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question_answer1)
Points \[(6,\,8),\,(3,7),(-2,-2)\] and \[(1,-1)\] are joined to form a quadrilateral. What will be the structure of quadrilateral?
A)
Rhombus done
clear
B)
Parallelogram done
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C)
Square done
clear
D)
Rectangle done
clear
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question_answer2)
Find the area (in square units) of the triangle whose vertices are \[(a,\,b+c),\] \[(a,\,b-c)\] and \[(-a,c)\].
A)
\[2ac\] done
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B)
\[2bc\] done
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C)
\[b(a+c)\] done
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D)
\[c(a-b)\] done
clear
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question_answer3)
Find the area of the quadrilateral, the coordinates of whose angular points taken in order are \[(1,1),\,(3,4),\,(5,-2)\] and \[(4,-7)\].
A)
\[20.5\]sq. units done
clear
B)
41 sq. units done
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C)
82 sq. units done
clear
D)
\[61.5\]sq. units done
clear
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question_answer4)
Four vertices of a parallelogram taken in order are \[(-3,-1),\,(a,b),\,(3,3)\]and\[(4,3)\]. What will be the ratio of a and b?
A)
\[4:1\] done
clear
B)
\[1:2\] done
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C)
\[1:3\] done
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D)
\[3:1\] done
clear
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question_answer5)
The points \[(1,1),\,(-1,5),\,(7,9)\] and \[(9,5)\] taken in such order that it will form a
A)
Rectangle done
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B)
Square done
clear
C)
Rhombus done
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D)
None of these done
clear
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question_answer6)
If the points (a, 0), (0. b} and (1,1) are collinear then which of the following is true?
A)
\[\frac{1}{a}+\frac{1}{b}=2\] done
clear
B)
\[\frac{1}{a}-\frac{1}{b}=1\] done
clear
C)
\[\frac{1}{a}-\frac{1}{b}=2\] done
clear
D)
\[\frac{1}{a}+\frac{1}{b}-1\] done
clear
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question_answer7)
Three points \[A(1,-2)\]\[B(3,4)\] and \[C(4,7)\]form
A)
A straight line done
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B)
An equilateral triangle done
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C)
A right-angled triangle done
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D)
None of these done
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question_answer8)
The coordinates of the mid-points of the sides of a triangle are (4, 2), (3, 3) and (2, 2). What will be the coordinates of the centroid of the triangle?
A)
\[\left( 3,\frac{7}{3} \right)\] done
clear
B)
\[\left( -3,\frac{-7}{3} \right)\] done
clear
C)
\[\left( 3,\frac{-7}{3} \right)\] done
clear
D)
\[\left( -3,\frac{7}{3} \right)\] done
clear
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question_answer9)
Area of quadrilateral formed by the vertices \[(-1,6),\,(-3,-9),\,(5,-8)\] and (3, 9) is _____ (sq. units).
A)
96 done
clear
B)
18 done
clear
C)
50 done
clear
D)
25 done
clear
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question_answer10)
Find the area of triangle whose vertices are \[(t,\,t-2),\,(t+2,\,t+2)\]and \[(t+3,\,\,\,t)\].
A)
14 sq. units done
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B)
2tsq. Units done
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C)
5 sq. units done
clear
D)
4 sq. units done
clear
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question_answer11)
The vertices of a \[\Delta ABC\] are\[A(2,1)\], \[B\,(6,-2),\]\[C\,(8,\,9)\]. If AD is angle bisector, where D meets on BC, then coordinates of D are
A)
\[\left( \frac{20}{3},\frac{5}{3} \right)\] done
clear
B)
\[(5,2)\] done
clear
C)
\[(4,3)\] done
clear
D)
\[\left( \frac{14}{3},\frac{7}{3} \right)\] done
clear
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question_answer12)
The coordinates of the third vertex of an equilateral triangle whose two vertices are at \[(3,\,4),\,\,(-2,\,3)\] are _____.
A)
\[(1,7)\] done
clear
B)
\[(5,1)\] done
clear
C)
\[\left( \frac{1+\sqrt{3}}{2},\frac{7-5\sqrt{3}}{2} \right)\] or \[\left( \frac{1-\sqrt{3}}{2},\frac{7+5\sqrt{3}}{2} \right)\] done
clear
D)
\[(-5,5)\] done
clear
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question_answer13)
In what ratio is the line segment joining the points (-3, 2) and (6, 1) is divided by Y-axis?
A)
\[1:3\] done
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B)
\[2:1\] done
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C)
\[1:2\] done
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D)
\[3:1\] done
clear
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question_answer14)
Find the coordinates of the point on X-axis which are equidistant from the points \[(-3,4)\] and (2, 5).
A)
\[(20,0)\] done
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B)
\[(-23,0)\] done
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C)
\[\left( \frac{4}{7},0 \right)\] done
clear
D)
None of these done
clear
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question_answer15)
If the centroid of the triangle formed by the points (a, b), (b, c) and (c. a) is at the origin, then \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=\]
A)
\[abc\] done
clear
B)
0 done
clear
C)
\[a+b+c\] done
clear
D)
\[3\text{ }abc\] done
clear
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question_answer16)
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter's school and then reaches the office. If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines)
A)
\[2.2\text{ }km\] done
clear
B)
\[2.7\text{ }km\] done
clear
C)
\[\text{11}\sqrt{3}\text{ }km\] done
clear
D)
\[2.40\text{ }km\] done
clear
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question_answer17)
DIRECTION: Students of a school are standing in rows and columns in their playground for drill practice. A, B, C and D are the position of the four students as shown in the figure. |
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What is the difference of distance between AC and AD?
A)
2 units done
clear
B)
\[2.14\]units done
clear
C)
8 units done
clear
D)
\[2.3\]units done
clear
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question_answer18)
DIRECTION: Students of a school are standing in rows and columns in their playground for drill practice. A, B, C and D are the position of the four students as shown in the figure. |
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If Mohit wants to stand in such a way that he is equidistance from each of the four students A, B, C and D then what are the coordinate of his position?
A)
(6, 6) done
clear
B)
(7, 5) done
clear
C)
(6, 4) done
clear
D)
(4, 6) done
clear
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question_answer19)
A well planned locality, has two straight roads perpendicular to each other. There are 5 lanes parallel to Road - I. Each lane has 8 houses as seen in figure. Chaitanya lives in the 6th house of the 5th lane and Hamida lives in the 2nd house of the 2nd lane. What will be the shortest distance between their houses?
A)
10 units done
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B)
12 units done
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C)
6 units done
clear
D)
5 units done
clear
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question_answer20)
To raise social awareness about the hazards of smoking, a school decided to start "No smoking campaign". A student is asked to prepare a campaign banner in the shape of a triangle shown in the figure. If cost of \[1\text{ }c{{m}^{2}}\]of banner is Rs. 2, find the cost of the banner.
A)
Rs.12 done
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B)
Rs.6 done
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C)
Rs.5 done
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D)
Rs.10 done
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question_answer21)
The coordinates of the centre of a circle passing through \[(1,2),(3,-4)\]and \[(5,-6)\] is _____.
A)
\[(2,11)\] done
clear
B)
\[(11,2)\] done
clear
C)
\[(11,-2)\] done
clear
D)
\[(-2,11)\] done
clear
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question_answer22)
If \[A(2,2),\,B(4,4)\] and \[C(2,6)\] are the vertices of a triangle ABC and D, E and F are the mid point of AB, BC and AC respectively, then
(i) Find the area of MBC. |
(ii) Find the area of ADEF. |
(iii) Find the ratio of area of ADEF to MSQ |
A)
B)
C)
D)
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question_answer23)
The values of t, if the area of the pentagon ABODE be \[\frac{45}{2}\] sq. units where \[A=(1,3),\] \[B=(-2,5),\] \[C=(-3,-1),\] \[D=(0,-2),\]\[D=(0,-2)\] and \[E=(2,t)\] are _____.
A)
\[-1.17\] done
clear
B)
\[-1,106\] done
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C)
\[1,17\] done
clear
D)
\[1,18\] done
clear
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question_answer24)
If \[(-2,1),\,(a,0),\,(4,b)\] and (1, 2) are the vertices of a parallelogram, then
(i) Find a |
(ii) Find b |
(iii) Area of the parallelogram. |
A)
B)
C)
D)
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question_answer25)
In the given figure, PQRS is a straight line R is the mid point of OS and 0 is the mid point of PS. S is (6, 5), R is (3, 5) and T is (4, 8). Find the length of median TU.
A)
\[\sqrt{13}\]units done
clear
B)
\[\sqrt{50}\]units done
clear
C)
\[2\sqrt{28}\]units done
clear
D)
\[\sqrt{58}\]units done
clear
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