IIT-JEE · Practice Sheet 27

1. 1.

   Mathematics

   If f(x) = 2x³ + 6x² + 8x, find f′(4).

   Formula:Derivative of a Polynomial

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

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2. 2.

   Mathematics

   Find the sum of the first 24 terms of an AP with first term 11 and common difference 1.

   Formula:AP Sum of n Terms

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

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3. 3.

   Mathematics

   Evaluate log base 2 of 16.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

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4. 4.

   Mathematics

   Find the sum of the first 7 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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5. 5.

   Physics

   Find the force required to accelerate a 10 kg mass at 12 m/s².

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

   $F = ma$

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6. 6.

   Physics

   Find the density of an object with mass 152 g and volume 40 cm³.

   Formula:Density

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

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7. 7.

   Physics

   Calculate the potential energy of a 13 kg object at a height of 44 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Chemistry

   89 mL of a 5 M solution is diluted to 339 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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9. 9.

   Chemistry

   How many moles are present in 220 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

   Formula:Number of Moles

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

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10. 10.

    Chemistry

    Find the molarity of a solution containing 3 mol of solute in 0.5 L of solution.

    Formula:Molarity

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

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11. 11.

    Physics

    Find the kinetic energy of a 10 kg object moving at 24 m/s.

    Formula:Kinetic Energy

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

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12. 12.

    Mathematics

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

    Formula:Slope of a Line

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

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13. 13.

    Physics

    Find the momentum of a 44 kg body moving at 29 m/s.

    Formula:Linear Momentum

    $p = mv$

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14. 14.

    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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15. 15.

    Mathematics

    For the quadratic 2x² − 4x + 0 = 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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16. 16.

    Mathematics

    Find the sum of the first 12 terms of an AP with first term 16 and common difference 2.

    Formula:AP Sum of n Terms

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

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17. 17.

    Quantitative Aptitude

    A vehicle covers 118 km in 2 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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18. 18.

    Physics

    A constant force of 91 N moves an object 50 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Mathematics

    Evaluate log base 3 of 81.

    Formula:Logarithm Evaluation

    $\log_{b}(b^{k}) = k$

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20. 20.

    Chemistry

    86 mL of a 1 M solution is diluted to 431 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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