GATE · Practice Sheet 8

1. 1.

   Physics

   If 2,505 J of work is done in 14 s, find the power.

   Formula:Power

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

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2. 2.

   Mathematics

   Find the sum of the first 25 terms of an AP with first term 8 and common difference 4.

   Formula:AP Sum of n Terms

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

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3. 3.

   Quantitative Aptitude

   A vehicle covers 172 km in 4 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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4. 4.

   Physics

   A force of 990 N acts on an area of 50 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Mathematics

   In an arithmetic progression with first term 5 and common difference 4, find term number 18.

   Formula:AP nth Term

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

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6. 6.

   Quantitative Aptitude

   Find the simple interest on ₹41,000 at 10% per annum for 5 year(s).

   Formula:Simple Interest

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

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7. 7.

   Physics

   If 1,381 J of work is done in 29 s, find the power.

   Formula:Power

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

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8. 8.

   Mathematics

   Evaluate ∫ from 0 to 4 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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9. 9.

   Physics

   Find the voltage across a 11 Ω resistor carrying a current of 17 A.

   Formula:Ohm's Law

   $V = IR$

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10. 10.

    Physics

    A projectile is launched at 25 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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11. 11.

    Mathematics

    For the quadratic 5x² + 4x + 1 = 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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12. 12.

    Quantitative Aptitude

    A vehicle covers 153 km in 3 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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13. 13.

    Mathematics

    Find the sum of the first 19 terms of an AP with first term 11 and common difference 2.

    Formula:AP Sum of n Terms

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

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14. 14.

    Physics

    Find the kinetic energy of a 10 kg object moving at 29 m/s.

    Formula:Kinetic Energy

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

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15. 15.

    Quantitative Aptitude

    Find the HCF and LCM of 15 and 15.

    Formula:LCM & HCF

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

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16. 16.

    Physics

    A constant force of 165 N moves an object 33 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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17. 17.

    Physics

    Find the voltage across a 28 Ω resistor carrying a current of 20 A.

    Formula:Ohm's Law

    $V = IR$

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18. 18.

    Physics

    An object starts at 9 m/s and accelerates at 1 m/s² for 5 s. Find its final velocity.

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

    $v = u + at$

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19. 19.

    Physics

    Find the force required to accelerate a 23 kg mass at 7 m/s².

    Formula:Newton's Second Law (F = ma)

    $F = ma$

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20. 20.

    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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