Engineering Entrance · Practice Sheet 27

1. 1.

   Physics

   Find the electrical power when 11 V drives a current of 9 A.

   Formula:Electrical Power

   $P = VI$

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2. 2.

   Physics

   An object starts at 16 m/s and accelerates at 7 m/s² for 8 s. Find its final velocity.

   Formula:Equation of Motion (v = u + at)

   $v = u + at$

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3. 3.

   Physics

   Find the voltage across a 10 Ω resistor carrying a current of 15 A.

   Formula:Ohm's Law

   $V = IR$

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4. 4.

   Physics

   Calculate the potential energy of a 41 kg object at a height of 48 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Chemistry

   Find the molarity of a solution containing 2 mol of solute in 2.5 L of solution.

   Formula:Molarity

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

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6. 6.

   Chemistry

   Find the pH of a solution with [H⁺] = 5×10⁻2 mol/L.

   Formula:pH of a Solution

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

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7. 7.

   Physics

   An object starts at 20 m/s and accelerates at 2 m/s² for 3 s. Find its final velocity.

   Formula:Equation of Motion (v = u + at)

   $v = u + at$

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8. 8.

   Mathematics

   Find the binomial coefficient C(7, 4) — the coefficient of x^4 in (1 + x)^7.

   Formula:Binomial Coefficient

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

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9. 9.

   Mathematics

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

   Formula:GP nth Term

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

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10. 10.

    Mathematics

    Find the slope of the line through (-2, 7) and (6, -8).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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11. 11.

    Physics

    Calculate the potential energy of a 33 kg object at a height of 42 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Physics

    Find the force required to accelerate a 3 kg mass at 18 m/s².

    Formula:Newton's Second Law (F = ma)

    $F = ma$

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13. 13.

    Mathematics

    Find the distance between the points (7, -7) and (4, 6).

    Formula:Distance Between Two Points

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

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14. 14.

    Mathematics

    Find the slope of the line through (4, 0) and (-4, -3).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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15. 15.

    Physics

    Find the density of an object with mass 10 g and volume 30 cm³.

    Formula:Density

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

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16. 16.

    Mathematics

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

    Formula:GP Sum of n Terms

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

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17. 17.

    Chemistry

    Find the pressure of 5 mol of an ideal gas at 274 K in a 20 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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18. 18.

    Chemistry

    Find the molarity of a solution containing 2 mol of solute in 4 L of solution.

    Formula:Molarity

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

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19. 19.

    Mathematics

    Evaluate log base 10 of 100,000.

    Formula:Logarithm Evaluation

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

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20. 20.

    Mathematics

    Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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