IIT-JEE · Practice Sheet 42

1. 1.

   Chemistry

   11 mL of a 1 M solution is diluted to 141 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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2. 2.

   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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3. 3.

   Physics

   A body moving at 10 m/s accelerates at 3 m/s² for 6 s. Find the distance travelled.

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

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

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4. 4.

   Mathematics

   Find term number 7 of a geometric progression with first term 4 and common ratio 3.

   Formula:GP nth Term

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

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5. 5.

   Chemistry

   54 mL of a 5 M solution is diluted to 239 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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6. 6.

   Mathematics

   Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.

   Formula:Binomial Coefficient

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

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7. 7.

   Mathematics

   Find the distance between the points (-1, -4) and (-8, -5).

   Formula:Distance Between Two Points

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

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8. 8.

   Mathematics

   If f(x) = 2x³ + 6x² + 9x, find f′(4).

   Formula:Derivative of a Polynomial

   $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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9. 9.

   Mathematics

   For the quadratic 3x² − 7x − 7 = 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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10. 10.

    Chemistry

    How many moles are present in 22 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

    Formula:Number of Moles

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

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11. 11.

    Mathematics

    Find the binomial coefficient C(5, 3) — the coefficient of x^3 in (1 + x)^5.

    Formula:Binomial Coefficient

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

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12. 12.

    Physics

    Calculate the potential energy of a 19 kg object at a height of 27 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Physics

    A constant force of 60 N moves an object 47 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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14. 14.

    Chemistry

    92 mL of a 10 M solution is diluted to 179 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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15. 15.

    Physics

    Find the kinetic energy of a 12 kg object moving at 26 m/s.

    Formula:Kinetic Energy

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

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16. 16.

    Physics

    Find the momentum of a 30 kg body moving at 22 m/s.

    Formula:Linear Momentum

    $p = mv$

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17. 17.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 5 and common ratio 2.

    Formula:GP Sum of n Terms

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

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18. 18.

    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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19. 19.

    Mathematics

    Find the sum of the first 11 terms of an AP with first term 12 and common difference 8.

    Formula:AP Sum of n Terms

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

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20. 20.

    Physics

    A force of 544 N acts on an area of 8 m². Find the pressure.

    Formula:Pressure

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

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