IIT-JEE · Practice Sheet 31

1. 1.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)

   Formula:Combinations

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

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2. 2.

   Physics

   A force of 75 N acts on an area of 17 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Physics

   Find the voltage across a 13 Ω resistor carrying a current of 15 A.

   Formula:Ohm's Law

   $V = IR$

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4. 4.

   Physics

   Find the density of an object with mass 202 g and volume 31 cm³.

   Formula:Density

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

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5. 5.

   Physics

   A body moving at 15 m/s accelerates at 8 m/s² for 10 s. Find the distance travelled.

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

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

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6. 6.

   Physics

   Find the force required to accelerate a 28 kg mass at 19 m/s².

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

   $F = ma$

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7. 7.

   Physics

   A projectile is launched at 34 m/s at 45° 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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8. 8.

   Physics

   A force of 732 N acts on an area of 36 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Physics

   An object starts at 20 m/s and accelerates at 5 m/s² for 10 s. Find its final velocity.

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

   $v = u + at$

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10. 10.

    Chemistry

    100 mL of a 2 M solution is diluted to 461 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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11. 11.

    Mathematics

    If f(x) = 1x³ + 6x² + 4x, find f′(4).

    Formula:Derivative of a Polynomial

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

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12. 12.

    Chemistry

    A solution is made by dissolving 21 g of solute in 69 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.

    Physics

    Find the force required to accelerate a 19 kg mass at 8 m/s².

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

    $F = ma$

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14. 14.

    Mathematics

    Find the binomial coefficient C(6, 4) — the coefficient of x^4 in (1 + x)^6.

    Formula:Binomial Coefficient

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

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15. 15.

    Mathematics

    Find the sum of the first 12 terms of an AP with first term 8 and common difference 4.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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16. 16.

    Mathematics

    Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.

    Formula:Binomial Coefficient

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

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17. 17.

    Mathematics

    If f(x) = 5x³ + 1x² + 7x, find f′(2).

    Formula:Derivative of a Polynomial

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

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18. 18.

    Mathematics

    Evaluate ∫ from 0 to 4 of 3x^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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19. 19.

    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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20. 20.

    Physics

    An object starts at 19 m/s and accelerates at 7 m/s² for 3 s. Find its final velocity.

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

    $v = u + at$

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