GATE · Practice Sheet 44

1. 1.

   Quantitative Aptitude

   Find the simple interest on ₹20,000 at 8% per annum for 6 year(s).

   Formula:Simple Interest

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

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2. 2.

   Mathematics

   In an arithmetic progression with first term 9 and common difference 10, find term number 22.

   Formula:AP nth Term

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

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3. 3.

   Mathematics

   If f(x) = 5x³ + 2x² + 3x, find f′(3).

   Formula:Derivative of a Polynomial

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

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4. 4.

   Physics

   Find the voltage across a 32 Ω resistor carrying a current of 13 A.

   Formula:Ohm's Law

   $V = IR$

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5. 5.

   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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6. 6.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)

   Formula:Combinations

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

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7. 7.

   Quantitative Aptitude

   Find the simple interest on ₹39,000 at 10% per annum for 6 year(s).

   Formula:Simple Interest

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

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8. 8.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)

   Formula:Combinations

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

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9. 9.

   Mathematics

   Find the distance between the points (0, -7) and (0, 2).

   Formula:Distance Between Two Points

   $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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10. 10.

    Mathematics

    Find term number 6 of a geometric progression with first term 4 and common ratio 3.

    Formula:GP nth Term

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

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11. 11.

    Physics

    Find the voltage across a 3 Ω resistor carrying a current of 18 A.

    Formula:Ohm's Law

    $V = IR$

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12. 12.

    Physics

    Find the force required to accelerate a 47 kg mass at 15 m/s².

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

    $F = ma$

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13. 13.

    Mathematics

    Find term number 7 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term

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

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14. 14.

    Quantitative Aptitude

    What is 10% of 120?

    Formula:Percentage of a Number

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

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15. 15.

    Mathematics

    Find term number 4 of a geometric progression with first term 6 and common ratio 3.

    Formula:GP nth Term

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

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16. 16.

    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation

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

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17. 17.

    Physics

    Find the electrical power when 123 V drives a current of 19 A.

    Formula:Electrical Power

    $P = VI$

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18. 18.

    Mathematics

    Evaluate log base 10 of 1,000,000.

    Formula:Logarithm Evaluation

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

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19. 19.

    Physics

    An object starts at 12 m/s and accelerates at 1 m/s² for 10 s. Find its final velocity.

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

    $v = u + at$

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20. 20.

    Physics

    Find the force required to accelerate a 49 kg mass at 7 m/s².

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

    $F = ma$

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