In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.

Concept: Areas of Sector and Segment of a Circle

If the quadratic equation px^{2} − 2√5px + 15 = 0 has two equal roots then find the value of p.

Concept: Nature of Roots

In the following figure, in ΔPQR, seg RS is the bisector of ∠PRQ. If PS = 6, SQ = 8, PR = 15, find QR.

Concept: Similarity of Triangles

Jaya borrowed Rs. 50,000 for 2 years. The rates of interest for two successive years are 12% and 15% respectively. She repays 33,000 at the end of the first year. Find the amount she must pay at the end of the second year to clear her debt.

Concept: Concept of Compound Interest > Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

Mr Lalit invested Rs. 5000 at a certain rate of interest, compounded annually for two years. At the end of the first year, it amounts to Rs. 5325. Calculate

1) The rate of interest

2) The amount at the end of the second year, to the nearest rupee.

Concept: Concept of Compound Interest > Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years

In what time will Rs. 1500 yield Rs. 496.50 as compound interest at 10% per annum compounded annually?

Concept: Concept of Compound Interest > Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years

The present population of the town is 2,00,000. The population is increased by 10% in the first year and 15% in the second year. Find the population of the town at the end of two years.

Concept: Concept of Compound Interest > Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years

If a, b, c are in continued proportion, prove that (a + b + c) (a – b + c) = a^{2} + b^{2} + c^{2}

Concept: Concept of Compound Interest > Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

Ranbir borrows Rs. 20,000 at 12% per annum compound interest. If he repays Rs. 8400 at the end of the first year and Rs. 9680 at the end of the second year, find the amount of loan outstanding at the beginning of the third year.

Concept: Concept of Compound Interest > Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years

The compound interest, calculated yearly, on a certain sum of money for the second year is Rs. 1320 and for the third year is Rs. 1452. Calculate the rate of interest and the original sum of money

Concept: Concept of Compound Interest > Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years

At what rate % p.a. will a sum of Rs. 4000 yield Rs. 1324 as compound interest in 3 years?

Concept: Concept of Compound Interest > Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5% p.a.?

Concept: Concept of Compound Interest > Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

Mr Kumar borrowed Rs. 15000 for two years. The rates of interest for two successive years are 8% and 10% respectively. If he repays Rs. 6200 at the end of the first year, find the outstanding amount at the end of the second year.

Concept: Concept of Compound Interest > Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

In what period of time will Rs. 12,000 yield Rs. 3972 as compound interest at 10% per annum, if compounded on a yearly basis?

Concept: Concept of Compound Interest > Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years

Nikita invests Rs. 6000 for two years at a certain rate of interest compounded annually. At the end of the first year, it amounts to Rs. 6720. Calculate:

1) the rate of interest.

2) the amount at the end of the second year.

Concept: Concept of Compound Interest > Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years

Rohit borrows Rs. 86,000 from Arun for two years at 5% per annum simple interest. He immediately lends out this money to Akshay at 5% compound interest compounded annually for the same period. Calculate Rohit’s profit in the transaction at the end of two years.

Concept: Concept of Compound Interest > Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

How much should a man invest in Rs. 50 shares selling at Rs. 60 to obtain an income of Rs. 450, if the rate of dividend declared is 10%. Also find his yield percent, to the nearest whole number.

Concept: Shares and Dividends Examples

Ashok invested Rs. 26,400 on 12%, Rs. 25 shares of a company. If he receives a dividend of Rs. 2,475. Find the :

1) number of shares he bought

2) The market value of each share

Concept: Shares and Dividends

A man invests Rs. 22,500 in Rs. 50 shares available at 10% discount. If the dividend paid by the company is 12%, calculate:

1) The number of shares purchased

2) The annual dividend received.

3) The rate of return he gets on his investment. Give your answer correct to the nearest whole number.

Concept: Shares and Dividends Examples

Rohit invested Rs. 9,600 on Rs. 100 shares at Rs. 20 premium paying 8% dividend. Rohit sold the shares when the price rose to Rs 160. He invested the proceeds (excluding dividend) in 10% Rs. 50 shares at Rs. 40. Find the:

1) original number of shares

2) sale proceeds

3) new number of shares

4) change in the two dividends.

Concept: Shares and Dividends

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