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JEE Advanced

Explore popular questions from Linear Inequalities for JEE Advanced. This collection covers Linear Inequalities previous year JEE Advanced questions hand picked by experienced teachers.

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Linear Inequalities

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Q 1. is

A

C

D

Explanation

We have,

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Q 2. The least perimeter of a cyclic quadrilateral of given area square units is

A

B

C

Explanation

If is the semi-perimeter of a cyclic quadrilateral of sides and units in length, then its area is given by

Using we have


Hence, the least perimeter is

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Q 3. If are positive real numbers such that then has

Minimum value 81

B

Maximum value 81

C

Minimum value 27

D

Maximum value 27

Explanation

We have,
Now,

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Q 4. The set of values of for which the inequalities hold simultaneously, is

A

(-2, 5)

B

(2, 8)

C

(-2, 8)

(2, 5)

Explanation

Given inequalities are
and
and
and

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Q 5. If then the minimum value of is

A

B

C

1

Explanation

Using we have


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Q 6. The number of solutions of the equation is

0

B

1

C

2

D

3

Explanation

Curves and do not intersect. So, the equation has no real root

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Q 7. If then

A

C

D

None of these

Explanation

Using we have


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Q 8. The minimum value of is

B

C

D

Explanation



and
Now,









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Q 9. The number of real solutions of the equation is

A

0

1

C

2

D

None of these

Explanation

We observe that and intersect at exactly one point. So, the equation has exactly one real root:

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Q 10. If and where and then the minimum value of is

A

C

D

None of these

Explanation

We have,



But,

Hence, the minimum value of is

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Q 11. The largest interval for which is

A

B

C

Explanation


When and

Positive for all
Again, when

Largest interval also the above inequality is true for

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Q 12. If then the solution set is

A

B

D

None of these

Explanation

By trial,
for
But for
Hence, solution set for is

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Q 13. The solution of the inequation < is

B

C

D

None of tnese

Explanation

The given inequation is

Let






As is an increasing function or

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Q 14. The set of all solutions of the inequation in is

A

B

D

Explanation

Given inequation is
Roots are

Roots are imaginary, therefore no real solutions exist

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Q 15. Let be a function defined by where is the greatest integer less than or equal to Then, the number of solutions of

A

0

Infinite

C

1

D

2

Explanation

Draw graphs of and
These two curves intersect it infinitely many points

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Q 16. If then

A

B

C

Explanation

Given,

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Q 17. Solution of the inequality is given by

A

B

D

None of these

Explanation



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Q 18. then belongs to

A

B

(5, 9)

D

Explanation

We have,




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Q 19. Let be an odd positive integer. Then, the number of real roots of the polynomial is

A

0

B

1

D

None of these

Explanation

As discussed in the above problem, if is odd, there is one change of sign in (i). Therefore, can have at most one negative real root. In this case, we have

So, the negative real root lies between and 0

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Q 20. If where the greatest integer less than or equal to then must be such that

A

B

C

Explanation

We have,





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Q 21. The total number of roots of the equation is

A

1

2

C

0

D

Infinitely many

Explanation

We have,



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Q 22. If are real numbers, then the largest value of the expression is

A

C

D

Explanation

Using we have