
Study Case : Q. 1 to 5 

Sonu went to the lab near to his home for COVID 19 test along with his family members. The seats in the waiting area were as per the norms of distancing during this pandemic (as shown in the above figure). His family members took their seats surrounded by black circular area. 
Based on the above information give the answer of the following questions. 
Considering O as the origin, what are the coordinates of seat of Sonu and Goru respectively?
A)
\[(2,3)\] and\[(6,5)\] done
clear
B)
\[(3,2)\] and \[(5,6)\] done
clear
C)
\[(3,6)\] and\[(5,2)\] done
clear
D)
\[(6,3)\] and \[(2,5)\] done
clear
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What is the distance between Golu and Monu?
A)
\[\sqrt{5}\] units done
clear
B)
\[2\sqrt{5}\] units done
clear
C)
\[3\sqrt{5}\] units done
clear
D)
\[4\sqrt{5}\] units done
clear
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What will be the coordinates of a point exactly between Sonu and Goru where a person can be seated?
A)
\[\left( \frac{5}{2},\frac{9}{2} \right)\] done
clear
B)
\[\left( \frac{11}{2},\frac{7}{2} \right)\] done
clear
C)
\[(4,4)\] done
clear
D)
\[\left( \frac{9}{2},4 \right)\] done
clear
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Find the area covered by Sonu and its members, if all four seats connected with a rope.
A)
\[\text{2}\sqrt{5}\,\text{sq}.\]units done
clear
B)
\[\sqrt{10}\,\text{sq}.\] units done
clear
C)
\[2\sqrt{10}\,\text{sq}.\] units done
clear
D)
\[10\,\text{sq}.\] units done
clear
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If the doctor divides the rope joining Sonu and Goru in the ratio \[1:2,\] then the coordinates of the seat of the doctor is:
A)
\[\left( \frac{10}{3},\frac{11}{3} \right)\] done
clear
B)
\[\left( \frac{11}{3},\frac{10}{3} \right)\] done
clear
C)
\[(4,4)\] done
clear
D)
\[(3,4)\] done
clear
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Study Case : Q. 6 to 10 
Centonion Public School Society, which has so many schools in different cities of India. One of the branch of Centonion Public School is in Meerut. In that School hundreds of students are in a classroom. 

Out of them one of the girl is standing in the ground having coordinates \[(3,4)\] facing towards west. She moves 5 units in straight line then take right and moves 4 units and stop. Now, she is at her coaching centre. The representation of the above situation on the coordinate axes is shown below: 

Based on the above information give the answer of the following questions. 
What is the shortest distance between her school and coaching centre?
A)
\[\sqrt{41}\] units done
clear
B)
3 units done
clear
C)
6 units done
clear
D)
7 units done
clear
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Suppose point \[D(1,4)\] divide the line segment AB in the ratio \[k:1,\] then find the value of k.
A)
\[3\] done
clear
B)
\[3/2\] done
clear
C)
\[2\] done
clear
D)
\[1/2\] done
clear
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If we draw perpendicular lines from points A and B to the Xaxis. the region covered by these perpendicular lines is:
A)
4 sq. units done
clear
B)
5 sq. units done
clear
C)
20 sq. units done
clear
D)
10 sq. units done
clear
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Find the area of \[\Delta ABC\].
A)
4 sq. units done
clear
B)
5 sq. units done
clear
C)
20 sq. units done
clear
D)
10 sq. units done
clear
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Find the image of the midpoint of AB with respect ro Xaxis.
A)
\[\left( \frac{1}{2},4 \right)\] done
clear
B)
\[\left( \frac{1}{2},4 \right)\] done
clear
C)
\[\left( \frac{1}{2},4 \right)\] done
clear
D)
\[\left( \frac{1}{2},4 \right)\] done
clear
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Study Case : Q. 11 to 15 
SLV3 was successfully launched on July 18, 1980 from Sriharikota Range (SHAR), when Rohini Satellite, RS1, was placed in orbit, thereby making India the sixth member of an exclusive club of spacefaring nations. 
SLV3 employed an open loop guidance (with stored pitch programme) to steer the vehicle in flight along a predetermined trajectory. The successful culmination of the SLV3 project showed the way to advanced launch vehicle projects such as the Augmented Satellite Launch Vehicle (ASLV), Polar Satellite Launch Vehicle (PSLV) and 
Geosynchronous Satellite Launch Vehicle (GSLV) Students of ClassXth made a mathematical model of a rocket as shown in the figure below: 
Based on the above information give the answer of the following questions: 

The coordinates of the point A are:
A)
\[(4,9)\] done
clear
B)
\[(5,9)\] done
clear
C)
\[\left( \frac{9}{2},9 \right)\] done
clear
D)
\[(4,8)\] done
clear
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The type of triangle ABC is:
A)
equilateral triangle done
clear
B)
isosceles triangle done
clear
C)
scalene triangle done
clear
D)
right triangle done
clear
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The area of triangle RBP is:
A)
2 sq. units done
clear
B)
4 sq. units done
clear
C)
\[\frac{3}{2}sq.\] units done
clear
D)
5 sq, units done
clear
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The area of rectangle BCED is:
A)
8 sq. units done
clear
B)
10 sq. units done
clear
C)
12 sq. units done
clear
D)
16 sq. units done
clear
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The area of trapezium DEGF is:
A)
8 sq. units done
clear
B)
10 sq. units done
clear
C)
12 sq. units done
clear
D)
16 sq. units done
clear
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Study Case : Q. 16 to 20 
All of the persons know that smoking is injurious to health. So, college students decided to make a campaign. 
To raise social awareness about hazards of smoking, school decided to start "NO SMOKING" campaign. 
Some students are asked to prepare campaign banners in the shape of triangle as shown in the figure: 

Based on the above information, give the answer of the following questions: 
The coordinates of the midpoint of Q and R are:
A)
\[(5,3)\] done
clear
B)
\[(6,3)\] done
clear
C)
\[\left( \frac{11}{2},3 \right)\] done
clear
D)
\[\left( 7,3 \right)\] done
clear
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The distance between P and R is:
A)
3 units done
clear
B)
\[3.5\]units done
clear
C)
\[3\sqrt{5}\] units done
clear
D)
\[5\sqrt{5}\]units done
clear
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The area of the triangle PQR is:
A)
21 sq. units done
clear
B)
35 sq. units done
clear
C)
42 sq, units done
clear
D)
45 sq, units done
clear
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The point on Xaxis, which is equidistant from points Q and R is:
A)
\[\left( \frac{11}{2},0 \right)\] done
clear
B)
\[(5,0)\] done
clear
C)
\[(6,0)\] done
clear
D)
\[(5,3)\] done
clear
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The centroid of the triangle PQR is:
A)
\[(5,5)\] done
clear
B)
\[(6,5)\] done
clear
C)
\[\left( \frac{17}{3},4 \right)\] done
clear
D)
\[\left( \frac{17}{3},5 \right)\] done
clear
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Study Case : Q. 21 to 25 
The class X students of a school in Rajinder Nagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Mango are planted on the boundary at the distance of 1 m from each other. 
There is a triangular grassy lawn in the plot as shown in figure. 

Based on the above figure, answer the following questions: 
Taking A as origin, the coordinates of vertices of the triangle are:
A)
\[(1,5),\,(4,6),\,(7,2)\] done
clear
B)
\[(2,4),\,(3,5),\,(6,3)\] done
clear
C)
\[(1,4),\,(4,5),\,(7,3)\] done
clear
D)
None of these done
clear
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The perimeter of \[\Delta PQR\] is:
A)
\[(\sqrt{10}+5+3\sqrt{5})\] units done
clear
B)
\[(\sqrt{10}+8\sqrt{5})\] units done
clear
C)
\[(10+3\sqrt{5})\] units done
clear
D)
\[(\sqrt{10}+5\sqrt{3})\] units done
clear
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The coordinates of the point M on PR such that \[\text{PM}:\text{MR}=\text{2}:\text{1},\]is:
A)
\[(4,3)\] done
clear
B)
\[(5,3)\] done
clear
C)
\[(5,4)\] done
clear
D)
\[(2,3)\] done
clear
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What will be the coordinates of the vertices of \[\Delta PQR\] if C is the origin?
A)
\[(14,3),\,(11,2),(8,6)\] done
clear
B)
\[(15,4),\,(12,3),(9,7)\] done
clear
C)
\[(14,2),\,(11,1),(8,5)\] done
clear
D)
\[(15,3),\,(12,2),(9,6)\] done
clear
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What are the coordinates of P if D is taken as the origin?
A)
\[(15,5)\] done
clear
B)
\[(15,5)\] done
clear
C)
\[(15,7)\] done
clear
D)
\[(15,3)\] done
clear
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Study Case : Q. 26 to 30 
On Annual Sports Day of a school, lines have been drawn with lime powder at a distance of 1 m each in the rectangular shaped school ground PLAY. 80 plastic cones have been placed at a distance of 1 m from each other along PY as shown in figure. 
Pushpendra runs \[\frac{1}{4}th\] the distance PY on the 3rd line and post a yellow flag. Pankaj runs \[\frac{1}{5}th\] the distance PY of the 7th line asnd posts a blue flag. 

Based on the given situation, answer the following questions: 
The coordinates of the yellow flag is:
A)
\[(20,3)\] done
clear
B)
\[(3,20)\] done
clear
C)
\[(80,3)\] done
clear
D)
\[(3,80)\] done
clear
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The coordinates of the blue flag is:
A)
\[(7,16)\] done
clear
B)
\[(16,7)\] done
clear
C)
\[(80,7)\] done
clear
D)
\[(7,80)\] done
clear
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What is the distance between both the flags?
A)
\[2\sqrt{2}m\] done
clear
B)
\[3\sqrt{2}m\] done
clear
C)
\[4\sqrt{2}m\] done
clear
D)
\[5\sqrt{2}m\] done
clear
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If Raman has to post a green flag exactly halfway between the line segment joining the two flags, where should he post his flag?
A)
16m on 4th line done
clear
B)
16m on 5th line done
clear
C)
18 m on 4th line done
clear
D)
18m on 5th line done
clear
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If Raman change his position and post a green flag at a point between the line segment joining the two flags, then the coordinate of the green flag which divides the Line : segment internally in the ratio \[1:2\] is:
A)
\[\left( \frac{13}{3},\frac{56}{3} \right)\] done
clear
B)
\[\left( \frac{56}{3},\frac{13}{3} \right)\] done
clear
C)
\[\left( \frac{13}{4},\frac{56}{3} \right)\] done
clear
D)
\[\left( \frac{56}{3},\frac{13}{4} \right)\] done
clear
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Study Case : Q. 31 to 35 
Four students of a class are standing at points P,Q,R and S in rows and columns in their playground for a drill practice (as shown in figure). 

Based on the above figure answer the following questions: 
The coordinates of the points P, Q, R and S (in order) are:
A)
\[(7,6),\,(4,5),(1,2)\]and \[(4,3)\] done
clear
B)
\[(1,2),(4,3),(7,6)\]and \[(4,5)\] done
clear
C)
\[(4,5),(7,6),(4,3)\]and \[(1,2)\] done
clear
D)
None of the above done
clear
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When the points P, Q, R and S (in order) join together, it form a quadrilateral PQRS. The relation between the sides of quadrilateral PQRS is:
A)
\[\text{QR}=S\text{P}\] and \[\text{PQ}=\text{RS}\] done
clear
B)
\[\text{PQ}=\text{QR}\] and \[\text{RS}=S\text{P}\] done
clear
C)
\[\text{PQ},\text{ QR},\text{ RS}\] and \[SP\] all are different done
clear
D)
None of the above done
clear
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The Length of the diagonals PR and QS are:
A)
\[\sqrt{10}\]and \[\sqrt{8}\]respectively done
clear
B)
\[2\] and \[\sqrt{52}\] respectively done
clear
C)
\[\sqrt{2}\] and \[\sqrt{10}\] respectively done
clear
D)
None of these done
clear
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The quadrilateral PQRS formed by these points is:
A)
a square done
clear
B)
a rectangle done
clear
C)
a parallelogram done
clear
D)
a trapezium done
clear
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The height of the quadrilateral PQRS taking SR as the base is:
A)
\[\frac{\sqrt{10}}{5}\]units done
clear
B)
\[\frac{2\sqrt{10}}{5}\]units done
clear
C)
\[3\sqrt{10}\]units done
clear
D)
\[\frac{3\sqrt{10}}{5}\]units done
clear
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