IIT-JEE · Practice Sheet 50

1. 1.

   Physics

   Find the voltage across a 39 Ω resistor carrying a current of 12 A.

   Formula:Ohm's Law

   $V = IR$

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2. 2.

   Chemistry

   How many moles are present in 234 g of sodium chloride (NaCl) (molar mass = 58.5 g/mol)?

   Formula:Number of Moles

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

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3. 3.

   Mathematics

   Evaluate ∫ from 0 to 5 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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4. 4.

   Mathematics

   Find term number 7 of a geometric progression with first term 5 and common ratio 3.

   Formula:GP nth Term

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

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5. 5.

   Quantitative Aptitude

   A vehicle covers 648 km in 9 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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6. 6.

   Mathematics

   If f(x) = 4x³ + 6x² + 1x, find f′(4).

   Formula:Derivative of a Polynomial

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

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7. 7.

   Physics

   A projectile is launched at 41 m/s at 30° 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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8. 8.

   Chemistry

   How many moles are present in 200 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

   Formula:Number of Moles

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

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9. 9.

   Physics

   Find the momentum of a 16 kg body moving at 21 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Physics

    A force of 668 N acts on an area of 9 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Physics

    Find the electrical power when 198 V drives a current of 1 A.

    Formula:Electrical Power

    $P = VI$

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12. 12.

    Chemistry

    A solution is made by dissolving 45 g of solute in 65 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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13. 13.

    Mathematics

    Find the distance between the points (-6, 4) and (-4, 3).

    Formula:Distance Between Two Points

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

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14. 14.

    Chemistry

    A solution is made by dissolving 6 g of solute in 155 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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15. 15.

    Chemistry

    40 mL of a 5 M solution is diluted to 180 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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16. 16.

    Physics

    Calculate the potential energy of a 10 kg object at a height of 29 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Physics

    A projectile is launched at 17 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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18. 18.

    Mathematics

    If f(x) = 2x³ + 5x² + 2x, find f′(1).

    Formula:Derivative of a Polynomial

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

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19. 19.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 372 K in a 6 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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20. 20.

    Chemistry

    Find the pH of a solution with [H⁺] = 1×10⁻2 mol/L.

    Formula:pH of a Solution

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

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