India · Class 12 · Practice Sheet 39

1. 1.

   Find the force needed to accelerate a 25 kg mass at 8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   In a triangle, a = 16, b = 13 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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3. 3.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 7 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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4. 4.

   Two masses 8,200 kg and 780 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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5. 5.

   A wave has frequency 668 Hz and wavelength 4.35 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A device runs at 127 V drawing 1.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   ₹1,000 is invested at 5% compound interest per annum for 2 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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8. 8.

   Find the sum of the first 3 terms of a geometric series with first term a = 8 and common ratio r = 4.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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9. 9.

   A body starts at 19 m/s and accelerates at 4.6 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    Find the momentum of a 43 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    Find the sum of the first 3 terms of a geometric series with first term a = 3 and common ratio r = 3.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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12. 12.

    In a triangle, a = 12, b = 12 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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13. 13.

    A wave has frequency 759 Hz and wavelength 4.53 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Two masses 8,700 kg and 790 kg are 5 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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15. 15.

    A wave has frequency 193 Hz and wavelength 3.44 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A current of 7.2 A flows through a 45 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    Find the population standard deviation of: 11, 5, 10, 6, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

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

    Formula:Quadratic Formula

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

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19. 19.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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20. 20.

    A force of 20 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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