IIT-JEE · Practice Sheet 8

1. 1.

   Mathematics

   Find term number 7 of a geometric progression with first term 5 and common ratio 2.

   Formula:GP nth Term

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

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2. 2.

   Chemistry

   49 mL of a 10 M solution is diluted to 228 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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3. 3.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)

   Formula:Combinations

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

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4. 4.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

   Formula:Probability (two dice)

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

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5. 5.

   Chemistry

   Find the pH of a solution with [H⁺] = 5×10⁻6 mol/L.

   Formula:pH of a Solution

   $pH = -\log_{10}[H^{+}]$

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6. 6.

   Physics

   Find the force required to accelerate a 44 kg mass at 19 m/s².

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

   $F = ma$

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7. 7.

   Physics

   A constant force of 25 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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8. 8.

   Chemistry

   Find the pH of a solution with [H⁺] = 5×10⁻3 mol/L.

   Formula:pH of a Solution

   $pH = -\log_{10}[H^{+}]$

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9. 9.

   Physics

   Calculate the potential energy of a 50 kg object at a height of 44 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Physics

    Find the electrical power when 131 V drives a current of 16 A.

    Formula:Electrical Power

    $P = VI$

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11. 11.

    Mathematics

    Evaluate log base 5 of 125.

    Formula:Logarithm Evaluation

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

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12. 12.

    Physics

    Find the density of an object with mass 23 g and volume 25 cm³.

    Formula:Density

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

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13. 13.

    Mathematics

    Find the distance between the points (-2, -3) and (-2, 4).

    Formula:Distance Between Two Points

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

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14. 14.

    Chemistry

    How many moles are present in 64 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

    Formula:Number of Moles

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

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15. 15.

    Mathematics

    Find the binomial coefficient C(6, 2) — the coefficient of x^2 in (1 + x)^6.

    Formula:Binomial Coefficient

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

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16. 16.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 9?

    Formula:Probability (two dice)

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

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17. 17.

    Physics

    An object starts at 10 m/s and accelerates at 10 m/s² for 9 s. Find its final velocity.

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

    $v = u + at$

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18. 18.

    Chemistry

    Find the molarity of a solution containing 2.5 mol of solute in 2 L of solution.

    Formula:Molarity

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

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19. 19.

    Physics

    An object starts at 16 m/s and accelerates at 1 m/s² for 8 s. Find its final velocity.

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

    $v = u + at$

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20. 20.

    Mathematics

    Evaluate ∫ from 1 to 5 of 2x^2 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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