GATE · Practice Sheet 32

1. 1.

   Physics

   Find the electrical power when 39 V drives a current of 2 A.

   Formula:Electrical Power

   $P = VI$

   View formula →
2. 2.

   Mathematics

   Find the sum of the first 14 terms of an AP with first term 20 and common difference 6.

   Formula:AP Sum of n Terms

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

   View formula →
3. 3.

   Physics

   A force of 498 N acts on an area of 15 m². Find the pressure.

   Formula:Pressure

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

   View formula →
4. 4.

   Physics

   Find the kinetic energy of a 12 kg object moving at 16 m/s.

   Formula:Kinetic Energy

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

   View formula →
5. 5.

   Physics

   If 3,034 J of work is done in 28 s, find the power.

   Formula:Power

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

   View formula →
6. 6.

   Mathematics

   Evaluate log base 5 of 3,125.

   Formula:Logarithm Evaluation

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

   View formula →
7. 7.

   Physics

   A constant force of 192 N moves an object 8 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

   View formula →
8. 8.

   Mathematics

   Find the distance between the points (2, 2) and (-4, 6).

   Formula:Distance Between Two Points

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

   View formula →
9. 9.

   Physics

   Find the electrical power when 148 V drives a current of 13 A.

   Formula:Electrical Power

   $P = VI$

   View formula →
10. 10.

    Mathematics

    Find the slope of the line through (-1, -1) and (0, -5).

    Formula:Slope of a Line

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

    View formula →
11. 11.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)

    Formula:Combinations

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

    View formula →
12. 12.

    Quantitative Aptitude

    A vehicle covers 135 km in 3 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

    View formula →
13. 13.

    Mathematics

    For the quadratic 4x² − 2x + 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 →
14. 14.

    Mathematics

    In an arithmetic progression with first term 20 and common difference 6, find term number 10.

    Formula:AP nth Term

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

    View formula →
15. 15.

    Physics

    A projectile is launched at 23 m/s at 60° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

    View formula →
16. 16.

    Mathematics

    In an arithmetic progression with first term 2 and common difference 10, find term number 13.

    Formula:AP nth Term

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

    View formula →
17. 17.

    Physics

    A projectile is launched at 47 m/s at 30° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

    View formula →
18. 18.

    Physics

    A force of 864 N acts on an area of 41 m². Find the pressure.

    Formula:Pressure

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

    View formula →
19. 19.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

    View formula →
20. 20.

    Quantitative Aptitude

    Find the simple interest on ₹16,000 at 8% per annum for 3 year(s).

    Formula:Simple Interest

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

    View formula →

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