Engineering Entrance · Practice Sheet 4

1. 1.

   Physics

   If 142 J of work is done in 37 s, find the power.

   Formula:Power

   $P = \dfrac{W}{t}$

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2. 2.

   Physics

   Find the density of an object with mass 24 g and volume 33 cm³.

   Formula:Density

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

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3. 3.

   Chemistry

   A solution is made by dissolving 29 g of solute in 157 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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4. 4.

   Physics

   A projectile is launched at 30 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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5. 5.

   Mathematics

   Find the sum of the first 10 terms of an AP with first term 11 and common difference 1.

   Formula:AP Sum of n Terms

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

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6. 6.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 5 and common ratio 2.

   Formula:GP Sum of n Terms

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

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7. 7.

   Mathematics

   For the quadratic 1x² − 7x − 3 = 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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8. 8.

   Mathematics

   Find the distance between the points (0, -8) and (-4, 6).

   Formula:Distance Between Two Points

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

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9. 9.

   Mathematics

   Find the sum of the first 3 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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10. 10.

    Mathematics

    In an arithmetic progression with first term 5 and common difference 3, find term number 30.

    Formula:AP nth Term

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

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11. 11.

    Physics

    Find the voltage across a 23 Ω resistor carrying a current of 1 A.

    Formula:Ohm's Law

    $V = IR$

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12. 12.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 3 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

    A solution is made by dissolving 33 g of solute in 132 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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14. 14.

    Physics

    Find the force required to accelerate a 20 kg mass at 4 m/s².

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

    $F = ma$

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15. 15.

    Physics

    A constant force of 38 N moves an object 35 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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16. 16.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻4 mol/L.

    Formula:pH of a Solution

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

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17. 17.

    Chemistry

    How many moles are present in 146.25 g of sodium chloride (NaCl) (molar mass = 58.5 g/mol)?

    Formula:Number of Moles

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

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18. 18.

    Physics

    A force of 873 N acts on an area of 24 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Physics

    Find the density of an object with mass 161 g and volume 19 cm³.

    Formula:Density

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

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20. 20.

    Mathematics

    Evaluate ∫ from 1 to 5 of 1x^2 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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