IIT-JEE · Practice Sheet 33

1. 1.

   Physics

   Find the electrical power when 133 V drives a current of 9 A.

   Formula:Electrical Power

   $P = VI$

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2. 2.

   Chemistry

   Find the pressure of 4 mol of an ideal gas at 242 K in a 3 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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3. 3.

   Mathematics

   If f(x) = 3x³ + 4x² + 1x, find f′(3).

   Formula:Derivative of a Polynomial

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

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4. 4.

   Mathematics

   Evaluate log base 2 of 64.

   Formula:Logarithm Evaluation

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

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5. 5.

   Mathematics

   Find term number 5 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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6. 6.

   Mathematics

   Find the slope of the line through (5, 1) and (-1, 6).

   Formula:Slope of a Line

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

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7. 7.

   Chemistry

   How many moles are present in 150 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

   Formula:Number of Moles

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

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8. 8.

   Physics

   Find the electrical power when 192 V drives a current of 12 A.

   Formula:Electrical Power

   $P = VI$

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9. 9.

   Physics

   Find the momentum of a 27 kg body moving at 22 m/s.

   Formula:Linear Momentum

   $p = mv$

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10. 10.

    Mathematics

    Evaluate log base 10 of 100.

    Formula:Logarithm Evaluation

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

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11. 11.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

    Formula:Permutations

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

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12. 12.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)

    Formula:Combinations

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

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13. 13.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

    Formula:Probability (two dice)

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

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14. 14.

    Chemistry

    How many moles are present in 50 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

    Formula:Number of Moles

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

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15. 15.

    Physics

    A force of 207 N acts on an area of 43 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Mathematics

    Find the sum of the first 7 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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17. 17.

    Chemistry

    Find the pressure of 2 mol of an ideal gas at 333 K in a 4 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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18. 18.

    Chemistry

    40 mL of a 5 M solution is diluted to 147 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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19. 19.

    Physics

    Find the momentum of a 29 kg body moving at 20 m/s.

    Formula:Linear Momentum

    $p = mv$

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20. 20.

    Physics

    Find the voltage across a 41 Ω resistor carrying a current of 3 A.

    Formula:Ohm's Law

    $V = IR$

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