India · Class 11 · Practice Sheet 20

1. 1.

   A triangle has sides a = 11 cm and b = 10 cm with an included angle C = 90°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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2. 2.

   Find the force needed to accelerate a 20 kg mass at 8.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A force of 64 N moves an object 10 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Find the momentum of a 23 kg object moving at 23 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A cone has base radius 8 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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6. 6.

   Solve using the quadratic formula: x² + 9x + 20 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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7. 7.

   Find the momentum of a 3 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Two masses 7,300 kg and 520 kg are 20 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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9. 9.

   A population of 6,100 grows 3% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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10. 10.

    ₹2,900 is invested at 5% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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11. 11.

    An object has mass 216 g and volume 30 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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12. 12.

    A device runs at 33 V drawing 0.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the momentum of a 42 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    ₹1,600 is invested at 4% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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15. 15.

    Find the gravitational potential energy of a 42 kg object raised 36 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A population of 1,500 grows 8% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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17. 17.

    Solve using the quadratic formula: x² − 6x + 5 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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18. 18.

    A population of 1,600 grows 8% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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19. 19.

    Find the force needed to accelerate a 29 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A force of 370 N acts on an area of 7 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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