IIT-JEE · Practice Sheet 10

1. 1.

   Physics

   Find the force required to accelerate a 49 kg mass at 19 m/s².

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

   $F = ma$

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2. 2.

   Chemistry

   Find the molarity of a solution containing 1 mol of solute in 4 L of solution.

   Formula:Molarity

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

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3. 3.

   Physics

   A body moving at 12 m/s accelerates at 4 m/s² for 9 s. Find the distance travelled.

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

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

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4. 4.

   Physics

   An object starts at 11 m/s and accelerates at 8 m/s² for 3 s. Find its final velocity.

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

   $v = u + at$

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5. 5.

   Mathematics

   Find the sum of the first 3 terms of a GP with first term 1 and common ratio 3.

   Formula:GP Sum of n Terms

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

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6. 6.

   Physics

   Calculate the potential energy of a 7 kg object at a height of 16 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Physics

   A projectile is launched at 33 m/s at 45° 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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8. 8.

   Physics

   Find the density of an object with mass 81 g and volume 39 cm³.

   Formula:Density

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

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9. 9.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

   Formula:Probability (two dice)

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

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10. 10.

    Physics

    An object starts at 7 m/s and accelerates at 6 m/s² for 10 s. Find its final velocity.

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

    $v = u + at$

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11. 11.

    Physics

    A body moving at 6 m/s accelerates at 1 m/s² for 10 s. Find the distance travelled.

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

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

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12. 12.

    Physics

    Find the voltage across a 23 Ω resistor carrying a current of 8 A.

    Formula:Ohm's Law

    $V = IR$

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13. 13.

    Mathematics

    Evaluate log base 10 of 100,000.

    Formula:Logarithm Evaluation

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

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14. 14.

    Chemistry

    77 mL of a 1 M solution is diluted to 352 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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15. 15.

    Mathematics

    For the quadratic 4x² − 3x − 4 = 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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16. 16.

    Mathematics

    Evaluate log base 3 of 81.

    Formula:Logarithm Evaluation

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

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17. 17.

    Quantitative Aptitude

    A vehicle covers 462 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.

    Physics

    A force of 182 N acts on an area of 38 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Physics

    Find the voltage across a 40 Ω resistor carrying a current of 2 A.

    Formula:Ohm's Law

    $V = IR$

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20. 20.

    Physics

    Find the kinetic energy of a 15 kg object moving at 30 m/s.

    Formula:Kinetic Energy

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

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