Questions and Answers
What is the value of ( \frac{p+q}{p-q} ) if ( \frac{p}{q} = 7 )?
If ( 2x+y = 2x-y = \sqrt{8} ), then the value of x and y are?
The equation ( x^3 - 3x^2 - 4x + 12 = 0 ) has three real roots, they are:
If ( \alpha ) and ( \beta ) are roots of the equation ( x^2 - 8x + 12 = 0 ), then ( \frac{1}{\alpha} + \frac{1}{\beta} = ) ____
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The roots of the equation ( x^2 - 7x + 10 = 0 ) are:
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Given that ( \log 10^2 = x ) and ( \log 10^3 = y ), the value of ( \log 10^{120} ) is expressed as:
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If four numbers 2, 3, 5, x are proportional, then x =
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If ( x = 2 + \sqrt{3} ) and ( y = 2 - \sqrt{3} ), then the value of ( x^2 + y^2 = )
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If the ratio of the roots of the equation ( 4x^2 - 6x + p = 0 ) is 1:2, then the value of p is:
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The ratio of the number of boys and number of girls in a school is found to be 15:3. How many boys and equal number of girls should be added to bring the ratio to 2/3?
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If ( 2x + 5 > 3x + 2 ) and ( 2x - 3 \leq 4x - 5 ), then x takes which of the following values?
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Solve for x of the inequalities ( 2 \leq \frac{3x - 2}{5} \leq 4 ) where ( x \in \mathbb{N} )
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The amount charged for a defined length of time for use of principal, generally on a yearly basis is known as:
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The sum required to earn a monthly interest of ` 1200 at 18% p.a. Simple Interest is?
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Sachin deposited ` 1,00,000 in his bank for 2 years at simple interest of 6%. How much interest would he earn? What would be the final value of the deposit?
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The ratio of principal and the compounded interest value for three years (Compounded annually) is 216:127. The rate of interest is:
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The compounded interest on `8000 for 6 months at 12% p.a. payable quarterly is:
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The annual birth and death rates per 1,000 are 39.4 and 19.4 respectively. The number of years in which the population will be doubled, assuming there is no immigration or emigration is:
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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% p.a. The ratio will be:
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Nominal rate of interest is 9.9 % p.a. If interest is compounded monthly, what will be the effective rate of interest?
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The population of a town increases by 2% of the population at the beginning of the year. The number of years by which the total increase in population would be 40% is:
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A stock pays annually an amount of ` 10 from the 6th year onwards. What is the present value of perpetuity, if the rate of return is 20%?
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A sum of money invested in compounded interest doubles itself in four years. In how many years does it become 32 times of itself at the same rate?
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Study Notes
Mock Test Information
- Mock Test Paper for July, 2024 scheduled for August 2nd, 2024.
- Time allocated for the paper: 2 hours, from 10:30 A.M. to 12:30 P.M.
- Focus of the paper: Quantitative Aptitude.
- Total marks available: 100.
Key Questions and Topics
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Expressions and Algebraic Equations
- Value of expression involving p and q when given specific conditions.
- Solving for x and y in simultaneous equations.
- Finding roots of polynomial equations.
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Roots and Ratios
- Calculating roots of quadratic equations using Vieta's formulas.
- Inverse relationships involving the roots of polynomial equations.
- Ratios and proportions in relation to given numbers.
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Logarithms
- Expressing logarithmic equations in terms of given variables.
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Inequalities
- Solving inequalities involving algebraic expressions and determining feasible values.
Interest and Finance Concepts
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Simple Interest Calculations
- Understanding how to calculate simple interest over time.
- Finding sums required to generate specific interest amounts.
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Compound Interest
- Distinguishing between nominal and effective interest rates.
- Understanding compounded interest calculations over specified time frames.
Population Growth and Ratios
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Population Doubling Time
- Calculating years required for a population to double based on birth and death rates.
- Managing assumptions of no immigration or emigration.
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Investment Returns
- Present value of perpetuity based on fixed annual returns.
- Understanding the growth of investment over time under compound interest.
Practical Applications
- Several mathematical concepts such as inequalities, algebraic expressions, and interest calculations to be applied in real-world financial scenarios.
- Importance of ratios and proportions in defining relationships among quantities in various contexts.
Additional Concepts
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Interest Rates and Compounding
- Importance of understanding effective interest rates compared to nominal rates.
- Key facts related to monthly versus annual compounding and its impact on financial growth.
Statistics and Trends
- Recognizing annual trends in demographic changes, such as birth and death rates.
- Application of statistics in predicting population growth based on historical rates.
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Description
Prepare for your upcoming exam with this mock test paper focused on Quantitative Aptitude. Designed for the Foundation Course, this test will challenge your mathematical skills and boost your confidence. Complete the paper to assess your readiness for the actual exam on August 2, 2024.
