GATE · Practice Sheet 28

1. 1.

   Mathematics

   Find the sum of the first 22 terms of an AP with first term 16 and common difference 1.

   Formula:AP Sum of n Terms

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

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2. 2.

   Mathematics

   Find the distance between the points (6, 1) and (7, 2).

   Formula:Distance Between Two Points

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

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3. 3.

   Physics

   Find the kinetic energy of a 15 kg object moving at 26 m/s.

   Formula:Kinetic Energy

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

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4. 4.

   Physics

   If 1,453 J of work is done in 6 s, find the power.

   Formula:Power

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

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5. 5.

   Mathematics

   If f(x) = 1x³ + 2x² + 4x, find f′(2).

   Formula:Derivative of a Polynomial

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

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6. 6.

   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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7. 7.

   Quantitative Aptitude

   Find the HCF and LCM of 28 and 13.

   Formula:LCM & HCF

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

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8. 8.

   Mathematics

   Evaluate log base 3 of 243.

   Formula:Logarithm Evaluation

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

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9. 9.

   Mathematics

   If f(x) = 1x³ + 1x² + 9x, find f′(5).

   Formula:Derivative of a Polynomial

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

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10. 10.

    Physics

    A constant force of 65 N moves an object 3 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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11. 11.

    Quantitative Aptitude

    Find the HCF and LCM of 10 and 11.

    Formula:LCM & HCF

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

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12. 12.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

    Formula:Permutations

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

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13. 13.

    Mathematics

    Evaluate log base 2 of 4.

    Formula:Logarithm Evaluation

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

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14. 14.

    Mathematics

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

    Formula:AP nth Term

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

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15. 15.

    Quantitative Aptitude

    Find the HCF and LCM of 10 and 9.

    Formula:LCM & HCF

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

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16. 16.

    Mathematics

    Evaluate ∫ from 1 to 5 of 5x^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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17. 17.

    Quantitative Aptitude

    Find the simple interest on ₹41,000 at 4% per annum for 1 year(s).

    Formula:Simple Interest

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

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18. 18.

    Mathematics

    For the quadratic 3x² + 7x + 7 = 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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19. 19.

    Quantitative Aptitude

    What is 10% of 1,140?

    Formula:Percentage of a Number

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

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20. 20.

    Physics

    Find the electrical power when 92 V drives a current of 5 A.

    Formula:Electrical Power

    $P = VI$

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