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QUESTION: 1

Find the pairs of consecutive even positive integers both of which are smaller than 10 and their sum of more than 11

Solution:

Let x be the smaller of the two consecutive even positive integers .

Then the other integer is x+2.

Since both the integers are smaller than 10,x<10 ....(1)

Also the sum of the two integers is more than 11.

x+(x+2)>11

⇒ 2x+2>11

⇒ 2x>11−2

⇒ 2x>9

⇒ x>9/2

⇒ x>4.5....(2)

From (1) and (2) we obtain 4.5>x>11

Since x is an even number, x can take the values 6,8 and 10.

Thus the required possible pairs are (6,8).

QUESTION: 2

The solution to |3x – 1| + 1 < 3 is

Solution:

|3x - 1| + 1 < 3

|3x -1| < 2

Opening mod, we get

3x - 1 < 2, -3x + 1 > 2

3x < 3, -3x > 1

x < 1, x > -1/3

-1/3 < x < 1

QUESTION: 3

Which of the following is not a linear inequality?

Solution:
A is a quadratic equation not a linear equality because square of a function can't be negative

QUESTION: 4

For a student to qualify for a certain course, the average of his marks in the permitted 3 attempts must be more than 60. His first two attempts yielded only 45 and 62 marks respectively. What is the minimum score required in the third attempt to qualify?

Solution:

No of attempts = 3

Average = (45+62+x)/3=60

x=73

QUESTION: 5

Which one of them is the solution for x, when x is integer and 12 x > 30?

Solution:

12x > 30

x > 30/12

x > 2.5

x is an integer. So, minimum value of x is 3.

QUESTION: 6

Find the value of x which satisfies 5x – 3 < 7, where x is a natural number.

Solution:

QUESTION: 7

If -5x+2<7x -4, then x is

Solution:

-5x + 2 < 7x - 4

6 < 12x

x > 1/2

QUESTION: 8

The solution to 5x-3<3x+1, when x is an integer, is

Solution:

We have 5x−3<3x+1

⇒5x−3+3<3x+1+3

⇒5x<3x+4

⇒5x−3×<3x+4−3x

⇒2x<4⇒x<2

When x is an integer the solutions of the given inequality are {.............,−4,−3,−2,−1,0,1}

Hence {x / xεZ, x<2}

QUESTION: 9

The inequations -4x+1≥0 and 3-4x<0 have the common solutions given by

Solution:

**-**4x+1≥0 and 3-4x<0

-4x ≥ -1 and 3 > 4x

1/4 ≥ x and 3/4 > x

{¾, ¼]

QUESTION: 10

Solve the following linear inequality for x:

Solution:

(2-3x)/5 ≤ (-x-6)/2

By cross multiply we get

4-6x ≤ -5x-30

-x ≤ -34

x ≥ 34

QUESTION: 11

A point P lies in the solution region of 3x – 7 > x + 3. So the possible coordinates of P are

Solution:

QUESTION: 12

A connected planar graph having 6 vertices, 7 edges contains _____________ regions.

Solution:

By euler’s formula the relation between vertices(n), edges(q) and regions(r) is given by n-q+r=2.

QUESTION: 13

If 5x+6<2x-3, then

Solution:

5x+6<2x-3

5x-2x < -3-6

3x < -9

x<-3

QUESTION: 14

The region x > -3 lies

Solution:

QUESTION: 15

If a < b then -a ______ - b

Solution:

QUESTION: 16

The solution of inequality 4x + 3 < 5x + 7 when x is a real number is

Solution:

4x+3<5x+7

4x+3−7<5x+7−7

4x−4<5x

4x−4−4x<5x−4x

−4<x

Thus, the solution set of the given inequality is (−4,∞).

QUESTION: 17

Two less than 5 times a number is greater than the third multiple of the number. So the number must be

Solution:

QUESTION: 18

What values of x satisfy -6x>24 and x is an integer?

Solution:

- 6x < 24

=> 6x < -24

x < - 4

QUESTION: 19

The solution set of , where x is a real

Solution:

X/3-x/2 > 1

-x/6 > 1

x/6

x < -6

therefore x belongs to the range (-∞,-6)

QUESTION: 20

Find the value of x when x is a natural number and 24x< 100.

Solution:

24x < 100

⇒ x < 100/24

⇒ x < 25/6

It is evident that 1,2,3 and 4 are the only natural numbers less than 25/6,

Thus when x is a natural number ,the solutions of the given inequality are 1,2,3 and 4.

Hence, in this case, the solution set is {1,2,3,4}.

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