IIT-JEE · Practice Sheet 7

1. 1.

   Physics

   A body moving at 1 m/s accelerates at 3 m/s² for 2 s. Find the distance travelled.

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

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

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2. 2.

   Chemistry

   Find the pressure of 5 mol of an ideal gas at 303 K in a 16 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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3. 3.

   Physics

   Find the density of an object with mass 209 g and volume 21 cm³.

   Formula:Density

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

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4. 4.

   Chemistry

   How many moles are present in 540 g of glucose (C₆H₁₂O₆) (molar mass = 180 g/mol)?

   Formula:Number of Moles

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

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5. 5.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 3 and common ratio 2.

   Formula:GP Sum of n Terms

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

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6. 6.

   Mathematics

   Find the distance between the points (-7, -3) and (-6, -8).

   Formula:Distance Between Two Points

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

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7. 7.

   Chemistry

   A solution is made by dissolving 50 g of solute in 134 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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8. 8.

   Mathematics

   For the quadratic 3x² + 1x − 5 = 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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9. 9.

   Physics

   Find the voltage across a 12 Ω resistor carrying a current of 10 A.

   Formula:Ohm's Law

   $V = IR$

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10. 10.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 2 and common ratio 2.

    Formula:GP Sum of n Terms

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

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11. 11.

    Chemistry

    56 mL of a 1 M solution is diluted to 412 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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12. 12.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 3.)

    Formula:Permutations

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

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13. 13.

    Chemistry

    How many moles are present in 48 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

    Formula:Number of Moles

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

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14. 14.

    Chemistry

    14 mL of a 5 M solution is diluted to 99 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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15. 15.

    Physics

    Find the force required to accelerate a 28 kg mass at 17 m/s².

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

    $F = ma$

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16. 16.

    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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17. 17.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

    Formula:Probability (two dice)

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

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18. 18.

    Physics

    Find the density of an object with mass 193 g and volume 23 cm³.

    Formula:Density

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

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19. 19.

    Mathematics

    For the quadratic 4x² + 0x − 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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20. 20.

    Mathematics

    In an arithmetic progression with first term 9 and common difference 5, find term number 18.

    Formula:AP nth Term

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

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