IIT-JEE · Practice Sheet 2

1. 1.

   Physics

   Find the voltage across a 26 Ω resistor carrying a current of 12 A.

   Formula:Ohm's Law

   $V = IR$

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2. 2.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)

   Formula:Permutations

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

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3. 3.

   Mathematics

   Find the slope of the line through (-7, -3) and (4, 8).

   Formula:Slope of a Line

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

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4. 4.

   Physics

   Find the momentum of a 42 kg body moving at 16 m/s.

   Formula:Linear Momentum

   $p = mv$

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5. 5.

   Physics

   If 1,943 J of work is done in 43 s, find the power.

   Formula:Power

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

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6. 6.

   Physics

   Find the density of an object with mass 58 g and volume 44 cm³.

   Formula:Density

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

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7. 7.

   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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8. 8.

   Physics

   A body moving at 4 m/s accelerates at 7 m/s² for 5 s. Find the distance travelled.

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

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

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9. 9.

   Physics

   An object starts at 16 m/s and accelerates at 2 m/s² for 2 s. Find its final velocity.

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

   $v = u + at$

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10. 10.

    Chemistry

    A solution is made by dissolving 41 g of solute in 95 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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11. 11.

    Mathematics

    For the quadratic 3x² − 5x + 1 = 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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12. 12.

    Mathematics

    Evaluate log base 5 of 3,125.

    Formula:Logarithm Evaluation

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

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13. 13.

    Physics

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

    Formula:Kinetic Energy

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

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14. 14.

    Physics

    Calculate the potential energy of a 43 kg object at a height of 5 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Physics

    A force of 100 N acts on an area of 26 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Mathematics

    Evaluate ∫ from 0 to 4 of 2x^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⁺] = 5×10⁻5 mol/L.

    Formula:pH of a Solution

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

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18. 18.

    Mathematics

    Evaluate ∫ from 0 to 5 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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19. 19.

    Physics

    Find the electrical power when 28 V drives a current of 3 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    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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