GATE · Practice Sheet 13

1. 1.

   Physics

   Find the force required to accelerate a 33 kg mass at 15 m/s².

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

   $F = ma$

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2. 2.

   Mathematics

   Find term number 6 of a geometric progression with first term 1 and common ratio 3.

   Formula:GP nth Term

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

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3. 3.

   Mathematics

   In an arithmetic progression with first term 2 and common difference 4, find term number 5.

   Formula:AP nth Term

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

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4. 4.

   Mathematics

   Find the sum of the first 15 terms of an AP with first term 1 and common difference 8.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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5. 5.

   Physics

   A projectile is launched at 40 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.

   Physics

   A body moving at 0 m/s accelerates at 7 m/s² for 9 s. Find the distance travelled.

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

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

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7. 7.

   Physics

   A projectile is launched at 23 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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8. 8.

   Physics

   An object starts at 9 m/s and accelerates at 4 m/s² for 9 s. Find its final velocity.

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

   $v = u + at$

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9. 9.

   Quantitative Aptitude

   A vehicle covers 245 km in 7 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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10. 10.

    Mathematics

    Find the distance between the points (0, -8) and (-3, -8).

    Formula:Distance Between Two Points

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

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11. 11.

    Mathematics

    Find term number 6 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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12. 12.

    Physics

    If 3,053 J of work is done in 21 s, find the power.

    Formula:Power

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

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13. 13.

    Physics

    Find the voltage across a 5 Ω resistor carrying a current of 20 A.

    Formula:Ohm's Law

    $V = IR$

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14. 14.

    Quantitative Aptitude

    What is 10% of 500?

    Formula:Percentage of a Number

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

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15. 15.

    Physics

    Find the voltage across a 29 Ω resistor carrying a current of 9 A.

    Formula:Ohm's Law

    $V = IR$

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16. 16.

    Quantitative Aptitude

    Find the simple interest on ₹20,000 at 5% per annum for 2 year(s).

    Formula:Simple Interest

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

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17. 17.

    Physics

    Find the kinetic energy of a 19 kg object moving at 10 m/s.

    Formula:Kinetic Energy

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

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18. 18.

    Physics

    If 4,049 J of work is done in 5 s, find the power.

    Formula:Power

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

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19. 19.

    Mathematics

    Find the slope of the line through (6, -5) and (3, 0).

    Formula:Slope of a Line

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

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20. 20.

    Mathematics

    Find the sum of the first 24 terms of an AP with first term 8 and common difference 8.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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