GATE · Practice Sheet 15

1. 1.

   Quantitative Aptitude

   A vehicle covers 112 km in 2 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 37 and 28.

   Formula:LCM & HCF

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

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3. 3.

   Quantitative Aptitude

   Find the simple interest on ₹11,000 at 6% per annum for 1 year(s).

   Formula:Simple Interest

   $SI = \dfrac{P\times R\times T}{100}$

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4. 4.

   Physics

   An object starts at 16 m/s and accelerates at 10 m/s² for 5 s. Find its final velocity.

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

   $v = u + at$

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5. 5.

   Mathematics

   Find the distance between the points (-6, 4) and (2, 2).

   Formula:Distance Between Two Points

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

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6. 6.

   Physics

   A projectile is launched at 14 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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7. 7.

   Quantitative Aptitude

   Find the HCF and LCM of 38 and 22.

   Formula:LCM & HCF

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

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8. 8.

   Physics

   If 312 J of work is done in 31 s, find the power.

   Formula:Power

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

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9. 9.

   Physics

   An object starts at 3 m/s and accelerates at 8 m/s² for 6 s. Find its final velocity.

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

   $v = u + at$

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10. 10.

    Physics

    If 287 J of work is done in 49 s, find the power.

    Formula:Power

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

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11. 11.

    Mathematics

    If f(x) = 2x³ + 1x² + 7x, find f′(3).

    Formula:Derivative of a Polynomial

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

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12. 12.

    Physics

    A constant force of 48 N moves an object 30 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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13. 13.

    Physics

    A projectile is launched at 38 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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14. 14.

    Physics

    An object starts at 6 m/s and accelerates at 7 m/s² for 5 s. Find its final velocity.

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

    $v = u + at$

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15. 15.

    Mathematics

    Find the slope of the line through (1, -1) and (-6, -2).

    Formula:Slope of a Line

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

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16. 16.

    Mathematics

    Find the distance between the points (4, 8) and (3, -6).

    Formula:Distance Between Two Points

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

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17. 17.

    Physics

    A force of 569 N acts on an area of 35 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Physics

    An object starts at 9 m/s and accelerates at 10 m/s² for 2 s. Find its final velocity.

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

    $v = u + at$

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19. 19.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 2.)

    Formula:Permutations

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

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20. 20.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 4.)

    Formula:Combinations

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

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