Engineering Entrance · Practice Sheet 46

1. 1.

   Chemistry

   89 mL of a 10 M solution is diluted to 389 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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2. 2.

   Physics

   A body moving at 8 m/s accelerates at 8 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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3. 3.

   Mathematics

   Evaluate ∫ from 1 to 4 of 3x^1 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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4. 4.

   Mathematics

   Find the distance between the points (-6, -8) and (5, -6).

   Formula:Distance Between Two Points

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

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5. 5.

   Chemistry

   A solution is made by dissolving 48 g of solute in 92 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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6. 6.

   Physics

   Find the voltage across a 36 Ω resistor carrying a current of 9 A.

   Formula:Ohm's Law

   $V = IR$

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7. 7.

   Physics

   Find the force required to accelerate a 15 kg mass at 3 m/s².

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

   $F = ma$

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8. 8.

   Mathematics

   Find the binomial coefficient C(5, 3) — the coefficient of x^3 in (1 + x)^5.

   Formula:Binomial Coefficient

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

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9. 9.

   Physics

   Find the momentum of a 17 kg body moving at 23 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Mathematics

    Find the sum of the first 20 terms of an AP with first term 6 and common difference 8.

    Formula:AP Sum of n Terms

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

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11. 11.

    Physics

    Find the density of an object with mass 168 g and volume 32 cm³.

    Formula:Density

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

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12. 12.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 6 and common ratio 2.

    Formula:GP Sum of n Terms

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

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13. 13.

    Chemistry

    How many moles are present in 175.5 g of sodium chloride (NaCl) (molar mass = 58.5 g/mol)?

    Formula:Number of Moles

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

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14. 14.

    Physics

    A force of 353 N acts on an area of 9 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Physics

    Find the momentum of a 29 kg body moving at 24 m/s.

    Formula:Linear Momentum

    $p = mv$

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16. 16.

    Physics

    A projectile is launched at 39 m/s at 60° 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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17. 17.

    Physics

    Find the electrical power when 225 V drives a current of 17 A.

    Formula:Electrical Power

    $P = VI$

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18. 18.

    Chemistry

    A solution is made by dissolving 45 g of solute in 106 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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19. 19.

    Chemistry

    41 mL of a 10 M solution is diluted to 337 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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20. 20.

    Physics

    Find the electrical power when 161 V drives a current of 10 A.

    Formula:Electrical Power

    $P = VI$

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