IIT-JEE · Practice Sheet 21

1. 1.

   Physics

   Find the force required to accelerate a 45 kg mass at 13 m/s².

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

   $F = ma$

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2. 2.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

   Formula:Permutations

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

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3. 3.

   Physics

   Find the voltage across a 33 Ω resistor carrying a current of 13 A.

   Formula:Ohm's Law

   $V = IR$

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4. 4.

   Physics

   Calculate the potential energy of a 50 kg object at a height of 43 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Chemistry

   How many moles are present in 176 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

   Formula:Number of Moles

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

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6. 6.

   Mathematics

   If f(x) = 2x³ + 1x² + 6x, find f′(3).

   Formula:Derivative of a Polynomial

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

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7. 7.

   Mathematics

   In an arithmetic progression with first term 17 and common difference 1, find term number 17.

   Formula:AP nth Term

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

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8. 8.

   Physics

   A projectile is launched at 31 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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9. 9.

   Mathematics

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

   Formula:GP Sum of n Terms

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

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10. 10.

    Physics

    Find the kinetic energy of a 16 kg object moving at 16 m/s.

    Formula:Kinetic Energy

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

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11. 11.

    Chemistry

    How many moles are present in 88 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

    Formula:Number of Moles

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

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12. 12.

    Chemistry

    A solution is made by dissolving 24 g of solute in 162 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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13. 13.

    Mathematics

    If f(x) = 4x³ + 3x² + 1x, find f′(5).

    Formula:Derivative of a Polynomial

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

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14. 14.

    Physics

    Find the force required to accelerate a 50 kg mass at 11 m/s².

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

    $F = ma$

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15. 15.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)

    Formula:Combinations

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

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16. 16.

    Physics

    Find the momentum of a 18 kg body moving at 32 m/s.

    Formula:Linear Momentum

    $p = mv$

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17. 17.

    Chemistry

    Find the molarity of a solution containing 0.5 mol of solute in 2.5 L of solution.

    Formula:Molarity

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

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18. 18.

    Chemistry

    A solution is made by dissolving 34 g of solute in 168 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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19. 19.

    Mathematics

    Find term number 6 of a geometric progression with first term 1 and common ratio 3.

    Formula:GP nth Term

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

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20. 20.

    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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