GATE · Practice Sheet 35

1. 1.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 2.)

   Formula:Permutations

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

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2. 2.

   Mathematics

   Evaluate ∫ from 0 to 3 of 4x^2 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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3. 3.

   Quantitative Aptitude

   Find the simple interest on ₹27,000 at 12% per annum for 6 year(s).

   Formula:Simple Interest

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

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4. 4.

   Physics

   A constant force of 114 N moves an object 41 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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5. 5.

   Mathematics

   In an arithmetic progression with first term 14 and common difference 2, find term number 16.

   Formula:AP nth Term

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

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6. 6.

   Mathematics

   Find the sum of the first 22 terms of an AP with first term 5 and common difference 8.

   Formula:AP Sum of n Terms

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

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7. 7.

   Mathematics

   Evaluate ∫ from 0 to 4 of 2x^2 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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8. 8.

   Mathematics

   Find the sum of the first 21 terms of an AP with first term 1 and common difference 9.

   Formula:AP Sum of n Terms

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

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9. 9.

   Quantitative Aptitude

   A vehicle covers 310 km in 5 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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10. 10.

    Physics

    A projectile is launched at 45 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.

    Quantitative Aptitude

    What is 15% of 960?

    Formula:Percentage of a Number

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

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12. 12.

    Quantitative Aptitude

    Find the HCF and LCM of 9 and 39.

    Formula:LCM & HCF

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

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13. 13.

    Physics

    A projectile is launched at 22 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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14. 14.

    Mathematics

    If f(x) = 3x³ + 4x² + 5x, find f′(4).

    Formula:Derivative of a Polynomial

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

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15. 15.

    Quantitative Aptitude

    Find the simple interest on ₹41,000 at 10% per annum for 1 year(s).

    Formula:Simple Interest

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

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16. 16.

    Physics

    Find the electrical power when 102 V drives a current of 1 A.

    Formula:Electrical Power

    $P = VI$

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17. 17.

    Quantitative Aptitude

    What is 20% of 940?

    Formula:Percentage of a Number

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

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18. 18.

    Quantitative Aptitude

    Find the HCF and LCM of 12 and 30.

    Formula:LCM & HCF

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

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19. 19.

    Physics

    An object starts at 13 m/s and accelerates at 9 m/s² for 9 s. Find its final velocity.

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

    $v = u + at$

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20. 20.

    Quantitative Aptitude

    Find the simple interest on ₹4,000 at 5% per annum for 1 year(s).

    Formula:Simple Interest

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

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