Engineering Entrance · Practice Sheet 18

1. 1.

   Chemistry

   How many moles are present in 450 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

   Formula:Number of Moles

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

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2. 2.

   Physics

   Find the voltage across a 46 Ω resistor carrying a current of 10 A.

   Formula:Ohm's Law

   $V = IR$

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3. 3.

   Mathematics

   Evaluate ∫ from 0 to 3 of 1x^2 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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4. 4.

   Chemistry

   59 mL of a 10 M solution is diluted to 173 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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5. 5.

   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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6. 6.

   Physics

   An object starts at 11 m/s and accelerates at 4 m/s² for 6 s. Find its final velocity.

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

   $v = u + at$

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7. 7.

   Physics

   Find the kinetic energy of a 12 kg object moving at 24 m/s.

   Formula:Kinetic Energy

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

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8. 8.

   Mathematics

   Evaluate ∫ from 1 to 5 of 1x^1 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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9. 9.

   Mathematics

   Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.

   Formula:Binomial Coefficient

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

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10. 10.

    Physics

    A force of 784 N acts on an area of 12 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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11. 11.

    Physics

    Find the momentum of a 48 kg body moving at 24 m/s.

    Formula:Linear Momentum

    $p = mv$

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12. 12.

    Physics

    Find the force required to accelerate a 28 kg mass at 5 m/s².

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

    $F = ma$

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13. 13.

    Physics

    A constant force of 139 N moves an object 4 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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14. 14.

    Physics

    Find the momentum of a 18 kg body moving at 10 m/s.

    Formula:Linear Momentum

    $p = mv$

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15. 15.

    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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16. 16.

    Physics

    Find the force required to accelerate a 2 kg mass at 1 m/s².

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

    $F = ma$

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17. 17.

    Chemistry

    94 mL of a 5 M solution is diluted to 178 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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18. 18.

    Mathematics

    Find the sum of the first 19 terms of an AP with first term 4 and common difference 1.

    Formula:AP Sum of n Terms

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

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19. 19.

    Mathematics

    Evaluate log base 5 of 25.

    Formula:Logarithm Evaluation

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

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20. 20.

    Physics

    Find the kinetic energy of a 5 kg object moving at 26 m/s.

    Formula:Kinetic Energy

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

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