On account of the disruption in education due to the corona pandemic, we're opening up our platform for teachers, free of cost. Know More →

JEE Main

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

Select Subject

Physics

Chemistry

Mathematics

Linear Inequalities

Correct Marks 4

Incorrectly Marks -1

Q 1. If {tex} x {/tex} is real number and {tex} | x | < 3 , {/tex} then

A

{tex} x \geq 3 {/tex}

{tex} - 3 < x < 3 {/tex}

C

{tex} x \leq - 3 {/tex}

D

{tex} - 3 \leq x \leq 3 {/tex}

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 2. Given that {tex} x ,\ y {/tex} and {tex} b {/tex} are real numbers and {tex} x < y ,\ b < 0 , {/tex} then

A

{tex} \frac { x } { b } < \frac { y } { b } {/tex}

B

{tex} \frac { x } { b } \leq \frac { y } { b } {/tex}

{tex} \frac { x } { b } > \frac { y } { b } {/tex}

D

{tex} \frac { x } { b } \geq \frac { y } { b } {/tex}

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 3. Solution of a linear inequality in variable {tex} x {/tex} is represented on number line is

A

{tex} x \in ( - \infty , 5 ) {/tex}

B

{tex} x \in ( - \infty , 5 ] {/tex}

C

{tex} x \in [ 5 , \infty ) {/tex}

{tex} x \in ( 5 , \infty ) {/tex}

Correct Marks 4

Incorrectly Marks -1

Q 4. If {tex} | x + 3 | \geq 10 {/tex}, then

A

{tex} x \in ( - 13,7 ] {/tex}

B

{tex} x \in ( - 13,7 ) {/tex}

C

{tex} x \in ( - \infty , 13 ] \cup [ - 7 , \infty ) {/tex}

{tex} x \in ( - \infty , - 13 ] \cup [ 7 , \infty ) {/tex}

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 5. Let {tex}\mathrm{ \frac { C } { 5 } = \frac { F - 32 } { 9 } } {/tex}. If {tex}\mathrm C {/tex} lies between {tex}10{/tex} and {tex}20{/tex}, then :

A

{tex} 50 < \mathrm{ F } < 78 {/tex}

{tex} 50 < \mathrm { F } < 68 {/tex}

C

{tex} 49 < \mathrm{ F } < 68 {/tex}

D

{tex} 49 < \mathrm { F } < 78 {/tex}

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 6. The solution set of the inequality {tex} 4 x + 3 < 6 x + 7 {/tex} is

A

{tex} [ - 2 , \infty ) {/tex}

B

{tex} ( - \infty , - 2 ) {/tex}

{tex} ( - 2 , \infty ) {/tex}

D

None of these

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 7. Which of the following is the solution set of {tex} 3 x - 7 > 5 x - 1\ \forall \ x \in R {/tex} ?

{tex} ( - \infty , - 3 ) {/tex}

B

{tex} ( - \infty , - 3 ] {/tex}

C

{tex} ( - 3 , \infty ) {/tex}

D

{tex} ( - 3,3 ) {/tex}

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 8. The solution set of the inequality {tex} 37 - ( 3 x + 5 ) \geq 9 x - 8 ( x - 3 ) {/tex} is

A

{tex} ( - \infty , 2 ) {/tex}

B

{tex} ( - \infty , - 2 ) {/tex}

{tex} ( - \infty , 2 ] {/tex}

D

{tex} ( - \infty , - 2 ] {/tex}

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 9. The graphical solution of {tex} 3 x - 6 \geq 0 {/tex} is

B

C

D

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 10. The solutions of the system of inequalities {tex} 3 x - 7 < 5 + x {/tex} and {tex} 11 - 5 x \leq 1 {/tex} on the number line is

A

C

D

None of the above

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 11. The solution set of the inequalities {tex} 3 x - 7 > 2 ( x - 6 ) {/tex} and {tex} 6 - x > 11 - 2 x , {/tex} is

A

{tex} ( - 5 , \infty ) {/tex}

B

{tex} [ 5 , \infty ) {/tex}

{tex} ( 5 , \infty ) {/tex}

D

{tex} [ - 5 , \infty ) {/tex}

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 12. If {tex} \frac { 3 x - 4 } { 2 } \geq \frac { x + 1 } { 4 } - 1 , {/tex} then {tex} x \in {/tex}

{tex} [ 1 , \infty ) {/tex}

B

{tex} ( 1 , \infty ) {/tex}

C

{tex} ( - 5,5 ) {/tex}

D

{tex} [ - 5,5 ] {/tex}

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 13. If {tex} - 5 \leq \frac { 5 - 3 x } { 2 } \leq 8 , {/tex} then {tex} x \in {/tex}

{tex} \left[ - \frac { 11 } { 3 } , 5 \right] {/tex}

B

{tex} [ - 5,5 ] {/tex}

C

{tex} \left[ - \frac { 11 } { 3 } , \infty \right) {/tex}

D

{tex} ( - \infty , \infty ) {/tex}

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 14. Solutions of the inequalities comprising a system in variable {tex} x {/tex} are represented on number lines as given below, then

{tex} x \in ( - \infty , - 4 ] \cup [ 3 , \infty ) {/tex}

B

{tex} x \in [ - 3,1 ] {/tex}

C

{tex} x \in ( - \infty , - 4 ) \cup [ 3 , \infty ) {/tex}

D

{tex} x \in [ - 4,3 ] {/tex}

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 15. The inequality {tex} \frac { 2 } { x } < 3 {/tex} is true, when {tex} x {/tex} belongs to

A

{tex} \left[ \frac { 2 } { 3 } , \infty \right) {/tex}

B

{tex} \left( - \infty , \frac { 2 } { 3 } \right] {/tex}

{tex} ( - \infty , 0 ) \cup \left( \frac { 2 } { 3 } , \infty \right) {/tex}

D

None of these

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 16. Solution of {tex} | 3 x + 2 | < 1 {/tex} is

A

{tex} \left[ - 1 , - \frac { 1 } { 3 } \right] {/tex}

B

{tex} \left\{ - \frac { 1 } { 3 } , - 1 \right\} {/tex}

{tex} \left( - 1 , - \frac { 1 } { 3 } \right) {/tex}

D

None of these

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 17. Solution of {tex} | x - 1 | \geq | x - 3 | {/tex} is

A

{tex} x \leq 2 {/tex}

{tex} x \geq 2 {/tex}

C

{tex} [ 1,3 ] {/tex}

D

None of these

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 18. If {tex} - 3 x + 17 < - 13 , {/tex} then

{tex} x \in ( 10 , \infty ) {/tex}

B

{tex} x \in [ 10 , \infty ) {/tex}

C

{tex} x \in ( - \infty , 10 ] {/tex}

D

{tex} x \in [ - 10,10 ) {/tex}

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 19. If {tex} | x + 2 | \leq 9 , {/tex} then

A

{tex} x \in ( - 7,11 ) {/tex}

{tex} x \in [ - 11,7 ] {/tex}

C

{tex} x \in ( - \infty , - 7 ) \cup ( 11 , \infty ) {/tex}

D

{tex} x \in ( - \infty , - 7 ) \cup [ 11 , \infty ) {/tex}

Explanation