Engineering Entrance · Practice Sheet 47

1. 1.

   Chemistry

   86 mL of a 1 M solution is diluted to 157 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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2. 2.

   Physics

   A projectile is launched at 34 m/s at 30° 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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3. 3.

   Physics

   A force of 867 N acts on an area of 22 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Physics

   A body moving at 11 m/s accelerates at 3 m/s² for 2 s. Find the distance travelled.

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

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

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5. 5.

   Physics

   A constant force of 120 N moves an object 21 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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6. 6.

   Mathematics

   Find the distance between the points (4, -7) and (-1, 5).

   Formula:Distance Between Two Points

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

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7. 7.

   Chemistry

   Find the molarity of a solution containing 1 mol of solute in 4 L of solution.

   Formula:Molarity

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

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8. 8.

   Mathematics

   Find the sum of the first 5 terms of an AP with first term 1 and common difference 1.

   Formula:AP Sum of n Terms

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

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9. 9.

   Chemistry

   A solution is made by dissolving 44 g of solute in 192 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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10. 10.

    Physics

    A projectile is launched at 20 m/s at 30° 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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11. 11.

    Chemistry

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

    Formula:Molarity

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

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12. 12.

    Mathematics

    Find the sum of the first 17 terms of an AP with first term 19 and common difference 8.

    Formula:AP Sum of n Terms

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

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13. 13.

    Physics

    Find the density of an object with mass 406 g and volume 47 cm³.

    Formula:Density

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

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14. 14.

    Chemistry

    24 mL of a 1 M solution is diluted to 283 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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15. 15.

    Chemistry

    A solution is made by dissolving 9 g of solute in 170 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.

    Mathematics

    Find the sum of the first 5 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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17. 17.

    Mathematics

    If f(x) = 2x³ + 1x² + 6x, find f′(3).

    Formula:Derivative of a Polynomial

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

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18. 18.

    Physics

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

    Formula:Linear Momentum

    $p = mv$

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19. 19.

    Physics

    Find the electrical power when 179 V drives a current of 13 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Chemistry

    Find the pH of a solution with [H⁺] = 1×10⁻4 mol/L.

    Formula:pH of a Solution

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

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