GATE · Practice Sheet 5

1. 1.

   Physics

   If 4,693 J of work is done in 3 s, find the power.

   Formula:Power

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

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2. 2.

   Physics

   Find the electrical power when 233 V drives a current of 15 A.

   Formula:Electrical Power

   $P = VI$

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3. 3.

   Mathematics

   For the quadratic 4x² + 2x − 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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4. 4.

   Mathematics

   Find the slope of the line through (1, -4) and (-8, -2).

   Formula:Slope of a Line

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

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5. 5.

   Physics

   A constant force of 143 N moves an object 2 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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6. 6.

   Physics

   If 4,571 J of work is done in 5 s, find the power.

   Formula:Power

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

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7. 7.

   Physics

   Find the voltage across a 2 Ω resistor carrying a current of 18 A.

   Formula:Ohm's Law

   $V = IR$

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8. 8.

   Physics

   A constant force of 150 N moves an object 12 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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9. 9.

   Mathematics

   Find term number 4 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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10. 10.

    Quantitative Aptitude

    Find the simple interest on ₹22,000 at 6% per annum for 1 year(s).

    Formula:Simple Interest

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

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11. 11.

    Physics

    Find the kinetic energy of a 1 kg object moving at 20 m/s.

    Formula:Kinetic Energy

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

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12. 12.

    Quantitative Aptitude

    Find the HCF and LCM of 26 and 17.

    Formula:LCM & HCF

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

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13. 13.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 2.)

    Formula:Combinations

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

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14. 14.

    Physics

    If 3,017 J of work is done in 31 s, find the power.

    Formula:Power

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

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15. 15.

    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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16. 16.

    Physics

    Find the kinetic energy of a 9 kg object moving at 16 m/s.

    Formula:Kinetic Energy

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

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17. 17.

    Mathematics

    For the quadratic 3x² + 3x − 6 = 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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18. 18.

    Physics

    A projectile is launched at 28 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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19. 19.

    Quantitative Aptitude

    What is 30% of 760?

    Formula:Percentage of a Number

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

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20. 20.

    Mathematics

    Find the slope of the line through (-3, 7) and (-2, -4).

    Formula:Slope of a Line

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

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