India · Class 11 · Practice Sheet 4

1. 1.

   A right-angled triangle has legs of 20 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   In a triangle, a = 9, b = 15 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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3. 3.

   Solve using the quadratic formula: x² + 3x + 0 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   An object has mass 132 g and volume 30 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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5. 5.

   A current of 5.3 A flows through a 28 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A wave has frequency 196 Hz and wavelength 4.07 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   An object has mass 184 g and volume 46 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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8. 8.

   Solve using the quadratic formula: x² − 1x + 0 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   A body starts at 14 m/s and accelerates at 3.6 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    A device runs at 24 V drawing 6.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the sum of the first 8 terms of a geometric series with first term a = 5 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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12. 12.

    A force of 74 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    ₹3,700 is invested at 3% 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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14. 14.

    Find the momentum of a 53 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Solve using the quadratic formula: x² − 8x + 12 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    In a triangle, a = 8, b = 5 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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17. 17.

    Find the force needed to accelerate a 53 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A device runs at 12 V drawing 2.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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20. 20.

    A body starts at 6 m/s and accelerates at 1.5 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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