Solve the following inequation and write down the solution set. 11 x - 4 < 15 x + 4 ≤ 13 x + 14 , x ∈ W Represent the solution on a real number line.

Given: 11 x - 4 < 15 x + 4 ≤ 13 x + 14 , x ∈ W Consider, 11 x - 4 < 15 x + 4 ⇒ 11 x - 4 - 4 < 15 x + 4 - 4 [subtract 4 from both sides] ⇒ 11 x - 8 < 15 x ⇒ 11 x - 8 - 11 x < 15 x - 11 x [subtract 11 x from both sides] ⇒ - 8 < 4 x ⇒ - 8 4 < 4 x 4 [divide both sides by 4 ] ⇒ x > - 2 . . . . . . . i Now, consider, 15 x + 4 ≤ 13 x + 14 ⇒ 15 x + 4 - 13 x ≤ 13 x + 4 - 13 x [subtract 13 x from both sides] ⇒ 2 x + 4 ≤ 14 ⇒ 2 x + 4 - 4 ≤ 14 - 4 [ subtract 4 from both sides] ⇒ 2 x ≤ 10 ⇒ 2 x 2 ≤ 10 2 [divide both sides by 5 ] ⇒ x ≤ 5 . . . . . . i i ∴ From equations i and i i , we get: - 2 < x ≤ 5 Since, x ∈ W . ∴ Solution set = 0 , 1 , 2 , 3 , 4 , 5 On the number line it can be represented as

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10th ICSE

IMPORTANT

Earn 100

Prove that the circle drawn with any side of a rhombus as a diameter, passes through the point of intersection of its diagonals.

Important Questions on Sample Question Paper

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 10

Use a ruler and a compass for this question.
Construct a

∆ ABC

in which

BC = 6.5 cm

∠ ABC = 60 °

AB = 5 cm

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 11

A shopkeeper in Rajasthan buys a scooty at the printed price of $₹ 30000$ from a wholesaler in Kerala. The shopkeeper sells scooty to a consumer in Rajasthan at a profit of $15 %$ on the basic cost price. If the rate of GST is $12 %$ , find the price (in rupees) inclusive of tax (under GST) at which the wholesaler sold the scooty.

Note: This question given in the book seems to have error and the modified question should be as given above.”

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 11

A shopkeeper in Rajasthan buys a scooty at the printed price of

₹ 30000

from a wholesaler in Kerala. The shopkeeper sells scooty to a consumer in Rajasthan at a profit of

15 %

on the basic cost price. If the rate of GST is

12 %

, find the amount (in rupees) which the consumer pays for the scooty.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 11

On plotting the points

O (0, 0), A (3, 0), B (3, 4), C (0, 4)

and joining

O A, A B, B C and C O

, which shape is obtained? Also, find the equations of

O B and A C

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 1

Solve the following inequation and write down the solution set.

$11 x - 4 < 15 x + 4 \leq 13 x + 14, x \in W$

Represent the solution on a real number line.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 1

A man invests $₹ 4500$ in shares of a company which is paying $7.5 %$ dividend. If $₹ 100$ shares are available at a discount of $10 %$ . Find number of shares he purchases.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 1

A man invests $₹ 4500$ in shares of a company which is paying $7.5 %$ dividend. If $₹ 100$ shares are available at a discount of $10 %$ . Find his annual income (in rupees upto one decimal place).

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 22 - Sample Question Paper>SAMPLE QUESTION PAPER>Q 2

Using the factor theorem, show that

(x - 2)

is a factor of

x^{3} + x^{2} - 4 x - 4

. Hence factorise the polynomial completely.

Prove that the circle drawn with any side of a rhombus as a diameter, passes through the point of intersection of its diagonals.

Important Questions on Sample Question Paper

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