IIT-JEE · Practice Sheet 41

1. 1.

   Chemistry

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

   Formula:pH of a Solution

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

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2. 2.

   Mathematics

   In an arithmetic progression with first term 2 and common difference 7, find term number 28.

   Formula:AP nth Term

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

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3. 3.

   Physics

   A force of 600 N acts on an area of 43 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Physics

   Find the force required to accelerate a 13 kg mass at 4 m/s².

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

   $F = ma$

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5. 5.

   Physics

   A projectile is launched at 14 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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6. 6.

   Physics

   A body moving at 10 m/s accelerates at 6 m/s² for 7 s. Find the distance travelled.

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

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

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7. 7.

   Physics

   Find the electrical power when 104 V drives a current of 7 A.

   Formula:Electrical Power

   $P = VI$

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8. 8.

   Mathematics

   Find term number 3 of a geometric progression with first term 2 and common ratio 3.

   Formula:GP nth Term

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

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9. 9.

   Chemistry

   89 mL of a 5 M solution is diluted to 148 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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10. 10.

    Mathematics

    Evaluate log base 5 of 125.

    Formula:Logarithm Evaluation

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

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11. 11.

    Physics

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

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Chemistry

    How many moles are present in 900 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

    Formula:Number of Moles

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

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13. 13.

    Physics

    An object starts at 3 m/s and accelerates at 8 m/s² for 8 s. Find its final velocity.

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

    $v = u + at$

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14. 14.

    Chemistry

    How many moles are present in 64 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

    Formula:Number of Moles

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

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15. 15.

    Physics

    If 2,300 J of work is done in 26 s, find the power.

    Formula:Power

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

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16. 16.

    Physics

    A force of 233 N acts on an area of 45 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Mathematics

    Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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18. 18.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)

    Formula:Permutations

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

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19. 19.

    Chemistry

    Find the molarity of a solution containing 2.5 mol of solute in 4 L of solution.

    Formula:Molarity

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

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20. 20.

    Physics

    Find the voltage across a 4 Ω resistor carrying a current of 5 A.

    Formula:Ohm's Law

    $V = IR$

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