IIT-JEE · Practice Sheet 14

1. 1.

   Chemistry

   A solution is made by dissolving 39 g of solute in 130 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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2. 2.

   Physics

   If 4,917 J of work is done in 16 s, find the power.

   Formula:Power

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

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3. 3.

   Physics

   Find the density of an object with mass 152 g and volume 12 cm³.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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4. 4.

   Physics

   Calculate the potential energy of a 10 kg object at a height of 6 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 4.)

   Formula:Permutations

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

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6. 6.

   Physics

   Find the kinetic energy of a 19 kg object moving at 7 m/s.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2}mv^{2}$

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7. 7.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)

   Formula:Combinations

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

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8. 8.

   Mathematics

   Evaluate ∫ from 2 to 3 of 1x^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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9. 9.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 5 and common ratio 2.

   Formula:GP Sum of n Terms

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

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10. 10.

    Mathematics

    In an arithmetic progression with first term 10 and common difference 6, find term number 19.

    Formula:AP nth Term

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

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11. 11.

    Chemistry

    97 mL of a 5 M solution is diluted to 405 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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12. 12.

    Mathematics

    Evaluate ∫ from 2 to 5 of 5x^2 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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13. 13.

    Mathematics

    Find the distance between the points (-1, 4) and (-7, -6).

    Formula:Distance Between Two Points

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

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14. 14.

    Physics

    Calculate the potential energy of a 32 kg object at a height of 6 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Mathematics

    Evaluate ∫ from 1 to 3 of 2x^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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16. 16.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 385 K in a 16 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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17. 17.

    Physics

    Calculate the potential energy of a 36 kg object at a height of 17 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Chemistry

    How many moles are present in 66 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

    Formula:Number of Moles

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

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19. 19.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 9?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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20. 20.

    Physics

    Find the voltage across a 24 Ω resistor carrying a current of 7 A.

    Formula:Ohm's Law

    $V = IR$

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