Engineering Entrance · Practice Sheet 17

1. 1.

   Physics

   Calculate the potential energy of a 44 kg object at a height of 26 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Physics

   A force of 583 N acts on an area of 16 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Physics

   Find the kinetic energy of a 13 kg object moving at 2 m/s.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2}mv^{2}$

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4. 4.

   Chemistry

   Find the pressure of 2 mol of an ideal gas at 387 K in a 18 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 distance between the points (-6, 1) and (-6, -7).

   Formula:Distance Between Two Points

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

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6. 6.

   Mathematics

   If f(x) = 4x³ + 2x² + 6x, find f′(4).

   Formula:Derivative of a Polynomial

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

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7. 7.

   Physics

   Calculate the potential energy of a 13 kg object at a height of 13 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Physics

   Find the momentum of a 47 kg body moving at 18 m/s.

   Formula:Linear Momentum

   $p = mv$

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9. 9.

   Mathematics

   Find the binomial coefficient C(7, 4) — the coefficient of x^4 in (1 + x)^7.

   Formula:Binomial Coefficient

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

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10. 10.

    Physics

    A projectile is launched at 44 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 2 mol of solute in 0.5 L of solution.

    Formula:Molarity

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

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12. 12.

    Physics

    Find the electrical power when 140 V drives a current of 13 A.

    Formula:Electrical Power

    $P = VI$

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13. 13.

    Physics

    Find the voltage across a 35 Ω resistor carrying a current of 7 A.

    Formula:Ohm's Law

    $V = IR$

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14. 14.

    Mathematics

    Find term number 7 of a geometric progression with first term 5 and common ratio 3.

    Formula:GP nth Term

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

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15. 15.

    Mathematics

    Evaluate ∫ from 1 to 3 of 4x^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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16. 16.

    Chemistry

    Find the pH of a solution with [H⁺] = 1×10⁻3 mol/L.

    Formula:pH of a Solution

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

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17. 17.

    Mathematics

    For the quadratic 5x² − 8x − 9 = 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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18. 18.

    Physics

    Find the voltage across a 22 Ω resistor carrying a current of 5 A.

    Formula:Ohm's Law

    $V = IR$

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19. 19.

    Physics

    Calculate the potential energy of a 37 kg object at a height of 33 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 3 and common ratio 3.

    Formula:GP Sum of n Terms

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

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