IIT-JEE · Practice Sheet 44

1. 1.

   Chemistry

   Find the pH of a solution with [H⁺] = 1×10⁻3 mol/L.

   Formula:pH of a Solution

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

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2. 2.

   Physics

   Find the force required to accelerate a 2 kg mass at 20 m/s².

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

   $F = ma$

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3. 3.

   Physics

   An object starts at 17 m/s and accelerates at 2 m/s² for 4 s. Find its final velocity.

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

   $v = u + at$

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4. 4.

   Mathematics

   Find term number 7 of a geometric progression with first term 2 and common ratio 3.

   Formula:GP nth Term

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

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5. 5.

   Mathematics

   Evaluate ∫ from 0 to 3 of 4x^1 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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6. 6.

   Chemistry

   A solution is made by dissolving 37 g of solute in 63 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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7. 7.

   Mathematics

   Find the sum of the first 5 terms of an AP with first term 9 and common difference 7.

   Formula:AP Sum of n Terms

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

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8. 8.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

   Formula:Probability (two dice)

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

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9. 9.

   Chemistry

   How many moles are present in 300 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

   Formula:Number of Moles

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

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10. 10.

    Mathematics

    Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.

    Formula:Binomial Coefficient

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

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11. 11.

    Mathematics

    Find the sum of the first 19 terms of an AP with first term 20 and common difference 3.

    Formula:AP Sum of n Terms

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

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12. 12.

    Physics

    Find the voltage across a 22 Ω resistor carrying a current of 17 A.

    Formula:Ohm's Law

    $V = IR$

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13. 13.

    Mathematics

    For the quadratic 2x² − 9x + 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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14. 14.

    Mathematics

    Find term number 7 of a geometric progression with first term 3 and common ratio 2.

    Formula:GP nth Term

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

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15. 15.

    Physics

    Find the momentum of a 18 kg body moving at 14 m/s.

    Formula:Linear Momentum

    $p = mv$

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16. 16.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

    Formula:Probability (two dice)

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

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17. 17.

    Mathematics

    Find the distance between the points (-6, 3) and (-2, -7).

    Formula:Distance Between Two Points

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

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18. 18.

    Mathematics

    Find the slope of the line through (-6, 3) and (5, 2).

    Formula:Slope of a Line

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

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19. 19.

    Physics

    Find the voltage across a 12 Ω resistor carrying a current of 5 A.

    Formula:Ohm's Law

    $V = IR$

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20. 20.

    Mathematics

    Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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