GATE · Practice Sheet 42

1. 1.

   Quantitative Aptitude

   Find the simple interest on ₹7,000 at 12% per annum for 5 year(s).

   Formula:Simple Interest

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

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2. 2.

   Physics

   A force of 336 N acts on an area of 20 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Physics

   Find the voltage across a 13 Ω resistor carrying a current of 12 A.

   Formula:Ohm's Law

   $V = IR$

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4. 4.

   Mathematics

   Evaluate ∫ from 1 to 3 of 2x^1 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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5. 5.

   Quantitative Aptitude

   A vehicle covers 608 km in 8 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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6. 6.

   Quantitative Aptitude

   Find the HCF and LCM of 34 and 37.

   Formula:LCM & HCF

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

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7. 7.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)

   Formula:Permutations

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

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8. 8.

   Mathematics

   If f(x) = 2x³ + 5x² + 6x, find f′(4).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Mathematics

   Find the sum of the first 23 terms of an AP with first term 13 and common difference 5.

   Formula:AP Sum of n Terms

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

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10. 10.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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11. 11.

    Quantitative Aptitude

    What is 75% of 100?

    Formula:Percentage of a Number

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

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12. 12.

    Quantitative Aptitude

    A vehicle covers 783 km in 9 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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13. 13.

    Physics

    Find the voltage across a 34 Ω resistor carrying a current of 7 A.

    Formula:Ohm's Law

    $V = IR$

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14. 14.

    Mathematics

    Find the slope of the line through (3, 8) and (-6, 3).

    Formula:Slope of a Line

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

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15. 15.

    Mathematics

    Evaluate log base 10 of 100,000.

    Formula:Logarithm Evaluation

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

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16. 16.

    Quantitative Aptitude

    Find the simple interest on ₹21,000 at 12% per annum for 1 year(s).

    Formula:Simple Interest

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

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17. 17.

    Mathematics

    If f(x) = 5x³ + 1x² + 7x, find f′(3).

    Formula:Derivative of a Polynomial

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

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18. 18.

    Quantitative Aptitude

    Find the simple interest on ₹18,000 at 6% per annum for 2 year(s).

    Formula:Simple Interest

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

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19. 19.

    Quantitative Aptitude

    What is 15% of 540?

    Formula:Percentage of a Number

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

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20. 20.

    Quantitative Aptitude

    A vehicle covers 534 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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