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Questions and Answers
What is the value of p + q?
What is the value of p + q?
If $\alpha$ and $\beta$ are roots of the equation $x^2 - 8x + 12 = 0$, then what is $\frac{1}{\alpha} + \frac{1}{\beta}$?
If $\alpha$ and $\beta$ are roots of the equation $x^2 - 8x + 12 = 0$, then what is $\frac{1}{\alpha} + \frac{1}{\beta}$?
2/3
If the ratio of the roots of the equation $4x^2 - 6x + p = 0$ is 1:2, what is the value of p?
If the ratio of the roots of the equation $4x^2 - 6x + p = 0$ is 1:2, what is the value of p?
3
The amount charged for a defined length of time for the use of principal, generally on a yearly basis, is known as?
The amount charged for a defined length of time for the use of principal, generally on a yearly basis, is known as?
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The simple interest on a sum of money at 6% p.a. for 7 years is equal to twice the simple interest on another sum for 9 years at 5%. The ratio will be?
The simple interest on a sum of money at 6% p.a. for 7 years is equal to twice the simple interest on another sum for 9 years at 5%. The ratio will be?
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Sinking fund factor is the reciprocal of?
Sinking fund factor is the reciprocal of?
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A user wants to create a password using 4 lowercase letters and 3 uppercase letters. If the password must start with an uppercase letter, how many ways can the password be created?
A user wants to create a password using 4 lowercase letters and 3 uppercase letters. If the password must start with an uppercase letter, how many ways can the password be created?
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In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together?
In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together?
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Study Notes
Algebra and Equations
- The sum p + q equals 4/3.
- If the equations 2x + y = 2x - y = √8, then x = 1 and y = ½.
- The roots of the cubic equation x³ - 3x² - 4x + 12 = 0 are -2, 2, and 3.
- For the quadratic x² - 8x + 12 = 0, the sum of the reciprocals of the roots is 2/3.
- The roots of the equation x² - 7x + 10 = 0 are 2 and 5.
Logarithms
- Given log₁₀2 = x and log₁₀3 = y, log₁₀120 can be expressed as 2x + y + 1.
Interest and Investments
- Rate of interest refers to the amount charged per year for use of principal.
- To earn a monthly interest of ₹1200 at 18% simple interest, a sum of ₹80,000 is required.
- For a ₹1,00,000 deposit at 6% SI for 2 years, the total amount after interest is ₹1,12,000.
- The principal and compounded interest ratio after three years is 216:127, indicating a rate of interest of 0.1666.
- Compounded interest for ₹8000 at 12% p.a. for 6 months is ₹487.20.
Population and Growth Rates
- With an annual birth rate of 39.4 and a death rate of 19.4, the population will double in 35 years.
- The total population increase of 40% at a 2% growth rate per annum takes 17 years.
Financial Formulas and Ratios
- In SI, the ratio of interest of two sums is 15:7 at 6% for 7 years and 5% for 9 years.
- The effective rate of interest, when compounded monthly at a nominal rate of 9.9%, is 10.35%.
- The projected real GDP after 6 years, assuming 17% growth and 9% inflation, would be 1.587 P.
Compound Interest Calculation
- A sum doubles in four years under compound interest; it will become 32 times in 20 years.
- The sinking fund factor is the reciprocal of the present value interest factor of a single cash flow.
Combinatorial Problems
- Password creation with 4 lowercase letters and 3 uppercase letters starting with an uppercase: 26 × 25 × 24 × 23 × 22 × 5 × 21.
- Arranging 5 boys and 3 girls in a row such that no two girls sit together results in 14,400 arrangements.
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Description
Test your knowledge of algebraic equations and their roots with this quiz designed for algebra class students. Answer questions involving linear equations, cubic equations, and properties of roots. Can you determine the correct values and roots quickly?
