IIT-JEE · Practice Sheet 3

1. 1.

   Mathematics

   If f(x) = 3x³ + 6x² + 3x, find f′(2).

   Formula:Derivative of a Polynomial

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

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2. 2.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)

   Formula:Permutations

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

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3. 3.

   Physics

   Find the electrical power when 183 V drives a current of 3 A.

   Formula:Electrical Power

   $P = VI$

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4. 4.

   Mathematics

   In an arithmetic progression with first term 9 and common difference 2, find term number 27.

   Formula:AP nth Term

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

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5. 5.

   Physics

   If 532 J of work is done in 5 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 33 g and volume 25 cm³.

   Formula:Density

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

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7. 7.

   Physics

   An object starts at 19 m/s and accelerates at 4 m/s² for 12 s. Find its final velocity.

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

   $v = u + at$

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8. 8.

   Physics

   Find the kinetic energy of a 19 kg object moving at 11 m/s.

   Formula:Kinetic Energy

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

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9. 9.

   Physics

   Find the electrical power when 56 V drives a current of 1 A.

   Formula:Electrical Power

   $P = VI$

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10. 10.

    Physics

    A constant force of 119 N moves an object 12 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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11. 11.

    Physics

    Calculate the potential energy of a 48 kg object at a height of 14 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Mathematics

    For the quadratic 5x² − 2x − 3 = 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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13. 13.

    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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14. 14.

    Physics

    A body moving at 14 m/s accelerates at 3 m/s² for 6 s. Find the distance travelled.

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

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

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15. 15.

    Physics

    A projectile is launched at 24 m/s at 30° 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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16. 16.

    Mathematics

    Evaluate log base 10 of 1,000,000.

    Formula:Logarithm Evaluation

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

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17. 17.

    Mathematics

    Find the sum of the first 6 terms of an AP with first term 14 and common difference 5.

    Formula:AP Sum of n Terms

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

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18. 18.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 216 K in a 7 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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19. 19.

    Physics

    Calculate the potential energy of a 41 kg object at a height of 44 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Physics

    An object starts at 4 m/s and accelerates at 5 m/s² for 11 s. Find its final velocity.

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

    $v = u + at$

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