IIT-JEE · Practice Sheet 5

1. 1.

   Mathematics

   Find the distance between the points (-8, -3) and (6, 4).

   Formula:Distance Between Two Points

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

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2. 2.

   Physics

   A body moving at 11 m/s accelerates at 4 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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3. 3.

   Mathematics

   Evaluate ∫ from 2 to 4 of 1x^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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4. 4.

   Physics

   Find the voltage across a 42 Ω resistor carrying a current of 11 A.

   Formula:Ohm's Law

   $V = IR$

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5. 5.

   Chemistry

   20 mL of a 5 M solution is diluted to 102 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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6. 6.

   Physics

   Find the density of an object with mass 388 g and volume 43 cm³.

   Formula:Density

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

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7. 7.

   Quantitative Aptitude

   A vehicle covers 72 km in 2 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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8. 8.

   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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9. 9.

   Mathematics

   If f(x) = 1x³ + 1x² + 6x, find f′(1).

   Formula:Derivative of a Polynomial

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

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10. 10.

    Quantitative Aptitude

    A vehicle covers 504 km in 9 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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11. 11.

    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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12. 12.

    Chemistry

    Find the pH of a solution with [H⁺] = 5×10⁻3 mol/L.

    Formula:pH of a Solution

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

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13. 13.

    Physics

    Find the force required to accelerate a 43 kg mass at 12 m/s².

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

    $F = ma$

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14. 14.

    Quantitative Aptitude

    A vehicle covers 328 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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15. 15.

    Physics

    Find the electrical power when 126 V drives a current of 4 A.

    Formula:Electrical Power

    $P = VI$

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16. 16.

    Physics

    Find the momentum of a 35 kg body moving at 21 m/s.

    Formula:Linear Momentum

    $p = mv$

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17. 17.

    Physics

    A projectile is launched at 18 m/s at 45° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

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18. 18.

    Mathematics

    If f(x) = 5x³ + 2x² + 2x, find f′(2).

    Formula:Derivative of a Polynomial

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

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19. 19.

    Physics

    Find the force required to accelerate a 5 kg mass at 2 m/s².

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

    $F = ma$

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20. 20.

    Chemistry

    Find the pH of a solution with [H⁺] = 2×10⁻6 mol/L.

    Formula:pH of a Solution

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

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