IIT-JEE · Practice Sheet 49

1. 1.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 4.)

   Formula:Combinations

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

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2. 2.

   Quantitative Aptitude

   A vehicle covers 336 km in 8 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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3. 3.

   Chemistry

   A solution is made by dissolving 16 g of solute in 140 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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4. 4.

   Mathematics

   If f(x) = 1x³ + 6x² + 7x, find f′(3).

   Formula:Derivative of a Polynomial

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

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5. 5.

   Physics

   An object starts at 10 m/s and accelerates at 6 m/s² for 5 s. Find its final velocity.

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

   $v = u + at$

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6. 6.

   Mathematics

   Find the slope of the line through (1, 0) and (2, 5).

   Formula:Slope of a Line

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

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7. 7.

   Mathematics

   For the quadratic 5x² − 1x − 6 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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8. 8.

   Chemistry

   A solution is made by dissolving 41 g of solute in 97 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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9. 9.

   Physics

   If 2,545 J of work is done in 25 s, find the power.

   Formula:Power

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

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10. 10.

    Physics

    A constant force of 157 N moves an object 23 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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11. 11.

    Physics

    An object starts at 2 m/s and accelerates at 6 m/s² for 10 s. Find its final velocity.

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

    $v = u + at$

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12. 12.

    Physics

    Find the force required to accelerate a 16 kg mass at 2 m/s².

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

    $F = ma$

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13. 13.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 5 and common ratio 2.

    Formula:GP Sum of n Terms

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

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14. 14.

    Physics

    Find the force required to accelerate a 43 kg mass at 8 m/s².

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

    $F = ma$

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15. 15.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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16. 16.

    Chemistry

    Find the pressure of 2 mol of an ideal gas at 308 K in a 14 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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17. 17.

    Chemistry

    A solution is made by dissolving 14 g of solute in 122 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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18. 18.

    Mathematics

    Find the slope of the line through (3, 0) and (-4, -2).

    Formula:Slope of a Line

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

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19. 19.

    Physics

    If 893 J of work is done in 9 s, find the power.

    Formula:Power

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

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20. 20.

    Mathematics

    Find the distance between the points (3, -6) and (-5, -7).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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