GATE · Practice Sheet 38

1. 1.

   Quantitative Aptitude

   A vehicle covers 175 km in 5 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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2. 2.

   Quantitative Aptitude

   Find the HCF and LCM of 17 and 31.

   Formula:LCM & HCF

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

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3. 3.

   Physics

   Find the electrical power when 105 V drives a current of 16 A.

   Formula:Electrical Power

   $P = VI$

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4. 4.

   Mathematics

   In an arithmetic progression with first term 7 and common difference 9, find term number 25.

   Formula:AP nth Term

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

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5. 5.

   Physics

   A constant force of 116 N moves an object 29 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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6. 6.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

   Formula:Permutations

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

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7. 7.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 3.)

   Formula:Combinations

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

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8. 8.

   Physics

   Find the force required to accelerate a 10 kg mass at 20 m/s².

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

   $F = ma$

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9. 9.

   Physics

   An object starts at 1 m/s and accelerates at 8 m/s² for 9 s. Find its final velocity.

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

   $v = u + at$

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10. 10.

    Physics

    Find the force required to accelerate a 15 kg mass at 12 m/s².

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

    $F = ma$

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11. 11.

    Quantitative Aptitude

    Find the HCF and LCM of 27 and 29.

    Formula:LCM & HCF

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

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12. 12.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)

    Formula:Combinations

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

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13. 13.

    Physics

    Find the kinetic energy of a 4 kg object moving at 3 m/s.

    Formula:Kinetic Energy

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

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14. 14.

    Quantitative Aptitude

    A vehicle covers 207 km in 3 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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15. 15.

    Quantitative Aptitude

    What is 50% of 1,080?

    Formula:Percentage of a Number

    $\text{Value} = \dfrac{P}{100}\times N$

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16. 16.

    Mathematics

    Find the slope of the line through (6, -6) and (7, 1).

    Formula:Slope of a Line

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

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17. 17.

    Quantitative Aptitude

    What is 40% of 280?

    Formula:Percentage of a Number

    $\text{Value} = \dfrac{P}{100}\times N$

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18. 18.

    Physics

    A projectile is launched at 20 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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19. 19.

    Physics

    Find the electrical power when 233 V drives a current of 17 A.

    Formula:Electrical Power

    $P = VI$

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20. 20.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 3.)

    Formula:Combinations

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

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