GATE · Practice Sheet 22

1. 1.

   Quantitative Aptitude

   Find the simple interest on ₹2,000 at 4% per annum for 6 year(s).

   Formula:Simple Interest

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

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2. 2.

   Physics

   A constant force of 168 N moves an object 49 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   Mathematics

   Find the distance between the points (1, -1) and (8, -2).

   Formula:Distance Between Two Points

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

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4. 4.

   Physics

   Find the electrical power when 84 V drives a current of 8 A.

   Formula:Electrical Power

   $P = VI$

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5. 5.

   Mathematics

   Find the distance between the points (5, 0) and (-1, -2).

   Formula:Distance Between Two Points

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

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6. 6.

   Quantitative Aptitude

   Find the HCF and LCM of 13 and 35.

   Formula:LCM & HCF

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

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7. 7.

   Physics

   An object starts at 20 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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8. 8.

   Quantitative Aptitude

   A vehicle covers 330 km in 5 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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9. 9.

   Mathematics

   If f(x) = 5x³ + 4x² + 5x, find f′(2).

   Formula:Derivative of a Polynomial

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

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10. 10.

    Mathematics

    Find the distance between the points (-5, 4) and (8, -6).

    Formula:Distance Between Two Points

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

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11. 11.

    Physics

    A projectile is launched at 36 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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12. 12.

    Physics

    Find the electrical power when 225 V drives a current of 7 A.

    Formula:Electrical Power

    $P = VI$

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13. 13.

    Mathematics

    Evaluate log base 2 of 64.

    Formula:Logarithm Evaluation

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

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14. 14.

    Physics

    A projectile is launched at 23 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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15. 15.

    Mathematics

    Find the distance between the points (0, 2) and (7, 6).

    Formula:Distance Between Two Points

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

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16. 16.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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17. 17.

    Mathematics

    Find term number 3 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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18. 18.

    Physics

    If 2,328 J of work is done in 26 s, find the power.

    Formula:Power

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

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19. 19.

    Mathematics

    Evaluate log base 3 of 729.

    Formula:Logarithm Evaluation

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

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20. 20.

    Quantitative Aptitude

    A vehicle covers 720 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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