GATE · Practice Sheet 3

1. 1.

   Physics

   Find the electrical power when 6 V drives a current of 7 A.

   Formula:Electrical Power

   $P = VI$

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2. 2.

   Physics

   Find the voltage across a 35 Ω resistor carrying a current of 20 A.

   Formula:Ohm's Law

   $V = IR$

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3. 3.

   Mathematics

   Find the sum of the first 13 terms of an AP with first term 6 and common difference 8.

   Formula:AP Sum of n Terms

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

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4. 4.

   Physics

   Find the voltage across a 11 Ω resistor carrying a current of 13 A.

   Formula:Ohm's Law

   $V = IR$

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5. 5.

   Physics

   A force of 768 N acts on an area of 30 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)

   Formula:Permutations

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

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7. 7.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)

   Formula:Combinations

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

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8. 8.

   Quantitative Aptitude

   Find the HCF and LCM of 16 and 13.

   Formula:LCM & HCF

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

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9. 9.

   Physics

   Find the kinetic energy of a 2 kg object moving at 29 m/s.

   Formula:Kinetic Energy

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

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10. 10.

    Mathematics

    In an arithmetic progression with first term 6 and common difference 10, find term number 6.

    Formula:AP nth Term

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

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11. 11.

    Physics

    A body moving at 10 m/s accelerates at 8 m/s² for 4 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.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 3.)

    Formula:Permutations

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

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13. 13.

    Mathematics

    Evaluate ∫ from 0 to 3 of 3x^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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14. 14.

    Mathematics

    Find term number 5 of a geometric progression with first term 5 and common ratio 2.

    Formula:GP nth Term

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

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15. 15.

    Physics

    A body moving at 7 m/s accelerates at 1 m/s² for 8 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^{2}$

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16. 16.

    Physics

    Find the voltage across a 46 Ω resistor carrying a current of 19 A.

    Formula:Ohm's Law

    $V = IR$

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17. 17.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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18. 18.

    Physics

    A constant force of 70 N moves an object 25 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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19. 19.

    Quantitative Aptitude

    Find the HCF and LCM of 29 and 6.

    Formula:LCM & HCF

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

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20. 20.

    Physics

    A projectile is launched at 12 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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