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Question Bank Solutions for ICSE Class 10 - CISCE - Mathematics

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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

[2.02] Quadratic Equations
Chapter: [2.02] Quadratic Equations
Concept: Quadratic Equations
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

[2.02] Quadratic Equations
Chapter: [2.02] Quadratic Equations
Concept: Quadratic Equations
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

[2.02] Quadratic Equations
Chapter: [2.02] Quadratic Equations
Concept: Quadratic Equations
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

2) The annual dividend received.

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.

[2.02] Quadratic Equations
Chapter: [2.02] Quadratic Equations
Concept: Quadratic Equations
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. of
Students
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`

[2.02] Quadratic Equations
Chapter: [2.02] Quadratic Equations
Concept: Quadratic Equations
Appears in 1 question paper
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Question Bank Solutions for ICSE Class 10 CISCE Mathematics. You can further filter Question Bank Solutions by subjects and chapters. Solutions for most of the questions for CISCE can be found here on shaalaa.com. You can use these solutions to prepare for your studies and ace in exams. Solving questions is a great way to practice and with shaalaa.com, you can answer a question and then also check your answer with the solutions provided.
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