GATE · Practice Sheet 33

1. 1.

   Mathematics

   Find the distance between the points (3, -1) and (-7, -1).

   Formula:Distance Between Two Points

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

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2. 2.

   Mathematics

   Find the sum of the first 21 terms of an AP with first term 15 and common difference 3.

   Formula:AP Sum of n Terms

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

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3. 3.

   Physics

   Find the voltage across a 25 Ω resistor carrying a current of 17 A.

   Formula:Ohm's Law

   $V = IR$

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4. 4.

   Quantitative Aptitude

   What is 10% of 860?

   Formula:Percentage of a Number

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

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5. 5.

   Quantitative Aptitude

   Find the simple interest on ₹26,000 at 12% per annum for 6 year(s).

   Formula:Simple Interest

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

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6. 6.

   Mathematics

   Evaluate log base 3 of 243.

   Formula:Logarithm Evaluation

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

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7. 7.

   Mathematics

   Find the slope of the line through (2, 3) and (3, 3).

   Formula:Slope of a Line

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

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8. 8.

   Mathematics

   If f(x) = 4x³ + 6x² + 5x, find f′(1).

   Formula:Derivative of a Polynomial

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

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9. 9.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 2.)

   Formula:Combinations

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

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10. 10.

    Mathematics

    For the quadratic 3x² − 7x + 9 = 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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11. 11.

    Physics

    If 3,689 J of work is done in 48 s, find the power.

    Formula:Power

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

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12. 12.

    Physics

    A force of 574 N acts on an area of 15 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    Physics

    A constant force of 29 N moves an object 6 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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14. 14.

    Physics

    If 566 J of work is done in 28 s, find the power.

    Formula:Power

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

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15. 15.

    Physics

    A force of 88 N acts on an area of 3 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Mathematics

    Evaluate ∫ from 2 to 5 of 5x^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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17. 17.

    Physics

    Find the voltage across a 6 Ω resistor carrying a current of 5 A.

    Formula:Ohm's Law

    $V = IR$

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18. 18.

    Physics

    A body moving at 6 m/s accelerates at 7 m/s² for 6 s. Find the distance travelled.

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

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

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19. 19.

    Physics

    A constant force of 152 N moves an object 46 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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20. 20.

    Mathematics

    Find the distance between the points (5, -2) and (3, -3).

    Formula:Distance Between Two Points

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

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