EmSAT Achieve · Practice Sheet 50

1. 1.

   Mathematics

   Find the sum of the first 11 terms of an AP with first term 18 and common difference 5.

   Formula:AP Sum of n Terms

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

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2. 2.

   Chemistry

   A solution is made by dissolving 17 g of solute in 134 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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3. 3.

   Chemistry

   Find the pH of a solution with [H⁺] = 2×10⁻6 mol/L.

   Formula:pH of a Solution

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

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4. 4.

   Physics

   A projectile is launched at 36 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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5. 5.

   Physics

   A constant force of 27 N moves an object 26 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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6. 6.

   Mathematics

   In an arithmetic progression with first term 8 and common difference 2, find term number 28.

   Formula:AP nth Term

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

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7. 7.

   Biology

   Under a microscope, an object of actual size 3.1 mm appears 120.9 mm. Find the magnification.

   Formula:Microscope Magnification

   $M = \dfrac{\text{image size}}{\text{actual size}}$

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8. 8.

   Biology

   Calculate the BMI of a person weighing 52 kg with height 1.56 m.

   Formula:Body Mass Index

   $BMI = \dfrac{m}{h^{2}}$

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9. 9.

   Physics

   Find the force required to accelerate a 31 kg mass at 3 m/s².

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

   $F = ma$

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10. 10.

    Physics

    Find the voltage across a 44 Ω resistor carrying a current of 8 A.

    Formula:Ohm's Law

    $V = IR$

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11. 11.

    Physics

    Find the momentum of a 21 kg body moving at 17 m/s.

    Formula:Linear Momentum

    $p = mv$

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12. 12.

    Physics

    Find the kinetic energy of a 2 kg object moving at 14 m/s.

    Formula:Kinetic Energy

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

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13. 13.

    Physics

    Find the force required to accelerate a 47 kg mass at 6 m/s².

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

    $F = ma$

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14. 14.

    Physics

    Find the momentum of a 29 kg body moving at 2 m/s.

    Formula:Linear Momentum

    $p = mv$

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15. 15.

    Chemistry

    How many moles are present in 90 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

    Formula:Number of Moles

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

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16. 16.

    Physics

    A projectile is launched at 28 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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17. 17.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 377 K in a 4 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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18. 18.

    Physics

    Find the density of an object with mass 90 g and volume 45 cm³.

    Formula:Density

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

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19. 19.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 5 and common ratio 3.

    Formula:GP Sum of n Terms

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

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20. 20.

    Mathematics

    In an arithmetic progression with first term 16 and common difference 10, find term number 26.

    Formula:AP nth Term

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

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