IIT-JEE · Practice Sheet 4

1. 1.

   Mathematics

   Evaluate log base 2 of 8.

   Formula:Logarithm Evaluation

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

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2. 2.

   Physics

   Find the momentum of a 10 kg body moving at 6 m/s.

   Formula:Linear Momentum

   $p = mv$

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3. 3.

   Chemistry

   How many moles are present in 110 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

   Formula:Number of Moles

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

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4. 4.

   Mathematics

   Find the slope of the line through (-4, -7) and (2, -2).

   Formula:Slope of a Line

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

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5. 5.

   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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6. 6.

   Physics

   A constant force of 125 N moves an object 30 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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7. 7.

   Mathematics

   For the quadratic 1x² − 1x + 0 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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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

   How many moles are present in 720 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

   Formula:Number of Moles

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

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10. 10.

    Mathematics

    Find the distance between the points (-8, -6) and (-6, 8).

    Formula:Distance Between Two Points

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

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11. 11.

    Mathematics

    Find the slope of the line through (7, -2) and (-2, 3).

    Formula:Slope of a Line

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

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12. 12.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

    Formula:Probability (two dice)

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

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13. 13.

    Physics

    Find the kinetic energy of a 4 kg object moving at 3 m/s.

    Formula:Kinetic Energy

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

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14. 14.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)

    Formula:Combinations

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

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15. 15.

    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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16. 16.

    Mathematics

    Evaluate ∫ from 1 to 4 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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17. 17.

    Chemistry

    Find the pH of a solution with [H⁺] = 2×10⁻3 mol/L.

    Formula:pH of a Solution

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

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18. 18.

    Mathematics

    If f(x) = 4x³ + 3x² + 5x, find f′(3).

    Formula:Derivative of a Polynomial

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

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19. 19.

    Mathematics

    Evaluate log base 5 of 3,125.

    Formula:Logarithm Evaluation

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

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20. 20.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 4.)

    Formula:Combinations

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

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