IIT-JEE · Practice Sheet 28

1. 1.

   Physics

   If 4,205 J of work is done in 50 s, find the power.

   Formula:Power

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

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2. 2.

   Chemistry

   84 mL of a 2 M solution is diluted to 260 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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3. 3.

   Mathematics

   If f(x) = 1x³ + 4x² + 9x, find f′(3).

   Formula:Derivative of a Polynomial

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

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4. 4.

   Chemistry

   94 mL of a 1 M solution is diluted to 182 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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5. 5.

   Physics

   Calculate the potential energy of a 12 kg object at a height of 38 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   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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7. 7.

   Physics

   A body moving at 0 m/s accelerates at 5 m/s² for 2 s. Find the distance travelled.

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

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

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8. 8.

   Chemistry

   A solution is made by dissolving 29 g of solute in 128 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.

   Mathematics

   For the quadratic 3x² − 2x + 7 = 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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10. 10.

    Mathematics

    Find term number 4 of a geometric progression with first term 3 and common ratio 3.

    Formula:GP nth Term

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

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11. 11.

    Mathematics

    Find the sum of the first 4 terms of a GP with first term 5 and common ratio 3.

    Formula:GP Sum of n Terms

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

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12. 12.

    Physics

    Find the momentum of a 40 kg body moving at 40 m/s.

    Formula:Linear Momentum

    $p = mv$

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13. 13.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 1 and common ratio 3.

    Formula:GP Sum of n Terms

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

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14. 14.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 3.)

    Formula:Combinations

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

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15. 15.

    Chemistry

    A solution is made by dissolving 6 g of solute in 179 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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16. 16.

    Mathematics

    Find the sum of the first 6 terms of an AP with first term 5 and common difference 5.

    Formula:AP Sum of n Terms

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

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17. 17.

    Mathematics

    In an arithmetic progression with first term 12 and common difference 6, find term number 28.

    Formula:AP nth Term

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

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18. 18.

    Mathematics

    Find term number 6 of a geometric progression with first term 5 and common ratio 2.

    Formula:GP nth Term

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

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19. 19.

    Physics

    Find the voltage across a 48 Ω resistor carrying a current of 8 A.

    Formula:Ohm's Law

    $V = IR$

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20. 20.

    Mathematics

    For the quadratic 1x² − 9x − 4 = 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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