GATE · Practice Sheet 31

1. 1.

   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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2. 2.

   Physics

   Find the kinetic energy of a 17 kg object moving at 27 m/s.

   Formula:Kinetic Energy

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

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3. 3.

   Physics

   Find the force required to accelerate a 21 kg mass at 16 m/s².

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

   $F = ma$

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4. 4.

   Quantitative Aptitude

   A vehicle covers 92 km in 2 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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5. 5.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 2.)

   Formula:Combinations

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

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6. 6.

   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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7. 7.

   Mathematics

   Evaluate ∫ from 1 to 4 of 5x^3 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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8. 8.

   Physics

   A body moving at 9 m/s accelerates at 3 m/s² for 2 s. Find the distance travelled.

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

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

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9. 9.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 2.)

   Formula:Combinations

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

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10. 10.

    Mathematics

    If f(x) = 3x³ + 1x² + 4x, find f′(5).

    Formula:Derivative of a Polynomial

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

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11. 11.

    Mathematics

    Find term number 3 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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12. 12.

    Quantitative Aptitude

    A vehicle covers 335 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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13. 13.

    Physics

    Find the electrical power when 24 V drives a current of 14 A.

    Formula:Electrical Power

    $P = VI$

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14. 14.

    Quantitative Aptitude

    Find the HCF and LCM of 7 and 6.

    Formula:LCM & HCF

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

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15. 15.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)

    Formula:Combinations

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

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16. 16.

    Quantitative Aptitude

    Find the HCF and LCM of 23 and 32.

    Formula:LCM & HCF

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

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17. 17.

    Mathematics

    In an arithmetic progression with first term 11 and common difference 9, find term number 7.

    Formula:AP nth Term

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

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18. 18.

    Quantitative Aptitude

    Find the simple interest on ₹18,000 at 12% per annum for 4 year(s).

    Formula:Simple Interest

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

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19. 19.

    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation

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

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20. 20.

    Mathematics

    Find the slope of the line through (-1, -6) and (-5, -1).

    Formula:Slope of a Line

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

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