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Find the value of a for which the area of the triangle formed by the points A(a, 2a), B(−2, 6) and C(3, 1) is 10 square units.
Concept: undefined >> undefined
From a solid cube of side 7 cm , a conical cavity of height 7 cm and radius 3 cm is hollowed out . Find the volume of the remaining solid.
Concept: undefined >> undefined
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Two solid cones A and B are placed in a cylindrical tube as shown in fig .16.76. The ratio of their capacities are 2: 1 . Find the heights and capacities of the cones . Also, find the volume of the remaining portion of the cylinder.
Concept: undefined >> undefined
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
Concept: undefined >> undefined
A solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is
Concept: undefined >> undefined
A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is
Concept: undefined >> undefined
A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, the total area of the canvas required in m2 is
Concept: undefined >> undefined
If three points (x1, y1) (x2, y2), (x3, y3) lie on the same line, prove that \[\frac{y_2 - y_3}{x_2 x_3} + \frac{y_3 - y_1}{x_3 x_1} + \frac{y_1 - y_2}{x_1 x_2} = 0\]
Concept: undefined >> undefined
Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + \[\sqrt{3}\] , 5) and C(2, 6).
Concept: undefined >> undefined
Find the value(s) of k for which the points (3k − 1, k − 2), (k, k − 7) and (k − 1, −k − 2) are collinear.
Concept: undefined >> undefined
If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c.
Concept: undefined >> undefined
If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.
Concept: undefined >> undefined
If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.
Concept: undefined >> undefined
If the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.
Concept: undefined >> undefined
\[A\left( 6, 1 \right) , B(8, 2) \text{ and } C(9, 4)\] are three vertices of a parallelogram ABCD . If E is the mid-point of DC , find the area of \[∆\] ADE.
Concept: undefined >> undefined
If \[D\left( - \frac{1}{5}, \frac{5}{2} \right), E(7, 3) \text{ and } F\left( \frac{7}{2}, \frac{7}{2} \right)\] are the mid-points of sides of \[∆ ABC\] , find the area of \[∆ ABC\] .
Concept: undefined >> undefined
Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).
Concept: undefined >> undefined
Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).
Concept: undefined >> undefined
Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.
Concept: undefined >> undefined
What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°)?
Concept: undefined >> undefined
