ACT · Practice Sheet 28

1. 1.

   Physics

   A force of 760 N acts on an area of 33 m². Find the pressure.

   Formula:Pressure

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

   View formula →
2. 2.

   Mathematics

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

   Formula:GP nth Term

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

   View formula →
3. 3.

   Quantitative Aptitude

   Two varieties costing $33 and $85 per kg are mixed to give a mixture worth $67 per kg. Find the mixing ratio.

   Formula:Alligation (Mixtures)

   $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

   View formula →
4. 4.

   Quantitative Aptitude

   A invests $3,000 and B invests $6,000 for the same period. If the total profit is $22,000, find A's share.

   Formula:Partnership (profit share)

   $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

   View formula →
5. 5.

   Physics

   Find the electrical power when 114 V drives a current of 9 A.

   Formula:Electrical Power

   $P = VI$

   View formula →
6. 6.

   Mathematics

   Find the sum of the first 6 terms of a GP with first term 4 and common ratio 2.

   Formula:GP Sum of n Terms

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

   View formula →
7. 7.

   Quantitative Aptitude

   A vehicle covers 376 km in 8 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

   View formula →
8. 8.

   Mathematics

   Evaluate log base 5 of 25.

   Formula:Logarithm Evaluation

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

   View formula →
9. 9.

   Quantitative Aptitude

   Find the HCF and LCM of 29 and 33.

   Formula:LCM & HCF

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

   View formula →
10. 10.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)

    Formula:Combinations

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

    View formula →
11. 11.

    Physics

    Find the density of an object with mass 123 g and volume 29 cm³.

    Formula:Density

    $\rho = \dfrac{m}{V}$

    View formula →
12. 12.

    Quantitative Aptitude

    Find the simple interest on $18,000 at 12% per annum for 3 year(s).

    Formula:Simple Interest

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

    View formula →
13. 13.

    Physics

    An object starts at 14 m/s and accelerates at 5 m/s² for 7 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

    View formula →
14. 14.

    Mathematics

    Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.

    Formula:Binomial Coefficient

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

    View formula →
15. 15.

    Physics

    A constant force of 20 N moves an object 6 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

    View formula →
16. 16.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

    View formula →
17. 17.

    Mathematics

    In an arithmetic progression with first term 11 and common difference 9, find term number 20.

    Formula:AP nth Term

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

    View formula →
18. 18.

    Mathematics

    Evaluate log base 3 of 81.

    Formula:Logarithm Evaluation

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

    View formula →
19. 19.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

    View formula →
20. 20.

    Quantitative Aptitude

    The marked price of an item is $400. After a 25% discount, find the selling price.

    Formula:Discount & Selling Price

    $SP = MP\left(1-\dfrac{d}{100}\right)$

    View formula →

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