India · Class 12 · Practice Sheet 29

1. 1.

   A force of 214 N acts on an area of 7.4 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Find the population standard deviation of: 13, 15, 16, 15, 19 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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3. 3.

   Find the gravitational potential energy of a 42 kg object raised 9 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   An object with initial velocity 10 m/s accelerates at 4 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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5. 5.

   A triangle has sides a = 9 cm and b = 10 cm with an included angle C = 30°. 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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6. 6.

   A population of 3,000 grows 2% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   Find the population standard deviation of: 16, 5, 5, 20, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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8. 8.

   A population of 4,900 grows 5% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   A triangle has sides a = 9 cm and b = 19 cm with an included angle C = 30°. 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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10. 10.

    Find the gravitational potential energy of a 6 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A device runs at 72 V drawing 7.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A 26 kg object moves at 19 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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13. 13.

    ₹3,300 is invested at 3% compound interest per annum for 3 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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14. 14.

    In a triangle, a = 18, b = 16 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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15. 15.

    Find the population standard deviation of: 5, 18, 15, 9, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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16. 16.

    In a triangle, a = 11, b = 8 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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17. 17.

    A wave has frequency 526 Hz and wavelength 2.64 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Two masses 6,300 kg and 710 kg are 9 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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19. 19.

    A wave has frequency 309 Hz and wavelength 2.43 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A body starts at 10 m/s and accelerates at 5.2 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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