India · Class 11 · Practice Sheet 47

1. 1.

   A triangle has sides a = 14 cm and b = 10 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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2. 2.

   A wave has frequency 299 Hz and wavelength 4.82 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the population standard deviation of: 14, 9, 11, 12, 9 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   A wave has frequency 575 Hz and wavelength 1.53 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   ₹700 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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6. 6.

   A force of 182 N acts on an area of 3.6 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Find the sum of the first 6 terms of a geometric series with first term a = 2 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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8. 8.

   A device runs at 168 V drawing 0.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Find the force needed to accelerate a 40 kg mass at 9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A population of 7,300 grows 3% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    Find the population standard deviation of: 16, 11, 14, 14, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A population of 4,700 grows 5% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    A force of 307 N acts on an area of 2 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A 29 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    A right-angled triangle has legs of 16 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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17. 17.

    A body starts at 14 m/s and accelerates at 1.7 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A wave has frequency 637 Hz and wavelength 4.24 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A cone has base radius 5 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    A triangle has sides a = 9 cm and b = 12 cm with an included angle C = 60°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

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

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