IIT-JEE · Practice Sheet 38

1. 1.

   Chemistry

   Find the pH of a solution with [H⁺] = 1×10⁻5 mol/L.

   Formula:pH of a Solution

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

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2. 2.

   Physics

   Find the momentum of a 47 kg body moving at 32 m/s.

   Formula:Linear Momentum

   $p = mv$

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3. 3.

   Physics

   If 4,707 J of work is done in 48 s, find the power.

   Formula:Power

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

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4. 4.

   Mathematics

   Evaluate ∫ from 1 to 4 of 5x^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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5. 5.

   Physics

   A projectile is launched at 37 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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6. 6.

   Physics

   A force of 530 N acts on an area of 35 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Mathematics

   In an arithmetic progression with first term 19 and common difference 9, find term number 11.

   Formula:AP nth Term

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

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8. 8.

   Mathematics

   Find the sum of the first 15 terms of an AP with first term 6 and common difference 1.

   Formula:AP Sum of n Terms

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

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9. 9.

   Physics

   A body moving at 12 m/s accelerates at 4 m/s² for 9 s. Find the distance travelled.

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

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

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10. 10.

    Mathematics

    If f(x) = 5x³ + 5x² + 3x, find f′(4).

    Formula:Derivative of a Polynomial

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

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11. 11.

    Physics

    A body moving at 13 m/s accelerates at 4 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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12. 12.

    Physics

    A projectile is launched at 19 m/s at 60° 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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13. 13.

    Mathematics

    For the quadratic 4x² + 7x + 8 = 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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14. 14.

    Physics

    If 3,898 J of work is done in 38 s, find the power.

    Formula:Power

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

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15. 15.

    Chemistry

    Find the pressure of 1 mol of an ideal gas at 237 K in a 4 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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16. 16.

    Mathematics

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

    Formula:AP nth Term

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

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17. 17.

    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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18. 18.

    Physics

    Find the momentum of a 41 kg body moving at 24 m/s.

    Formula:Linear Momentum

    $p = mv$

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19. 19.

    Physics

    Calculate the potential energy of a 38 kg object at a height of 7 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Chemistry

    59 mL of a 2 M solution is diluted to 225 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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