IIT-JEE · Practice Sheet 16

1. 1.

   Mathematics

   Find the distance between the points (3, -7) and (-7, -1).

   Formula:Distance Between Two Points

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

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2. 2.

   Mathematics

   Find the slope of the line through (-2, 4) and (-7, -3).

   Formula:Slope of a Line

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

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3. 3.

   Physics

   Find the density of an object with mass 78 g and volume 20 cm³.

   Formula:Density

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

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4. 4.

   Physics

   A constant force of 167 N moves an object 49 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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5. 5.

   Physics

   Calculate the potential energy of a 39 kg object at a height of 4 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   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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7. 7.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

   Formula:Probability (two dice)

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

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8. 8.

   Physics

   Find the voltage across a 26 Ω resistor carrying a current of 15 A.

   Formula:Ohm's Law

   $V = IR$

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9. 9.

   Chemistry

   73 mL of a 2 M solution is diluted to 152 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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10. 10.

    Physics

    A force of 767 N acts on an area of 26 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Mathematics

    For the quadratic 3x² + 6x + 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

    Find the sum of the first 13 terms of an AP with first term 5 and common difference 5.

    Formula:AP Sum of n Terms

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

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13. 13.

    Physics

    A constant force of 62 N moves an object 10 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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14. 14.

    Chemistry

    A solution is made by dissolving 13 g of solute in 59 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

    Find the pressure of 5 mol of an ideal gas at 319 K in a 19 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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16. 16.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)

    Formula:Permutations

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

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17. 17.

    Physics

    If 2,086 J of work is done in 34 s, find the power.

    Formula:Power

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

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18. 18.

    Mathematics

    Find term number 6 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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19. 19.

    Physics

    If 4,862 J of work is done in 35 s, find the power.

    Formula:Power

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

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20. 20.

    Mathematics

    Evaluate ∫ from 2 to 3 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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