IIT-JEE · Practice Sheet 46

1. 1.

   Mathematics

   Find term number 6 of a geometric progression with first term 6 and common ratio 2.

   Formula:GP nth Term

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

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2. 2.

   Physics

   Find the electrical power when 21 V drives a current of 18 A.

   Formula:Electrical Power

   $P = VI$

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3. 3.

   Mathematics

   Find the distance between the points (-1, -7) and (-6, -3).

   Formula:Distance Between Two Points

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

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4. 4.

   Physics

   Find the force required to accelerate a 38 kg mass at 10 m/s².

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

   $F = ma$

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5. 5.

   Mathematics

   Evaluate log base 3 of 9.

   Formula:Logarithm Evaluation

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

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6. 6.

   Mathematics

   Find the distance between the points (3, -7) and (-5, 1).

   Formula:Distance Between Two Points

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

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7. 7.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)

   Formula:Permutations

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

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8. 8.

   Quantitative Aptitude

   A vehicle covers 528 km in 8 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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9. 9.

   Mathematics

   Find the binomial coefficient C(5, 4) — the coefficient of x^4 in (1 + x)^5.

   Formula:Binomial Coefficient

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

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10. 10.

    Physics

    A constant force of 166 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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11. 11.

    Physics

    An object starts at 18 m/s and accelerates at 2 m/s² for 12 s. Find its final velocity.

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

    $v = u + at$

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12. 12.

    Physics

    Calculate the potential energy of a 32 kg object at a height of 20 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Mathematics

    Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.

    Formula:Binomial Coefficient

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

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14. 14.

    Chemistry

    A solution is made by dissolving 30 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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15. 15.

    Physics

    Find the electrical power when 61 V drives a current of 15 A.

    Formula:Electrical Power

    $P = VI$

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16. 16.

    Physics

    Find the momentum of a 27 kg body moving at 20 m/s.

    Formula:Linear Momentum

    $p = mv$

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17. 17.

    Physics

    A projectile is launched at 47 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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18. 18.

    Physics

    Find the momentum of a 36 kg body moving at 26 m/s.

    Formula:Linear Momentum

    $p = mv$

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19. 19.

    Physics

    Find the kinetic energy of a 1 kg object moving at 8 m/s.

    Formula:Kinetic Energy

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

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20. 20.

    Physics

    Calculate the potential energy of a 11 kg object at a height of 15 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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