Engineering Entrance · Practice Sheet 1

1. 1.

   Chemistry

   Find the pressure of 4 mol of an ideal gas at 365 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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2. 2.

   Chemistry

   Find the molarity of a solution containing 1 mol of solute in 2.5 L of solution.

   Formula:Molarity

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

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3. 3.

   Chemistry

   Find the pH of a solution with [H⁺] = 5×10⁻4 mol/L.

   Formula:pH of a Solution

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

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4. 4.

   Physics

   Find the momentum of a 35 kg body moving at 19 m/s.

   Formula:Linear Momentum

   $p = mv$

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5. 5.

   Mathematics

   Find the sum of the first 6 terms of an AP with first term 19 and common difference 1.

   Formula:AP Sum of n Terms

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

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6. 6.

   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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7. 7.

   Mathematics

   If f(x) = 5x³ + 4x² + 8x, find f′(3).

   Formula:Derivative of a Polynomial

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

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8. 8.

   Chemistry

   Find the pH of a solution with [H⁺] = 5×10⁻4 mol/L.

   Formula:pH of a Solution

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

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9. 9.

   Physics

   Find the force required to accelerate a 38 kg mass at 16 m/s².

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

   $F = ma$

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10. 10.

    Physics

    A constant force of 34 N moves an object 12 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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11. 11.

    Physics

    An object starts at 0 m/s and accelerates at 3 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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12. 12.

    Physics

    Find the density of an object with mass 239 g and volume 36 cm³.

    Formula:Density

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

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13. 13.

    Mathematics

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

    Formula:GP nth Term

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

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14. 14.

    Mathematics

    Find the distance between the points (7, 8) and (2, 8).

    Formula:Distance Between Two Points

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

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15. 15.

    Physics

    A body moving at 11 m/s accelerates at 4 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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16. 16.

    Physics

    Find the force required to accelerate a 34 kg mass at 20 m/s².

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

    $F = ma$

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17. 17.

    Physics

    Find the momentum of a 10 kg body moving at 29 m/s.

    Formula:Linear Momentum

    $p = mv$

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18. 18.

    Mathematics

    In an arithmetic progression with first term 20 and common difference 10, find term number 9.

    Formula:AP nth Term

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

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19. 19.

    Chemistry

    63 mL of a 2 M solution is diluted to 163 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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20. 20.

    Physics

    A constant force of 15 N moves an object 10 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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