Engineering Entrance · Practice Sheet 25

1. 1.

   Physics

   Find the force required to accelerate a 40 kg mass at 1 m/s².

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

   $F = ma$

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2. 2.

   Chemistry

   A solution is made by dissolving 45 g of solute in 98 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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3. 3.

   Mathematics

   Evaluate log base 3 of 243.

   Formula:Logarithm Evaluation

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

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4. 4.

   Mathematics

   Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.

   Formula:Binomial Coefficient

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

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5. 5.

   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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6. 6.

   Mathematics

   Evaluate log base 10 of 100,000.

   Formula:Logarithm Evaluation

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

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7. 7.

   Mathematics

   Evaluate ∫ from 0 to 5 of 4x^3 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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8. 8.

   Mathematics

   Find the distance between the points (-2, -5) and (8, 8).

   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 11 terms of an AP with first term 6 and common difference 2.

   Formula:AP Sum of n Terms

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

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10. 10.

    Chemistry

    How many moles are present in 32 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

    Formula:Number of Moles

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

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11. 11.

    Physics

    Find the voltage across a 43 Ω resistor carrying a current of 9 A.

    Formula:Ohm's Law

    $V = IR$

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12. 12.

    Mathematics

    In an arithmetic progression with first term 13 and common difference 9, find term number 15.

    Formula:AP nth Term

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

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13. 13.

    Chemistry

    A solution is made by dissolving 17 g of solute in 90 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.

    Mathematics

    For the quadratic 2x² − 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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15. 15.

    Mathematics

    Find the distance between the points (3, -1) and (-4, -2).

    Formula:Distance Between Two Points

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

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16. 16.

    Physics

    An object starts at 9 m/s and accelerates at 7 m/s² for 2 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

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17. 17.

    Physics

    A body moving at 15 m/s accelerates at 8 m/s² for 4 s. Find the distance travelled.

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

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

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18. 18.

    Physics

    An object starts at 3 m/s and accelerates at 7 m/s² for 12 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

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19. 19.

    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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20. 20.

    Chemistry

    38 mL of a 10 M solution is diluted to 302 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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