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question_answer1)
PQOR is a rectangle whose vertices are Q (0, 7), O (0, 0) and R (- 5, 0). Find the length of its diagonal.
A)
\[\sqrt{84}\] done
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B)
8 done
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C)
12 done
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D)
\[\sqrt{74}\] done
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E)
None of these done
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question_answer2)
The point which lies on the perpendicular bisector of the line segmen joining the points P (- 3, - 5) and Q (3, 5) is
A)
(-3, 4) done
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B)
(2, -5) done
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C)
(0, 0) done
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D)
(-1, 4) done
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E)
None of these done
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question_answer3)
The points (- 5, 0), (0, 4) and (5, 1) are the vertices of a _______
A)
right triangle done
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B)
isosceles triangle done
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C)
equilateral triangle done
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D)
scalene triangle done
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E)
None of these done
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question_answer4)
The points (4, 5), (6, 7) and (8, 9) are ________
A)
collinear done
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B)
not collinear done
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C)
the vertices of a right triangle done
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D)
vertices of an isosceles triangle done
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E)
None of these done
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question_answer5)
If a point (x, y) is equidistant from the points (p + q, q - p) and (p - q, p + q), then ________
A)
\[qx+yp=0\] done
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B)
\[qx=yp\] done
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C)
\[px=qy\] done
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D)
\[px+qy=0\] done
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E)
None of these done
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question_answer6)
If M and N are the points whose coordinates are \[\left( \mathbf{a}{{\mathbf{p}}^{\mathbf{2}}},\text{ }\mathbf{2ap} \right)\] and \[\left( \frac{\mathbf{a}}{{{\mathbf{p}}^{\mathbf{2}}}}\mathbf{,}\frac{\mathbf{2a}}{\mathbf{p}} \right)\] respectively and S is the point (a, 0), then \[\frac{\mathbf{1}}{\mathbf{SM}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{SN}}\] is equal to _________
A)
a done
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B)
ap done
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C)
\[\frac{1}{a}\] done
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D)
\[\frac{1}{ap}\] done
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E)
None of these done
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question_answer7)
The coordinates of circumcentre of the triangle whose vertices are (3, 6),(4, -4) and (3, -5) are
A)
\[\left( \frac{-3}{2},\,\,0 \right)\] done
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B)
\[\left( \frac{-3}{2},\,\,\frac{1}{2} \right)\] done
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C)
\[\left( \frac{1}{2},\,\,-3 \right)\] done
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D)
\[\left( \frac{1}{3},\,\,\frac{3}{2} \right)\] done
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E)
None of these done
clear
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question_answer8)
The ratio in which the line \[2x+3y-9=0\] the points (2, 3) and (4, 7) is _________
A)
3 : 1 done
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B)
\[-\]5 : 4 done
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C)
\[-\]1 : 5 done
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D)
2 : 5 done
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E)
None of these done
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question_answer9)
The area of a triangle, whose vertices are (a, a - 2), (a + 2, a + 2) and (a + 3, a), is _________
A)
1 sq unit done
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B)
2 sq units done
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C)
3 sq units done
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D)
4 sq units done
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E)
None of these done
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question_answer10)
If the points (p, 0), (0, q) and (1, 1) are collinear, then \[\frac{\mathbf{1}}{\mathbf{p}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{q}}\] equals to _______
A)
1 unit done
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B)
2 unit done
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C)
3 unit done
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D)
4 unit done
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E)
None of these done
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question_answer11)
The distance between the points\[(\cos \theta ,\sin \theta ,)\] and \[(\cos \theta ,-\sin \theta ,)\] is _______
A)
\[\sqrt{3}\] done
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B)
\[\sqrt{2}\] done
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C)
2 done
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D)
1 done
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E)
None of these done
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question_answer12)
If A \[\left( \frac{\mathbf{7}}{\mathbf{3}}\mathbf{,}\frac{\mathbf{m}}{\mathbf{5}} \right)\] is the midpoint of the line segment joining the points B (3, -2) and C (4, 6), then the value of m is _______
A)
4 done
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B)
10 done
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C)
\[-\]4 done
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D)
\[-\]8 done
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E)
None of these done
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question_answer13)
If the point A (-3, m) divides the line segment joining the points B (-8, -5) and C (1, - 4) in the ratio a : b, then m equals to
A)
\[\frac{-5}{3}\] done
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B)
\[\frac{40}{3}\] done
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C)
\[\frac{-40}{9}\] done
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D)
\[\frac{30}{7}\] done
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E)
None of these done
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question_answer14)
The ratio, in which the line 5x + 3y = - 9 divides the segment joining the points (2, 3) and (- 3, 4), is ________
A)
4 : 3 done
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B)
\[-\]4 : 3 done
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C)
\[-\]14 : 5 done
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D)
\[-\]14 : 3 done
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E)
None of these done
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question_answer15)
If a point A (-1, 3) divides internally the line segment joining B (3, 4) and ( in ratio 2 : 3, then the coordinates of point C is ______
A)
(2,-3) done
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B)
\[\left( 2,\frac{3}{2} \right)\] done
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C)
\[\left( -1,\frac{3}{2} \right)\] done
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D)
(-2, 3) done
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E)
None of these done
clear
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question_answer16)
The points (6, 1), (8, 2), (9, 4) and (7, 3) are the vertices of a
A)
trapezium done
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B)
rectangle done
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C)
square done
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D)
rhombus done
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E)
None of these done
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question_answer17)
If the coordinates of mid-point of the sides of a triangle are (21, 7), (- 5, 8, 5) and (10, 8.5), then which among the following is not a vertex of this triangle?
A)
(\[-\]16, 10) done
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B)
(7, 6) done
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C)
(36, 7) done
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D)
(6, 7) done
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E)
None of these done
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question_answer18)
The third vertex of a triangle, if two of its vertices are (- 5, 2) and (1, - 3) and the centroid is at (- 2, 3), is
A)
(- 2, 5) done
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B)
(- 2, 10) done
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C)
(0, 5) done
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D)
(10, - 2) done
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E)
None of these done
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question_answer19)
The vertices of a \[\Delta \]PQR are P (1, 2), Q (- 3, 2) and R (5 - 6). Which among the following is a true statement for this triangle PQR?
A)
Circumcentre of \[\Delta \]PQR is (- 1, - 4) done
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B)
Circumradius of\[\Delta \]PQR is 740 unit done
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C)
The point where perpendicular bisectors of PQ and PR intersects, is the circumcentre of the triangle PQR. done
clear
D)
All the above done
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E)
None of these done
clear
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question_answer20)
Find the orthecentre of the triangle ABC having its vertices as A (- 2, - 3), B (2, 1) and C (5, - 2).
A)
(\[-\]3, 5) done
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B)
(\[-\]4, 6) done
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C)
(2, 1) done
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D)
(0, 0) done
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E)
None of these done
clear
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question_answer21)
The equation of a line whose inclination is \[60{}^\circ \] an of 5 units on x-axis, is
A)
\[\sqrt{3}x-y=\sqrt{3}\] done
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B)
\[\sqrt{3}x-y=5\sqrt{3}\] done
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C)
\[x-\sqrt{3}y=\sqrt{3}\] done
clear
D)
\[x-\sqrt{3}y=5\sqrt{3}\] done
clear
E)
None of these done
clear
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question_answer22)
The area of a triangle formed by the line \[\mathbf{4x}-\mathbf{3y}+\mathbf{12}=\mathbf{0}\] with the coordinate axes is __________
A)
3 sq unit done
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B)
4 sq unit done
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C)
5 sq unit done
clear
D)
6 sq unit done
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E)
None of these done
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question_answer23)
The equation of a line which is parallel to the line \[\mathbf{3x}-\mathbf{5y}+\mathbf{8}=\mathbf{0}\] and making an intercept - 3 on x-axis is
A)
\[5y-3x=9\] done
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B)
\[5y+3x=9\] done
clear
C)
\[3x+5y=9\] done
clear
D)
\[3x-5y=9\] done
clear
E)
None of these done
clear
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question_answer24)
Which among the following can be the vertices of an equilateral triangle?
A)
(2, 3), (5, 4), (7, 8) done
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B)
(3, - 6), (5,-9), (6, - 12) done
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C)
(3,-3), (-3, 3), \[(-3\sqrt{3},-3\sqrt{3)}\] done
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D)
All the above done
clear
E)
None of these done
clear
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question_answer25)
If the vertices of a triangle have integral coordinates, then the triangle cannot be
A)
an equilateral triangle done
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B)
a right triangle done
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C)
an isosceles triangle done
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D)
All the above done
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E)
None of these done
clear
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question_answer26)
If three vertices (in order) of a parallelogram are (p + q, p - q), (2p + q, 2p q) and (p - q, p + q), then its fourth vertex is _________
A)
\[\left( q,\,\,-q \right)\] done
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B)
\[\left( 2q,\,\,-2q \right)\] done
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C)
\[\left( -\,q,\,\,q \right)\] done
clear
D)
\[\left( p,\,-p \right)\] done
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E)
None of these done
clear
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question_answer27)
The equation of median drawn from the vertex P to the side QR of a \[\Delta \]PQR, whose vertices are P (2, 3), Q (- 3, - 5) and R (6, 2), is _______.
A)
\[9x-y=18\] done
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B)
\[9x-y=15\] done
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C)
\[3x-8y=18\] done
clear
D)
\[3x+8y=15\] done
clear
E)
None of these done
clear
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question_answer28)
A line \[\mathbf{6x}+\mathbf{5y}=\mathbf{30}\] intersects the coordinate axes. Find the length of the smallest side of the triangle so formed by the axis.
A)
3 units done
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B)
4 units done
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C)
5 units done
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D)
6 units done
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E)
None of these done
clear
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question_answer29)
The line segment joining the points (3, - 2) and (4, - 6) is divided by the line \[\mathbf{2x}+\mathbf{3y}-\mathbf{11}=\mathbf{0}\] in the ratio m: n externally at point (a, b). Which among the following is true for the given information?
A)
m = 11 done
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B)
n = 21 done
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C)
\[a-b=\frac{89}{10}\] done
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D)
All the above done
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E)
None of these done
clear
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question_answer30)
If the mid-points of sides of a \[\Delta \]ABC are P (2, 5), Q (- 3, 8) and R (6, 12), then its vertices are ________
A)
(13, 10), (\[-\]9, 2), (2, 14) done
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B)
(12, 9), (\[-\]8, 1), (1, 15) done
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C)
(11, 9), (\[-\]7, 1), (1, 15) done
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D)
(\[-\]12, 8), (\[-\]7, 2), (\[-\]2, 15) done
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E)
None of these done
clear
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question_answer31)
The three medians of a \[\Delta \]PQR intersect at a point S. If the medians are PM, QN & RT and the area of \[\Delta \]PQR is 90\[c{{m}^{2}}\], then the area of the quadrilateral MSRN is ________
A)
45 \[c{{m}^{2}}\] done
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B)
30 \[c{{m}^{2}}\] done
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C)
15 \[c{{m}^{2}}\] done
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D)
60 \[c{{m}^{2}}\] done
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E)
None of these done
clear
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question_answer32)
The length of the side of a at the of the angle of Pythagorean triangle of 8 cm, 15 cm 17 cm the hypotenuse is ________
A)
\[5\frac{5}{23}cm\] done
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B)
\[6\frac{4}{23}cm\] done
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C)
\[7\frac{3}{23}cm\] done
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D)
\[4\frac{2}{23}cm\] done
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E)
None of these done
clear
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question_answer33)
The length of the diagonal of a square, which can be inscribed in a right triangle of sides 5 cm, 12 cm and 13 cm, is ______
A)
\[\frac{30\sqrt{2}}{17}cm\] done
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B)
\[\frac{60\sqrt{2}}{17}cm\] done
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C)
15 cm done
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D)
10\[\sqrt{2}\] cm done
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E)
None of these done
clear
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question_answer34)
The equation of a line, which passes through (3, 4) and the product of whose intercepts on the coordinate axes is 48, is _________
A)
\[6x+9y=48\] done
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B)
\[8x+9y=48\] done
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C)
\[4x+3y=24\] done
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D)
\[3x+4y=24\] done
clear
E)
None of these done
clear
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question_answer35)
If the equations of three concurrent lines are \[\mathbf{px}+\mathbf{6y}-\mathbf{8}=\mathbf{0},\] \[\mathbf{qx}+\mathbf{5y}-\mathbf{8}=\mathbf{0}\] and \[\mathbf{rx}+\mathbf{4y}-\mathbf{8}=\mathbf{0},\] then the value of p + r is __________
A)
q done
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B)
2q done
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C)
3q done
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D)
4q done
clear
E)
None of these done
clear
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question_answer36)
The point (p, q) divides the line formed by joining the points (p + q, p + q) and (p - q, q - p) in the ratio _______
A)
p : q internally done
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B)
q : p externally done
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C)
2 : 1 done
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D)
1 : 1 done
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E)
None of these done
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question_answer37)
The radius of the circle which passes through the origin (0, 6) and (6, 0) is
A)
12cm done
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B)
6 cm done
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C)
3\[\sqrt{2}\]cm done
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D)
4\[\sqrt{2}\] done
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E)
None of these done
clear
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question_answer38)
Area of the region formed by the lines \[3|x|+\,2|y|\,=6\] is
A)
8\[c{{m}^{2}}\] done
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B)
10\[c{{m}^{2}}\] done
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C)
12\[c{{m}^{2}}\] done
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D)
14\[c{{m}^{2}}\] done
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E)
None of these done
clear
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question_answer39)
The orthecentre of the triangle formed by the lines \[\mathbf{5x}-\mathbf{8y}=\mathbf{10},\] \[\mathbf{16x}+\mathbf{10y}=\mathbf{13}\] and y-axis, is _____
A)
\[\left( \frac{102}{89},\frac{-95}{178} \right)\] done
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B)
\[\left( \frac{51}{89},\frac{89}{95} \right)\] done
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C)
\[\left( \frac{102}{89},\frac{95}{178} \right)\] done
clear
D)
\[\left( \frac{51}{89},\frac{-95}{89} \right)\] done
clear
E)
None of these done
clear
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question_answer40)
The line which is perpendicular to \[\mathbf{5x}+\mathbf{2y}-\mathbf{3}=\mathbf{0}\] is _________
A)
\[2x-5y+8=0\] done
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B)
\[3x-5y=9\] done
clear
C)
\[4x-3y=7\] done
clear
D)
\[5x-2y=3\] done
clear
E)
None of these done
clear
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