Engineering Entrance · Practice Sheet 49

1. 1.

   Chemistry

   Find the pressure of 4 mol of an ideal gas at 324 K in a 8 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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2. 2.

   Mathematics

   Evaluate log base 3 of 81.

   Formula:Logarithm Evaluation

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

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3. 3.

   Mathematics

   Find the distance between the points (7, -6) and (3, 2).

   Formula:Distance Between Two Points

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

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4. 4.

   Mathematics

   Find the sum of the first 17 terms of an AP with first term 6 and common difference 5.

   Formula:AP Sum of n Terms

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

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5. 5.

   Physics

   A projectile is launched at 12 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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6. 6.

   Physics

   A force of 844 N acts on an area of 35 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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7. 7.

   Mathematics

   If f(x) = 5x³ + 4x² + 4x, find f′(3).

   Formula:Derivative of a Polynomial

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

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8. 8.

   Chemistry

   A solution is made by dissolving 11 g of solute in 181 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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9. 9.

   Mathematics

   Find the sum of the first 25 terms of an AP with first term 13 and common difference 9.

   Formula:AP Sum of n Terms

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

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10. 10.

    Mathematics

    Find the slope of the line through (8, 5) and (5, -7).

    Formula:Slope of a Line

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

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11. 11.

    Mathematics

    In an arithmetic progression with first term 15 and common difference 4, find term number 5.

    Formula:AP nth Term

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

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12. 12.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻6 mol/L.

    Formula:pH of a Solution

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

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13. 13.

    Mathematics

    Find the distance between the points (7, -3) and (-4, 5).

    Formula:Distance Between Two Points

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

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14. 14.

    Physics

    Find the electrical power when 141 V drives a current of 19 A.

    Formula:Electrical Power

    $P = VI$

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15. 15.

    Mathematics

    Evaluate log base 10 of 100.

    Formula:Logarithm Evaluation

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

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16. 16.

    Chemistry

    14 mL of a 5 M solution is diluted to 148 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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17. 17.

    Chemistry

    Find the molarity of a solution containing 3 mol of solute in 2 L of solution.

    Formula:Molarity

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

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18. 18.

    Mathematics

    Find term number 5 of a geometric progression with first term 2 and common ratio 3.

    Formula:GP nth Term

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

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19. 19.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻6 mol/L.

    Formula:pH of a Solution

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

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20. 20.

    Physics

    Find the electrical power when 176 V drives a current of 18 A.

    Formula:Electrical Power

    $P = VI$

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