IIT-JEE · Practice Sheet 17

1. 1.

   Chemistry

   Find the pressure of 1 mol of an ideal gas at 370 K in a 20 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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2. 2.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)

   Formula:Combinations

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

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3. 3.

   Mathematics

   In an arithmetic progression with first term 20 and common difference 2, find term number 23.

   Formula:AP nth Term

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

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4. 4.

   Physics

   A body moving at 13 m/s accelerates at 3 m/s² for 3 s. Find the distance travelled.

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

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

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5. 5.

   Physics

   Find the force required to accelerate a 42 kg mass at 15 m/s².

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

   $F = ma$

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6. 6.

   Chemistry

   A solution is made by dissolving 26 g of solute in 103 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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7. 7.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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8. 8.

   Mathematics

   Evaluate log base 2 of 64.

   Formula:Logarithm Evaluation

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

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9. 9.

   Physics

   If 5,000 J of work is done in 50 s, find the power.

   Formula:Power

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

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10. 10.

    Physics

    An object starts at 18 m/s and accelerates at 4 m/s² for 8 s. Find its final velocity.

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

    $v = u + at$

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11. 11.

    Physics

    A body moving at 13 m/s accelerates at 2 m/s² for 4 s. Find the distance travelled.

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

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

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12. 12.

    Mathematics

    Find term number 6 of a geometric progression with first term 2 and common ratio 2.

    Formula:GP nth Term

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

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13. 13.

    Chemistry

    91 mL of a 10 M solution is diluted to 335 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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14. 14.

    Physics

    A body moving at 0 m/s accelerates at 2 m/s² for 2 s. Find the distance travelled.

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

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

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15. 15.

    Chemistry

    43 mL of a 2 M solution is diluted to 302 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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16. 16.

    Chemistry

    How many moles are present in 500 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

    Formula:Number of Moles

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

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17. 17.

    Physics

    A constant force of 136 N moves an object 33 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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18. 18.

    Chemistry

    Find the molarity of a solution containing 1 mol of solute in 2 L of solution.

    Formula:Molarity

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

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19. 19.

    Physics

    Find the kinetic energy of a 20 kg object moving at 7 m/s.

    Formula:Kinetic Energy

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

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20. 20.

    Physics

    Find the density of an object with mass 46 g and volume 26 cm³.

    Formula:Density

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

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