Engineering Entrance · Practice Sheet 39

1. 1.

   Mathematics

   If f(x) = 1x³ + 3x² + 4x, find f′(4).

   Formula:Derivative of a Polynomial

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

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2. 2.

   Physics

   A body moving at 9 m/s accelerates at 1 m/s² for 10 s. Find the distance travelled.

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

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

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3. 3.

   Physics

   Find the force required to accelerate a 6 kg mass at 19 m/s².

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

   $F = ma$

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4. 4.

   Mathematics

   Find the sum of the first 24 terms of an AP with first term 19 and common difference 5.

   Formula:AP Sum of n Terms

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

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5. 5.

   Mathematics

   Find term number 6 of a geometric progression with first term 5 and common ratio 2.

   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 a GP with first term 4 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.

   Physics

   Calculate the potential energy of a 38 kg object at a height of 18 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Physics

   A projectile is launched at 17 m/s at 60° 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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9. 9.

   Chemistry

   Find the molarity of a solution containing 1 mol of solute in 2 L of solution.

   Formula:Molarity

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

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10. 10.

    Mathematics

    Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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11. 11.

    Physics

    Find the momentum of a 12 kg body moving at 40 m/s.

    Formula:Linear Momentum

    $p = mv$

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12. 12.

    Mathematics

    Find term number 5 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term

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

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13. 13.

    Chemistry

    A solution is made by dissolving 39 g of solute in 105 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 kinetic energy of a 15 kg object moving at 19 m/s.

    Formula:Kinetic Energy

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

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15. 15.

    Physics

    A body moving at 5 m/s accelerates at 1 m/s² for 10 s. Find the distance travelled.

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

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

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16. 16.

    Mathematics

    Find the sum of the first 23 terms of an AP with first term 1 and common difference 4.

    Formula:AP Sum of n Terms

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

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17. 17.

    Chemistry

    How many moles are present in 150 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

    Formula:Number of Moles

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

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18. 18.

    Mathematics

    Evaluate log base 10 of 100,000.

    Formula:Logarithm Evaluation

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

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19. 19.

    Mathematics

    Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

    Formula:Binomial Coefficient

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

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20. 20.

    Mathematics

    Evaluate log base 5 of 15,625.

    Formula:Logarithm Evaluation

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

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