IIT-JEE · Practice Sheet 6

1. 1.

   Physics

   Find the momentum of a 21 kg body moving at 9 m/s.

   Formula:Linear Momentum

   $p = mv$

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2. 2.

   Physics

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

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

   $v = u + at$

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3. 3.

   Mathematics

   Find the sum of the first 23 terms of an AP with first term 17 and common difference 9.

   Formula:AP Sum of n Terms

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

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4. 4.

   Quantitative Aptitude

   A vehicle covers 511 km in 7 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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5. 5.

   Chemistry

   Find the pressure of 2 mol of an ideal gas at 365 K in a 17 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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6. 6.

   Chemistry

   Find the pH of a solution with [H⁺] = 5×10⁻4 mol/L.

   Formula:pH of a Solution

   $pH = -\log_{10}[H^{+}]$

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7. 7.

   Chemistry

   A solution is made by dissolving 33 g of solute in 172 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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8. 8.

   Chemistry

   63 mL of a 2 M solution is diluted to 390 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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9. 9.

   Mathematics

   In an arithmetic progression with first term 8 and common difference 10, find term number 19.

   Formula:AP nth Term

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

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10. 10.

    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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11. 11.

    Physics

    Calculate the potential energy of a 23 kg object at a height of 5 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Mathematics

    Find the sum of the first 3 terms of a GP with first term 2 and common ratio 2.

    Formula:GP Sum of n Terms

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

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13. 13.

    Physics

    A body moving at 6 m/s accelerates at 5 m/s² for 3 s. Find the distance travelled.

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

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

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14. 14.

    Mathematics

    Evaluate ∫ from 2 to 4 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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15. 15.

    Mathematics

    Find the distance between the points (5, -6) and (4, -2).

    Formula:Distance Between Two Points

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

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16. 16.

    Physics

    Find the voltage across a 50 Ω resistor carrying a current of 16 A.

    Formula:Ohm's Law

    $V = IR$

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17. 17.

    Physics

    A body moving at 14 m/s accelerates at 5 m/s² for 3 s. Find the distance travelled.

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

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

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18. 18.

    Mathematics

    Find term number 6 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term

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

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19. 19.

    Mathematics

    In an arithmetic progression with first term 13 and common difference 7, find term number 28.

    Formula:AP nth Term

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

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20. 20.

    Chemistry

    A solution is made by dissolving 28 g of solute in 168 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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