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Questions and Answers
What is the value of p + q?
What is the value of p + q?
- 7/8
- 2/6
- 2/3
- 4/3 (correct)
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?
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?
Sinking fund factor is the reciprocal of?
Sinking fund factor is the reciprocal of?
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?
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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