# Model Activity Task 1 Maths Solution

### Share solution sheet

1. Write the condition for the roots to become equal in the equation ax2bx + c = 0, (a, b, c are
real, a ≠ 0).
Ans: b² – 4ac = 0

2. The radius of a circle is 10 cm and the length of a chord is 12 cm. Then, calculate the distance
between the chord and centre of the circle.
Ans:

3. If the ratio of the volumes of two cubes is 1 : 8, then find the ratio of the total surface areas
of the two cubes.
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4. If the amount of Rs. 400/- for 2 years is 441 then find the annual rate of compound interest.
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5. If x, 12, y, 27 are in continued proportion then find the values of x and y.
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6. If each side of a cube increases 50% by length, then what is the parcentage increase in total
surface area of the cube?
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7. Solve: (2x+1)+(3/2x+1) = 4 (x ≠ 1/2)
Ans:

8. The total interest of a principal in n yrs. at the rate of simple interest of r % per annum is 25
pnr ,
the principal will be
(a) Rs. 2p
(b) Rs. 4p
(c) Rs. 2p
(d) Rs. 4p
Ans:

9. If the height of two right circular cylinders are in the ratio 3 : 4 and perimeters are in the ratio
1 : 2, then find the ratio of their volumes.
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10. AB and AC are two chords of a circle which are perpendicular to each other. If AB = 4 cm. and
AC = 3 cm., then find the length of the radius of the circle.
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11. If simple interest and compound interest of a certain sum of money for two years are Rs. 8400 and
Rs. 8652, then find the sum of money and the rate of interest.
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12. If the ratio of two roots of the quadratic equation ax²+bx+c=0 [a ≠ 0] 1 : r, then show that (r+1)²/r = b²/ac.
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13. Prove that if any straight line passing through the centre of a circle bisects any chord, which is not
a diameter, then the straight line will be perpendicular on that chord.
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14. AB is a radius of a circle with centre O. C is a point on the circle. If ∠OBC = 60º then find the
value of ∠OCA.
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15. Height of a right circular cylinder is twice of its radius. If the height would be 6 times of its radius,
then the volume of the cylinder would be greater by 539 cubic dcm., find the height of the cylinder.
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