GATE · Practice Sheet 7

1. 1.

   Mathematics

   Evaluate log base 5 of 625.

   Formula:Logarithm Evaluation

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

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2. 2.

   Physics

   A body moving at 2 m/s accelerates at 2 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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3. 3.

   Physics

   Find the force required to accelerate a 42 kg mass at 9 m/s².

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

   $F = ma$

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4. 4.

   Physics

   A projectile is launched at 33 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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5. 5.

   Physics

   A constant force of 14 N moves an object 36 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

   Find the HCF and LCM of 22 and 24.

   Formula:LCM & HCF

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

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7. 7.

   Physics

   A force of 270 N acts on an area of 43 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Physics

   Find the kinetic energy of a 10 kg object moving at 4 m/s.

   Formula:Kinetic Energy

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

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9. 9.

   Mathematics

   Find the slope of the line through (-8, -7) and (5, 3).

   Formula:Slope of a Line

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

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10. 10.

    Quantitative Aptitude

    Find the simple interest on ₹43,000 at 12% per annum for 3 year(s).

    Formula:Simple Interest

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

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11. 11.

    Mathematics

    Find term number 4 of a geometric progression with first term 6 and common ratio 3.

    Formula:GP nth Term

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

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12. 12.

    Quantitative Aptitude

    A vehicle covers 414 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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13. 13.

    Quantitative Aptitude

    What is 25% of 980?

    Formula:Percentage of a Number

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

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14. 14.

    Mathematics

    Find the distance between the points (6, 7) and (6, -6).

    Formula:Distance Between Two Points

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

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15. 15.

    Mathematics

    In an arithmetic progression with first term 9 and common difference 7, find term number 30.

    Formula:AP nth Term

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

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16. 16.

    Physics

    A constant force of 119 N moves an object 50 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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17. 17.

    Physics

    Find the force required to accelerate a 24 kg mass at 16 m/s².

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

    $F = ma$

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18. 18.

    Mathematics

    Find the slope of the line through (2, 7) and (-1, 5).

    Formula:Slope of a Line

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

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19. 19.

    Physics

    A body moving at 14 m/s accelerates at 8 m/s² for 10 s. Find the distance travelled.

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

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

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20. 20.

    Quantitative Aptitude

    What is 40% of 300?

    Formula:Percentage of a Number

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

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