GATE · Practice Sheet 24

1. 1.

   Physics

   A body moving at 15 m/s accelerates at 4 m/s² for 5 s. Find the distance travelled.

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

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

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2. 2.

   Physics

   A projectile is launched at 33 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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3. 3.

   Mathematics

   Find term number 5 of a geometric progression with first term 6 and common ratio 2.

   Formula:GP nth Term

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

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4. 4.

   Physics

   Find the voltage across a 39 Ω resistor carrying a current of 8 A.

   Formula:Ohm's Law

   $V = IR$

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5. 5.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 2.)

   Formula:Permutations

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

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6. 6.

   Mathematics

   Find the sum of the first 5 terms of an AP with first term 19 and common difference 1.

   Formula:AP Sum of n Terms

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

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7. 7.

   Quantitative Aptitude

   A vehicle covers 444 km in 6 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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8. 8.

   Physics

   If 522 J of work is done in 30 s, find the power.

   Formula:Power

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

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9. 9.

   Mathematics

   Evaluate log base 2 of 32.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

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10. 10.

    Mathematics

    In an arithmetic progression with first term 17 and common difference 3, find term number 18.

    Formula:AP nth Term

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

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11. 11.

    Mathematics

    Evaluate ∫ from 1 to 4 of 2x^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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12. 12.

    Physics

    An object starts at 8 m/s and accelerates at 2 m/s² for 5 s. Find its final velocity.

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

    $v = u + at$

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13. 13.

    Quantitative Aptitude

    Find the HCF and LCM of 26 and 11.

    Formula:LCM & HCF

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

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14. 14.

    Physics

    A body moving at 7 m/s accelerates at 4 m/s² for 5 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

    In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)

    Formula:Combinations

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

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16. 16.

    Physics

    Find the kinetic energy of a 13 kg object moving at 13 m/s.

    Formula:Kinetic Energy

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

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17. 17.

    Quantitative Aptitude

    A vehicle covers 204 km in 4 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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18. 18.

    Mathematics

    Evaluate log base 2 of 8.

    Formula:Logarithm Evaluation

    $\log_{b}(b^{k}) = k$

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19. 19.

    Physics

    Find the kinetic energy of a 7 kg object moving at 10 m/s.

    Formula:Kinetic Energy

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

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20. 20.

    Physics

    A projectile is launched at 19 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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