GATE · Practice Sheet 26

1. 1.

   Physics

   A body moving at 15 m/s accelerates at 8 m/s² for 5 s. Find the distance travelled.

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

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

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2. 2.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 2.)

   Formula:Permutations

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

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3. 3.

   Physics

   A constant force of 72 N moves an object 27 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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4. 4.

   Quantitative Aptitude

   Find the HCF and LCM of 12 and 12.

   Formula:LCM & HCF

   $\text{LCM}\times\text{HCF} = a\times b$

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5. 5.

   Physics

   Find the electrical power when 26 V drives a current of 10 A.

   Formula:Electrical Power

   $P = VI$

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6. 6.

   Physics

   Find the force required to accelerate a 23 kg mass at 4 m/s².

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

   $F = ma$

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7. 7.

   Mathematics

   If f(x) = 1x³ + 3x² + 1x, find f′(3).

   Formula:Derivative of a Polynomial

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

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8. 8.

   Mathematics

   Evaluate log base 10 of 100.

   Formula:Logarithm Evaluation

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

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9. 9.

   Physics

   Find the voltage across a 9 Ω resistor carrying a current of 18 A.

   Formula:Ohm's Law

   $V = IR$

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10. 10.

    Physics

    A constant force of 67 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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11. 11.

    Physics

    Find the kinetic energy of a 20 kg object moving at 24 m/s.

    Formula:Kinetic Energy

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

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12. 12.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)

    Formula:Permutations

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

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13. 13.

    Mathematics

    Evaluate log base 3 of 9.

    Formula:Logarithm Evaluation

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

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14. 14.

    Physics

    A body moving at 12 m/s accelerates at 3 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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15. 15.

    Mathematics

    If f(x) = 4x³ + 1x² + 8x, find f′(2).

    Formula:Derivative of a Polynomial

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

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16. 16.

    Physics

    A force of 214 N acts on an area of 41 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Mathematics

    Evaluate ∫ from 2 to 5 of 4x^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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18. 18.

    Physics

    If 3,521 J of work is done in 21 s, find the power.

    Formula:Power

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

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19. 19.

    Quantitative Aptitude

    A vehicle covers 264 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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20. 20.

    Physics

    A constant force of 77 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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