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questions
List of practice Questions
The shaded plane given below is rotated clockwise around the given axis, up to an angle of 270 degrees. Draw the solid form resulting from this rotation.
JEE Advanced - 2024
JEE Advanced
Architecture
Three-Dimensional Perception
The schematic plan, front elevation, and side elevation, of an office building block are given below. The direction of the incident sunrays is indicated as ‘S’. Sketch the shading and shadows that would be generated by the sunrays in the view of the building block provided in Figure J.
JEE Advanced - 2024
JEE Advanced
Architecture
Geometrical Drawing
Certain cities across the globe are known by their uniquely coloured street façades. Colour the given street façade with minimum three colours of your choice. The façade elements such as cornice, entry steps, door, window, parapet etc. are to be considered while planning the colour scheme for the street façade.
JEE Advanced - 2024
JEE Advanced
Architecture
Imagination and Aesthetic Sensitivity
Below is the story of a hare and a tortoise
narrated in four scenes. Fill up the blank frames with appropriate illustrations to complete the narration. You may add text balloons, if required.
\newpage
JEE Advanced - 2024
JEE Advanced
Architecture
Imagination and Aesthetic Sensitivity
Match the representative skylines in Column I, with their corresponding cities in Column II.
JEE Advanced - 2024
JEE Advanced
Architecture
Architectural Knowledge
Match the architectural landmarks of India in Column I, with their corresponding descriptions in Column II.
JEE Advanced - 2024
JEE Advanced
Architecture
Architectural Knowledge
The front elevation of a city hoarding is shown in Figure H. Given below (Figure I) is the outline of the human-eye view of the hoarding.
Fill it up with text and graphic elements indicated in Figure H, maintaining geometry and proportion. Use the indicative grid provided.
JEE Advanced - 2024
JEE Advanced
Architecture
Geometrical Drawing
A rod AB of length 8 units, having mid-point at S, is in a vertical position as shown below. The end A is sliding vertically down, while end B is moving horizontally to your right till it reaches the point C, which is 8 units from the point B. Draw the locus of the mid-point S, using a minimum of 8 positions of AB.
JEE Advanced - 2024
JEE Advanced
Architecture
Geometrical Drawing
You have sprained your ankle and are on a wheelchair. You want to join your friends for a party at the food court located on the top floor of a shopping mall, which you are visiting for the first time. Since you are alone, and also do not know your way around, signs would help you. \textit{Which of the following signs will you require to conveniently reach your destination on your own?
}
JEE Advanced - 2024
JEE Advanced
Architecture
Imagination and Aesthetic Sensitivity
Identify the last figure in the sequence shown in Figure G.
JEE Advanced - 2024
JEE Advanced
Architecture
Geometrical Drawing
A building designed by the famous Indian architect Raj Rewal was demolished in the year 2017, after much controversy. \textit{Identify the building from the given options.
}
JEE Advanced - 2024
JEE Advanced
Architecture
Architectural Knowledge
Which of the following graphics represents the United Nations’ ‘Sustainable Development Goal 3 (SDG 3): Good Health and Well-being’?
JEE Advanced - 2024
JEE Advanced
Architecture
Architectural Knowledge
A hemispherical vessel of radius 30 cm is full of mixture to prepare kulfis. Kulfi-moulds are right circular cones of 5 cm diameter at base, having a height of 10 cm. Maximum how many kulfis can be prepared by filling the moulds up to the brim?
JEE Advanced - 2024
JEE Advanced
Architecture
Geometrical Drawing
You overheard a conversation between X and Y in a building. The conversations were as follows:
\begin{quote} X: I am a part of a window and can be appreciated from outside.
Y: Well, I might be invisible, but I carry the building load.
X: While I ensure light inside the room, I am not affected by the weather.
Y: I am not exposed to the weather, and people take advantage of my strength, which you don’t have much. \end{quote}
Identify X and Y from the options given below.
JEE Advanced - 2024
JEE Advanced
Architecture
Architectural Knowledge
With respect to 'Green Buildings', consider the following statements and select the appropriate option.
JEE Advanced - 2024
JEE Advanced
Architecture
Architectural Knowledge
Let \( \vec{a} = \hat{i} - \hat{j} \), \( \vec{b} = \hat{j} - \hat{k} \), and \( \vec{c} = \hat{k} - \hat{i} \), then the value of \( \vec{b} \cdot (\vec{a} + \vec{c}) \) is:
KEAM - 2024
KEAM
Mathematics
Sequence and Series
Let \( \mathbf{u}, \mathbf{v}, \mathbf{w} \) be vectors such that \( \mathbf{u} + \mathbf{v} + \mathbf{w} = \mathbf{0} \). If \( |\mathbf{u}| = 3 \), \( |\mathbf{v}| = 4 \), and \( |\mathbf{w}| = 5 \), then \( \mathbf{u} \cdot \mathbf{v} + \mathbf{w} \cdot \mathbf{u} \) is:
KEAM - 2024
KEAM
Mathematics
Vectors
If a vector makes angles \( \frac{\pi}{3}, \frac{\pi}{4} \) and \( \gamma \) with \( \hat{i}, \hat{j} \), and \( \hat{k} \), respectively, where \( \gamma \in \left( \frac{\pi}{2}, \pi \right) \), then the angle \( \gamma \) is:
KEAM - 2024
KEAM
Mathematics
Sequence and Series
Evaluate \( \cos \left( \cot^{-1} \left( \frac{7}{24} \right) \right) \):
KEAM - 2024
KEAM
Mathematics
Sequence and Series
If \( 3 \sin \theta + 5 \cos \theta = 5 \), then the value of \( 5 \sin \theta - 3 \cos \theta \) is:
KEAM - 2024
KEAM
Mathematics
Sequence and Series
The value of \( \tan \left[ \tan^{-1} \left( \frac{3}{4} \right) + \tan^{-1} \left( \frac{2}{3} \right) \right] \) is:
KEAM - 2024
KEAM
Mathematics
Sequence and Series
If \( \alpha = \tan^2 x + \cot^2 x \), where \( x \in \left( 0, \frac{\pi}{2} \right) \), then \( \alpha \) lies in the interval:
KEAM - 2024
KEAM
Mathematics
Sequence and Series
The domain of the function \( f(x) = \frac{\sin^{-1} \left( x-3 \right)}{\sqrt{9 - x^2}} \) is:
KEAM - 2024
KEAM
Mathematics
Sequence and Series
If \( \sin \theta = \frac{b}{a} \), then \( \frac{\sqrt{a+b}} {\sqrt{a-b}} + \frac{\sqrt{a-b}} {\sqrt{a+b}} \) is equal to:
KEAM - 2024
KEAM
Mathematics
Sequence and Series
If \( \frac{\sec^2 15^\circ - 1}{\sec^2 15^\circ} \) equals:
KEAM - 2024
KEAM
Mathematics
Sequence and Series
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