GATE · Practice Sheet 50

1. 1.

   Quantitative Aptitude

   Find the simple interest on ₹37,000 at 5% per annum for 3 year(s).

   Formula:Simple Interest

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

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2. 2.

   Physics

   Find the electrical power when 26 V drives a current of 6 A.

   Formula:Electrical Power

   $P = VI$

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3. 3.

   Physics

   A projectile is launched at 38 m/s at 60° 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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4. 4.

   Physics

   Find the force required to accelerate a 26 kg mass at 2 m/s².

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

   $F = ma$

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5. 5.

   Physics

   A constant force of 90 N moves an object 32 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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6. 6.

   Mathematics

   In an arithmetic progression with first term 19 and common difference 7, find term number 25.

   Formula:AP nth Term

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

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7. 7.

   Mathematics

   Evaluate ∫ from 0 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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8. 8.

   Mathematics

   Find the slope of the line through (6, -3) and (4, 3).

   Formula:Slope of a Line

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

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9. 9.

   Mathematics

   Evaluate ∫ from 0 to 4 of 1x^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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10. 10.

    Quantitative Aptitude

    Find the HCF and LCM of 11 and 23.

    Formula:LCM & HCF

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

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11. 11.

    Mathematics

    Find the distance between the points (1, -8) and (0, 5).

    Formula:Distance Between Two Points

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

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12. 12.

    Physics

    If 4,400 J of work is done in 30 s, find the power.

    Formula:Power

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

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13. 13.

    Physics

    Find the voltage across a 15 Ω resistor carrying a current of 14 A.

    Formula:Ohm's Law

    $V = IR$

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14. 14.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 4.)

    Formula:Combinations

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

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15. 15.

    Mathematics

    For the quadratic 4x² + 6x − 5 = 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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16. 16.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)

    Formula:Permutations

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

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17. 17.

    Physics

    Find the force required to accelerate a 49 kg mass at 16 m/s².

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

    $F = ma$

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18. 18.

    Mathematics

    Find the sum of the first 22 terms of an AP with first term 13 and common difference 5.

    Formula:AP Sum of n Terms

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

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19. 19.

    Mathematics

    In an arithmetic progression with first term 11 and common difference 8, find term number 26.

    Formula:AP nth Term

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

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20. 20.

    Physics

    A force of 699 N acts on an area of 47 m². Find the pressure.

    Formula:Pressure

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

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