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Question Bank Solutions for ICSE Class 10 - CISCE - Mathematics

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Construct a regular hexagon of side 5 cm. Construct a circle circumscribing the hexagon. All traces of construction must be clearly shown.

[3.03] Constructions
Chapter: [3.03] Constructions
Concept: Circumscribing and Inscribing a Circle on a Regular Hexagon
Appears in 1 question paper

If a, b, c are in continued proportion, prove that (a + b + c) (a – b + c) = a2 + b2 + c2

[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

A wholesaler buys a TV from the manufacturer for Rs. 25,000. He marks the price of TV 20% above his cost price and sells it to a retailer at a 10% discount on the market price. If the rate of the VAT is 8%, find the :

1) Market price

2) Retailer’s cost price inclusive of tax.

3) VAT paid by the wholesaler.

[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

ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that:

1) ΔADE ~ ΔACB

2) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.

3) Find. Area of ΔADE: area of quadrilateral BCED

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

Sum of two natural numbers is 8 and the difference of their reciprocal is `2/15`. Find the numbers.

[2.02] Quadratic Equations
Chapter: [2.02] Quadratic Equations
Concept: Quadratic Equations
Appears in 1 question paper

Calculate the ratio in which the line joining A(-4,2) and B(3,6 is divided by a point P(x, 3). Also, find (i) x (ii) Length of AP.

[2.04] Ratio and Proportion
Chapter: [2.04] Ratio and Proportion
Concept: Ratios
Appears in 1 question paper

The numbers 6, 8, 10, 12, 13 and x are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of x

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

A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being Rs. 18,000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the rate of sales tax is 8%, find:

1) the VAT paid by the shopkeeper.

2) the total amount that the consumer pays for the washing machine

[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

In Δ ABC, ∠ABC = ∠DAC. AB = 8 cm, AC = 4 cm, AD = 5 cm.

1) Prove that Δ ACD is similar to Δ BCA.

2) Find BC and CD

3) Find- area of Δ ACD : area of Δ BCA

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

If (x - 9) : (3x + 6) is the duplicate ratio of 4: 9, find the value of x.

[2.04] Ratio and Proportion
Chapter: [2.04] Ratio and Proportion
Concept: Ratios
Appears in 1 question paper

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

[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 median of the following observations
11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24.
Find the value of x and hence find the mean.

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

If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.

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

Solve the following equation and calculate the answer correct to two decimal places:

x2 – 5x – 10 = 0.

[2.02] Quadratic Equations
Chapter: [2.02] Quadratic Equations
Concept: Quadratic Equations
Appears in 1 question paper

In the given figure, AB and DE are perpendicular to BC.

1) Prove that ΔABC ∼ ΔDEC

2) If AB = 6 cm; DE = 4 cm and AC = 15 cm. Calculate CD.

3) Find the ratio of area of ΔABC: area of ΔDEC

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

A shopkeeper sells an article at the listed price of Rs. 1500 and the rate of the VAT is 12% at each stage of the sale. If the shopkeeper pays a VAT of Rs. 36 to the Government, what was the price, inclusive to TAX, at which the shopkeeper purchased the article from the wholesaler?

[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 solving the following quadratic equation, find the value of ‘p' for which the given equation has real and equal roots: 

x2 + (p – 3)x + p = 0.

[2.02] Quadratic Equations
Chapter: [2.02] Quadratic Equations
Concept: Quadratic Equations
Appears in 1 question paper

A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and solve it to find the original cost of the books.

[2.02] Quadratic Equations
Chapter: [2.02] Quadratic Equations
Concept: Quadratic Equations
Appears in 1 question paper

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.?

[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

ABC is an isosceles right-angled triangle with ∠ABC = 90°. A semi-circle is drawn with AC as the diameter. If AB = BC = 7 cm, find the area of the shaded region. [Take Π = 22/7]

[4] Mensuration
Chapter: [4] Mensuration
Concept: Perimeter and Area of a Circle
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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