IIT-JEE · Practice Sheet 48

1. 1.

   Physics

   A constant force of 125 N moves an object 41 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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2. 2.

   Chemistry

   Find the pressure of 4 mol of an ideal gas at 213 K in a 5 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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3. 3.

   Mathematics

   Find term number 5 of a geometric progression with first term 2 and common ratio 3.

   Formula:GP nth Term

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

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4. 4.

   Physics

   Find the electrical power when 133 V drives a current of 7 A.

   Formula:Electrical Power

   $P = VI$

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5. 5.

   Chemistry

   A solution is made by dissolving 38 g of solute in 139 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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6. 6.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

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7. 7.

   Physics

   Find the momentum of a 17 kg body moving at 4 m/s.

   Formula:Linear Momentum

   $p = mv$

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8. 8.

   Quantitative Aptitude

   A vehicle covers 540 km in 6 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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9. 9.

   Physics

   Find the voltage across a 15 Ω resistor carrying a current of 4 A.

   Formula:Ohm's Law

   $V = IR$

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10. 10.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)

    Formula:Combinations

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

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11. 11.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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12. 12.

    Physics

    A body moving at 0 m/s accelerates at 7 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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13. 13.

    Physics

    Find the kinetic energy of a 17 kg object moving at 30 m/s.

    Formula:Kinetic Energy

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

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14. 14.

    Physics

    A constant force of 80 N moves an object 10 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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15. 15.

    Mathematics

    Find the slope of the line through (8, -1) and (-2, 5).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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16. 16.

    Physics

    Find the electrical power when 158 V drives a current of 9 A.

    Formula:Electrical Power

    $P = VI$

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17. 17.

    Physics

    Find the momentum of a 30 kg body moving at 10 m/s.

    Formula:Linear Momentum

    $p = mv$

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18. 18.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)

    Formula:Combinations

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

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19. 19.

    Physics

    If 2,871 J of work is done in 44 s, find the power.

    Formula:Power

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

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20. 20.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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