IIT-JEE · Practice Sheet 36

1. 1.

   Mathematics

   Evaluate ∫ from 2 to 4 of 3x^3 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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2. 2.

   Physics

   A force of 724 N acts on an area of 38 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Mathematics

   In an arithmetic progression with first term 7 and common difference 3, find term number 6.

   Formula:AP nth Term

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

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4. 4.

   Physics

   Calculate the potential energy of a 44 kg object at a height of 38 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Physics

   Find the voltage across a 34 Ω resistor carrying a current of 14 A.

   Formula:Ohm's Law

   $V = IR$

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6. 6.

   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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7. 7.

   Mathematics

   Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.

   Formula:Binomial Coefficient

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

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8. 8.

   Physics

   Find the density of an object with mass 90 g and volume 32 cm³.

   Formula:Density

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

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9. 9.

   Mathematics

   Find the sum of the first 7 terms of a GP with first term 1 and common ratio 3.

   Formula:GP Sum of n Terms

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

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10. 10.

    Physics

    If 3,901 J of work is done in 24 s, find the power.

    Formula:Power

    $P = \dfrac{W}{t}$

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11. 11.

    Physics

    Find the electrical power when 134 V drives a current of 14 A.

    Formula:Electrical Power

    $P = VI$

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12. 12.

    Mathematics

    Find the distance between the points (1, -5) and (-3, 7).

    Formula:Distance Between Two Points

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

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13. 13.

    Chemistry

    Find the molarity of a solution containing 1.5 mol of solute in 4 L of solution.

    Formula:Molarity

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

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14. 14.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻4 mol/L.

    Formula:pH of a Solution

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

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15. 15.

    Chemistry

    Find the molarity of a solution containing 0.5 mol of solute in 4 L of solution.

    Formula:Molarity

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

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16. 16.

    Mathematics

    If f(x) = 5x³ + 3x² + 3x, find f′(5).

    Formula:Derivative of a Polynomial

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

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17. 17.

    Physics

    A force of 192 N acts on an area of 44 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Physics

    Find the density of an object with mass 45 g and volume 16 cm³.

    Formula:Density

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

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19. 19.

    Mathematics

    Evaluate log base 5 of 3,125.

    Formula:Logarithm Evaluation

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

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20. 20.

    Physics

    Find the kinetic energy of a 14 kg object moving at 8 m/s.

    Formula:Kinetic Energy

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

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