IIT-JEE · Practice Sheet 12

1. 1.

   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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2. 2.

   Mathematics

   Evaluate log base 5 of 25.

   Formula:Logarithm Evaluation

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

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3. 3.

   Physics

   A projectile is launched at 27 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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4. 4.

   Physics

   Find the voltage across a 46 Ω resistor carrying a current of 6 A.

   Formula:Ohm's Law

   $V = IR$

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5. 5.

   Mathematics

   Find term number 7 of a geometric progression with first term 6 and common ratio 2.

   Formula:GP nth Term

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

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6. 6.

   Physics

   A constant force of 197 N moves an object 41 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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7. 7.

   Chemistry

   Find the pH of a solution with [H⁺] = 1×10⁻6 mol/L.

   Formula:pH of a Solution

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

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8. 8.

   Mathematics

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

   Formula:GP Sum of n Terms

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

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9. 9.

   Chemistry

   Find the pressure of 4 mol of an ideal gas at 282 K in a 12 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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10. 10.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

    Formula:Permutations

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

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11. 11.

    Physics

    If 2,860 J of work is done in 31 s, find the power.

    Formula:Power

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

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12. 12.

    Physics

    An object starts at 4 m/s and accelerates at 3 m/s² for 4 s. Find its final velocity.

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

    $v = u + at$

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13. 13.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 3.)

    Formula:Permutations

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

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14. 14.

    Chemistry

    How many moles are present in 16 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

    Formula:Number of Moles

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

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15. 15.

    Mathematics

    In an arithmetic progression with first term 11 and common difference 9, find term number 29.

    Formula:AP nth Term

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

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16. 16.

    Physics

    Calculate the potential energy of a 32 kg object at a height of 35 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Chemistry

    A solution is made by dissolving 14 g of solute in 162 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.

    Physics

    A projectile is launched at 25 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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19. 19.

    Mathematics

    Evaluate log base 5 of 25.

    Formula:Logarithm Evaluation

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

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20. 20.

    Physics

    Find the force required to accelerate a 36 kg mass at 5 m/s².

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

    $F = ma$

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