IIT-JEE · Practice Sheet 1

1. 1.

   Mathematics

   Find the distance between the points (5, 8) and (4, 5).

   Formula:Distance Between Two Points

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

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2. 2.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 2.)

   Formula:Permutations

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

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3. 3.

   Mathematics

   Find term number 6 of a geometric progression with first term 1 and common ratio 2.

   Formula:GP nth Term

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

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4. 4.

   Mathematics

   Find the sum of the first 12 terms of an AP with first term 17 and common difference 3.

   Formula:AP Sum of n Terms

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

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5. 5.

   Chemistry

   How many moles are present in 22 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

   Formula:Number of Moles

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

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6. 6.

   Chemistry

   Find the molarity of a solution containing 3 mol of solute in 2 L of solution.

   Formula:Molarity

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

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7. 7.

   Mathematics

   Find the sum of the first 5 terms of an AP with first term 14 and common difference 5.

   Formula:AP Sum of n Terms

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

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8. 8.

   Chemistry

   A solution is made by dissolving 5 g of solute in 150 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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9. 9.

   Mathematics

   Evaluate ∫ from 2 to 5 of 4x^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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10. 10.

    Mathematics

    In an arithmetic progression with first term 4 and common difference 2, find term number 18.

    Formula:AP nth Term

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

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11. 11.

    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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12. 12.

    Chemistry

    Find the pressure of 2 mol of an ideal gas at 375 K in a 17 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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13. 13.

    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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14. 14.

    Physics

    Calculate the potential energy of a 37 kg object at a height of 20 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Physics

    Find the kinetic energy of a 3 kg object moving at 2 m/s.

    Formula:Kinetic Energy

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

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16. 16.

    Quantitative Aptitude

    A vehicle covers 264 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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17. 17.

    Mathematics

    In an arithmetic progression with first term 17 and common difference 8, find term number 14.

    Formula:AP nth Term

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

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18. 18.

    Mathematics

    Find the slope of the line through (-2, 2) and (-1, 8).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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19. 19.

    Physics

    Find the force required to accelerate a 32 kg mass at 8 m/s².

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

    $F = ma$

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20. 20.

    Mathematics

    Find term number 3 of a geometric progression with first term 1 and common ratio 3.

    Formula:GP nth Term

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

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