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22 questions · timed · auto-graded

Question 11 Mark
If the centroid of the triangle formed by the points (a, b), (1, a) and (b, 1) is at the origin, then $\frac{a^3+b^3+1}{a b}$ = ____________ .
Answer
3
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Question 21 Mark
The coordinates of the point equidistant from the vertices O(0, 0) A(6, 0) and B(0, 8) of $\triangle OAB$ are ____________ .
Answer
(3, 4)
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Question 31 Mark
If the distance of the point (4, a) from x-axis is half its distance from y-axis, then ____________ .
Answer
2
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Question 41 Mark
The coordinates of the point which is equidistant from the vertices of the triangle formed by the points O(0, 0) A(a, 0) and B(0, b) are ____________ .
Answer
$(a / 2, b / 2)$
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Question 51 Mark
It (2, -2) and (5, 2) are opposite vertices of a square, then the length of the side of the square is ____________ .
Answer
$5 / \sqrt{2}$
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Question 61 Mark
The number of points on x-axis which are at a distance of $2 \sqrt{5}$ from the point (7, -4), is ____________ .
Answer
2
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Question 71 Mark
The ratio in which the point $P\left(\frac{3}{4}, \frac{5}{12}\right)$ divides the line segment joining the points $A(1/2, 3/2)$ and B(2, - 5) is ____________ .
Answer
$1: 5$
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Question 81 Mark
If the distance between the points A(- 3, - 14) and B(a, - 5) is 9 units, then a = ____________ .
Answer
$-3$
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Question 91 Mark
The x-coordinate of the point lying on the perpendicular bisector of the line segment joining the points A(- 2, - 5) and B(2, 5) is ____________ .
Answer
Zero
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Question 121 Mark
The values of y for which the point (2,-4) is equidistant from the points (3, 8) and (-10, y), are ____________ .
Answer
$-3,-5$
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Question 131 Mark
If P($(a / 3$, 4) is the mid-point of the line segment joining the points Q(- 6, 5) and R(- 2, 3) then the value of $' a^{\prime}$ is ____________ .
Answer
$-12$
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Question 141 Mark
If the distance between the points (4, p) and (1, 0) is 5, then the values of p are ____________ .
Answer
$\pm 4$
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Question 151 Mark
The quadrant in which the point dividing the line segment joining the points (7, -6) and (3, 4) internally in the ratio 1 : 2 is ____________ .
Answer
IV
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Question 161 Mark
The x-axis divides the line segment joining the points (-4, -6) and (-1, 7) in the ratio ____________ .
Answer
$6: 7$
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Question 171 Mark
If the distance between the points (2,-2) and (- 1, x) is 5, then the values of x are ____________ .
Answer
2, -6
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Question 191 Mark
The distance between the points (1, 0) and (2, $\cot \theta$) is ____________ .
Answer
$|\operatorname{cosec} \theta|$
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Question 201 Mark
If the centroid of the triangle whose vertices are (2, 4), (3, a) (4, 2) is (a, 3) then a = ____________ .
Answer
3
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Fill In The Blanks[1 Marks ] - Maths STD 10 Questions - Vidyadip