Linear Inequalities Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. |2x – 3| < |x + 5|, then x belongs to
(a) (–3, 5)
(b) (5, 9)
(c)
(d)
2. If x satisfies the inequalities x + 7 < 2x + 3 and
2x + 4 < 5x + 3, then x lies in the interval
(a) (– 8, 3)
(b) (1, 3)
(c) (4, 8)
(d) (–8, –1)
3. The shaded region shown in the figure is given by the inequations
Page 2


PART-I (Single Correct MCQs)
1. |2x – 3| < |x + 5|, then x belongs to
(a) (–3, 5)
(b) (5, 9)
(c)
(d)
2. If x satisfies the inequalities x + 7 < 2x + 3 and
2x + 4 < 5x + 3, then x lies in the interval
(a) (– 8, 3)
(b) (1, 3)
(c) (4, 8)
(d) (–8, –1)
3. The shaded region shown in the figure is given by the inequations
(a) 14x + 5y   70, y   14 and x – y   5
(b) 14x + 5y  70, y   14 and x – y   5
(c) 14x + 5y  70, y   14 and x – y   5
(d) 14x + 5y  70, y  14 and x – y   5
4. The region represented by the inequation system x, y = 0, y = 6, x + y =
3, is
(a) Unbounded in first quadrant
(b) Unbounded in first and second quadrants
(c) Bounded in first quadrant
(d) None of these
5. If –7 < x < 18 and 9 < y < 20, then the range of x + y is:
(a) [2, 38]
(b) (2, 38]
(c) [2, 38)
(d) (2, 38)
6. The region represented by 2x + 3y – 5 = 0 and
4x – 3y + 2 = 0, is
(a) Not in first quadrant
(b) Bounded in first quadrant
(c) Unbounded in first quadrant
(d) None of these
7. The set of  real values of x satisfying and is
(a) [2, 4]
(b)
(c)
(d) None of these
8. IQ of a person is given by the formula
Page 3


PART-I (Single Correct MCQs)
1. |2x – 3| < |x + 5|, then x belongs to
(a) (–3, 5)
(b) (5, 9)
(c)
(d)
2. If x satisfies the inequalities x + 7 < 2x + 3 and
2x + 4 < 5x + 3, then x lies in the interval
(a) (– 8, 3)
(b) (1, 3)
(c) (4, 8)
(d) (–8, –1)
3. The shaded region shown in the figure is given by the inequations
(a) 14x + 5y   70, y   14 and x – y   5
(b) 14x + 5y  70, y   14 and x – y   5
(c) 14x + 5y  70, y   14 and x – y   5
(d) 14x + 5y  70, y  14 and x – y   5
4. The region represented by the inequation system x, y = 0, y = 6, x + y =
3, is
(a) Unbounded in first quadrant
(b) Unbounded in first and second quadrants
(c) Bounded in first quadrant
(d) None of these
5. If –7 < x < 18 and 9 < y < 20, then the range of x + y is:
(a) [2, 38]
(b) (2, 38]
(c) [2, 38)
(d) (2, 38)
6. The region represented by 2x + 3y – 5 = 0 and
4x – 3y + 2 = 0, is
(a) Not in first quadrant
(b) Bounded in first quadrant
(c) Unbounded in first quadrant
(d) None of these
7. The set of  real values of x satisfying and is
(a) [2, 4]
(b)
(c)
(d) None of these
8. IQ of a person is given by the formula
where, MA is mental age and CA is chronological age.If 80 = IQ = 140 for a
group of 12 years children, then the range of their mental age is
(a) 9.8 = MA = 16.8
(b) 10 = MA = 16
(c) 9.6 = MA = 16.8
(d) 9.6 = MA = 16.6
9. Find the range of values of x that satisfy the following system of in-
equations.
–17 = 3x + 10 = –2;
–22 = 5x + 13 = 3 and
–19 = 2x – 9 = –3
(a) (–5, –4)
(b) [–5, –4]
(c) [–5, –3)
(d) (–5, –3)
10. The vertex of common graph of inequalities 2x + y = 2 and x – y = 3, is
(a) (0, 0)
(b)
(c)
(d)
11. Ankur appeared in an examination which has 5 subjects, out of five, in
four subjects he got 90, 70, 75, 65 marks respectively. The minimum &
maximum marks he should score in fifth subject so that the average
mark is greater than or equal to 70 and less than or equal to 75 is
(a) 55, 75
(b) 55, 70
(c) 50, 75
(d) 50, 70
Page 4


PART-I (Single Correct MCQs)
1. |2x – 3| < |x + 5|, then x belongs to
(a) (–3, 5)
(b) (5, 9)
(c)
(d)
2. If x satisfies the inequalities x + 7 < 2x + 3 and
2x + 4 < 5x + 3, then x lies in the interval
(a) (– 8, 3)
(b) (1, 3)
(c) (4, 8)
(d) (–8, –1)
3. The shaded region shown in the figure is given by the inequations
(a) 14x + 5y   70, y   14 and x – y   5
(b) 14x + 5y  70, y   14 and x – y   5
(c) 14x + 5y  70, y   14 and x – y   5
(d) 14x + 5y  70, y  14 and x – y   5
4. The region represented by the inequation system x, y = 0, y = 6, x + y =
3, is
(a) Unbounded in first quadrant
(b) Unbounded in first and second quadrants
(c) Bounded in first quadrant
(d) None of these
5. If –7 < x < 18 and 9 < y < 20, then the range of x + y is:
(a) [2, 38]
(b) (2, 38]
(c) [2, 38)
(d) (2, 38)
6. The region represented by 2x + 3y – 5 = 0 and
4x – 3y + 2 = 0, is
(a) Not in first quadrant
(b) Bounded in first quadrant
(c) Unbounded in first quadrant
(d) None of these
7. The set of  real values of x satisfying and is
(a) [2, 4]
(b)
(c)
(d) None of these
8. IQ of a person is given by the formula
where, MA is mental age and CA is chronological age.If 80 = IQ = 140 for a
group of 12 years children, then the range of their mental age is
(a) 9.8 = MA = 16.8
(b) 10 = MA = 16
(c) 9.6 = MA = 16.8
(d) 9.6 = MA = 16.6
9. Find the range of values of x that satisfy the following system of in-
equations.
–17 = 3x + 10 = –2;
–22 = 5x + 13 = 3 and
–19 = 2x – 9 = –3
(a) (–5, –4)
(b) [–5, –4]
(c) [–5, –3)
(d) (–5, –3)
10. The vertex of common graph of inequalities 2x + y = 2 and x – y = 3, is
(a) (0, 0)
(b)
(c)
(d)
11. Ankur appeared in an examination which has 5 subjects, out of five, in
four subjects he got 90, 70, 75, 65 marks respectively. The minimum &
maximum marks he should score in fifth subject so that the average
mark is greater than or equal to 70 and less than or equal to 75 is
(a) 55, 75
(b) 55, 70
(c) 50, 75
(d) 50, 70
12. The set of real values of x satisfying  is
(a)
(b) [0, 2]
(c) [–1, 1]
(d) None of these
13. The cost and revenue functions of a product are given by C(x) =2x + 80
and R(x) = 5x + 20  respectively, where x is the number of items
produced by the manufacture. How many items the manufacturer must
sell to realize some profit?
(a) more than 20
(b) more than or equal to 20
(c) more than 25
(d) None of these
14. A man wants to cut three lengths from a single piece of board of length
91 cm. The second length is to be 3 cm longer than the shortest and the
third length is to be twice as long as the shortest. The possible length of
the shortest board, if the third piece is to be at least 5 cm longer than the
second, is
(a) less than 8 cm
(b) greater than or equal to 8 cm but less than or equal to 22 cm
(c) less than 22 cm
(d) greater than 22 cm
15. The true statement for the graph of inequations 3x + 2y = 6 and 6x + 4y =
20, is
(a) Both graphs are disjoint
(b) Both do not contain origin
(c) Both contain point (1, 1)
(d) None of these
16. Solve for x, 
(a) x ? (–5, –2) ? (–1, 8)
(b) x ? (5, 2) ? (–1, 8)
Page 5


PART-I (Single Correct MCQs)
1. |2x – 3| < |x + 5|, then x belongs to
(a) (–3, 5)
(b) (5, 9)
(c)
(d)
2. If x satisfies the inequalities x + 7 < 2x + 3 and
2x + 4 < 5x + 3, then x lies in the interval
(a) (– 8, 3)
(b) (1, 3)
(c) (4, 8)
(d) (–8, –1)
3. The shaded region shown in the figure is given by the inequations
(a) 14x + 5y   70, y   14 and x – y   5
(b) 14x + 5y  70, y   14 and x – y   5
(c) 14x + 5y  70, y   14 and x – y   5
(d) 14x + 5y  70, y  14 and x – y   5
4. The region represented by the inequation system x, y = 0, y = 6, x + y =
3, is
(a) Unbounded in first quadrant
(b) Unbounded in first and second quadrants
(c) Bounded in first quadrant
(d) None of these
5. If –7 < x < 18 and 9 < y < 20, then the range of x + y is:
(a) [2, 38]
(b) (2, 38]
(c) [2, 38)
(d) (2, 38)
6. The region represented by 2x + 3y – 5 = 0 and
4x – 3y + 2 = 0, is
(a) Not in first quadrant
(b) Bounded in first quadrant
(c) Unbounded in first quadrant
(d) None of these
7. The set of  real values of x satisfying and is
(a) [2, 4]
(b)
(c)
(d) None of these
8. IQ of a person is given by the formula
where, MA is mental age and CA is chronological age.If 80 = IQ = 140 for a
group of 12 years children, then the range of their mental age is
(a) 9.8 = MA = 16.8
(b) 10 = MA = 16
(c) 9.6 = MA = 16.8
(d) 9.6 = MA = 16.6
9. Find the range of values of x that satisfy the following system of in-
equations.
–17 = 3x + 10 = –2;
–22 = 5x + 13 = 3 and
–19 = 2x – 9 = –3
(a) (–5, –4)
(b) [–5, –4]
(c) [–5, –3)
(d) (–5, –3)
10. The vertex of common graph of inequalities 2x + y = 2 and x – y = 3, is
(a) (0, 0)
(b)
(c)
(d)
11. Ankur appeared in an examination which has 5 subjects, out of five, in
four subjects he got 90, 70, 75, 65 marks respectively. The minimum &
maximum marks he should score in fifth subject so that the average
mark is greater than or equal to 70 and less than or equal to 75 is
(a) 55, 75
(b) 55, 70
(c) 50, 75
(d) 50, 70
12. The set of real values of x satisfying  is
(a)
(b) [0, 2]
(c) [–1, 1]
(d) None of these
13. The cost and revenue functions of a product are given by C(x) =2x + 80
and R(x) = 5x + 20  respectively, where x is the number of items
produced by the manufacture. How many items the manufacturer must
sell to realize some profit?
(a) more than 20
(b) more than or equal to 20
(c) more than 25
(d) None of these
14. A man wants to cut three lengths from a single piece of board of length
91 cm. The second length is to be 3 cm longer than the shortest and the
third length is to be twice as long as the shortest. The possible length of
the shortest board, if the third piece is to be at least 5 cm longer than the
second, is
(a) less than 8 cm
(b) greater than or equal to 8 cm but less than or equal to 22 cm
(c) less than 22 cm
(d) greater than 22 cm
15. The true statement for the graph of inequations 3x + 2y = 6 and 6x + 4y =
20, is
(a) Both graphs are disjoint
(b) Both do not contain origin
(c) Both contain point (1, 1)
(d) None of these
16. Solve for x, 
(a) x ? (–5, –2) ? (–1, 8)
(b) x ? (5, 2) ? (–1, 8)
(c) x ? (5, 2)
(d) x ? (–1, 8)
17. A vertex of bounded region of inequalities x = 0, x + 2y = 0 and 2x + y =
4, is
(a) (1, 1)
(b) (0, 1)
(c) (3, 0)
(d) (0, 0)
18. The set of real values of x  for which is
(a)
(b)
(c)
(d) none of these
19. Shaded region is represented by
(a) 2x + 5y = 80, x + y = 20, x = 0, y = 0
(b) 2x + 5y = 80, x + y = 20, x = 0, y = 0
(c) 2x + 5y = 80, x + y = 20, x = 0, y = 0
(d) 2x + 5y = 80, x + y = 20, x = 0, y = 0