Engineering Entrance · Practice Sheet 31

1. 1.

   Physics

   Find the electrical power when 169 V drives a current of 20 A.

   Formula:Electrical Power

   $P = VI$

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2. 2.

   Chemistry

   How many moles are present in 110 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

   Formula:Number of Moles

   $n = \dfrac{m}{M}$

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3. 3.

   Mathematics

   Find the sum of the first 3 terms of a GP with first term 4 and common ratio 2.

   Formula:GP Sum of n Terms

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

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4. 4.

   Mathematics

   Evaluate log base 3 of 27.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

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5. 5.

   Mathematics

   For the quadratic 2x² + 1x − 3 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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6. 6.

   Mathematics

   Find the distance between the points (-1, -7) and (-2, 1).

   Formula:Distance Between Two Points

   $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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7. 7.

   Physics

   Find the voltage across a 33 Ω resistor carrying a current of 15 A.

   Formula:Ohm's Law

   $V = IR$

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8. 8.

   Mathematics

   Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

   Formula:Binomial Coefficient

   $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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9. 9.

   Chemistry

   Find the pressure of 5 mol of an ideal gas at 238 K in a 7 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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10. 10.

    Physics

    A projectile is launched at 20 m/s at 45° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

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11. 11.

    Physics

    A constant force of 195 N moves an object 35 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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12. 12.

    Mathematics

    Find the distance between the points (-4, 5) and (-5, -4).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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13. 13.

    Physics

    A body moving at 5 m/s accelerates at 8 m/s² for 8 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)

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

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14. 14.

    Chemistry

    A solution is made by dissolving 15 g of solute in 67 g of solvent. Find the mass percentage of the solute.

    Formula:Mass Percentage

    $\%\,\text{mass} = \dfrac{\text{solute}}{\text{solution}}\times 100$

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15. 15.

    Physics

    A constant force of 40 N moves an object 30 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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16. 16.

    Physics

    Find the momentum of a 10 kg body moving at 34 m/s.

    Formula:Linear Momentum

    $p = mv$

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17. 17.

    Physics

    Find the electrical power when 206 V drives a current of 20 A.

    Formula:Electrical Power

    $P = VI$

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18. 18.

    Physics

    Find the kinetic energy of a 13 kg object moving at 23 m/s.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2}mv^{2}$

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19. 19.

    Chemistry

    How many moles are present in 27 g of water (H₂O) (molar mass = 18 g/mol)?

    Formula:Number of Moles

    $n = \dfrac{m}{M}$

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20. 20.

    Physics

    Find the kinetic energy of a 18 kg object moving at 6 m/s.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2}mv^{2}$

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