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Section I: Numerical Answer Type Questions
Q.01 Solid 1, Solid 2 and Solid 3 are joined together to form a cuboid as shown in Figure 1. The cuboid is then painted from all the sides. How many surfaces are there without the paint when you separate all the three solids?
Answer : 27
Step 1 : Count the total surface of all 3 objects, i.e. 45 (solid 1 and 2 has 16 side and solid 3 has 13 sides)
Step 2 : Count total painted surface in figure 1, i.e. 18
Step 3 : Subtract Total surface and painted surface. You will get answer 27 Q.02 An irregular solid is cut into seven pieces as shown. The pieces are neither rotated nor scaled, but are kept in a random sequence. Find the correct sequence to get the smooth form. The sequence should be written from left to right.
Answer : 3214765
Q.03 What are the least number of lines required to generate a 3D form such that it creates shadows similar to the figure shown below?
Answer : 5
Q.04 In the square ABCD, line XY is drawn parallel to the base as shown in the figure below. P and Q are any two arbitrary points on XY, forming triangles ABQ and CDP. What fraction of the area of the square is the total green shaded area?
Answer : 0.5
Q.05 Five square pyramids are stacked as shown in the figure below with the bottom layer consisting of four pyramids in a 2 x 2 grid. If the bottom layer consists of pyramids in 6 x 7 grid, and they are stacked in a similar manner to its maximum height, how many pyramids will the formation contain?
Answer : 112
Q.06 A bank needs to upgrade its ATM kiosks to be wheel-chair accessible. An ATM kiosk entrance has four steps rising up to reach the floor level of the kiosk. Each step is 1000 mm in length, 300 mm in breadth, and 150 mm in height. The bank proposes to create a wheelchair accessible ramp with a slope of 1:12, adjacent to the steps. What is the minimum horizontal length of the ramp in metre?
Answer : 7.2
Q.07 A system of frictionless and massless pulleys is being used to pull up a load of 2520 N. What is the minimum force (in Newtons) required at the end of the rope (shown in dashed lines)?
Answer : 420
Amount of load required to lift total weight is divided by half of total number of pulleys.
Since total pulley count is 8, so we will divide total load i.e. 2520 N by 4 to calculate required force at the end of rope i.e. 420 N
Q.08 Shown below are three views of the same solid. Count the number of edges.
Answer : 14
Section II: Multiple Select Questions
Q.09 A virus has two variants P and Q. Two treatments L and M were developed against
variant P and Q and tested through four independent trials. The table shows the
results. Assuming that both variants are equally prevalent, and both treatments cost
about the same, but a given patient can be treated with only one treatment, which of
the options is/are true?
A. If the patient is known to be infected by variant P, both the treatments will be equally effective
B. If we can determine that the patient is infected by variant Q, treatment L has a higher chance of success
C. If the variant that the patient is infected by is not known, then both the treatments can be equally effective
D. If a hospital can stock only one of the two treatments, they should stock treatment L
Answer : B & D
A. Not Possible, For Variant P Treatment M is more effective as it have more successes
B. Possible, For Variant Q Treatment L is more effective as it have more successes
C. Not Possible, As successes in variant P and Q is different in both treatment.
D. Possible, though both treatment has equal successes in total but treatment L has almost similar success in both variants so that should be preference.
Q.10 Figure shows the plan of a one-way road passing next to a primary school. Which of the options can be the location(s) to set up a bus stop for the school bus in Indian context?
Answer : D
Since it is one way road so only possible options could be C or D and from these two also option D is best place for bus stop as there is road cross and driver can easily see people crossing road in front.
Q.11 Mobile sculptures are created by tying fish-shaped cut-outs of different colours using blue strings on brown sticks of negligible weight, as shown below. All the fish cut-outs are of the same size and weight. Which of the options will remain balanced after suspending from a ceiling?
Answer : B,D
Carefully examine the placement of blue string and calculate the distribution of load on both side by giving some value to length of brown stick and weight of fish.
Q.12 Which of the graphs shown below represent(s) the equation XY = 25?
Answer : A,C,D
Multiply the value of X and Y of all the graphs it comes 25 except the value of graphs of B is -25.
Q.13 Which of the following rocking chairs will NOT topple while rocking 15 degree?
Answer: B, C
Q.14 Shown on the left are the front and top views of a 3D object. Which option(s) can be the side view?
Answer: A, B
In Figure C the line highlighted by red colour (coming from Top View) is not matching with the figure.
In Figure D the line highlighted by red colour represents a vertex which is not available in front view of drawing.
Q.15 Figure P can be divided into four identical pieces. Assuming that the pieces can be rotated and flipped, which of the options will fit?
Answer: B, C
Q.16 An animation of shapes morphing from one to another is shown in the GIF below.
Which of the shapes shown in the options can be found in this animation sequence in
its exact orientation and size?
Answer: C, D
It is clear from animation that C and D are only possible options.
Q.17 Tile X was used to create a pattern which is seamless (without gaps) when arranged
as shown in Y. Which tile(s) from the options will create a seamless pattern?
Answer: A, C, D
Q.18 Some configurations for the pair of scissors are shown below. If concentric circles
represent hinges, which of the options will work?
Answer: A, C, D
Part A – Section III: Multiple Choice Questions
Q.19 Shown in the box are the orthographic views of a 3D object. Which option represents
that object?
Answer: D
Q.20 A washbasin is to be installed in a college canteen in India. Which of the options can
help derive the appropriate height of the washbasin from the floor?
A. Average height of the adult Indian male and female population
B. Average height of the tallest 50% adult Indian female population
C. Average height of the shortest 5% adult Indian female population
D. Average height of the shortest 5% adult Indian male population
Answer: C
Height of Washbasin should be such that It is is reachable to every person so the person having shortest height in the group will be considered to finalise height here. And in given option Option C is one with the shortest height so that is the correct answer.
Q.21 Image X represents the six faces of a cube. Image Y shows a composition using five
such cubes. What could be the rear view of the shown composition?
Answer: D
Check the Opposite faces of each number and match opposite face of Image Y with given options.
1 is opposite to 2 & 5
2 is opposite to 1 & 3
3 is opposite to 2
5 is opposite to 1
Q 22 Shown below are two parts of a mould. Mould is closed and material is poured into
the cavity. What would be the resultant moulded part?
Q.23 Three leaves are falling from a tree. Figure 1 shows the way a leaf falls. Figure 2
illustrates the starting orientation of the three leaves. If the blue colour leaf is at 200 cm, the
red colour leaf is at 425 cm and the yellow colour leaf is at 375 cm from the ground, then
what would be the orientation of all the leaves when they reach the ground?
Answer: C
Q.24 Which option resembles an angry person when flipped vertically?
Q.25 Eleven identical circles are linked together by line segments that connect the centres
of adjoining circles as shown in the figure below. Which of the statements is TRUE?
A. Purple area is equal to the green area
B. Purple area is greater than green area by one circle
C. Purple area is greater than green area by two circles
D. Purple area is greater than green area by three circles
Answer : C
Q.26 Identify the odd one.
Q.27 Shown on the left is a woven mat using threads of two colours. The mat is flipped at
the edge Q to reveal the back side. Identify the back side of the mat from the given
options.
Answer: D
Q.28
Q.29 A folding fan shown in the image is made of bamboo and paper painted on one side.
Which option is the closest representation of the same fan in the folded position?
(dotted lines indicate the folds)
Answer: B
Q.30 Roads are generally made with an angle on the curvatures to counter the centrifugal
force on vehicles moving with speed. This is called ‘Banking of Road’. Figure shows
two one-way roads P and Q from top view. If the maximum safe speed limit is same
for both the roads, which option shows the schematic cross section of P and Q at the
position SS?
Q.31 Which option will fold into the pack shown in the image below?
Answer: D
Answer: C
Q.32 A closed loop is made of a metal pipe and is rolling between two fixed pulleys as
shown in the image on the left. What would be the path traced by point P when the
loop completes one turn?
Q.33 Biomimicry is the practice of looking to nature for inspiration to solve design
problems. Shown below are plants and animals (top row) that have inspired the design of
products (bottom row).
Which of the options listed below correctly identifies the plant and/or animal with the
product that it inspired?
A. P – 3, Q – 1, R – 4, S – 2
B. P – 4, Q – 2, R – 1, S – 3
C. P – 3, Q – 4, R – 1, S – 2
D. P – 1, Q – 3, R – 2, S – 4
Answer : C
Q.34 Image below shows configurations of jars filled with water. Which option will work as
an air filter?
Q.35 Which of the options, when combined with block shown on top, will result in perfect
4x4x4 cube?
Answer: D
Q.36 Which of the options will result in the form shown on the left, when revolved around
x-x’ axis?
Answer: B
Q.37 Figure 1 shows the skeleton of a T-rex dinosaur. Identify the correct distorted
silhouette from the given options.
Q.38 Circles of how many different radii are needed to construct the following figure?
A. 4
B. 5
C. 6
D. 7
Answer : D
Q.39 A printed transparent sticker (as shown on the left) is applied onto a glass cylinder
such that the vertical edges meet. Which option is the correct representation?
Answer: A
Q.40 Image on the left shows a cylinder kept on the top of a cube. Height of the cylinder
and side of the cube are equal. Parallel rays of light are falling on them at an angle of
45 degree. Which option shows the correct shadow?
Q.41 Shown on the left is a futon that becomes a mattress when opened and folds into a
seat. Which option CANNOT be folded as a seat?
Answer : C
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