
Direction: Q. 1 to 5 
Sanjeev wants to measure a garden during the visit to his native. He marks points P and Q on the opposite edges of a garden as shown in the figure. 
To find the distance between the points, he makes a rightangled triangle using rope connecting Q with another point R at a distance of \[\text{4m},\] connecting R to point 5 at a distance of \[\text{15m}\] from point R and connecting S to the point P which is at a distance of \[\text{8m}\] from S such that triangle PRS is a right angled triangle with \[\angle S=90{}^\circ \]. 

Based on the above information, give the answer of the following questions: 
Which property of geometry will be used to find the distance PR?
A)
Similarity of triangles done
clear
B)
Thales theorem done
clear
C)
Pythagoras theorem done
clear
D)
Area of similar triangles done
clear
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What is the distance (PQ) of garden?
A)
\[10\,m\] done
clear
B)
\[11\,m\] done
clear
C)
\[12\,m\] done
clear
D)
\[13\,m\] done
clear
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What is the distance PR?
A)
\[12\,m\] done
clear
B)
\[17\,m\] done
clear
C)
\[10\,m\] done
clear
D)
\[9\,m\] done
clear
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Find the Length of the rope used.
A)
\[26\,m\] done
clear
B)
\[25\,m\] done
clear
C)
\[27\,m\] done
clear
D)
\[23\,m\] done
clear
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Which of the following forms a Pythagoras triplet?
A)
\[(5,11,13)\] done
clear
B)
\[(9,15,18)\] done
clear
C)
\[(17,24,25)\] done
clear
D)
\[(20,21,29)\] done
clear
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Direction: Q. 6 to 10 
Anika is studying in class X. She observe two poles DC and BA. The heights of these poles are x m and y m respectively as shown in figure below: 

These poles are z metres apart and O is the point o: 
intersection of the lines joining the top of each pole to the foot of opposite pole and the distance between point 0 and L is a Few questions came" to his mind while observing the poles Give answer to his questions by looking at figure. 
Which is the correct similarity criteria applicable in \[\Delta CAB\] and \[\Delta CLO\]?
A)
AA done
clear
B)
SSS done
clear
C)
SAS done
clear
D)
RHS done
clear
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If \[\text{CL}=\text{a},\]then find o In terms of x, y and d.
A)
\[\frac{xd}{z}\] done
clear
B)
\[\frac{xz}{d}\] done
clear
C)
\[\frac{zd}{x}\] done
clear
D)
\[xzd\] done
clear
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If \[\text{AL}=\text{b},\]then find b in terms of x, y and d is:
A)
\[\frac{zd}{y}\] done
clear
B)
\[\frac{yd}{z}\] done
clear
C)
\[xyd\] done
clear
D)
\[xzd\] done
clear
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Find d in terms of x and y.
A)
\[\frac{x+y}{xy}\] done
clear
B)
\[\frac{xy}{x+y}\] done
clear
C)
\[xy\] done
clear
D)
\[\frac{x}{y}\] done
clear
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If \[\text{x}=\text{7 m}\] and \[\text{y}=\text{1}0\text{ m},\]then find d.
A)
\[\frac{30}{13}m\] done
clear
B)
\[\frac{50}{17}m\] done
clear
C)
\[\frac{70}{17}m\] done
clear
D)
\[\frac{90}{19}m\] done
clear
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Direction: Q. 11 to 15 
Gaurav placed a light bulb at a point O on the ceiling and directly below it placed a table. He cuts a polygon, say a quadrilateral PQRS, from a plane cardboard and place this cardboard parallel to the ground between the lighted bulb and the table. Then a shadow of PQRS is cast on the table as PQRS. Quadrilateral P'Q'R'S' is an enlargement of the quadrilateral PQRS with scale factor \[\text{1}:\text{3}\] Given that \[\text{PQ}=\text{2}.\text{5cm},\] \[\text{QR}=\text{3}.\text{5 cm}\]. \[\text{RS}=\text{3}.\text{4 cm}\] and \[\text{PS}=\text{3}.\text{1 cm};\] \[\angle P=115{}^\circ ,\] \[\angle Q=95{}^\circ ,\] \[\angle R=65{}^\circ \]and \[\angle S=85{}^\circ \]. 

Based on the given information, give the answer of the following questions: 
The length of R'S' is:
A)
\[\text{3}.\text{4 cm}\] done
clear
B)
\[\text{1}0.\text{2 cm}\] done
clear
C)
\[\text{6}.\text{8 cm}\] done
clear
D)
\[\text{9}.\text{5 cm}\] done
clear
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The ratio of sides P'Q' and Q'R' is:
A)
\[\text{5}:7\] done
clear
B)
\[7:5\] done
clear
C)
\[7:2\] done
clear
D)
\[2:7\] done
clear
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The measurement of angle Q is:
A)
\[115{}^\circ \] done
clear
B)
\[95{}^\circ \] done
clear
C)
\[65{}^\circ \] done
clear
D)
\[85{}^\circ \] done
clear
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The sum of the length Q'R' and P'S' is:
A)
\[\text{12}.\text{3 cm}\] done
clear
B)
\[\text{6}.\text{7 cm}\] done
clear
C)
\[\text{19}.\text{8 cm}\] done
clear
D)
\[\text{9 cm}\] done
clear
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The sum of angles of quadrilateral P'Q'R'S' is:
A)
\[180{}^\circ \] done
clear
B)
\[270{}^\circ \] done
clear
C)
\[300{}^\circ \] done
clear
D)
\[360{}^\circ \] done
clear
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Direction: Q. 16 to 20 
There is a staircase as shown in figure, connecting points A and B. Measurement of steps are marked in the figure. Give answers of the following questions by looking at the figure. 

The common angle in each staircase is:
A)
\[30{}^\circ \] done
clear
B)
\[60{}^\circ \] done
clear
C)
\[90{}^\circ \] done
clear
D)
nothing done
clear
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Which is the correct similarity criteria applicable for staircase II and III?
A)
RHS done
clear
B)
SAS done
clear
C)
SSA done
clear
D)
AAS done
clear
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Which concept is used to find the distance between A and S?
A)
Pythagoras theorem done
clear
B)
Thales theorem done
clear
C)
Converse of Thales theorem done
clear
D)
Converse of pythagoras theorem, done
clear
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The straight line distance between A and B is:
A)
\[\sqrt{5}+\sqrt{6.56}+\sqrt{6.56}+\sqrt{7.24}\] done
clear
B)
\[\sqrt{5.15}+\sqrt{6.21}+\sqrt{6.21}+\sqrt{7}\] done
clear
C)
\[\sqrt{5}+\sqrt{6}+\sqrt{6}+\sqrt{7}\] done
clear
D)
None of the above done
clear
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The sum of the area of each staircase is:
A)
6 square unit done
clear
B)
12 square unit done
clear
C)
10 square unit done
clear
D)
None of these done
clear
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Direction: Q. 21 to 25 
Nazima is fly fishing in a stream. The tip of her fishing rod is \[\text{1}.\text{8 m}\] above the surface of the water and the fly at the end of the string rests on the water \[3.6\text{ m}\]away and \[2.4\text{ m}\] from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, answer the following questions given below: 

How much string does she have out?
A)
\[1\,m\] done
clear
B)
\[1.5\,m\] done
clear
C)
\[2.5\,m\] done
clear
D)
\[3\,m\] done
clear
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If she pulls in the string at the rate of \[\text{5 cm}/\text{s}\] then the Length of the string pulled in 12 seconds is:
A)
\[0.\text{6 m}\] done
clear
B)
\[1.\text{6 m}\] done
clear
C)
\[0.8\text{ m}\] done
clear
D)
\[1.2\text{ m}\] done
clear
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Length of the remaining string left out after 12 seconds is:
A)
\[1.2\text{ m}\] done
clear
B)
C)
D)
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The distance of fly at the end of the string from the point over the water surface just below the tip of fishing rod, after 12 seconds is:
A)
\[\text{1}.\text{2 m}\] done
clear
B)
\[\text{2}.\text{52 m}\] done
clear
C)
\[\text{1}.\text{59 m}\] done
clear
D)
\[\text{2}.\text{79 m}\] done
clear
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The horizontal distance of the fly from Nazima after 12 seconds is:
A)
\[1.2\,m\] done
clear
B)
\[\text{2}.\text{52 m}\] done
clear
C)
\[\text{1}.\text{59 m}\] done
clear
D)
\[\text{2}.\text{79 m}\] done
clear
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Direction: Q. 26 to 30 
Two buildings I and II are of heights \[\text{19 m}\] and \[\text{4}0\text{ m}\] respectively \[20\text{ m}\] apart. 

Based on the above information, give the answer of the following questions: 
The distance between their tops can be found out by using which of the following theorems?
A)
Similarity of triangles done
clear
B)
Converse of Pythagoras Theorem done
clear
C)
Thales Theorem done
clear
D)
Pythagoras Theorem done
clear
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The distance between their tops i.e., Length of AB is:
A)
\[\sqrt{1961}\,m\] done
clear
B)
\[\sqrt{802}\,m\] done
clear
C)
\[29\,m\] done
clear
D)
\[41\,m\] done
clear
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In a \[\Delta ABC,\] \[BD\bot AC\] such that \[B{{D}^{2}}=DC.\] AD, then :
A)
\[\angle A=90{}^\circ \] done
clear
B)
\[\angle B=90{}^\circ \] done
clear
C)
\[\angle C=90{}^\circ \] done
clear
D)
ABC is not a right angled triangle done
clear
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In the given figure, the side PQ of a right triangle \[\Delta PQR\]where \[\text{OP}=\text{6 cm},\] \[\text{OR}=\text{8 cm}\] and \[\text{QR}=\text{26 cm},\]is : 

A)
\[21\,cm\] done
clear
B)
\[23\,cm\] done
clear
C)
\[24\,cm\] done
clear
D)
\[36\,cm\] done
clear
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Hypotenuse of a right triangle is \[\text{25 cm}\] and out of the remaining two sides, one is longer than the other by \[\text{5 cm}\]. Then the length of the longer side is:
A)
\[20\,cm\] done
clear
B)
\[15\,cm\] done
clear
C)
\[12.5\,cm\] done
clear
D)
\[10\,cm\] done
clear
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Direction: Q. 31 to 35 
The Louvre Pyramid (Pyramide du Louvre) is a large glass and Chinese American architect I. 
M. Pei, surrounded by three smaller pyramids, in the maincourtyard (Cour Napoleon) of the Louvre Palace (Palais du Louvre) in Paris. The large pyramid serves as the main entrance to the Louvre Museum. 
Completed in 1989., it has become a landmark of the city of Paris. As can be seen, two triangles ABC and DEF have been marked in the image, where \[\left. DE \right\AB\] and \[\left. EF \right\BC\]. 

Based on the given information, give the answer of the following questions: 
Which of the following is not a criteria for similarity of two triangles?
A)
SSS done
clear
B)
ASA done
clear
C)
SAS done
clear
D)
AA done
clear
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Select the correct statement from the statements given below:
A)
\[\Delta ABC\tilde{\ }\Delta DEF\] by SSS similarity criterion done
clear
B)
\[\Delta ABC\tilde{\ }\Delta DEF\] by SAS similarity criterion done
clear
C)
\[\Delta ABC\tilde{\ }\Delta EDF\] by AA similarity criterion done
clear
D)
\[\Delta ABC\tilde{\ }\Delta DEF\] by AA similarity criterion done
clear
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If the measures of sides AB, BC and DE are \[\text{15 m},\] \[\text{21 m},\] and \[\text{10 m}\] respectively, then measure of side EF is:
A)
\[\text{14 m}\] done
clear
B)
\[\frac{50}{7}\text{ m}\] done
clear
C)
\[\text{12 m}\] done
clear
D)
\[\text{7 m}\] done
clear
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In relation to the part \[(3),\] the ratio of sides \[\text{DF}:\text{AC}\] is:
A)
\[2:5\] done
clear
B)
\[5:2\] done
clear
C)
\[2:3\] done
clear
D)
\[3:2\] done
clear
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In relation to the part \[(3),\] the ratio of areas of triangles ABC and DEF is:
A)
\[9:4\] done
clear
B)
\[3:2\] done
clear
C)
\[4:9\] done
clear
D)
\[2:3\] done
clear
View Solution play_arrow