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# Question Bank Solutions for ICSE Class 10 - CISCE - Mathematics

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

[3.05] Similarity
Chapter: [3.05] Similarity
Concept: Similarity of Triangles
Appears in 2 question papers

Solve the equation 4x2 – 5x – 3 = 0 and give your answer correct to two decimal places

Appears in 1 question paper

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.

[1.01] Compound Interest
Chapter: [1.01] Compound Interest
Concept: Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
Appears in 1 question paper

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.

[1.04] Sales Tax and Value Added Tax
Chapter: [1.04] Sales Tax and Value Added Tax
Concept: Introduction to Sales Tax and Value Added Tax
Appears in 1 question paper

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.

[2.01] Co-ordinate Geometry Distance and Section Formula
Chapter: [2.01] Co-ordinate Geometry Distance and Section Formula
Concept: Co-ordinates Expressed as (x,y)
Appears in 1 question paper

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.

[1.02] Shares and Dividends
Chapter: [1.02] Shares and Dividends
Concept: Shares and Dividends Examples
Appears in 1 question paper

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.

[1.04] Sales Tax and Value Added Tax
Chapter: [1.04] Sales Tax and Value Added Tax
Concept: Introduction to Sales Tax and Value Added Tax
Appears in 1 question paper

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.

[6] Statistics
Chapter: [6] Statistics
Concept: Median of Grouped Data
Appears in 1 question paper

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).

[2.1] Co-ordinate Geometry Equation of a Line
Chapter: [2.1] Co-ordinate Geometry Equation of a Line
Concept: Slope of a Line
Appears in 1 question paper

Solve the quadratic equation x2 -  3(x + 3) = 0; Give your answer correct two significant figures

Appears in 1 question paper

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

[1.04] Sales Tax and Value Added Tax
Chapter: [1.04] Sales Tax and Value Added Tax
Concept: Introduction to Sales Tax and Value Added Tax
Appears in 1 question paper

If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of 'a' and b'.

[2.03] Factorization
Chapter: [2.03] Factorization
Concept: Factor Theorem
Appears in 1 question paper

Solve x2 + 7x = 7 and give your answer correct to two decimal places

Appears in 1 question paper

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

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

[1.02] Shares and Dividends
Chapter: [1.02] Shares and Dividends
Concept: Shares and Dividends Examples
Appears in 1 question paper

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.

Appears in 1 question paper

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

[3.05] Similarity
Chapter: [3.05] Similarity
Concept: Similarity of Triangles
Appears in 1 question paper

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

[1.04] Sales Tax and Value Added Tax
Chapter: [1.04] Sales Tax and Value Added Tax
Concept: Introduction to Sales Tax and Value Added Tax
Appears in 1 question paper

Without using trigonometric tables evaluate:

(sin 65^@)/(cos 25^@) + (cos 32^@)/(sin 58^@) - sin 28^2. sec 62^@ + cosec^2 30^@

[5] Trigonometry
Chapter: [5] Trigonometry
Concept: Trigonometric Ratios of Complementary Angles
Appears in 1 question paper

The marks obtained by 30 students in a class assignment of 5 marks are given below.

 Marks 0 1 2 3 4 5 No. ofStudents 1 3 6 10 5 5

Calculate the mean, median and mode of the above distribution

[6] Statistics
Chapter: [6] Statistics
Concept: Median of Grouped Data
Appears in 1 question paper

Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation

(K + 2)x^2 - kx + 6 = 0`