Test: Linear Inequalities- 1 - JEE MCQ

# Test: Linear Inequalities- 1 - JEE MCQ

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## 25 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Linear Inequalities- 1

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Test: Linear Inequalities- 1 - Question 1

### By solving the inequality 3(a - 6) < 4 + a, the answer will be

Test: Linear Inequalities- 1 - Question 2

### What is the solution set for

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Test: Linear Inequalities- 1 - Question 3

### Identify the solution set for

Detailed Solution for Test: Linear Inequalities- 1 - Question 3

6<3(x-5)-5(x-1)
15
90<-2x-10
100<-2x
-50>x

Test: Linear Inequalities- 1 - Question 4

What is the solution set for

Detailed Solution for Test: Linear Inequalities- 1 - Question 4

check for interval (7/3, ∞ ) the whole would be +ve
check for interval (-∞,3/2 ) the whole would be +ve

Test: Linear Inequalities- 1 - Question 5

Identify the solution set for

Detailed Solution for Test: Linear Inequalities- 1 - Question 5

(7x-5)/(8x+3) > 4
(7x-5)/(8x+3) - 4 >0
7x - 5 - 4 ( 8x + 3 ) / 8x + 3 > 0
- 25 x - 17 / 8x + 3 > 0
Now furthermore solving for general range :
x ∈ ( -17/ 25, - 3/8)

Test: Linear Inequalities- 1 - Question 6

What is the solution set for

Test: Linear Inequalities- 1 - Question 7

Identify solution set for | 4 − x | + 1 < 3?

Detailed Solution for Test: Linear Inequalities- 1 - Question 7

|4 − x| + 1 < 3
⇒ 4 − x + 1 < 3
Add −4 and −1 on both sides, we get
4 − x + 1 − 4 − 1 < 3 − 4 − 1
⇒ − x < −2
Multiply both sides by −1, we get
x > 2
Also,|4−x| + 1 < 3
⇒ −(4−x) + 1 < 3
⇒ − 4 + x + 1 < 3
Add 4 and −1 on both sides, we get
− 4 + x + 1 + 4 − 1 < 3 + 4 − 1
⇒ x < 6
Thus, x ∈ (2,6).

Test: Linear Inequalities- 1 - Question 8

What is the solution set for

Detailed Solution for Test: Linear Inequalities- 1 - Question 8

|x-2|/(x-2) > 0
=> x - 2 > 0
x > 2
x denotes (2,∞)

Test: Linear Inequalities- 1 - Question 9

Identify the solution set for

Detailed Solution for Test: Linear Inequalities- 1 - Question 9

x−13+4<x−55−2

Multiply by 15 both side we get

x−13×15+4×15<x−55×15−2×15

⇒5(x−1)+60<3(x−5)−30

⇒5x−5+60<3x−15−30

⇒5x+55<3x−45

Add −3x and −55 on both sides, we get

5x+55−3x−55<3x−45−3x−55

⇒5x−3x<−45−55

⇒2x<−100

Divided by 2 we get

x<−50

Then x is (−∞,−50)

Test: Linear Inequalities- 1 - Question 10

What is the solution set for

Detailed Solution for Test: Linear Inequalities- 1 - Question 10

|(2x-1)/(x-1)| > 2
|x| > a
⇒ x > a
or x < -a
(2x-1)/(x-1) > 2 and (2x-1)/(x-1) < -2
(2x-2+1)/(x-1) > 2
⇒ (2(x-1) + 1)/(x-1) > 2
⇒ 2 + (1/(x-1)) > 2
1/(x-1) > 0
x-1 < 0
x < 1...........(1)
Now taking, (2x-1)/(x-1) < -2
2 + (1/(x-1) < -2
= 1/(x-1) < -4
x-1 > -1/4
x > -1/4 + 1
x > 3/4.......(2)
From (1) and (2)
x implies (3/4, 1)∪ (⁡1,∞)

Test: Linear Inequalities- 1 - Question 11

In the first four papers each of 100 marks, Rishi got 95, 72, 73, 83 marks. If he wants an average of greater than or equal to 75 marks and less than 80 marks, find the range of marks he should score in the fifth paper .

Detailed Solution for Test: Linear Inequalities- 1 - Question 11

Let marks in 5th paper be x
Average = (95 + 72 + 73 + 53 + x)/5
= (323 + x)/5
(75 ≤ 323 + x)/5 < 80
375 ≤ 323 + x < 400
52 ≤ x < 77
[52,77).

Test: Linear Inequalities- 1 - Question 12

A man wants to cut three lengths from a single piece of board of length 91cm. The second length is to be 3 cm longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for the shortest board if the third piece is to be at least 5 cm longer than the second?

Test: Linear Inequalities- 1 - Question 13

Find all pairs of consecutive odd natural numbers, both of which are larger than 10, such that their sum is less than 40.

Test: Linear Inequalities- 1 - Question 14

The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of atleast 65 marks.

Test: Linear Inequalities- 1 - Question 15

A solution is to be kept between 30C and 35C What is the range of temperature in degree Fahrenheit ?

Test: Linear Inequalities- 1 - Question 16

The longest side of a triangle is three times the shortest side and the third side is 2cm shorter than the longest side if the perimeter of the triangles at least 61cm, find the minimum length of the shortest side.

Test: Linear Inequalities- 1 - Question 17

Which of the following is correct ?

Test: Linear Inequalities- 1 - Question 18

Solve the inequality 3 − 2x ≤ 9

Detailed Solution for Test: Linear Inequalities- 1 - Question 18

3 − 2x ≤ 9
-2x ≤ 6
-x ≤ 3
-3 ≤ x

Test: Linear Inequalities- 1 - Question 19

Given that x is an integer, find the values of x which satisfy both 2x + 3 > 7 and x + 4 < 10

Test: Linear Inequalities- 1 - Question 20

The solution of 4x-2 > 6 is

Test: Linear Inequalities- 1 - Question 21

x = 4 , 5 and 6 are the solutions for :

Test: Linear Inequalities- 1 - Question 22

What are the integer values of x which satisfy the inequalities x > − 2 and x ≤ 2 ?

Test: Linear Inequalities- 1 - Question 23

Given that x is an integer, find the values of x which satisfy the simultaneous linear inequalities 2 + x < 6 and 2 −3x < − 1.

Test: Linear Inequalities- 1 - Question 24

Solve : 30x < 200, when x is a natural number :

Test: Linear Inequalities- 1 - Question 25

The solution set for : 3x − 7 > x + 3.

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests