GATE · Practice Sheet 41

1. 1.

   Physics

   If 4,374 J of work is done in 45 s, find the power.

   Formula:Power

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

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2. 2.

   Mathematics

   In an arithmetic progression with first term 12 and common difference 9, find term number 25.

   Formula:AP nth Term

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

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3. 3.

   Quantitative Aptitude

   Find the HCF and LCM of 25 and 6.

   Formula:LCM & HCF

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

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4. 4.

   Physics

   A force of 110 N acts on an area of 36 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Quantitative Aptitude

   Find the HCF and LCM of 27 and 12.

   Formula:LCM & HCF

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

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6. 6.

   Physics

   Find the voltage across a 32 Ω resistor carrying a current of 19 A.

   Formula:Ohm's Law

   $V = IR$

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7. 7.

   Physics

   A force of 726 N acts on an area of 34 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Quantitative Aptitude

   What is 40% of 320?

   Formula:Percentage of a Number

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

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9. 9.

   Mathematics

   In an arithmetic progression with first term 11 and common difference 10, find term number 9.

   Formula:AP nth Term

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

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10. 10.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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11. 11.

    Mathematics

    In an arithmetic progression with first term 4 and common difference 4, find term number 27.

    Formula:AP nth Term

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

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12. 12.

    Physics

    Find the voltage across a 13 Ω resistor carrying a current of 2 A.

    Formula:Ohm's Law

    $V = IR$

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13. 13.

    Quantitative Aptitude

    What is 60% of 720?

    Formula:Percentage of a Number

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

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14. 14.

    Physics

    A projectile is launched at 26 m/s at 30° 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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15. 15.

    Mathematics

    Evaluate ∫ from 1 to 5 of 4x^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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16. 16.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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17. 17.

    Physics

    Find the voltage across a 22 Ω resistor carrying a current of 17 A.

    Formula:Ohm's Law

    $V = IR$

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18. 18.

    Mathematics

    Find the slope of the line through (-7, 0) and (-2, 6).

    Formula:Slope of a Line

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

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19. 19.

    Physics

    An object starts at 1 m/s and accelerates at 7 m/s² for 12 s. Find its final velocity.

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

    $v = u + at$

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20. 20.

    Physics

    Find the kinetic energy of a 15 kg object moving at 12 m/s.

    Formula:Kinetic Energy

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

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