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GATE · Practice Sheet 29

Sheet code: GATE-S29 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Physics

    A force of 519 N acts on an area of 13 m². Find the pressure.

    Formula:Pressure
    P=FAP = \dfrac{F}{A}
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  2. 2.
    Physics

    A body moving at 13 m/s accelerates at 3 m/s² for 3 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)
    s=ut+12at2s = ut + \tfrac{1}{2}at^{2}
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  3. 3.
    Physics

    If 375 J of work is done in 27 s, find the power.

    Formula:Power
    P=WtP = \dfrac{W}{t}
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  4. 4.
    Mathematics

    Find term number 3 of a geometric progression with first term 5 and common ratio 2.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  5. 5.
    Mathematics

    Find the sum of the first 20 terms of an AP with first term 1 and common difference 1.

    Formula:AP Sum of n Terms
    Sn=n2 [2a+(n−1)d]S_n = \dfrac{n}{2}\,[2a+(n-1)d]
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  6. 6.
    Mathematics

    Find term number 4 of a geometric progression with first term 1 and common ratio 3.

    Formula:GP nth Term
    an=a r n−1a_n = a\,r^{\,n-1}
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  7. 7.
    Quantitative Aptitude

    Find the simple interest on ₹15,000 at 6% per annum for 3 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  8. 8.
    Physics

    If 1,866 J of work is done in 16 s, find the power.

    Formula:Power
    P=WtP = \dfrac{W}{t}
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  9. 9.
    Quantitative Aptitude

    Find the HCF and LCM of 31 and 29.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  10. 10.
    Physics

    A force of 979 N acts on an area of 30 m². Find the pressure.

    Formula:Pressure
    P=FAP = \dfrac{F}{A}
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  11. 11.
    Physics

    A projectile is launched at 42 m/s at 45° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range
    R=u2sin⁡2θgR = \dfrac{u^{2}\sin 2\theta}{g}
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  12. 12.
    Mathematics

    Find the distance between the points (-4, 3) and (-6, 5).

    Formula:Distance Between Two Points
    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
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  13. 13.
    Physics

    Find the kinetic energy of a 13 kg object moving at 13 m/s.

    Formula:Kinetic Energy
    KE=12mv2KE = \tfrac{1}{2}mv^{2}
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  14. 14.
    Physics

    A projectile is launched at 22 m/s at 60° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range
    R=u2sin⁡2θgR = \dfrac{u^{2}\sin 2\theta}{g}
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  15. 15.
    Physics

    A force of 827 N acts on an area of 49 m². Find the pressure.

    Formula:Pressure
    P=FAP = \dfrac{F}{A}
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  16. 16.
    Quantitative Aptitude

    A vehicle covers 322 km in 7 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  17. 17.
    Mathematics

    If f(x) = 5x³ + 6x² + 8x, find f′(1).

    Formula:Derivative of a Polynomial
    ddxxn=n x n−1\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}
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  18. 18.
    Mathematics

    Evaluate ∫ from 1 to 4 of 5x^2 dx.

    Formula:Definite Integral of a Power
    ∫pqaxn dx=an+1[xn+1]pq\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}
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  19. 19.
    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
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  20. 20.
    Mathematics

    Evaluate ∫ from 2 to 4 of 5x^1 dx.

    Formula:Definite Integral of a Power
    ∫pqaxn dx=an+1[xn+1]pq\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}
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