India · Class 10 · Practice Sheet 38

1. 1.

   A right-angled triangle has legs of 13 cm and 15 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A bag has 27 equally likely marbles, of which 6 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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3. 3.

   Find the gravitational potential energy of a 39 kg object raised 26 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   An object has mass 42 g and volume 14 cm³. Find its density.

   Formula:Density

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

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5. 5.

   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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6. 6.

   An object with initial velocity 8 m/s accelerates at 4.6 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   ₹1,000 is invested at 6% 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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8. 8.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   Solve using the quadratic formula: x² + 5x + 6 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A current of 7.9 A flows through a 56 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Find the force needed to accelerate a 58 kg mass at 3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    ₹2,900 is invested at 6% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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13. 13.

    A force of 106 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 9 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    A bag has 19 equally likely marbles, of which 9 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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16. 16.

    In a triangle, a = 16, b = 10 and the included angle C = 70°. 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.

    A force of 101 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    Solve using the quadratic formula: x² + 7x + 10 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    A right-angled triangle has legs of 17 cm and 5 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    Find the gravitational potential energy of a 46 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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