GATE · Practice Sheet 16

1. 1.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 2.)

   Formula:Permutations

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

   View formula →
2. 2.

   Mathematics

   Find the sum of the first 24 terms of an AP with first term 7 and common difference 8.

   Formula:AP Sum of n Terms

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

   View formula →
3. 3.

   Mathematics

   Evaluate log base 5 of 15,625.

   Formula:Logarithm Evaluation

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

   View formula →
4. 4.

   Mathematics

   Find the slope of the line through (-8, 6) and (6, -4).

   Formula:Slope of a Line

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

   View formula →
5. 5.

   Mathematics

   For the quadratic 5x² − 4x − 3 = 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 →
6. 6.

   Physics

   A force of 157 N acts on an area of 8 m². Find the pressure.

   Formula:Pressure

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

   View formula →
7. 7.

   Mathematics

   Evaluate ∫ from 1 to 5 of 2x^3 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

   View formula →
8. 8.

   Physics

   Find the voltage across a 47 Ω resistor carrying a current of 5 A.

   Formula:Ohm's Law

   $V = IR$

   View formula →
9. 9.

   Physics

   Find the force required to accelerate a 36 kg mass at 13 m/s².

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

   $F = ma$

   View formula →
10. 10.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

    View formula →
11. 11.

    Mathematics

    Find term number 3 of a geometric progression with first term 6 and common ratio 2.

    Formula:GP nth Term

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

    View formula →
12. 12.

    Mathematics

    If f(x) = 3x³ + 5x² + 2x, find f′(4).

    Formula:Derivative of a Polynomial

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

    View formula →
13. 13.

    Physics

    If 3,081 J of work is done in 17 s, find the power.

    Formula:Power

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

    View formula →
14. 14.

    Physics

    Find the electrical power when 34 V drives a current of 10 A.

    Formula:Electrical Power

    $P = VI$

    View formula →
15. 15.

    Physics

    If 3,180 J of work is done in 33 s, find the power.

    Formula:Power

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

    View formula →
16. 16.

    Mathematics

    Find the distance between the points (6, -1) and (1, 5).

    Formula:Distance Between Two Points

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

    View formula →
17. 17.

    Mathematics

    Find the slope of the line through (6, 8) and (-5, 3).

    Formula:Slope of a Line

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

    View formula →
18. 18.

    Quantitative Aptitude

    A vehicle covers 108 km in 3 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

    View formula →
19. 19.

    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

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

    View formula →
20. 20.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 4.)

    Formula:Combinations

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

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.