GATE · Practice Sheet 20

1. 1.

   Quantitative Aptitude

   Find the simple interest on ₹10,000 at 5% per annum for 1 year(s).

   Formula:Simple Interest

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

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2. 2.

   Physics

   A force of 609 N acts on an area of 44 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Mathematics

   Evaluate log base 2 of 8.

   Formula:Logarithm Evaluation

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

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4. 4.

   Quantitative Aptitude

   A vehicle covers 534 km in 6 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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5. 5.

   Mathematics

   Find term number 4 of a geometric progression with first term 4 and common ratio 2.

   Formula:GP nth Term

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

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6. 6.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 2.)

   Formula:Permutations

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

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7. 7.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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8. 8.

   Physics

   An object starts at 0 m/s and accelerates at 5 m/s² for 8 s. Find its final velocity.

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

   $v = u + at$

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9. 9.

   Physics

   A projectile is launched at 50 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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10. 10.

    Mathematics

    Find the sum of the first 24 terms of an AP with first term 13 and common difference 6.

    Formula:AP Sum of n Terms

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

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11. 11.

    Mathematics

    Find term number 5 of a geometric progression with first term 4 and common ratio 3.

    Formula:GP nth Term

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

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12. 12.

    Mathematics

    If f(x) = 2x³ + 5x² + 7x, find f′(1).

    Formula:Derivative of a Polynomial

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

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13. 13.

    Physics

    A force of 872 N acts on an area of 12 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Mathematics

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

    Formula:GP nth Term

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

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15. 15.

    Quantitative Aptitude

    A vehicle covers 210 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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16. 16.

    Mathematics

    Find the distance between the points (4, 2) and (1, -8).

    Formula:Distance Between Two Points

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

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17. 17.

    Mathematics

    Find the sum of the first 12 terms of an AP with first term 13 and common difference 3.

    Formula:AP Sum of n Terms

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

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18. 18.

    Physics

    Find the kinetic energy of a 17 kg object moving at 2 m/s.

    Formula:Kinetic Energy

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

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19. 19.

    Physics

    If 2,021 J of work is done in 3 s, find the power.

    Formula:Power

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

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20. 20.

    Physics

    Find the electrical power when 130 V drives a current of 13 A.

    Formula:Electrical Power

    $P = VI$

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