⇒ y - 2x - 2 = 0​

So, distance of the origin (0, 0) from normal is;

D = \(\rm \left|{ap+bq+c\over\sqrt{a^2+b^2}}\right|\)

⇒ D = \(\rm \left|{1\times0+(-2)\times0+(-2)\over\sqrt{1^2+(-2)^2}}\right|\) 

⇒ D = \(\boldsymbol{\rm \left|{-2\over\sqrt5}\right| = {2\over\sqrt5}}\)