Engineering Entrance · Practice Sheet 37

1. 1.

   Physics

   An object starts at 1 m/s and accelerates at 9 m/s² for 9 s. Find its final velocity.

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

   $v = u + at$

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2. 2.

   Chemistry

   Find the pressure of 5 mol of an ideal gas at 396 K in a 7 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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3. 3.

   Chemistry

   74 mL of a 10 M solution is diluted to 474 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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4. 4.

   Mathematics

   For the quadratic 5x² + 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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5. 5.

   Mathematics

   Find the sum of the first 5 terms of a GP with first term 5 and common ratio 3.

   Formula:GP Sum of n Terms

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

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6. 6.

   Physics

   Find the electrical power when 179 V drives a current of 17 A.

   Formula:Electrical Power

   $P = VI$

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7. 7.

   Physics

   Find the force required to accelerate a 38 kg mass at 20 m/s².

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

   $F = ma$

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8. 8.

   Mathematics

   Find the slope of the line through (-6, -4) and (-3, 3).

   Formula:Slope of a Line

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

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9. 9.

   Physics

   A body moving at 12 m/s accelerates at 4 m/s² for 9 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.

    Mathematics

    If f(x) = 2x³ + 3x² + 9x, find f′(1).

    Formula:Derivative of a Polynomial

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

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11. 11.

    Chemistry

    How many moles are present in 300 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

    Formula:Number of Moles

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

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12. 12.

    Physics

    Calculate the potential energy of a 17 kg object at a height of 39 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Chemistry

    How many moles are present in 270 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

    Formula:Number of Moles

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

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14. 14.

    Mathematics

    In an arithmetic progression with first term 13 and common difference 9, find term number 8.

    Formula:AP nth Term

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

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15. 15.

    Chemistry

    A solution is made by dissolving 27 g of solute in 105 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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16. 16.

    Chemistry

    How many moles are present in 100 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

    Formula:Number of Moles

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

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17. 17.

    Mathematics

    Evaluate log base 3 of 27.

    Formula:Logarithm Evaluation

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

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18. 18.

    Physics

    A constant force of 57 N moves an object 4 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Mathematics

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

    Formula:GP nth Term

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

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20. 20.

    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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