Engineering Entrance · Practice Sheet 30

1. 1.

   Mathematics

   Find term number 7 of a geometric progression with first term 4 and common ratio 2.

   Formula:GP nth Term

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

   View formula →
2. 2.

   Mathematics

   Find the sum of the first 5 terms of a GP with first term 3 and common ratio 3.

   Formula:GP Sum of n Terms

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

   View formula →
3. 3.

   Physics

   Calculate the potential energy of a 37 kg object at a height of 33 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
4. 4.

   Chemistry

   A solution is made by dissolving 22 g of solute in 104 g of solvent. Find the mass percentage of the solute.

   Formula:Mass Percentage

   $\%\,\text{mass} = \dfrac{\text{solute}}{\text{solution}}\times 100$

   View formula →
5. 5.

   Physics

   Find the force required to accelerate a 30 kg mass at 11 m/s².

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

   $F = ma$

   View formula →
6. 6.

   Mathematics

   Evaluate ∫ from 1 to 3 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 →
7. 7.

   Mathematics

   Find term number 3 of a geometric progression with first term 1 and common ratio 3.

   Formula:GP nth Term

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

   View formula →
8. 8.

   Chemistry

   75 mL of a 5 M solution is diluted to 333 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

   View formula →
9. 9.

   Physics

   If 1,409 J of work is done in 40 s, find the power.

   Formula:Power

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

   View formula →
10. 10.

    Mathematics

    Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.

    Formula:Binomial Coefficient

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

    View formula →
11. 11.

    Physics

    An object starts at 14 m/s and accelerates at 1 m/s² for 5 s. Find its final velocity.

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

    $v = u + at$

    View formula →
12. 12.

    Physics

    Find the density of an object with mass 491 g and volume 2 cm³.

    Formula:Density

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

    View formula →
13. 13.

    Physics

    Find the momentum of a 14 kg body moving at 7 m/s.

    Formula:Linear Momentum

    $p = mv$

    View formula →
14. 14.

    Physics

    A constant force of 198 N moves an object 17 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

    View formula →
15. 15.

    Physics

    A force of 613 N acts on an area of 25 m². Find the pressure.

    Formula:Pressure

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

    View formula →
16. 16.

    Physics

    Find the electrical power when 178 V drives a current of 6 A.

    Formula:Electrical Power

    $P = VI$

    View formula →
17. 17.

    Mathematics

    Find the sum of the first 16 terms of an AP with first term 11 and common difference 1.

    Formula:AP Sum of n Terms

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

    View formula →
18. 18.

    Physics

    A force of 655 N acts on an area of 28 m². Find the pressure.

    Formula:Pressure

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

    View formula →
19. 19.

    Mathematics

    For the quadratic 4x² − 4x − 1 = 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 →
20. 20.

    Physics

    Find the voltage across a 40 Ω resistor carrying a current of 18 A.

    Formula:Ohm's Law

    $V = IR$

    View formula →

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