Daily Practice Problems

Class 11 Maths

Linear Inequalities

Class 11 Maths

Linear Inequalities

**Question 1:**

Solve 5x – 3 < 3x + 1 where x is an integer.

**Question 2:**

Solve: (5 – 2x)/3 ≤ x/6 - 5

**Question 3:**

Ravi scored 70 and 75 marks in the first two-unit test. Calculate the minimum marks he should get in the third test to have an average of at least 60 marks.

**Question 4:**

Solve: (x - 4)/2 ≥ (x + 1)/4 - 1

**Question 5:**

Solve the equation, 4x - 2 ≤ 6 and 9x + 3 ≥ -15

**Question 6:**

Consider a triangle where the longest side of the triangle is three times the shortest side. Third side of the triangle is 3 cm smaller than the longest side. Parameter of the triangle is at least 61 cm. What will be the minimum length of the shortest side?

**Question 7:**

For the pool, the average water acidity is considered normal when in the range of 7.2 and 7.8 pH when measured for three days continuously. What will be the pH for the third day when acidity for the first two days is 7.52 and 7.1. Consider the pH of the pool in normal.

**Question 8:**

In T20 series, Raj scored 30 and 85 runs in the first two matches. Calculate the minimum runs required in his third match to form an average of at least 50 runs.

**Question 9:**

Find the pairs of consecutive odd natural numbers both of which are larger than 10 such that their sum is less than 50.

**Question 10:**

While drilling hole it was found that temperature (T) changes at (x) km below the surface. It was given by T = 30 + 25(x - 3) and 3 < x < 15. Determine the depth at which temperature will be between 400°C and 700°C.

**Question 11:**

Let x is an integer. Solve 5x – 3 ≤ 3x + 1

**Question 12:**

Solve for x: 2x – 1 ≤ 3, 3x + 1 ≥ -5

**Question 13:**

If (x + 3)/(x – 2) > 1/2 then x lies in the interval _____.

**Question 14:**

The interval in which f(x) = (x – 1)(x – 2)(x – 3) is negative is _____.

**Question 15:**

The solution of the inequality |x – 1| < 2 is ____.

**Question 16:**

If | x − 1| > 5, then range of x is _____.

**Question 17:**

The solution of |2/(x – 4)| > 1 where x ≠ 4 is

**Question 18:**

The graph of the inequations x ≥ 0, y ≥ 0, 3x + 4y ≤ 12 is

**Question 19:**

Solve: f(x) = {(x – 1)(2 – x)}/(x – 3) ≥ 0

**Question 20:**

The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then breadth ______.

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