IIT-JEE · Practice Sheet 39

1. 1.

   Mathematics

   Find the slope of the line through (-4, 7) and (6, -2).

   Formula:Slope of a Line

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

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2. 2.

   Physics

   A projectile is launched at 30 m/s at 60° to the horizontal. Find its range (g = 9.8 m/s²).

   Formula:Projectile Range

   $R = \dfrac{u^{2}\sin 2\theta}{g}$

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3. 3.

   Physics

   Find the voltage across a 27 Ω resistor carrying a current of 15 A.

   Formula:Ohm's Law

   $V = IR$

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4. 4.

   Physics

   Calculate the potential energy of a 18 kg object at a height of 47 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Chemistry

   A solution is made by dissolving 16 g of solute in 170 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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6. 6.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 3.)

   Formula:Combinations

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

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7. 7.

   Chemistry

   Find the molarity of a solution containing 2 mol of solute in 4 L of solution.

   Formula:Molarity

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

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8. 8.

   Quantitative Aptitude

   A vehicle covers 198 km in 3 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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9. 9.

   Physics

   Find the density of an object with mass 169 g and volume 44 cm³.

   Formula:Density

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

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10. 10.

    Physics

    An object starts at 1 m/s and accelerates at 2 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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11. 11.

    Mathematics

    For the quadratic 5x² + 6x − 7 = 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.

    Physics

    An object starts at 19 m/s and accelerates at 4 m/s² for 6 s. Find its final velocity.

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

    $v = u + at$

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13. 13.

    Mathematics

    Evaluate ∫ from 2 to 4 of 3x^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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14. 14.

    Physics

    Find the voltage across a 23 Ω resistor carrying a current of 19 A.

    Formula:Ohm's Law

    $V = IR$

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15. 15.

    Mathematics

    Find the sum of the first 22 terms of an AP with first term 2 and common difference 8.

    Formula:AP Sum of n Terms

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

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16. 16.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 3 and common ratio 2.

    Formula:GP Sum of n Terms

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

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17. 17.

    Quantitative Aptitude

    A vehicle covers 480 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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18. 18.

    Mathematics

    Evaluate log base 3 of 243.

    Formula:Logarithm Evaluation

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

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19. 19.

    Mathematics

    In an arithmetic progression with first term 2 and common difference 6, find term number 10.

    Formula:AP nth Term

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

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20. 20.

    Physics

    If 4,514 J of work is done in 48 s, find the power.

    Formula:Power

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

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