Engineering Entrance · Practice Sheet 8

1. 1.

   Mathematics

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

   Formula:Distance Between Two Points

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

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2. 2.

   Mathematics

   Find the slope of the line through (1, 5) and (2, 5).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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3. 3.

   Mathematics

   In an arithmetic progression with first term 18 and common difference 1, find term number 6.

   Formula:AP nth Term

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

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4. 4.

   Physics

   Find the kinetic energy of a 2 kg object moving at 12 m/s.

   Formula:Kinetic Energy

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

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5. 5.

   Physics

   Calculate the potential energy of a 15 kg object at a height of 3 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Mathematics

   Find the sum of the first 7 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.

   Physics

   Find the electrical power when 111 V drives a current of 13 A.

   Formula:Electrical Power

   $P = VI$

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8. 8.

   Mathematics

   Find the slope of the line through (-2, 3) and (1, -4).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

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9. 9.

   Mathematics

   Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

   Formula:Binomial Coefficient

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

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10. 10.

    Mathematics

    If f(x) = 4x³ + 5x² + 3x, find f′(1).

    Formula:Derivative of a Polynomial

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

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11. 11.

    Physics

    A constant force of 49 N moves an object 5 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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12. 12.

    Mathematics

    Find the sum of the first 23 terms of an AP with first term 9 and common difference 2.

    Formula:AP Sum of n Terms

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

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13. 13.

    Physics

    An object starts at 13 m/s and accelerates at 7 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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14. 14.

    Physics

    Calculate the potential energy of a 48 kg object at a height of 6 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Physics

    Find the force required to accelerate a 28 kg mass at 1 m/s².

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

    $F = ma$

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16. 16.

    Mathematics

    Find the binomial coefficient C(6, 2) — the coefficient of x^2 in (1 + x)^6.

    Formula:Binomial Coefficient

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

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17. 17.

    Physics

    Calculate the potential energy of a 48 kg object at a height of 48 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Physics

    Find the voltage across a 18 Ω resistor carrying a current of 19 A.

    Formula:Ohm's Law

    $V = IR$

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19. 19.

    Physics

    Find the electrical power when 215 V drives a current of 18 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Chemistry

    How many moles are present in 22 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

    Formula:Number of Moles

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

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