ACT · Practice Sheet 7

1. 1.

   Mathematics

   Find term number 3 of a geometric progression with first term 5 and common ratio 2.

   Formula:GP nth Term

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

   View formula →
2. 2.

   Physics

   Find the voltage across a 24 Ω resistor carrying a current of 20 A.

   Formula:Ohm's Law

   $V = IR$

   View formula →
3. 3.

   Quantitative Aptitude

   Pipe A fills a tank in 13 hours and pipe B in 6 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

   View formula →
4. 4.

   Quantitative Aptitude

   Find the simple interest on $42,000 at 6% per annum for 4 year(s).

   Formula:Simple Interest

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

   View formula →
5. 5.

   Mathematics

   Find the distance between the points (-4, 8) and (4, 3).

   Formula:Distance Between Two Points

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

   View formula →
6. 6.

   Physics

   Find the kinetic energy of a 20 kg object moving at 6 m/s.

   Formula:Kinetic Energy

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

   View formula →
7. 7.

   Quantitative Aptitude

   Two varieties costing $34 and $87 per kg are mixed to give a mixture worth $57 per kg. Find the mixing ratio.

   Formula:Alligation (Mixtures)

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

   View formula →
8. 8.

   Mathematics

   In an arithmetic progression with first term 14 and common difference 6, find term number 27.

   Formula:AP nth Term

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

   View formula →
9. 9.

   Physics

   A constant force of 156 N moves an object 48 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

   View formula →
10. 10.

    Quantitative Aptitude

    An item is bought for $200 and sold for $240. Find the profit percentage.

    Formula:Profit Percentage

    $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

    View formula →
11. 11.

    Mathematics

    Find the binomial coefficient C(5, 3) — the coefficient of x^3 in (1 + x)^5.

    Formula:Binomial Coefficient

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

    View formula →
12. 12.

    Physics

    If 791 J of work is done in 23 s, find the power.

    Formula:Power

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

    View formula →
13. 13.

    Quantitative Aptitude

    What is 10% of 700?

    Formula:Percentage of a Number

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

    View formula →
14. 14.

    Mathematics

    Find the sum of the first 9 terms of an AP with first term 3 and common difference 8.

    Formula:AP Sum of n Terms

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

    View formula →
15. 15.

    Mathematics

    If f(x) = 1x³ + 1x² + 7x, find f′(1).

    Formula:Derivative of a Polynomial

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

    View formula →
16. 16.

    Quantitative Aptitude

    Find the compound interest on $17,000 at 10% per annum compounded annually for 3 years.

    Formula:Compound Interest

    $A = P\left(1+\dfrac{R}{100}\right)^{T}$

    View formula →
17. 17.

    Quantitative Aptitude

    Two varieties costing $18 and $98 per kg are mixed to give a mixture worth $30 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

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

    View formula →
18. 18.

    Physics

    A projectile is launched at 23 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 →
19. 19.

    Quantitative Aptitude

    What is 40% of 900?

    Formula:Percentage of a Number

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

    View formula →
20. 20.

    Physics

    Find the electrical power when 19 V drives a current of 15 A.

    Formula:Electrical Power

    $P = VI$

    View formula →

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