GATE · Practice Sheet 36

1. 1.

   Quantitative Aptitude

   Find the HCF and LCM of 6 and 12.

   Formula:LCM & HCF

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

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2. 2.

   Physics

   An object starts at 5 m/s and accelerates at 1 m/s² for 12 s. Find its final velocity.

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

   $v = u + at$

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3. 3.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 4.)

   Formula:Combinations

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

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4. 4.

   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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5. 5.

   Mathematics

   Evaluate log base 3 of 729.

   Formula:Logarithm Evaluation

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

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6. 6.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)

   Formula:Combinations

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

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7. 7.

   Physics

   A force of 767 N acts on an area of 35 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Mathematics

   For the quadratic 3x² − 6x − 8 = 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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9. 9.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 2.)

   Formula:Combinations

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

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10. 10.

    Physics

    A constant force of 15 N moves an object 35 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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11. 11.

    Physics

    A body moving at 3 m/s accelerates at 1 m/s² for 5 s. Find the distance travelled.

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

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

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12. 12.

    Physics

    A force of 268 N acts on an area of 37 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    Mathematics

    Find the distance between the points (-5, -1) and (-3, 6).

    Formula:Distance Between Two Points

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

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14. 14.

    Physics

    A constant force of 187 N moves an object 42 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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15. 15.

    Physics

    Find the force required to accelerate a 2 kg mass at 6 m/s².

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

    $F = ma$

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16. 16.

    Physics

    A projectile is launched at 31 m/s at 60° 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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17. 17.

    Physics

    A force of 953 N acts on an area of 8 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Mathematics

    In an arithmetic progression with first term 11 and common difference 2, find term number 5.

    Formula:AP nth Term

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

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19. 19.

    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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20. 20.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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