GATE · Practice Sheet 46

1. 1.

   Physics

   Find the voltage across a 37 Ω resistor carrying a current of 17 A.

   Formula:Ohm's Law

   $V = IR$

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2. 2.

   Mathematics

   Evaluate ∫ from 2 to 5 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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3. 3.

   Mathematics

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

   Formula:Slope of a Line

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

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4. 4.

   Physics

   A constant force of 121 N moves an object 13 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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5. 5.

   Physics

   A projectile is launched at 13 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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6. 6.

   Mathematics

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

   Formula:Distance Between Two Points

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

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7. 7.

   Mathematics

   For the quadratic 3x² + 2x + 0 = 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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8. 8.

   Mathematics

   In an arithmetic progression with first term 4 and common difference 10, find term number 24.

   Formula:AP nth Term

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

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9. 9.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 2.)

   Formula:Combinations

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

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10. 10.

    Physics

    A projectile is launched at 37 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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11. 11.

    Mathematics

    Find the distance between the points (-5, -2) and (-1, -2).

    Formula:Distance Between Two Points

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

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12. 12.

    Physics

    A body moving at 0 m/s accelerates at 3 m/s² for 8 s. Find the distance travelled.

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

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

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13. 13.

    Physics

    Find the force required to accelerate a 24 kg mass at 11 m/s².

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

    $F = ma$

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14. 14.

    Quantitative Aptitude

    A vehicle covers 136 km in 4 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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15. 15.

    Physics

    A force of 468 N acts on an area of 15 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Physics

    A projectile is launched at 25 m/s at 30° 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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17. 17.

    Mathematics

    For the quadratic 1x² + 0x + 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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18. 18.

    Physics

    Find the force required to accelerate a 43 kg mass at 10 m/s².

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

    $F = ma$

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19. 19.

    Physics

    A projectile is launched at 23 m/s at 30° 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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20. 20.

    Physics

    A force of 585 N acts on an area of 49 m². Find the pressure.

    Formula:Pressure

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

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