Engineering Entrance · Practice Sheet 33

1. 1.

   Chemistry

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

   Formula:Molarity

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

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2. 2.

   Chemistry

   Find the pressure of 2 mol of an ideal gas at 343 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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3. 3.

   Mathematics

   Evaluate log base 2 of 4.

   Formula:Logarithm Evaluation

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

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4. 4.

   Physics

   A force of 955 N acts on an area of 10 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Mathematics

   In an arithmetic progression with first term 8 and common difference 4, find term number 17.

   Formula:AP nth Term

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

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6. 6.

   Physics

   Find the density of an object with mass 118 g and volume 10 cm³.

   Formula:Density

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

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7. 7.

   Mathematics

   Find the sum of the first 7 terms of an AP with first term 13 and common difference 2.

   Formula:AP Sum of n Terms

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

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8. 8.

   Physics

   Find the momentum of a 49 kg body moving at 2 m/s.

   Formula:Linear Momentum

   $p = mv$

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9. 9.

   Physics

   A body moving at 2 m/s accelerates at 7 m/s² for 7 s. Find the distance travelled.

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

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

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10. 10.

    Physics

    Find the kinetic energy of a 13 kg object moving at 23 m/s.

    Formula:Kinetic Energy

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

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11. 11.

    Chemistry

    30 mL of a 5 M solution is diluted to 249 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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12. 12.

    Physics

    A constant force of 123 N moves an object 6 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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13. 13.

    Chemistry

    Find the pH of a solution with [H⁺] = 2×10⁻3 mol/L.

    Formula:pH of a Solution

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

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14. 14.

    Physics

    Find the voltage across a 15 Ω resistor carrying a current of 6 A.

    Formula:Ohm's Law

    $V = IR$

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15. 15.

    Physics

    A constant force of 182 N moves an object 13 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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16. 16.

    Physics

    Find the momentum of a 20 kg body moving at 8 m/s.

    Formula:Linear Momentum

    $p = mv$

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17. 17.

    Mathematics

    Find the sum of the first 14 terms of an AP with first term 2 and common difference 6.

    Formula:AP Sum of n Terms

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

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18. 18.

    Mathematics

    For the quadratic 5x² − 6x − 9 = 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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19. 19.

    Mathematics

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

    Formula:GP Sum of n Terms

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

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20. 20.

    Mathematics

    Find the slope of the line through (-6, -4) and (5, -2).

    Formula:Slope of a Line

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

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