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

If A, B, C are the interior angles of a triangle ABC, prove that `\tan \frac{B+C}{2}=\cot \frac{A}{2}`

Concept: Trigonometric Ratios of Complementary Angles

Solve the equation 4x^{2} – 5x – 3 = 0 and give your answer correct to two decimal places

Concept: Quadratic Equations

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

The catalogue price of a computer set is Rs. 42,000. The shopkeeper gives a discount of

10% on the listed price. He further gives an off-season discount of 5% on the discounted

price. However, sales tax at 8% is charged on the remaining price after the two successive

discounts. Find

1)the amount of sales tax a customer has to pay

2)the total price to be paid by the customer for the computer set.

Concept: Sales Tax, Value Added Tax, and Good and Services Tax

P(1, -2) is a point on the line segment A(3, -6) and B(x, y) such that AP : PB is equal to 2 : 3. Find the coordinates of B.

Concept: Co-ordinates Expressed as (x,y)

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

The printed price of an air conditioner is Rs. 45000/-. The wholesaler allows a discount of 10%

to the shopkeeper. The shopkeeper sells the article to the customer at a discount of 5% of the

marked price. Sales tax (under VAT) is charged at the rate of 12% at every stage. Find:

1) VAT paid by the shopkeeper to the government

2) The total amount paid by the customer inclusive of tax.

Concept: Sales Tax, Value Added Tax, and Good and Services Tax

The mean of following numbers is 68. Find the value of ‘x’.

45, 52, 60, x, 69, 70, 26, 81 and 94

Hence estimate the median.

Concept: Median of Grouped Data

The slope of a line joining P(6, k) and Q (1-3k, 3) is `1/2` Find

1) k

2) A midpoint of PQ, using the value of ‘k’ found in (1).

Concept: Slope of a Line

If (3a + 2b) : (5a + 3b) = 18 : 29. Find a : b

Concept: Concept of Ratio

Solve the quadratic equation x^{2} - 3(x + 3) = 0; Give your answer correct two significant figures

Concept: Quadratic Equations

A dealer buys an article at a discount of 30% from the wholesaler, the marked price being Rs. 6000. The dealer sells it to a shopkeeper at a discount of 10% on the marked price. If the rate of the VAT is 6%, find

1) The price paid by the shopkeeper including the tax.

2) The VAT paid by the dealer

Concept: Sales Tax, Value Added Tax, and Good and Services Tax

If (x + 2) and (x + 3) are factors of x^{3} + ax + b, find the values of 'a' and `b'.

Concept: Factor Theorem

Solve x^{2} + 7x = 7 and give your answer correct to two decimal places

Concept: Quadratic Equations

The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series

Concept: Concept of Ratio

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

Rs. 7500 were divided equally among a certain number of children. Had there been 20 less children, each would have received Rs. 100 more. Find the original number of children.

Concept: Quadratic Equations

In ΔPQR, MN is parallel to QR and `(PM)/(MQ) = 2/3`

1) Find `(MN)/(QR)`

2) Prove that ΔOMN and ΔORQ are similar.

3) Find, Area of ΔOMN : Area of ΔORQ

Concept: Similarity of Triangles

A shopkeeper bought an article for Rs. 3,450. He marks the price of the article 16% above the cost price. The rate of sales tax charged in the article is 10%

Find the:

1) market price of the article.

2) price paid by a customer who buys the article

Concept: Sales Tax, Value Added Tax, and Good and Services Tax