IIT-JEE · Practice Sheet 45

1. 1.

   Physics

   A constant force of 66 N moves an object 41 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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2. 2.

   Mathematics

   Find the distance between the points (-5, 5) and (3, -4).

   Formula:Distance Between Two Points

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

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3. 3.

   Mathematics

   Find the slope of the line through (1, 2) and (-5, 8).

   Formula:Slope of a Line

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

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4. 4.

   Physics

   A projectile is launched at 16 m/s at 60° 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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5. 5.

   Physics

   A constant force of 144 N moves an object 19 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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6. 6.

   Mathematics

   Evaluate ∫ from 1 to 3 of 4x^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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7. 7.

   Mathematics

   Find the slope of the line through (5, -1) and (-5, 8).

   Formula:Slope of a Line

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

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8. 8.

   Physics

   Find the voltage across a 44 Ω resistor carrying a current of 2 A.

   Formula:Ohm's Law

   $V = IR$

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9. 9.

   Mathematics

   If f(x) = 4x³ + 6x² + 9x, find f′(1).

   Formula:Derivative of a Polynomial

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

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10. 10.

    Physics

    Find the force required to accelerate a 38 kg mass at 8 m/s².

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

    $F = ma$

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11. 11.

    Mathematics

    Find the sum of the first 14 terms of an AP with first term 18 and common difference 2.

    Formula:AP Sum of n Terms

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

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12. 12.

    Physics

    A constant force of 100 N moves an object 37 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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13. 13.

    Chemistry

    67 mL of a 2 M solution is diluted to 283 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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14. 14.

    Chemistry

    How many moles are present in 90 g of water (H₂O) (molar mass = 18 g/mol)?

    Formula:Number of Moles

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

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15. 15.

    Quantitative Aptitude

    A vehicle covers 520 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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16. 16.

    Mathematics

    Find the sum of the first 6 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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17. 17.

    Physics

    A force of 919 N acts on an area of 20 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Physics

    Find the voltage across a 3 Ω resistor carrying a current of 8 A.

    Formula:Ohm's Law

    $V = IR$

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19. 19.

    Mathematics

    Find term number 5 of a geometric progression with first term 3 and common ratio 3.

    Formula:GP nth Term

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

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20. 20.

    Physics

    Find the voltage across a 50 Ω resistor carrying a current of 8 A.

    Formula:Ohm's Law

    $V = IR$

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