IIT-JEE · Practice Sheet 25

1. 1.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 4.)

   Formula:Permutations

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

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2. 2.

   Mathematics

   Find the binomial coefficient C(6, 4) — the coefficient of x^4 in (1 + x)^6.

   Formula:Binomial Coefficient

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

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3. 3.

   Mathematics

   Find the slope of the line through (-1, -1) and (1, 4).

   Formula:Slope of a Line

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

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4. 4.

   Mathematics

   In an arithmetic progression with first term 3 and common difference 2, find term number 16.

   Formula:AP nth Term

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

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5. 5.

   Physics

   Find the density of an object with mass 195 g and volume 31 cm³.

   Formula:Density

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

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6. 6.

   Mathematics

   Find the slope of the line through (-4, 8) and (-5, -8).

   Formula:Slope of a Line

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

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7. 7.

   Physics

   An object starts at 14 m/s and accelerates at 9 m/s² for 3 s. Find its final velocity.

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

   $v = u + at$

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8. 8.

   Physics

   Find the voltage across a 18 Ω resistor carrying a current of 8 A.

   Formula:Ohm's Law

   $V = IR$

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9. 9.

   Physics

   Find the force required to accelerate a 17 kg mass at 12 m/s².

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

   $F = ma$

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10. 10.

    Mathematics

    Find the binomial coefficient C(8, 3) — the coefficient of x^3 in (1 + x)^8.

    Formula:Binomial Coefficient

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

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11. 11.

    Mathematics

    Evaluate log base 5 of 25.

    Formula:Logarithm Evaluation

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

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12. 12.

    Physics

    A force of 289 N acts on an area of 29 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    Physics

    A constant force of 183 N moves an object 45 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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14. 14.

    Physics

    A projectile is launched at 23 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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15. 15.

    Mathematics

    In an arithmetic progression with first term 15 and common difference 5, find term number 25.

    Formula:AP nth Term

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

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16. 16.

    Mathematics

    Evaluate log base 2 of 8.

    Formula:Logarithm Evaluation

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

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17. 17.

    Chemistry

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

    Formula:Molarity

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

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18. 18.

    Mathematics

    Find the sum of the first 20 terms of an AP with first term 3 and common difference 10.

    Formula:AP Sum of n Terms

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

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19. 19.

    Physics

    Find the voltage across a 29 Ω resistor carrying a current of 20 A.

    Formula:Ohm's Law

    $V = IR$

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20. 20.

    Chemistry

    16 mL of a 10 M solution is diluted to 263 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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