GATE · Practice Sheet 2

1. 1.

   Physics

   If 2,140 J of work is done in 34 s, find the power.

   Formula:Power

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

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2. 2.

   Physics

   Find the voltage across a 22 Ω resistor carrying a current of 10 A.

   Formula:Ohm's Law

   $V = IR$

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3. 3.

   Physics

   If 3,063 J of work is done in 44 s, find the power.

   Formula:Power

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

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4. 4.

   Mathematics

   Evaluate ∫ from 1 to 3 of 2x^2 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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5. 5.

   Mathematics

   Find the slope of the line through (1, -6) and (-5, 8).

   Formula:Slope of a Line

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

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6. 6.

   Physics

   Find the kinetic energy of a 9 kg object moving at 25 m/s.

   Formula:Kinetic Energy

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

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7. 7.

   Physics

   A body moving at 4 m/s accelerates at 6 m/s² for 7 s. Find the distance travelled.

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

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

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8. 8.

   Mathematics

   Find the distance between the points (4, 0) and (6, 1).

   Formula:Distance Between Two Points

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

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9. 9.

   Physics

   An object starts at 19 m/s and accelerates at 4 m/s² for 7 s. Find its final velocity.

   Formula:Equation of Motion (v = u + at)

   $v = u + at$

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10. 10.

    Physics

    Find the electrical power when 178 V drives a current of 20 A.

    Formula:Electrical Power

    $P = VI$

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11. 11.

    Mathematics

    If f(x) = 5x³ + 4x² + 4x, find f′(2).

    Formula:Derivative of a Polynomial

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

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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.

    Physics

    Find the voltage across a 20 Ω resistor carrying a current of 15 A.

    Formula:Ohm's Law

    $V = IR$

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14. 14.

    Physics

    A projectile is launched at 28 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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15. 15.

    Quantitative Aptitude

    A vehicle covers 267 km in 3 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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16. 16.

    Mathematics

    Find term number 7 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term

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

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17. 17.

    Physics

    A force of 205 N acts on an area of 40 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Mathematics

    Evaluate log base 2 of 4.

    Formula:Logarithm Evaluation

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

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19. 19.

    Physics

    Find the kinetic energy of a 17 kg object moving at 2 m/s.

    Formula:Kinetic Energy

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

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20. 20.

    Physics

    Find the force required to accelerate a 17 kg mass at 1 m/s².

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

    $F = ma$

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