IIT-JEE · Practice Sheet 37

1. 1.

   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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2. 2.

   Physics

   Find the electrical power when 198 V drives a current of 14 A.

   Formula:Electrical Power

   $P = VI$

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3. 3.

   Physics

   Find the kinetic energy of a 16 kg object moving at 27 m/s.

   Formula:Kinetic Energy

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

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4. 4.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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5. 5.

   Physics

   Find the momentum of a 34 kg body moving at 26 m/s.

   Formula:Linear Momentum

   $p = mv$

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6. 6.

   Physics

   Find the voltage across a 26 Ω resistor carrying a current of 18 A.

   Formula:Ohm's Law

   $V = IR$

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7. 7.

   Chemistry

   80 mL of a 1 M solution is diluted to 203 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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8. 8.

   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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9. 9.

   Quantitative Aptitude

   A vehicle covers 192 km in 3 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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10. 10.

    Physics

    Calculate the potential energy of a 38 kg object at a height of 18 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Mathematics

    Find the binomial coefficient C(8, 3) — the coefficient of x^3 in (1 + x)^8.

    Formula:Binomial Coefficient

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

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12. 12.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 2.)

    Formula:Combinations

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

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13. 13.

    Chemistry

    Find the molarity of a solution containing 1 mol of solute in 2.5 L of solution.

    Formula:Molarity

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

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14. 14.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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15. 15.

    Physics

    Find the voltage across a 13 Ω resistor carrying a current of 8 A.

    Formula:Ohm's Law

    $V = IR$

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16. 16.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 4.)

    Formula:Permutations

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

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17. 17.

    Mathematics

    Evaluate ∫ from 2 to 3 of 4x^1 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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18. 18.

    Physics

    Find the electrical power when 230 V drives a current of 5 A.

    Formula:Electrical Power

    $P = VI$

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19. 19.

    Physics

    If 3,568 J of work is done in 29 s, find the power.

    Formula:Power

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

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20. 20.

    Physics

    A projectile is launched at 34 m/s at 30° 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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