GATE · Practice Sheet 18

1. 1.

   Quantitative Aptitude

   What is 40% of 820?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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2. 2.

   Physics

   An object starts at 9 m/s and accelerates at 5 m/s² for 6 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 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 4.)

   Formula:Combinations

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

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4. 4.

   Mathematics

   Find term number 3 of a geometric progression with first term 5 and common ratio 3.

   Formula:GP nth Term

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

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5. 5.

   Mathematics

   For the quadratic 3x² + 8x − 7 = 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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6. 6.

   Quantitative Aptitude

   What is 10% of 640?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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7. 7.

   Mathematics

   Evaluate log base 5 of 15,625.

   Formula:Logarithm Evaluation

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

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8. 8.

   Physics

   A force of 594 N acts on an area of 31 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Quantitative Aptitude

   Find the HCF and LCM of 33 and 29.

   Formula:LCM & HCF

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

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10. 10.

    Physics

    Find the kinetic energy of a 13 kg object moving at 23 m/s.

    Formula:Kinetic Energy

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

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11. 11.

    Physics

    A body moving at 12 m/s accelerates at 7 m/s² for 7 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

    Find the kinetic energy of a 9 kg object moving at 29 m/s.

    Formula:Kinetic Energy

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

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13. 13.

    Mathematics

    For the quadratic 4x² − 7x − 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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14. 14.

    Physics

    A force of 575 N acts on an area of 4 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Mathematics

    If f(x) = 3x³ + 6x² + 1x, find f′(2).

    Formula:Derivative of a Polynomial

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

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16. 16.

    Mathematics

    Evaluate ∫ from 2 to 5 of 3x^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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17. 17.

    Physics

    Find the voltage across a 24 Ω resistor carrying a current of 20 A.

    Formula:Ohm's Law

    $V = IR$

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18. 18.

    Physics

    An object starts at 8 m/s and accelerates at 9 m/s² for 7 s. Find its final velocity.

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

    $v = u + at$

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19. 19.

    Mathematics

    Evaluate log base 3 of 27.

    Formula:Logarithm Evaluation

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

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20. 20.

    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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