Engineering Entrance · Practice Sheet 19

1. 1.

   Chemistry

   Find the pressure of 1 mol of an ideal gas at 315 K in a 9 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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2. 2.

   Chemistry

   How many moles are present in 234 g of sodium chloride (NaCl) (molar mass = 58.5 g/mol)?

   Formula:Number of Moles

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

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3. 3.

   Mathematics

   Find the slope of the line through (5, -6) and (6, -1).

   Formula:Slope of a Line

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

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4. 4.

   Physics

   Find the momentum of a 42 kg body moving at 8 m/s.

   Formula:Linear Momentum

   $p = mv$

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5. 5.

   Chemistry

   Find the pressure of 2 mol of an ideal gas at 363 K in a 11 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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6. 6.

   Physics

   A force of 644 N acts on an area of 50 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Mathematics

   In an arithmetic progression with first term 4 and common difference 9, find term number 8.

   Formula:AP nth Term

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

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8. 8.

   Physics

   A body moving at 3 m/s accelerates at 7 m/s² for 10 s. Find the distance travelled.

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

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

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9. 9.

   Mathematics

   Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.

   Formula:Binomial Coefficient

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

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10. 10.

    Mathematics

    Find the sum of the first 19 terms of an AP with first term 4 and common difference 6.

    Formula:AP Sum of n Terms

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

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11. 11.

    Physics

    Find the momentum of a 6 kg body moving at 17 m/s.

    Formula:Linear Momentum

    $p = mv$

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12. 12.

    Mathematics

    For the quadratic 1x² + 7x + 7 = 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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13. 13.

    Mathematics

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

    Formula:Slope of a Line

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

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14. 14.

    Chemistry

    Find the pressure of 5 mol of an ideal gas at 387 K in a 2 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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15. 15.

    Mathematics

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

    Formula:GP nth Term

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

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16. 16.

    Physics

    Find the force required to accelerate a 3 kg mass at 16 m/s².

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

    $F = ma$

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17. 17.

    Physics

    A force of 641 N acts on an area of 11 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 394 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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19. 19.

    Physics

    Find the kinetic energy of a 9 kg object moving at 3 m/s.

    Formula:Kinetic Energy

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

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20. 20.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻3 mol/L.

    Formula:pH of a Solution

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

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