GATE · Practice Sheet 40

1. 1.

   Mathematics

   If f(x) = 3x³ + 3x² + 8x, find f′(1).

   Formula:Derivative of a Polynomial

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

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2. 2.

   Mathematics

   Evaluate ∫ from 1 to 4 of 3x^3 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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3. 3.

   Physics

   Find the voltage across a 4 Ω resistor carrying a current of 13 A.

   Formula:Ohm's Law

   $V = IR$

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4. 4.

   Mathematics

   In an arithmetic progression with first term 18 and common difference 2, find term number 12.

   Formula:AP nth Term

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

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5. 5.

   Mathematics

   Evaluate ∫ from 1 to 5 of 3x^3 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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6. 6.

   Quantitative Aptitude

   What is 50% of 380?

   Formula:Percentage of a Number

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

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7. 7.

   Mathematics

   Find the sum of the first 15 terms of an AP with first term 6 and common difference 1.

   Formula:AP Sum of n Terms

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

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8. 8.

   Physics

   Find the voltage across a 32 Ω resistor carrying a current of 2 A.

   Formula:Ohm's Law

   $V = IR$

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9. 9.

   Physics

   An object starts at 17 m/s and accelerates at 9 m/s² for 9 s. Find its final velocity.

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

   $v = u + at$

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10. 10.

    Quantitative Aptitude

    Find the simple interest on ₹30,000 at 6% per annum for 3 year(s).

    Formula:Simple Interest

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

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11. 11.

    Physics

    If 2,205 J of work is done in 41 s, find the power.

    Formula:Power

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

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12. 12.

    Physics

    Find the kinetic energy of a 18 kg object moving at 24 m/s.

    Formula:Kinetic Energy

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

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13. 13.

    Mathematics

    Find the sum of the first 20 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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14. 14.

    Physics

    A body moving at 12 m/s accelerates at 4 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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15. 15.

    Quantitative Aptitude

    Find the HCF and LCM of 38 and 36.

    Formula:LCM & HCF

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

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16. 16.

    Quantitative Aptitude

    What is 75% of 480?

    Formula:Percentage of a Number

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

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17. 17.

    Quantitative Aptitude

    Find the simple interest on ₹29,000 at 10% per annum for 5 year(s).

    Formula:Simple Interest

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

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18. 18.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

    Formula:Permutations

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

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19. 19.

    Physics

    A body moving at 9 m/s accelerates at 3 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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20. 20.

    Physics

    An object starts at 17 m/s and accelerates at 3 m/s² for 4 s. Find its final velocity.

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

    $v = u + at$

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