Engineering Entrance · Practice Sheet 10

1. 1.

   Physics

   A force of 64 N acts on an area of 22 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Physics

   Calculate the potential energy of a 27 kg object at a height of 43 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Physics

   If 3,772 J of work is done in 46 s, find the power.

   Formula:Power

   $P = \dfrac{W}{t}$

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4. 4.

   Physics

   Find the force required to accelerate a 38 kg mass at 8 m/s².

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

   $F = ma$

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5. 5.

   Mathematics

   In an arithmetic progression with first term 4 and common difference 1, find term number 16.

   Formula:AP nth Term

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

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6. 6.

   Chemistry

   Find the molarity of a solution containing 2.5 mol of solute in 2 L of solution.

   Formula:Molarity

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

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7. 7.

   Chemistry

   A solution is made by dissolving 36 g of solute in 97 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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8. 8.

   Physics

   A projectile is launched at 37 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.

   Mathematics

   Find the sum of the first 25 terms of an AP with first term 16 and common difference 3.

   Formula:AP Sum of n Terms

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

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10. 10.

    Mathematics

    Evaluate ∫ from 2 to 4 of 4x^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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11. 11.

    Physics

    If 3,718 J of work is done in 49 s, find the power.

    Formula:Power

    $P = \dfrac{W}{t}$

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12. 12.

    Mathematics

    In an arithmetic progression with first term 17 and common difference 4, find term number 30.

    Formula:AP nth Term

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

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13. 13.

    Physics

    Find the electrical power when 202 V drives a current of 18 A.

    Formula:Electrical Power

    $P = VI$

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14. 14.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻2 mol/L.

    Formula:pH of a Solution

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

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15. 15.

    Chemistry

    52 mL of a 2 M solution is diluted to 419 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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16. 16.

    Mathematics

    Find the distance between the points (6, 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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17. 17.

    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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18. 18.

    Mathematics

    Find term number 5 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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19. 19.

    Mathematics

    Find the sum of the first 6 terms of an AP with first term 7 and common difference 8.

    Formula:AP Sum of n Terms

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

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20. 20.

    Physics

    A projectile is launched at 22 m/s at 45° 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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