ACT · Practice Sheet 39

1. 1.

   Mathematics

   Find the sum of the first 12 terms of an AP with first term 18 and common difference 6.

   Formula:AP Sum of n Terms

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

   View formula →
2. 2.

   Quantitative Aptitude

   Find the simple interest on $2,000 at 8% per annum for 1 year(s).

   Formula:Simple Interest

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

   View formula →
3. 3.

   Mathematics

   Find the distance between the points (-3, -7) and (3, -5).

   Formula:Distance Between Two Points

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

   View formula →
4. 4.

   Physics

   Find the density of an object with mass 26 g and volume 33 cm³.

   Formula:Density

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

   View formula →
5. 5.

   Mathematics

   In an arithmetic progression with first term 17 and common difference 10, find term number 8.

   Formula:AP nth Term

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

   View formula →
6. 6.

   Physics

   If 284 J of work is done in 30 s, find the power.

   Formula:Power

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

   View formula →
7. 7.

   Quantitative Aptitude

   Pipe A fills a tank in 13 hours and pipe B in 12 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

   $T = \dfrac{xy}{x+y}$

   View formula →
8. 8.

   Physics

   Find the force required to accelerate a 34 kg mass at 10 m/s².

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

   $F = ma$

   View formula →
9. 9.

   Mathematics

   Evaluate log base 2 of 64.

   Formula:Logarithm Evaluation

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

   View formula →
10. 10.

    Physics

    Calculate the potential energy of a 20 kg object at a height of 17 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
11. 11.

    Mathematics

    If f(x) = 2x³ + 2x² + 9x, find f′(2).

    Formula:Derivative of a Polynomial

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

    View formula →
12. 12.

    Quantitative Aptitude

    Divide $1,757 between two people in the ratio 5:2. How much does each receive?

    Formula:Sharing in a Ratio

    $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

    View formula →
13. 13.

    Quantitative Aptitude

    Pipe A fills a tank in 15 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

    $T = \dfrac{xy}{x+y}$

    View formula →
14. 14.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

    View formula →
15. 15.

    Mathematics

    Evaluate log base 5 of 25.

    Formula:Logarithm Evaluation

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

    View formula →
16. 16.

    Physics

    An object starts at 10 m/s and accelerates at 2 m/s² for 5 s. Find its final velocity.

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

    $v = u + at$

    View formula →
17. 17.

    Quantitative Aptitude

    Divide $1,722 between two people in the ratio 2:5. How much does each receive?

    Formula:Sharing in a Ratio

    $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

    View formula →
18. 18.

    Quantitative Aptitude

    Two varieties costing $24 and $75 per kg are mixed to give a mixture worth $44 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

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

    View formula →
19. 19.

    Mathematics

    Find the distance between the points (4, -2) and (-7, -3).

    Formula:Distance Between Two Points

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

    View formula →
20. 20.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

    Formula:Probability (two dice)

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

    View formula →

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