GATE · Practice Sheet 34

1. 1.

   Mathematics

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

   Formula:Slope of a Line

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

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2. 2.

   Physics

   A force of 689 N acts on an area of 49 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Quantitative Aptitude

   Find the HCF and LCM of 20 and 6.

   Formula:LCM & HCF

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

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4. 4.

   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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5. 5.

   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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6. 6.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

   Formula:Permutations

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

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7. 7.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)

   Formula:Combinations

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

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8. 8.

   Physics

   Find the electrical power when 150 V drives a current of 16 A.

   Formula:Electrical Power

   $P = VI$

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9. 9.

   Mathematics

   Evaluate ∫ from 0 to 4 of 2x^2 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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10. 10.

    Physics

    An object starts at 4 m/s and accelerates at 3 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.

    Physics

    If 4,545 J of work is done in 2 s, find the power.

    Formula:Power

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

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12. 12.

    Physics

    A force of 793 N acts on an area of 9 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    Mathematics

    Find the distance between the points (-4, -6) and (-6, 8).

    Formula:Distance Between Two Points

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

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14. 14.

    Physics

    An object starts at 16 m/s and accelerates at 3 m/s² for 8 s. Find its final velocity.

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

    $v = u + at$

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15. 15.

    Mathematics

    Find the distance between the points (6, 4) and (-3, -4).

    Formula:Distance Between Two Points

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

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16. 16.

    Quantitative Aptitude

    Find the HCF and LCM of 39 and 25.

    Formula:LCM & HCF

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

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17. 17.

    Mathematics

    Find the distance between the points (6, 8) and (-6, 4).

    Formula:Distance Between Two Points

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

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18. 18.

    Quantitative Aptitude

    A vehicle covers 364 km in 7 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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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.

    Quantitative Aptitude

    Find the HCF and LCM of 24 and 31.

    Formula:LCM & HCF

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

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