Engineering Entrance · Practice Sheet 34

1. 1.

   Mathematics

   In an arithmetic progression with first term 7 and common difference 6, find term number 26.

   Formula:AP nth Term

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

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2. 2.

   Physics

   Find the density of an object with mass 93 g and volume 29 cm³.

   Formula:Density

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

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3. 3.

   Chemistry

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

   Formula:pH of a Solution

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

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4. 4.

   Mathematics

   In an arithmetic progression with first term 2 and common difference 3, find term number 17.

   Formula:AP nth Term

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

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5. 5.

   Mathematics

   Find term number 5 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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6. 6.

   Mathematics

   Find the sum of the first 6 terms of an AP with first term 1 and common difference 9.

   Formula:AP Sum of n Terms

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

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7. 7.

   Physics

   Find the force required to accelerate a 37 kg mass at 2 m/s².

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

   $F = ma$

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8. 8.

   Mathematics

   Find the distance between the points (-4, -2) and (0, -3).

   Formula:Distance Between Two Points

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

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9. 9.

   Mathematics

   Evaluate log base 5 of 25.

   Formula:Logarithm Evaluation

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

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10. 10.

    Physics

    Find the kinetic energy of a 18 kg object moving at 5 m/s.

    Formula:Kinetic Energy

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

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11. 11.

    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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12. 12.

    Chemistry

    17 mL of a 10 M solution is diluted to 410 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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13. 13.

    Mathematics

    For the quadratic 3x² − 1x + 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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14. 14.

    Mathematics

    If f(x) = 3x³ + 2x² + 2x, find f′(4).

    Formula:Derivative of a Polynomial

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

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15. 15.

    Physics

    A constant force of 152 N moves an object 6 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 molarity of a solution containing 1 mol of solute in 1 L of solution.

    Formula:Molarity

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

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17. 17.

    Physics

    Find the voltage across a 38 Ω resistor carrying a current of 19 A.

    Formula:Ohm's Law

    $V = IR$

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18. 18.

    Physics

    A constant force of 138 N moves an object 22 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Physics

    Calculate the potential energy of a 50 kg object at a height of 10 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Mathematics

    Find the distance between the points (0, 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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