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(sec A − cos A) (cot A + tan A)

= sec A . cot A + sec A . tan A - cos A.cot A - cosA . tan A

= \(\frac{1}{cos\,A}\) . \(\frac{cos\,A}{sin\,A}\) + sec A . tan A - cos A . \(\frac{cos\, A}{sin\,A}-cos\,A.\frac{sin\,A}{cos\,A}\)

= \(\frac{1}{sin\,A}-sin\,A-\frac{cos^2A}{sin\,A}+sec\,A.tan\,A\)

= \(\frac{1-sin^2\,A-cos^2\,A}{sin\,A}\) + sec A . tan A

= \(\frac{1-1}{sin\,A}\) + sec A . tan A

(∵ sin²A + cos²A = 1)

= sec A . tan A

let CP of one article be = x
CP of 5 articles = 5x

SP of 3 articles = 5x 
SP of one article = 5x/3

So the gain = (0.66x/x)*100 = 66%.

There are two angles of projection for the same horizontal range, i.e; theta and 90 - theta with the horizontal. The projectile will cover the same horizontal range whether it is thrown at an angle of theta or 90 - theta with the horizontal. 

Here when the gun is fired, the shell moves with a certain velocity and the angle of elevation is 5pi/36 = 25 deg 

To overcome the hill which prevents the trajectory, the shell be elevation at an angle of 90 - 25 = 65 deg = 13pi/36, to cover the same range.

Pyrophosphoric acid, also known under the name diphosphoric acid, is colorless, odorless, hygroscopic and is soluble in water, diethyl ether, and ethyl alcohol.

Chemical formula‎: ‎H₄P₂O₇

Correct option is A) do

Correct option is C) pushing

You can work with color in Maya in so many different ways: 

· Change the basic color of an object by adjusting the color attribute of a material applied to the object. See Set a color for the object for a visual demonstration. 

· Apply a texture as a color map to the material’s color attribute. See Map a texture to any of the material attributes for a visual demonstration, and Map a 2D or 3D texture to a material for more information. 

· Use a Ramp Shader for extra control over the way color changes with light and view angle. You can simulate a variety of exotic materials and tweak traditional shading in subtle ways. 

· Expand, enhance, or manipulate colors in applied textures using utilities such as Blend Colors, Clamp, Gamma Correct, and so forth. For example, you can blend colors, adjust contrast, and convert HSV to RGB. For a description of each of the utilities and what you can use them for, see Utility nodes.

1. Create a sphere and a plane, and position the sphere over the plane. Create a light to illuminate both surfaces. 

2. Create a specular material (a Phong or PhongE) and assign it to the sphere. The sphere is reflected in the plane. 

3. Create a second material and assign it to the plane. The plane reflects the sphere. 

4. Make each surface a different color so you can see the reflection of one in the other. 

5. In the Raytracing Quality section of the Render Settings window, turn on Raytracing. This tells Maya to raytrace any surface whose Visible in Reflections/Refractions is toggled on. These attributes are on by default for all surfaces, but raytracing only works when you turn on Raytracing in the Render Settings window. To learn more about the Render Settings, see Render Settings window. 

6. Perform a test render to visualize the results. If you want the sphere to reflect the plane, open the plane’s Attribute Editor and turn on Render Stats > Visible in Reflections. To test iterations of a scene, see Visualize interactively with IPR

Anisotropy reflects and transmits light with a directional bias and causes materials to appear rougher or glossier in certain directions. The default value for Anisotropy is 0, which means 'isotropic.' As you move the control towards 1.0, the surface is made more anisotropic in the U axis.

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.

Roughness controls the glossiness of the specular reflections. The lower the value, the sharper the reflection. In the limit, a value of 0 will give you a perfectly sharp mirror reflection, while 1.0 will create reflections that are close to a diffuse reflection. You should connect a map here to get variation in the specular highlight.

Correct answer is (a) c

One of the velocity V₁ = V; Other velocity V₂ = -V

 Relative velocity (V_rel) = \(\frac{V_1 - V_2}{[1 + \frac{V^2}{C^2}]}\) = \(\frac{V- (-V)}{[1 + \frac{v^2}{C^2}]}\) = \(\frac{2v}{2}\)

V = C

V_relative = C

(a) L_A = L_B

Magnitude of L is, L = mvr sin ϕ = mvd 

d = r sin ϕ is the distance of closest approach of the particle so the origin, as ‘d’ is same for both particles. So, L_A = L_B

Correct answer is (b) Poles

(a) Inertia of passenger

1. Weight W = mg

= 70 × 10 = 700 N.

2. W = mg – ma

= 70 × 10 – 70 × 5

= 700 – 350

= 350 N

3. W = mg + ma

= 70 × 10 + 70 × 5

= 700 + 350

= 1050N.

This question is based on the concept of g_eff i.e. the effective g. In such questions, go in the frame of the lift and find g_eff and then solve like a normal ground frame question by using g_eff instead of g.

1) As the lift is moving with a constant velocity, it already is an inertial frame and so g_eff = g

So, weight = 70*10 = 700 N

2) In the frame of lift, g_eff = 10-5 = 5 

So, weight = 70*5 = 350 N

3) In the frame of lift, g_eff = 10+5 = 15

So, weight = 70*15 = 1050 N

Hope it helps

Ask if any doubt

Correct option is (c) mg 

μmg cosθ = mg sinθ

∴ Total force on plank 

= mg sinθ (along the incline) 

mg cosθ⁺ (⟂to incline)

= mg (resultant)

Correct option is C) them

Colourless  – Adjective

Correct option is C) bowl

Swami rose silently and tiptoed to his bed in the passage; Granny was sitting up in her bed and remarked, “Boy are you already feeling sleepy? Don’t you want to hear a story?”

Correct option is C) I’ll carry

Correct option is A) hot

Correct option is B) so as not to

Correct option is D) Would you like to go

Correct option is D) would

Correct option is C) so as to

Correct option is  B) during

Correct option is A) gave

Correct option is C) would you like

Correct option is  A) while

Correct option is D) set out

Correct option is  D) in

Correct option is  C) for

Correct option is  B) during

Galvanometer: A device i.e., used to detect current in the circuit. It can be converted into Ammeter to measure current and Voltmeter to measure potential difference between any two points in the circuit.

(a) 1.5 x 10⁸ m/s

μ = √∈_r μ_r = √1 x 4 = 2

⇒ v = c/μ = 3 x 10⁸ /2

= 1.5 x 10⁸ m/s

Answer is (3)

V = 1/√{μɛ}

n = √{μ_rɛ_r} = 2

sin c = 1/2

c = 30º

Correct option is C) changing

First aunt polly ran upstairs at her heels. After looking at tom,she sank down into a chair and then laughed a little then cried a little and then did both together.

Mentality is represented by disjoining Half-length M and N hook.