Engineering Entrance · Practice Sheet 50

1. 1.

   Chemistry

   94 mL of a 1 M solution is diluted to 257 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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2. 2.

   Physics

   An object starts at 2 m/s and accelerates at 8 m/s² for 2 s. Find its final velocity.

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

   $v = u + at$

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3. 3.

   Chemistry

   How many moles are present in 9 g of water (H₂O) (molar mass = 18 g/mol)?

   Formula:Number of Moles

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

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4. 4.

   Chemistry

   Find the pressure of 2 mol of an ideal gas at 334 K in a 17 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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5. 5.

   Mathematics

   Find the sum of the first 15 terms of an AP with first term 8 and common difference 2.

   Formula:AP Sum of n Terms

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

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6. 6.

   Mathematics

   Find the slope of the line through (-5, 8) and (7, -2).

   Formula:Slope of a Line

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

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7. 7.

   Physics

   Find the force required to accelerate a 17 kg mass at 1 m/s².

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

   $F = ma$

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8. 8.

   Mathematics

   In an arithmetic progression with first term 17 and common difference 3, find term number 27.

   Formula:AP nth Term

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

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9. 9.

   Physics

   Find the electrical power when 225 V drives a current of 4 A.

   Formula:Electrical Power

   $P = VI$

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10. 10.

    Mathematics

    Find the slope of the line through (-6, 6) and (-2, -7).

    Formula:Slope of a Line

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

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11. 11.

    Physics

    An object starts at 4 m/s and accelerates at 10 m/s² for 7 s. Find its final velocity.

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

    $v = u + at$

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12. 12.

    Mathematics

    If f(x) = 4x³ + 5x² + 6x, find f′(4).

    Formula:Derivative of a Polynomial

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

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13. 13.

    Mathematics

    Evaluate log base 10 of 1,000.

    Formula:Logarithm Evaluation

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

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14. 14.

    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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15. 15.

    Physics

    A projectile is launched at 23 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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16. 16.

    Physics

    A force of 722 N acts on an area of 23 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 353 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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18. 18.

    Mathematics

    Evaluate log base 3 of 729.

    Formula:Logarithm Evaluation

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

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19. 19.

    Physics

    A constant force of 51 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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20. 20.

    Chemistry

    A solution is made by dissolving 43 g of solute in 128 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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