GATE · Practice Sheet 48

1. 1.

   Physics

   If 2,405 J of work is done in 47 s, find the power.

   Formula:Power

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

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2. 2.

   Physics

   An object starts at 1 m/s and accelerates at 2 m/s² for 3 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 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)

   Formula:Permutations

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

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4. 4.

   Physics

   A constant force of 192 N moves an object 16 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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5. 5.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 2.)

   Formula:Permutations

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

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6. 6.

   Mathematics

   In an arithmetic progression with first term 13 and common difference 6, find term number 16.

   Formula:AP nth Term

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

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7. 7.

   Mathematics

   Evaluate log base 3 of 729.

   Formula:Logarithm Evaluation

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

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8. 8.

   Quantitative Aptitude

   A vehicle covers 414 km in 9 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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9. 9.

   Mathematics

   Evaluate log base 5 of 15,625.

   Formula:Logarithm Evaluation

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

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10. 10.

    Physics

    An object starts at 0 m/s and accelerates at 7 m/s² for 5 s. Find its final velocity.

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

    $v = u + at$

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11. 11.

    Physics

    Find the voltage across a 34 Ω resistor carrying a current of 4 A.

    Formula:Ohm's Law

    $V = IR$

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12. 12.

    Quantitative Aptitude

    Find the simple interest on ₹17,000 at 5% per annum for 5 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

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13. 13.

    Quantitative Aptitude

    What is 10% of 920?

    Formula:Percentage of a Number

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

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14. 14.

    Physics

    A constant force of 107 N moves an object 4 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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15. 15.

    Physics

    A force of 522 N acts on an area of 8 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Mathematics

    Find term number 6 of a geometric progression with first term 3 and common ratio 3.

    Formula:GP nth Term

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

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17. 17.

    Mathematics

    Find the sum of the first 20 terms of an AP with first term 16 and common difference 3.

    Formula:AP Sum of n Terms

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

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18. 18.

    Physics

    Find the voltage across a 42 Ω resistor carrying a current of 6 A.

    Formula:Ohm's Law

    $V = IR$

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19. 19.

    Mathematics

    Evaluate log base 3 of 81.

    Formula:Logarithm Evaluation

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

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20. 20.

    Physics

    A projectile is launched at 11 m/s at 45° 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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