Class 9 Pearson - Linear Equations and InequationsContact Number: 9667591930 / 8527521718

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1.

How many pairs of *x* and *y* satisfy the equations 2*x* + 4*y* = 8 and 6*x* +12*y* = 24?

(1) 0

(2) 1

(3) Infinite

(4) None of these

2.

Find the value of ‘*k*’ for which the system of linear equations *kx* + 2*y* = 5 and 3*x* + *y* = 1 has zero solutions.

(1) *k* = 6

(2) *k *= 3

(3) *k *= 4

(4) None of these

3.

Find the minimum value of |*x* – 3| + 11.

(1) 8

(2) 11

(3) 0

(4) –8

4.

The maximum value of 23 – |2*x* + 3| is

(1) 20

(2) 26

(3) 17

(4) 23

5.

The product of a number and 72 exceeds the product of the number and 27 by 360. Find the number.

(1) 12

(2) 7

(3) 8

(4) 11

6.

The total cost of 10 erasers and 5 sharpeners is at least ₹65. The cost of each eraser cannot exceed ₹4. Find the minimum possible cost of each sharpener.

(1) ₹6

(2) ₹5.50

(3) ₹5

(4) ₹6.50

7.

If the system of linear equations *px* + 3*y* = 9 and 4*x* +*py* = 8 has unique solution, then

(1) $p=\pm 2\sqrt{3}$

(2) $p\ne \pm 3\sqrt{2}$

(3) $p\ne \pm 2\sqrt{3}$

(4) $p=\pm 3\sqrt{2}$

8.

In a group of goats and hens, the total number of legs is 12 more than twice the total number of heads. The number of goats is

(1) 8

(2) 6

(3) 2

(4) Cannot be determined

9.

If $\frac{x+3}{x-3}<1,$ then which of the following cannot be the value of *x*?

(1) 0

(2) 1

(3) 2

(4) 4

10.

The system of equations *px* + 4*y* = 32 and 2*qy* + 15*x* =96 has infinite solutions. The value of *p* – *q* is

(1) –1

(2) 1

(3) 0

(4) 11

11.

If *x* and *y* are two integers where *x* ≥ 0 and *y* ≥ 0, then the number of ordered pairs satisfying the inequation 2*x* + 3*y* ≤ 1 is ______.

(1) 1

(2) 2

(3) 3

(4) 4

12.

The common solution set of the inequations $\frac{x}{2}+\frac{y}{2}\le 1$ and *x* + *y* > 2 is _____.

(1) {(*x*, *y*)/*x* < 2 and *y*> 2}

(2) {(*x*, *y*)/*x* < 1 and *y* >1}

(3) an empty set

(4) {(*x*, *y*)/*x* < 2 and *y* < 1}

13.

If (1, 4) is the point of intersection of the lines 2*x* + *by* = 6 and 3*y* = 8 + *ax*, then find the value of *a* – *b*.

(1) 2

(2) 3

(3) 4

(4) –3

14.

If *x* be a negative integer, then the solution of the inequatiou 1 ≤ 2*x* + 8 ≤ 11 is

(1) {–5, –3, –4, –2, –1}

(2) {–4, –2, –1}

(3) {–6, –3, –1}

(4) {–3, –2, –1}

15.

If 5*u* + 3*v* = 13*uv* and *u* – *v* = *uv*, then (*u*, *v*) = _____.

(1) (2, 1)

(2) $\left(\frac{1}{2},\text{\hspace{0.17em}\hspace{0.17em}}1\right)$

(3) $\left(1,\text{\hspace{0.17em}\hspace{0.17em}}\frac{1}{2}\right)$

(4) (1, 2)

16.

Solve the equations: 4 (2^{x}^{ – 1}) + 9(3^{y}^{ – 1}) = 17 and 3(2* ^{x}*) – 2(3

(1) (*x*, *y*) = (2, 1)

(2) (*x*, *y*) = (–2, –1)

(3) (*x*, *y*) = (1, 2)

(4) (*x*, *y*) = (2, –1)

17.

The solution set of $\frac{2}{x}+\frac{3}{y}=2$ and $\frac{3}{x}+\frac{4}{y}=20$ is

(1) (4, –2)

(2) $\left(-\frac{1}{2},\text{\hspace{0.17em}\hspace{0.17em}}\frac{1}{4}\right)$

(3) (2, –4)

(4) $\left(\frac{1}{4},\text{\hspace{0.17em}\hspace{0.17em}}\frac{-1}{\text{\hspace{0.17em}\hspace{0.17em}}2}\right)$

18.

Cost of 5 pens and 7 note books is ₹82 and cost of 4 pens and 4 note books is ₹52. Find the cost of 2 note books and 3 pens.

(1) ₹34.50

(2) ₹30.50

(3) ₹32.50

(4) ₹36.50

19.

If (*a* + *b*, *a* – *b*) is the solution of the equations 3*x* + 2*y* = 20 and 4*x* – 5*y* = 42, then find the value of *b*.

(1) 8

(2) –2

(3) –4

(4) 5

20.

Number of integral values of *x* that do not satisfy the inequation $\frac{x-7}{x-9}>0$ is______.

(1) 4

(2) 3

(3) 2

(4) 0

21.

The solution set formed by the regions *x* + *y* > 7 and *x* + *y* < 10 in the first quadrant represents a ________.

(1) triangle

(2) rectangle

(3) trapezium

(4) rhombus

22.

Solve $\left|3-\frac{{\displaystyle 2x}}{{\displaystyle 5}}\right|\le 4.$

(1) $\frac{5}{2}\le x\le \frac{35}{2}$

(2) $\frac{-5}{\text{\hspace{0.17em}\hspace{0.17em}}2}\le x\le \frac{35}{2}$

(3) $\frac{-35}{\text{\hspace{0.17em}\hspace{0.17em}}2}\le x\le \frac{-5}{\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}2}$

(4) None of these

23.

In a fraction, if numerator is increased by 2 and denominator is increased by 3, it becomes $\frac{3}{4}$ and if numerator is decreased by 3 and denominator is decreased by 6, it becomes $\frac{4}{3}$. Find the sum of the numerator and denominator.

(1) 16

(2) 18

(3) 20

(4) 14

24.

If 100 cm is divided into two parts such that the sum of 2 times the smaller part and $\frac{1}{3}$ of the larger part, is less than 100 cm, then which of the following is correct?

(1) Larger portion is always less than 60.

(2) Smaller portion is always less than 60 and more than 40.

(3) Larger portion is always greater than 60.

(4) Smaller portion is always greater than 40.

25.

If 2*a* – 3*b* = 1 and 5*a* + 2*b* = 50, then what is the value of *a* – *b*?

(1) 10

(2) 6

(3) 7

(4) 3

26.

The fair of 3 full tickets and 2 half tickets ₹204 and the fair of 2 full tickets and 3 half tickets is ₹186. Find the fair of a full ticket and a half ticket.

(1) ₹94

(2) ₹78

(3) ₹86

(4) ₹62

27.

If $\frac{3}{2}x+2y=\frac{x}{4}-\frac{y}{2}=1,$ then *x* – *y* =

(1) 1

(2) 3

(3) 2

(4) 0

28.

If we add 1 to the numerator and subtract 1 from the denominator a fraction becomes 1. It also becomes $\frac{1}{2}$ if we add 1 to the denominator. Then the sum of the numerator and denominator of the fraction is

(1) 7

(2) 8

(3) 2

(4) 11

29.

If 4*x* – 3*y* = 7*xy* and 3*x* + 2*y* = 18*xy* then (*x*, *y*) =

(1) $\left(\frac{1}{2},\text{\hspace{0.17em}\hspace{0.17em}}\frac{1}{3}\right)$

(2) (3, 4)

(3) (4, 3)

(4) $\left(\frac{1}{3},\text{\hspace{0.17em}\hspace{0.17em}}\frac{1}{4}\right)$

30.

Jeevesh had 92 currency notes in all, some of which were of ₹100 denomination and the remaining of ₹50 denomination. The total value of amount of all these currency notes was ₹6350. How much amount in rupees did lie have in the denomination of ₹50?

(1) 3500

(2) 3350

(3) 2850

(4) 2600

31.

The solution set of the inequation $\frac{1}{5+3x}\le 0$ is

(1) $x\in (\frac{-5}{\text{\hspace{0.17em}\hspace{0.17em}}3},\text{\hspace{0.17em}\hspace{0.17em}}\infty )$

(2) $x\in (-\infty ,\frac{5}{3})$

(3) $x\in (\frac{5}{3},\text{\hspace{0.17em}\hspace{0.17em}}\infty )$

(4) $x\in (-\infty ,\frac{-5}{\text{\hspace{0.17em}\hspace{0.17em}}3})$

32.

If 2|*x*| – |*y*| = 3 and 4|*x*| + |*y*| =3, then number of possible ordered pairs of the form (*x*, *y*) is

(1) 0

(2) 1

(3) 2

(4) 4

33.

The solution set formed by the inequations *x* ≥ –7 and *y* ≥ –7 in the third quadrant represents a

(1) trapezium

(2) rectangle

(3) square

(4) rhombus

34.

Find the solution of the inequation $\frac{1}{|3x-5|}>2,$ where *x* is a positive integer.

(1) {2, 3}

(2) {2, 3, 4}

(3) *x* = 2

(4) Null set

35.

A father wants to divide ₹200 into two parts between two sons such that by adding three times the smaller part to half of the larger part, then this will always be less than ₹200. How will he divide this amount?

(1) Smaller part is always less than 50.

(2) Larger part is always greater than 160.

(3) Larger part is always less than 160.

(4) Smaller part is always greater than 40.

36.

Solve |7 – 2*x*| ≤ 13.

(1) 3 ≤ *x* ≤ 10

(2) –3 < *x* < 10

(3) –10 ≤ *x* ≤ 3

(4) –3 ≤ *x* ≤ 10

37.

If an ordered pair, satisfying the equations *x* + *y* = 7 and 3*x* –2*y* = 11, is also satisfies the equation 3*x* + *py* – 17 = 0, then the value of *p* is __________.

(1) 2

(2) –2

(3) 1

(4) 3

38.

Solve for *x*: |2*x* + 3| < 2*x* + 4.

(1) *x* > –2

(2) $x>-\frac{7}{4}$

(3) $x<-\frac{7}{4}$

(4) *x* < –2

39.

Find the values of *x* and *y*, which satisfy the simultaneous equations 1010*x* + 1011*y* = 4040 and 1011*x* + 1010*y* = 4044.

(1) *x* = 2, *y* = –4

(2) *x* = 0, *y* = 4

(3) *x* = 4, *y* = 4

(4) *x* = 4, *y* = 0

40.

A bus conductor gets a total of 220 coins of 25 paise, 50 paise and ₹1 daily. One day he got ₹110 and next day he got ₹80 in that the number of coins of 25 paise and 50 paise coins are interchanged then find the total number of 50 paise coins and 25 paise coins.

(1) 180

(2) 190

(3) 160

(4) 200

41.

The common solution set of the inequations 5 ≤ 2*x* + 7 ≤ 8 and 7 ≤ 3*x* + 5 ≤ 9 is ______.

(1) $\frac{2}{3}\le x\le \frac{4}{3}$

(2) $-1\le x\le \frac{4}{3}$

(3) $\frac{2}{3}\le x\le \frac{1}{2}$

(4) Null set

42.

The solution set formed by the inequations *x* + *y* ≥ 3, *x* + *y* ≥ 4, *x* ≤ 2 in the first quadrant represents a

(1) triangle

(2) parallelogram

(3) rectangle

(4) rhombus

43.

Shiva's age is three times that of Ram. After 10 years Shiva's age becomes less than twice the age of Ram. What can be the maximum present age (in complete years) of Shiva?

(1) 30

(2) 10

(3) 9

(4) 29

44.

In an ICC Champions trophy series, Sachin scores 68 runs and 74 runs out of three matches. A player can be placed in Grade A of ICC rankings if the average score of three matches is at least 75 and at most 85. Sachin is placed in Grade A. What Is the maximum runs that he should score in the third match?

(1) 105

(2) 83

(3) 113

(4) 97

45.

The sum of predecessors of two numbers is 36 and their difference is 4. Find the numbers. The following are the steps involved in solving the above problem. Arrange them in sequential order.

(A) *X* – 1 + *Y* – 1 = 36 and *X* – *Y*'= 4

(B) Solve for *X* and *Y*

(C) Let *X* > *Y*

(D) Let the numbers be *X* and *Y*

(1) CDAB

(2) CDBA

(3) DCAB

(4) DCBA

46.

The following are the steps involved in solving the equations 2* ^{x}* + 3

(A) Rewrite the given equation in terms of *p* and *q*

(B) Let *p* = 2* ^{x}* and

(C) Find *x* and *y*

(D) Solve for *p* and *q*

(1) ABCD

(2) ABDC

(3) BACD

(4) BADC

47.

There are two numbers. The predecessor of the larger number exceeds the successor of the smaller number by 6. The sum of the numbers is 32. Find the numbers.

The following are the steps involved in solving the above problem. Arrange them in sequential order.

(A) *M* + *N* = 32 and *M* – 1 – (*N* + 1) = 6

(B) Let *N* < *M*

(C) Solve for *M* and *N*

(D) Let the numbers be *M* and *N*

(1) BDCA

(2) BDAC

(3) DBCA

(4) DBAC

48.

The following are the two steps involved in finding the values of *p* and *q* from 3* ^{p}* + 5

(A) Let *x* = 3*p* and *y* = 5^{q}

(B) Solve for *x* and *y*

(C) Find *p* and *q*

(D) Rewrite the given equations in terms of *x* and *y*

(1) ABCD

(2) ADCB

(3) ACBD

(4) ADBC

49.

Solve for *x*: 2*x* – 3 ≤ 5*x* + 9.

(1) *x* ≥ –4

(2) *x* ≥ –3

(3) *x* ≥ –2

(4) *x* ≥ –1

50.

*X* is an integer satisfying 1 ≤ 2*X* + 3 ≤ 7. How many values can it take?

(1) 4

(2) 3

(3) 5

(4) 6

51.

Solve for *x*: 5*x* + 4 ≥ *x* + 12.

(1) *x* ≥ 0

(2) *x* ≥ 1

(3) *x* ≥ 2

(4) *x* ≥ 3

52.

*Y* is an integer satisfying –3 ≤ 4*Y* –7 ≤ 5. How many value can it take?

(1) 2

(2) 4

(3) 3

(4) 5

53.

*N* is a three-digit number. It exceeds the number formed by reversing the digits by 792. Its hundreds digit can be

(1) 9

(2) 8

(3) Either (1) or (2)

(4) Neither (1) nor (2)

54.

*X* is a three-digit number. The number formed by reversing the digits of *X* is 891 less than *X*. Find its units digit.

(1) 0

(2) 1

(3) 2

(4) Cannot be determined

55.

An examination consists of 160 questions. One mark is given for every correct option. If one-fourth mark is deducted for every wrong option and half mark is deducted for every question left, then one person scores 79. And if half mark is deducted for every wrong option and one-fourth mark is deducted for every left question, the person scores 76, then find the number of questions he attempted correctly.

(1) 80

(2) 100

(3) 120

(4) 140

56.

Runs scored by Sachin in a charity match is 10 more than the balls faced by Lara. The number of balls faced by Sachin is 5 less than the runs scored by Lara. Together they have scored 105 runs and Sachin faced 10 balls less than the balls faced by Lara. How many runs were scored by Sachin?

(1) 45

(2) 60

(3) 50

(4) 55

57.

The number of ordered pairs of different prime numbers whose sum is not exceeding 26 and difference between second number and first number cannot be less than 10.

(1) 8

(2) 9

(3) 10

(4) 11

58.

The number of possible pairs of successive prime numbers, such that each of them is greater than 40 and their sum is utmost 100, is

(1) 3

(2) 2

(3) 4

(4) 1

59.

In an election the supporters of two candidates A and B were taken to polling booth in two different vehicles, capable of carrying 10 and 15 voters respectively. If at least 90 vehicles were required to carry a total of 1200 voters, then find the maximum number of votes by which the elections could be won by the Candidate B.

(1) 900

(2) 600

(3) 300

(4) 500

60.

A test has 60 questions. For each correct answer 2 marks are awarded and each wrong answer 1 mark is deducted. A candidate attempted all the questions in the test and scored 90 marks. Find the number of questions he attempted correctly.

(1) 54

(2) 48

(3) 49

(4) 50

61.

Krishna and Sudheer have some marbles with them. If Sudheer gives 10 marbles to Krishna, Krishna will have 40 more marbles than Sudheer. If Sudheer gives 40 marbles to Krishna, Krishna will have 5 times as many marbles as Sudheer. Find the number of marbles with Sudheer.

(1) 65

(2) 55

(3) 70

(4) 50

62.

In a test, for each correct answer 1 mark is awarded and each wrong answer half a mark is deducted. The test has 70 questions. A candidate attempted all the questions m the test and scored 40 marks.

How many questions did he attempt wrongly?

(1) 15

(2) 20

(3) 25

(4) 10

63.

Amar and Bhavan have a certain amount with them. If Bhavan gives ₹20 to Amar, he will have half the amount with Amar. If Amar gives ₹40 to Bhavan. he will have half the amount with Bhavan. Find the amount with Bhavan.

(1) ₹70

(2) ₹90

(3) ₹60

(4) ₹80

64.

Solve for $z:4x+5y+9z=36,\text{\hspace{0.17em}\hspace{0.17em}}6x+\frac{15}{2}y+11z=49.$

(1) 2

(2) 1

(3) 3

(4) Cannot be determined

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