GATE · Practice Sheet 47

1. 1.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 4.)

   Formula:Permutations

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

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2. 2.

   Mathematics

   If f(x) = 4x³ + 6x² + 6x, find f′(2).

   Formula:Derivative of a Polynomial

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

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3. 3.

   Quantitative Aptitude

   Find the HCF and LCM of 18 and 21.

   Formula:LCM & HCF

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

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4. 4.

   Mathematics

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

   Formula:GP nth Term

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

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5. 5.

   Physics

   An object starts at 1 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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6. 6.

   Physics

   Find the electrical power when 166 V drives a current of 12 A.

   Formula:Electrical Power

   $P = VI$

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7. 7.

   Physics

   A projectile is launched at 21 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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8. 8.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)

   Formula:Combinations

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

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9. 9.

   Quantitative Aptitude

   Find the HCF and LCM of 6 and 22.

   Formula:LCM & HCF

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

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10. 10.

    Physics

    An object starts at 1 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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11. 11.

    Quantitative Aptitude

    A vehicle covers 385 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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12. 12.

    Mathematics

    Find the distance between the points (-5, 8) and (7, 5).

    Formula:Distance Between Two Points

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

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13. 13.

    Mathematics

    Evaluate log base 5 of 15,625.

    Formula:Logarithm Evaluation

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

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14. 14.

    Mathematics

    Find the distance between the points (-4, 1) and (6, -1).

    Formula:Distance Between Two Points

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

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15. 15.

    Quantitative Aptitude

    What is 15% of 980?

    Formula:Percentage of a Number

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

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16. 16.

    Physics

    A body moving at 6 m/s accelerates at 6 m/s² for 3 s. Find the distance travelled.

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

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

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17. 17.

    Quantitative Aptitude

    What is 60% of 440?

    Formula:Percentage of a Number

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

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18. 18.

    Physics

    A constant force of 131 N moves an object 29 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)

    Formula:Combinations

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

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20. 20.

    Mathematics

    Find the sum of the first 13 terms of an AP with first term 6 and common difference 10.

    Formula:AP Sum of n Terms

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

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