GATE · Practice Sheet 11

1. 1.

   Quantitative Aptitude

   Find the HCF and LCM of 39 and 32.

   Formula:LCM & HCF

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

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2. 2.

   Mathematics

   For the quadratic 4x² − 9x + 6 = 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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3. 3.

   Mathematics

   If f(x) = 4x³ + 5x² + 4x, find f′(2).

   Formula:Derivative of a Polynomial

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

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4. 4.

   Mathematics

   Find term number 3 of a geometric progression with first term 1 and common ratio 3.

   Formula:GP nth Term

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

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5. 5.

   Mathematics

   Find the slope of the line through (8, 1) and (-1, -2).

   Formula:Slope of a Line

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

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6. 6.

   Physics

   Find the electrical power when 94 V drives a current of 13 A.

   Formula:Electrical Power

   $P = VI$

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7. 7.

   Mathematics

   Find term number 7 of a geometric progression with first term 5 and common ratio 3.

   Formula:GP nth Term

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

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8. 8.

   Physics

   A body moving at 9 m/s accelerates at 7 m/s² for 9 s. Find the distance travelled.

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

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

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9. 9.

   Physics

   Find the kinetic energy of a 15 kg object moving at 7 m/s.

   Formula:Kinetic Energy

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

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10. 10.

    Mathematics

    Find the sum of the first 7 terms of an AP with first term 13 and common difference 4.

    Formula:AP Sum of n Terms

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

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11. 11.

    Physics

    Find the electrical power when 83 V drives a current of 7 A.

    Formula:Electrical Power

    $P = VI$

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12. 12.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)

    Formula:Permutations

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

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13. 13.

    Physics

    Find the electrical power when 14 V drives a current of 9 A.

    Formula:Electrical Power

    $P = VI$

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14. 14.

    Mathematics

    In an arithmetic progression with first term 15 and common difference 8, find term number 12.

    Formula:AP nth Term

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

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15. 15.

    Quantitative Aptitude

    Find the HCF and LCM of 25 and 25.

    Formula:LCM & HCF

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

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16. 16.

    Physics

    A projectile is launched at 25 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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17. 17.

    Physics

    Find the kinetic energy of a 8 kg object moving at 8 m/s.

    Formula:Kinetic Energy

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

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18. 18.

    Mathematics

    For the quadratic 5x² − 9x − 4 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

    $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

    View formula →
19. 19.

    Mathematics

    In an arithmetic progression with first term 1 and common difference 2, find term number 17.

    Formula:AP nth Term

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

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20. 20.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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