Nepal · Class 12 · Practice Sheet 7

1. 1.

   Find the sum of the first 5 terms of a geometric series with first term a = 4 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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2. 2.

   A current of 7.8 A flows through a 24 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 10 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   Rs 2,600 is invested at 3% 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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5. 5.

   Find the force needed to accelerate a 21 kg mass at 8.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A force of 75 N moves an object 14 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Find the momentum of a 29 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A body starts at 3 m/s and accelerates at 5 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   A device runs at 51 V drawing 2.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the momentum of a 16 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    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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12. 12.

    A 2 kg object moves at 22 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A wave has frequency 320 Hz and wavelength 1.8 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A cone has base radius 12 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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15. 15.

    Rs 2,400 is invested at 8% 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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16. 16.

    Find the force needed to accelerate a 7 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A device runs at 68 V drawing 0.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    An object with initial velocity 2 m/s accelerates at 4.2 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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19. 19.

    A current of 4.8 A flows through a 39 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    Rs 2,500 is invested at 5% 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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