GATE · Practice Sheet 14

1. 1.

   Mathematics

   Find the slope of the line through (-6, -2) and (7, -1).

   Formula:Slope of a Line

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

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2. 2.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 3.)

   Formula:Permutations

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

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3. 3.

   Physics

   A body moving at 0 m/s accelerates at 1 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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4. 4.

   Mathematics

   Find term number 3 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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5. 5.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 2.)

   Formula:Combinations

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

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6. 6.

   Physics

   Find the force required to accelerate a 37 kg mass at 12 m/s².

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

   $F = ma$

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7. 7.

   Mathematics

   If f(x) = 2x³ + 3x² + 5x, find f′(4).

   Formula:Derivative of a Polynomial

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

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8. 8.

   Mathematics

   Find term number 3 of a geometric progression with first term 1 and common ratio 2.

   Formula:GP nth Term

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

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9. 9.

   Mathematics

   In an arithmetic progression with first term 3 and common difference 3, find term number 17.

   Formula:AP nth Term

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

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10. 10.

    Physics

    Find the electrical power when 39 V drives a current of 1 A.

    Formula:Electrical Power

    $P = VI$

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11. 11.

    Physics

    Find the kinetic energy of a 13 kg object moving at 10 m/s.

    Formula:Kinetic Energy

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

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12. 12.

    Physics

    Find the force required to accelerate a 26 kg mass at 19 m/s².

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

    $F = ma$

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13. 13.

    Quantitative Aptitude

    A vehicle covers 210 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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14. 14.

    Physics

    Find the voltage across a 27 Ω resistor carrying a current of 13 A.

    Formula:Ohm's Law

    $V = IR$

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15. 15.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)

    Formula:Combinations

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

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16. 16.

    Mathematics

    Find the distance between the points (7, 1) and (5, 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 term number 3 of a geometric progression with first term 2 and common ratio 2.

    Formula:GP nth Term

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

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18. 18.

    Mathematics

    If f(x) = 5x³ + 3x² + 2x, find f′(4).

    Formula:Derivative of a Polynomial

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

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19. 19.

    Mathematics

    Find term number 6 of a geometric progression with first term 2 and common ratio 2.

    Formula:GP nth Term

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

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20. 20.

    Mathematics

    For the quadratic 1x² + 9x + 4 = 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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