Engineering Entrance · Practice Sheet 29

1. 1.

   Physics

   Find the momentum of a 11 kg body moving at 38 m/s.

   Formula:Linear Momentum

   $p = mv$

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2. 2.

   Physics

   Find the density of an object with mass 19 g and volume 26 cm³.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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3. 3.

   Mathematics

   Evaluate ∫ from 1 to 4 of 3x^3 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.

   Mathematics

   Find term number 4 of a geometric progression with first term 6 and common ratio 3.

   Formula:GP nth Term

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

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5. 5.

   Mathematics

   Find the sum of the first 7 terms of an AP with first term 1 and common difference 1.

   Formula:AP Sum of n Terms

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

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6. 6.

   Physics

   Find the voltage across a 34 Ω resistor carrying a current of 11 A.

   Formula:Ohm's Law

   $V = IR$

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7. 7.

   Mathematics

   In an arithmetic progression with first term 11 and common difference 2, find term number 30.

   Formula:AP nth Term

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

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8. 8.

   Mathematics

   Find term number 7 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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9. 9.

   Chemistry

   A solution is made by dissolving 9 g of solute in 192 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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10. 10.

    Chemistry

    Find the molarity of a solution containing 3 mol of solute in 4 L of solution.

    Formula:Molarity

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

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11. 11.

    Mathematics

    In an arithmetic progression with first term 18 and common difference 7, find term number 26.

    Formula:AP nth Term

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

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12. 12.

    Physics

    If 825 J of work is done in 25 s, find the power.

    Formula:Power

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

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13. 13.

    Physics

    A body moving at 13 m/s accelerates at 6 m/s² for 9 s. Find the distance travelled.

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

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

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14. 14.

    Mathematics

    For the quadratic 4x² + 1x + 0 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

    $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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15. 15.

    Mathematics

    Find the sum of the first 4 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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16. 16.

    Mathematics

    Find the distance between the points (-4, -2) and (0, 5).

    Formula:Distance Between Two Points

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

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17. 17.

    Physics

    Find the kinetic energy of a 11 kg object moving at 13 m/s.

    Formula:Kinetic Energy

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

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18. 18.

    Physics

    An object starts at 4 m/s and accelerates at 6 m/s² for 12 s. Find its final velocity.

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

    $v = u + at$

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19. 19.

    Chemistry

    Find the pressure of 5 mol of an ideal gas at 321 K in a 7 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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20. 20.

    Physics

    Find the voltage across a 9 Ω resistor carrying a current of 15 A.

    Formula:Ohm's Law

    $V = IR$

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