Engineering Entrance · Practice Sheet 7

1. 1.

   Mathematics

   In an arithmetic progression with first term 17 and common difference 7, find term number 14.

   Formula:AP nth Term

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

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2. 2.

   Chemistry

   Find the pH of a solution with [H⁺] = 1×10⁻6 mol/L.

   Formula:pH of a Solution

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

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3. 3.

   Physics

   Calculate the potential energy of a 50 kg object at a height of 21 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Physics

   If 3,308 J of work is done in 15 s, find the power.

   Formula:Power

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

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5. 5.

   Physics

   Find the momentum of a 16 kg body moving at 27 m/s.

   Formula:Linear Momentum

   $p = mv$

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6. 6.

   Mathematics

   Find the sum of the first 3 terms of a GP with first term 2 and common ratio 3.

   Formula:GP Sum of n Terms

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

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7. 7.

   Mathematics

   If f(x) = 5x³ + 2x² + 3x, find f′(3).

   Formula:Derivative of a Polynomial

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

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8. 8.

   Mathematics

   Evaluate ∫ from 0 to 5 of 3x^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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9. 9.

   Physics

   A force of 582 N acts on an area of 6 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Mathematics

    For the quadratic 1x² + 8x − 1 = 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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11. 11.

    Physics

    A projectile is launched at 22 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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12. 12.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 1 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

    51 mL of a 5 M solution is diluted to 134 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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14. 14.

    Physics

    A constant force of 92 N moves an object 16 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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15. 15.

    Chemistry

    A solution is made by dissolving 26 g of solute in 167 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

    Evaluate log base 10 of 1,000,000.

    Formula:Logarithm Evaluation

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

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17. 17.

    Physics

    A projectile is launched at 36 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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18. 18.

    Physics

    If 4,976 J of work is done in 11 s, find the power.

    Formula:Power

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

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19. 19.

    Mathematics

    Find term number 6 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term

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

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20. 20.

    Mathematics

    For the quadratic 1x² − 9x − 1 = 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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