India · Class 12 · Practice Sheet 40

1. 1.

   A triangle has sides a = 18 cm and b = 20 cm with an included angle C = 60°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

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

   View formula →
2. 2.

   Find the gravitational potential energy of a 3 kg object raised 27 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
3. 3.

   Find the force needed to accelerate a 43 kg mass at 7.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
4. 4.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
5. 5.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 8 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

   View formula →
6. 6.

   Find the force needed to accelerate a 27 kg mass at 8.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
7. 7.

   A triangle has sides a = 10 cm and b = 6 cm with an included angle C = 90°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

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

   View formula →
8. 8.

   Find the population standard deviation of: 14, 8, 4, 16, 18 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
9. 9.

   A population of 1,900 grows 3% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
10. 10.

    A force of 185 N acts on an area of 5.2 m². Find the pressure.

    Formula:Pressure

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

    View formula →
11. 11.

    A wave has frequency 61 Hz and wavelength 0.38 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
12. 12.

    A device runs at 90 V drawing 3.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
13. 13.

    Two masses 1,600 kg and 200 kg are 13 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

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

    View formula →
14. 14.

    A cone has base radius 4 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
15. 15.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

    View formula →
16. 16.

    An object with initial velocity 7 m/s accelerates at 3.9 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
17. 17.

    Find the force needed to accelerate a 33 kg mass at 3 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
18. 18.

    A wave has frequency 71 Hz and wavelength 0.45 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
19. 19.

    A device runs at 42 V drawing 0.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
20. 20.

    ₹1,700 is invested at 5% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

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

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.