Engineering Entrance · Practice Sheet 11

1. 1.

   Physics

   Find the electrical power when 24 V drives a current of 6 A.

   Formula:Electrical Power

   $P = VI$

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2. 2.

   Physics

   A body moving at 2 m/s accelerates at 3 m/s² for 6 s. Find the distance travelled.

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

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

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3. 3.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 6 and common ratio 3.

   Formula:GP Sum of n Terms

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

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4. 4.

   Physics

   Find the voltage across a 8 Ω resistor carrying a current of 18 A.

   Formula:Ohm's Law

   $V = IR$

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5. 5.

   Physics

   Find the electrical power when 131 V drives a current of 3 A.

   Formula:Electrical Power

   $P = VI$

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6. 6.

   Physics

   Calculate the potential energy of a 14 kg object at a height of 38 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Physics

   Find the voltage across a 47 Ω resistor carrying a current of 4 A.

   Formula:Ohm's Law

   $V = IR$

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8. 8.

   Mathematics

   In an arithmetic progression with first term 17 and common difference 6, find term number 16.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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9. 9.

   Physics

   Find the kinetic energy of a 9 kg object moving at 13 m/s.

   Formula:Kinetic Energy

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

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10. 10.

    Mathematics

    For the quadratic 1x² − 2x + 6 = 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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11. 11.

    Physics

    Find the electrical power when 29 V drives a current of 14 A.

    Formula:Electrical Power

    $P = VI$

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12. 12.

    Chemistry

    A solution is made by dissolving 7 g of solute in 195 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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13. 13.

    Mathematics

    Find the sum of the first 16 terms of an AP with first term 13 and common difference 1.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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14. 14.

    Mathematics

    Find term number 5 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term

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

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15. 15.

    Mathematics

    If f(x) = 3x³ + 4x² + 2x, find f′(4).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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16. 16.

    Chemistry

    87 mL of a 5 M solution is diluted to 430 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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17. 17.

    Chemistry

    Find the pH of a solution with [H⁺] = 2×10⁻4 mol/L.

    Formula:pH of a Solution

    $pH = -\log_{10}[H^{+}]$

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18. 18.

    Mathematics

    Find term number 7 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term

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

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19. 19.

    Physics

    A body moving at 6 m/s accelerates at 7 m/s² for 3 s. Find the distance travelled.

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

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

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20. 20.

    Mathematics

    If f(x) = 4x³ + 3x² + 3x, find f′(1).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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