IIT-JEE · Practice Sheet 47

1. 1.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

   Formula:Probability (two dice)

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

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2. 2.

   Mathematics

   Find the binomial coefficient C(6, 2) — the coefficient of x^2 in (1 + x)^6.

   Formula:Binomial Coefficient

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

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3. 3.

   Physics

   Calculate the potential energy of a 34 kg object at a height of 2 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Mathematics

   Evaluate ∫ from 1 to 5 of 1x^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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5. 5.

   Physics

   A force of 493 N acts on an area of 33 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Physics

   Find the kinetic energy of a 5 kg object moving at 6 m/s.

   Formula:Kinetic Energy

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

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7. 7.

   Chemistry

   A solution is made by dissolving 18 g of solute in 96 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 body moving at 9 m/s accelerates at 6 m/s² for 5 s. Find the distance travelled.

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

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

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9. 9.

   Quantitative Aptitude

   A vehicle covers 380 km in 5 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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10. 10.

    Physics

    A force of 117 N acts on an area of 36 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Chemistry

    A solution is made by dissolving 11 g of solute in 105 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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12. 12.

    Physics

    Find the force required to accelerate a 8 kg mass at 1 m/s².

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

    $F = ma$

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13. 13.

    Chemistry

    A solution is made by dissolving 46 g of solute in 132 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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14. 14.

    Physics

    An object starts at 1 m/s and accelerates at 4 m/s² for 7 s. Find its final velocity.

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

    $v = u + at$

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15. 15.

    Chemistry

    55 mL of a 1 M solution is diluted to 248 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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16. 16.

    Physics

    Find the kinetic energy of a 15 kg object moving at 30 m/s.

    Formula:Kinetic Energy

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

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17. 17.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

    Formula:Probability (two dice)

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

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18. 18.

    Physics

    Find the force required to accelerate a 2 kg mass at 15 m/s².

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

    $F = ma$

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19. 19.

    Physics

    Find the electrical power when 20 V drives a current of 14 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Physics

    Find the momentum of a 27 kg body moving at 15 m/s.

    Formula:Linear Momentum

    $p = mv$

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