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If the vertices of a triangles are O(0, 0), A (a, 0) and B(0, a). Then, the distance between its circumcenter and orthocenter is:
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If𝑎≠𝑏, then (𝑎,𝑏)≠(𝑏,𝑎) Reason R. (4,-3) lies in quadrant IV. In the light of the above statements, choose the correct answer from the options given below
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If two circles intersect at two points, then the line joining their centres is prependicular to the common chord Reason R: The perpendicular bisectors of two chords of a circle intersect at its centre. In the light of the above statements, choose the correct answer from the options given below:
A straight line has equation 𝑦=−𝑥+6 which of the following line is parallel to it?
If a Chord which is normal to the parabola at one end subtends a right angle at the vertex, then its slope is -
Match List I with List II
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LIST I |
LIST II |
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(A) |
The angle between the straight lines, 2x2+3y2-7xy = 0 is |
(i) |
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(B) |
The circles x2+y2+x+y = 0 and x2+y2+x-y = 0 intersect at angle |
(ii) |
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(C) |
The area of circle centred at (1, 2) and passing through (4, 6) is |
(iii) |
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(D) |
The parabolas y2= 4x and x2= 32y intersect at point (16, 8) at angle |
(iv) |
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Choose the correct answer from the options given below:
A triangle with vertices (4, 0), (-1,-1), (3, 5) is
If the vertices of a triangle are (1,2), (2,5) and (4,3) then the area of the triangle is
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