GATE · Practice Sheet 19

1. 1.

   Physics

   A constant force of 70 N moves an object 31 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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2. 2.

   Physics

   A body moving at 2 m/s accelerates at 5 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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3. 3.

   Quantitative Aptitude

   Find the simple interest on ₹32,000 at 12% per annum for 5 year(s).

   Formula:Simple Interest

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

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4. 4.

   Physics

   If 2,982 J of work is done in 35 s, find the power.

   Formula:Power

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

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5. 5.

   Physics

   Find the force required to accelerate a 36 kg mass at 17 m/s².

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

   $F = ma$

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6. 6.

   Physics

   If 1,846 J of work is done in 5 s, find the power.

   Formula:Power

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

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7. 7.

   Mathematics

   For the quadratic 1x² + 5x + 9 = 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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8. 8.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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9. 9.

   Quantitative Aptitude

   Find the simple interest on ₹30,000 at 8% per annum for 3 year(s).

   Formula:Simple Interest

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

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10. 10.

    Physics

    Find the kinetic energy of a 11 kg object moving at 26 m/s.

    Formula:Kinetic Energy

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

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11. 11.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 2.)

    Formula:Permutations

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

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12. 12.

    Mathematics

    For the quadratic 4x² − 7x + 2 = 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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13. 13.

    Mathematics

    If f(x) = 5x³ + 2x² + 1x, find f′(4).

    Formula:Derivative of a Polynomial

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

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14. 14.

    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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15. 15.

    Mathematics

    Evaluate log base 2 of 32.

    Formula:Logarithm Evaluation

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

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16. 16.

    Physics

    Find the voltage across a 27 Ω resistor carrying a current of 6 A.

    Formula:Ohm's Law

    $V = IR$

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17. 17.

    Mathematics

    Find the sum of the first 24 terms of an AP with first term 9 and common difference 6.

    Formula:AP Sum of n Terms

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

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18. 18.

    Mathematics

    If f(x) = 1x³ + 5x² + 3x, find f′(3).

    Formula:Derivative of a Polynomial

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

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19. 19.

    Mathematics

    Evaluate log base 3 of 9.

    Formula:Logarithm Evaluation

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

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20. 20.

    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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