GATE · Practice Sheet 23

1. 1.

   Physics

   Find the kinetic energy of a 19 kg object moving at 27 m/s.

   Formula:Kinetic Energy

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

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2. 2.

   Mathematics

   Find the slope of the line through (2, -1) and (1, 6).

   Formula:Slope of a Line

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

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3. 3.

   Physics

   Find the voltage across a 22 Ω resistor carrying a current of 2 A.

   Formula:Ohm's Law

   $V = IR$

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4. 4.

   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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5. 5.

   Mathematics

   Find the distance between the points (-7, -6) and (-5, 3).

   Formula:Distance Between Two Points

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

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6. 6.

   Mathematics

   Find the slope of the line through (-4, 1) and (-6, 0).

   Formula:Slope of a Line

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

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7. 7.

   Mathematics

   Find the sum of the first 11 terms of an AP with first term 1 and common difference 5.

   Formula:AP Sum of n Terms

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

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8. 8.

   Physics

   A body moving at 11 m/s accelerates at 6 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.

   Mathematics

   For the quadratic 5x² − 1x − 3 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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10. 10.

    Quantitative Aptitude

    A vehicle covers 488 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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11. 11.

    Physics

    A constant force of 66 N moves an object 18 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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12. 12.

    Physics

    If 3,827 J of work is done in 17 s, find the power.

    Formula:Power

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

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13. 13.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)

    Formula:Permutations

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

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14. 14.

    Physics

    Find the force required to accelerate a 31 kg mass at 10 m/s².

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

    $F = ma$

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15. 15.

    Mathematics

    If f(x) = 4x³ + 5x² + 9x, find f′(5).

    Formula:Derivative of a Polynomial

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

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16. 16.

    Mathematics

    For the quadratic 3x² + 5x − 1 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

    $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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17. 17.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 4.)

    Formula:Combinations

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

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18. 18.

    Quantitative Aptitude

    Find the HCF and LCM of 12 and 29.

    Formula:LCM & HCF

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

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19. 19.

    Mathematics

    Evaluate log base 10 of 1,000,000.

    Formula:Logarithm Evaluation

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

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20. 20.

    Physics

    A constant force of 89 N moves an object 17 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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