India · Class 12 · Practice Sheet 36

1. 1.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 11 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A current of 6.9 A flows through a 6 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the gravitational potential energy of a 36 kg object raised 8 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A device runs at 61 V drawing 4.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the force needed to accelerate a 43 kg mass at 3.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A triangle has sides a = 9 cm and b = 12 cm with an included angle C = 120°. 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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7. 7.

   A cone has base radius 6 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A force of 469 N acts on an area of 1 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A wave has frequency 198 Hz and wavelength 4.6 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A current of 4.4 A flows through a 8 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    A force of 157 N acts on an area of 8.6 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A body starts at 11 m/s and accelerates at 6 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    A force of 20 N acts on an area of 9.5 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    A body starts at 9 m/s and accelerates at 5 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A population of 7,500 grows 10% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    A current of 7.3 A flows through a 14 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the force needed to accelerate a 3 kg mass at 4.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Find the gravitational potential energy of a 40 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A force of 75 N acts on an area of 1.1 m². Find the pressure.

    Formula:Pressure

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

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