Engineering Entrance · Practice Sheet 26

1. 1.

   Mathematics

   In an arithmetic progression with first term 5 and common difference 6, find term number 6.

   Formula:AP nth Term

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

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2. 2.

   Physics

   Find the electrical power when 72 V drives a current of 2 A.

   Formula:Electrical Power

   $P = VI$

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3. 3.

   Chemistry

   How many moles are present in 900 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

   Formula:Number of Moles

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

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4. 4.

   Mathematics

   Find the distance between the points (6, -6) and (3, 4).

   Formula:Distance Between Two Points

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

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5. 5.

   Physics

   Find the electrical power when 177 V drives a current of 16 A.

   Formula:Electrical Power

   $P = VI$

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6. 6.

   Mathematics

   In an arithmetic progression with first term 20 and common difference 9, find term number 15.

   Formula:AP nth Term

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

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7. 7.

   Physics

   Find the kinetic energy of a 12 kg object moving at 21 m/s.

   Formula:Kinetic Energy

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

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8. 8.

   Physics

   A constant force of 110 N moves an object 2 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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9. 9.

   Mathematics

   Find the binomial coefficient C(9, 2) — the coefficient of x^2 in (1 + x)^9.

   Formula:Binomial Coefficient

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

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10. 10.

    Physics

    A body moving at 3 m/s accelerates at 1 m/s² for 7 s. Find the distance travelled.

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

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

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11. 11.

    Mathematics

    Evaluate log base 2 of 32.

    Formula:Logarithm Evaluation

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

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12. 12.

    Physics

    A projectile is launched at 21 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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13. 13.

    Physics

    Find the momentum of a 17 kg body moving at 29 m/s.

    Formula:Linear Momentum

    $p = mv$

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14. 14.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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15. 15.

    Chemistry

    Find the molarity of a solution containing 1 mol of solute in 4 L of solution.

    Formula:Molarity

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

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16. 16.

    Chemistry

    Find the pressure of 5 mol of an ideal gas at 296 K in a 16 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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17. 17.

    Chemistry

    How many moles are present in 100 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

    Find the sum of the first 6 terms of a GP with first term 5 and common ratio 2.

    Formula:GP Sum of n Terms

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

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19. 19.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻6 mol/L.

    Formula:pH of a Solution

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

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20. 20.

    Mathematics

    In an arithmetic progression with first term 20 and common difference 9, find term number 19.

    Formula:AP nth Term

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

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