Question Set B

CBSE 9th Standard Mathematics Lines and Angles Important Questions And Answers Study Material - QB365

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Questions:

Multiple Choice Question

25 x 1 = 25

In a ΔDEF, ∠F > ∠E then which of the following is true?

(a)

EF > DF

(b)

DE > DF

(c)

DE < DF

(d)

EF < DF

In figure, if AB = AC and BD = DC, ΔABD and ΔACD are congruent by which criterion.

(a)

SSS

(b)

ASA

(c)

SAS

(d)

RHS

If AB = QR, BC = PR and CA = PQ then:

(a)

ΔABC ≅ ΔPQR

(b)

ΔCBA ≅ ΔPRQ

(c)

ΔBAC ≅ ΔRPQ

(d)

ΔPQR ≅ ΔBCA

In ΔPQR, PQ = PR and ㄥQ = 65⁰, then ㄥP is :

(a)

55⁰

(b)

130⁰

(c)

65⁰

(d)

50⁰

In two triangles ABC and DEF, ㄥA = ㄥD, ㄥB = ㄥE and AB = EF, then are the two triangles congruent? If yes, by which congruency rule?

(a)

yes, by AA

(b)

(c)

yes, by ASA

(d)

Yes, by RHS

The side of an equilateral triangle is 4cm.An equilateral triangle, congruent to it, has the side length

(a)

1 cm

(b)

2 cm

(c)

3 cm

(d)

4 cm

Each angle of an equilateral triangle is :

(a)

\(50^{ 0 }\)

(b)

\(90^{ 0 }\)

(c)

\(80^{ 0 }\)

(d)

\(60^{ 0 }\)

A pair of angles is called linear pair if the sum of two adjacent angles is:

(a)

\(90^{ 0 }\)

(b)

\(180^{ 0 }\)

(c)

\(230^{ 0 }\)

(d)

\(360^{ 0 }\)

The compliment of (\(90^{ 0 }\)-\(a^{ 0 }\)) is

(a)

\(-a^{ 0 }\)

(b)

\(90^{ 0 }\)+\(a^{ 0 }\)

(c)

\(90^{ 0 }\)-\(a^{ 0 }\)

(d)

\(a^{ 0 }\)

10.

A reflex angle

(a)

is greater than \(180^{ 0 }\) but less than \(360^{ 0 }\)

(b)

is exactly equal to \(180^{ 0 }\)

(c)

is exactly equal to \(90^{ 0 }\)

(d)

is greater than \(90^{ 0 }\) but less than \(180^{ 0 }\)

11.

The minimum number of points required to draw a line is

(a)

(b)

(c)

(d)

12.

If the point P lies in between M and N, and C is mid point of MP, then:

(a)

MC + PN + = MN

(b)

MP + CP = MN

(c)

MC + CN + MN

(d)

CP + CN = MN

13.

How many numbers of lines do pass through two distinct points?

(a)

(b)

(c)

(d)

14.

Pythagoras was a student of

(a)

Thales

(b)

Euclid

(c)

both (a) and (b)

(d)

Archimedes

15.

In Indus Valley Civilisation (about 300 b.C), The brick used for construction work were having dimension in the ration

(a)

1 : 3 : 4

(b)

4 : 2 : 1

(c)

4 : 4 : 1

(d)

4 : 3 : 2

16.

If x=3-3y and y=-2 is a solution of the equation 4px-3y=12, then the value of p is:

(a)

(b)

\(1\over2\)

(c)

(d)

17.

Straight line passing through the points (-1, 1), (0,0) and (1, -1) has equation:

(a)

y=x

(b)

x+y=0

(c)

y=2x

(d)

2+3y=7x

18.

The equation whose graph is

(a)

y=x

(b)

x+y=0

(c)

x+y=1

(d)

y-x=1

19.

The equation of y-axis is

(a)

x=0

(b)

y=0

(c)

x=1

(d)

y=1

20.

The line y=mx+c

(a)

passes through origin

(b)

does not pass through origin

(c)

is parallel to x-axis

(d)

is parallel to y-axis

21.

The distance of a point (0,-3) from the origin is:

(a)

(b)

(c)

-1

(d)

None of these

22.

If the point A(0,2), B(0,-6) aand C(a,3) lie on y - axis, then the value of a is:

(a)

(b)

(c)

(d)

-6

23.

In which quadrant does the point (-1,-1) lie?

(a)

(b)

(c)

III

(d)

24.

The line of intersection of IV and I quadrants is

(a)

x - axis

(b)

y - axis

(c)

vertical axis

(d)

None of these

25.

The line of intersection of III and IV quadrants is

(a)

y - axis

(b)

x - axis

(c)

horizontal axis

(d)

None of these

Case Study Questions

4 x 4 = 16

26.

Sanjay bought 5 notebooks and 2 pens for Rs. 120. He told to guess the cost of each notebook and pen to his friends Mohan and Anil. Sanjay has given the clue that both the costs are positive integers and divisible by 5 such that the cost of a notebook is greater than that of a pen.

Now, Mohan and Anil tried to guess.
Mohan said that price of each notebook could be Rs. 18. Then five notebooks would cost Rs.90, the two pens would cost Rs.30 and each pen could be for Rs. 15. Anil felt that Rs. 18 for one notebook was too little. It should be at least Rs. 20. Then the price of each pen would also be Rs.10.
(i) Form the linear equations in two variables from this situation by taking cost of one notebook as Rs. x and cost of one pen as Rs. y.

(a) 2x + 5y = 120	(b) 5x + y = 120
(c) x + y = 120	(d) 5x + 2y = 120

(ii) Which is the solution of the equations formed in (i)?

(a) x = 10, y = 20	(b) x = 20, y = 10
(c) x = 15, y = 15	(d) none of these

(i) Rs. 120	(ii) Rs. 95
(iii) Rs. 105	(iv) Rs. 125

(d) If the cost of one notebook is twice the cost of one pen, then find the cost of one pen?

(a) Rs. 20	(b) Rs. 10
(c) Rs. 5	(d) Rs. 15

(e) Which is the standard form of linear equations y = 4 ?

(i) y – 4 = 0	(ii) 1.y + 4 = 0
(iii) 0.x + 1.y + 4 = 0	(iv) 0.x + 1.y – 4 = 0

27.

Aditya is a Class IX student residing in a village. One day, he went to a city Hospital along with his grandfather for general checkup. From there he visited three places - School, Library and Police Station. After returning to his village, he plotted a graph by taking Hospital as origin and marked three places on the graph as per his direction of movement and distance. The graph is shown below:

(i) What are the coordinates of School?

(a) (3, 2)	(b) (2, 3)
(c) (3, 5)	(d) (5, 3)

(ii) What are the coordinates of Police Station?

(a) (2, -1)	(b) (2, 1)
(c) (-2, -1)	(d) (-2, 1)

(iii) Distance between school and police station:

(a) 4

(b) 3

(c) 2

(d) 1

(iv) What are the coordinates of Library?

(a) (2, 6)	(b) (2, -6)
(c) (6, -2)	(d) (6, 2)

(v) In which quadrant the point (-1, 4) lies?

(a) I	(b) II
(c) III	(d) IV

28.

Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in the figure.

(a) What are the coordinates of A and B respectively?

(i) A(3, 5); B(7, 8)	(ii) A(5, 3); B(8, 7)
(iii) A(3, 5); B(7, 9)	(iv) A(5, 3); B(9, 7)

(b) What are the coordinates of C and D respectively?

(i) C(11, 5); D(7, 1)	(ii) C(5, 11); D(1, 7)
(iii) C(5, 11); D(7, 1)	(iv) C(5, 11); D(-1, 7)

(i) 5 units	(ii) 14 units
(iii) 8 units	(iv) 10 units

(d) What is the distance between A and C?

(i) 5 units	(ii) 14 units
(iii) 8 units	(iv) 10 units

(e) What are the coordinates of the point of intersection of AC and BD?

(i) (7, 5)	(ii) (5, 7)
(iii) (7, 7)	(iv) (5, 5)

29.

In the below given layout, the design and measurements has been made such that area of two bedrooms and Kitchen together is 95 sq. m.

(i) The area of two bedrooms and kitchen are respectively equal to

(a) 5x, 5y	(b) 10x, 5y
(c) 5x, 10y	(c) x, y

(ii) Find the length of the outer boundary of the layout.

(a) 27 m

(b) 15 m

(c) 50 m

(d) 54 m

(iii) The pair of linear equation in two variables formed from the statements are
(a) x + y = 13, x + y = 9
(b) 2x + y = 13, x + y = 9
(c) x + y = 13, 2x + y = 9
(d) None of the above
(iv) Which is the solution satisfying both the equations formed in (iii)?

(a) x = 7, y = 6	(b) x = 8, y = 5
(c) x = 6, y = 7	(d) x = 5, y = 8

(v) Find the area of each bedroom.

(a) 30 sq. m	(b) 35 sq. m
(c) 65 sq. m	(d) 42 sq. m

Assertion and reason

9 x 1 = 9

30.

Assertion : In ∆ABC and ∆PQR, AB = PQ, AC = PR and ∠BAC = ∠QPR then ∆ABC ≅ ∆PQR
Reason : Both the triangles are congruent by SSS congruence.
Codes:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d)Assertion (A) is false but reason (R) is true.

31.

Assertion : Angles opposite to equal sides of a triangle are not equal.
Reason : Sides opposite to equal angles of a triangle are equal.
Codes:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A)
(c) Assertion (A) is true but reason (R) is false.
(d)Assertion (A) is false but reason (R) is true.

32.

Assertion : In ∆ABC, D is the midpoint of BC. If DL ⊥ AB and DM ⊥ AC such that DL = DM, then BL = CM
Reason : If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent.

33.

Assertion : The angles of a triangle are in the ration 3 : 5 : 7. The triangle is acute- angled
Reason : The sum of angles that are formed on a straight line is equal to 180°.
Codes
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

34.

Assertion : If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 5 : 4, then the greater of the two angles is 100^о.
Reason : If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 180^о.
Codes
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

35.

Assertion : The graph of the linear equation 2x – y = 1 passes through the point (2, 3).
Reason : Every point lying on graph is not a solution of 2x – y = 1.
Codes:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

36.

Assertion : There are infinite number of lines which passes through (3, 2).
Reason : A linear equation in two variables has infinitely many solutions.
Codes:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

37.

Assertion : The points (-1, 2) and (2,- 1) are at different positions in the coordinate plane.
Reason : Point (-1, 2) lies in II-quadrant and (2,- 1) lies in IV quadrant
Codes:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

38.

Assertion: Point (4, -2) lies in IV quadrant.
Reason: The perpendicular distance of a point from y-axis is called its abscissa.
Codes:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

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Answers Key:

Multiple Choice Question

25 x 1 = 25

(b)
DE > DF

AB=AC
BD=CD
AD=AD
ΔABD ≅ ΔACD

AB=QR
BC=PR=RP
CA=PQ
∴ A ↔ Q
B ↔ R
C ↔ P
∴ ΔCBA ≅ ΔPRQ

(d)
50⁰

Two equilateral triangles of the same side length are congruent

\(\angle A+\angle B+\angle C\)
\(\therefore \angle A=\angle B=\angle C=60^{ 0 }\)

Linear Pair Axiom

Complement of (\(90^{ 0 }\)-\(a^{ 0 }\))
=\(90^{ 0 }\)-(\(90^{ 0 }\)-\(a^{ 0 }\))=\(a^{ 0 }\)

10.

Definition of a reflex angle

11.

(b)
2

12.

13.

(a)
1

14.

(a)
Thales

15.

(b)
4 : 2 : 1

16.

4p(3)-3(-2)=12 ⇒ \(p={1\over2}\)

17.

All the points satisfy x+y=0

18.

(1,1) satisfies y=x

19.

(a)
x=0

20.

O(0,0) does not satisfy y=mx+c

21.

(a)
1

22.

(a)
0

23.

24.

(a)
x - axis

25.

(a)
y - axis

Case Study Questions

4 x 4 = 16

26.

(i) (d) 5x + 2y = 120
Here, the cost of one notebook be Rs. x and that of pen be Rs. y.
According to the statement, we have 5x + 2y = 120
(ii) (b) x = 20, y = 10
5x + 2y = 5(10) + 2(20) = 50 + 40 = 90 ≠ 120
5x + 2y = 5(20) + 2(10) = 100 + 20 = 120
5x + 2y = 5(15) + 2(15) = 75 + 30 = 105 ≠ 120
(c) (ii) Rs. 95
5x + 2y = 5(15) + 2(10) = 75 + 20 = 95
(d) (b) Rs. 10
Here, x = 2y
5(2y) + 2y
= 10y + 2y = 12y = 120
⇒ y = 10
(e) (iv) 0.x + 1.y – 4 = 0
Since, y = 4 ⇒ y – 4 = 0
Thus, standard form of y = 4 is 0.x + 1.y – 4 = 0

27.

(i) (b) (2, 3)
(ii) (a) (2, -1)
(iii) (a) 4
(iv) (d) (6, 2)
(v) (b) II

28.

(a) (iii) A(3, 5); B(7, 9)
(b) (i) C(11, 5); D(7, 1)
(c) (iii) 8 units
(d) (iii) 8 units
(e) (i) (7, 5)

29.

(i) (b) 10x, 5y
Area of one bedroom = 5x sq.m
Area of two bedrooms = 10x sq.m
Area of kitchen = 5y sq. m
(ii) (d) 54 m
Length of outer boundary = 12 + 15 + 12 + 15 = 54 m
(iii) (d) None of the above
Area of two bedrooms = 10x sq.m
Area of kitchen = 5y sq. m
So, 10x + 5y = 95  2x + y = 19
Also, x + 2 + y = 15 x + y = 13
(iv) (c) x = 6, y = 7
x + y = 6 + 7 = 13
2x + y = 2(6) + 7 = 19
x = 6, y = 7
x + y = 6 + 7 = 13
2x + y = 2(6) + 7 = 19
x = 6, y = 7
(v) (a) 30 sq. m
Area of living room = (15 x 7) – 30
= 105 – 30 =75 sq. m

Assertion and reason

9 x 1 = 9

30.

In ∆ABC and ∆PQR,
AB = PQ, AC = PR and ∠BAC = ∠QPR (Given)
then ∆ABC ≅ ∆PQR by ASA Congruence Rule So, Assertion (A) is true.
But Reason (R) is false.
Correct option is (c) Assertion (A) is true but reason (R) is false.

31.

We know that Angles opposite to equal sides of a triangle are equal.
So, Assertion is not correct.
Also, we know that Sides opposite to equal angles of a triangle are equal.
So, Reason is correct.
Correct option is (d) Assertion (A) is false but reason (R) is true.

32.

We know that “If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then triangles are congruent.” - This is ASA Congruence Rule.
So, Reason is correct.
In △BDL and △CDM, we have
BD = CD (D is midpoint)
DL = DM (Given)
and ∠BLD = ∠CMD (90° each)
∴ △BDL ≅ △CDM (RHS criterion)
⇒ BL = CM (CPCT)
So, Assertion is also correct
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).

33.

We know that the sum of angles that are formed on a straight line is equal to 180°.
So, Reason is correct
Also, the sum of all the interior angles of a triangle is 1800 Let the angles measure (3x)°, (5x)° and (7x)°.
Then,3x + 5x + 7x = 180° ⇒15x = 180° ⇒x = 12°
Therefore, the angles are 3(12)°=36°, 5(12)°=60° and 7(12)° = 84°. Hence, the triangle is acute-angled.
So, Assertion (A) is also true.
But reason (R) is not the correct explanation of assertion (A). Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).

34.

We know If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 180^о
hat the solution of the line will satisfy the equation of the line. So, Reason is correct.
Let the angles be 5x and 4x
Since, these two angles are co-interior angles. So, we
have 5x + 4x = 180^о
⇒ 9x = 180^о ⇒ x = 20^о
Hence, greater angle = 5x = 5 x 200 = 100^о
So, Assertion is also correct
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

35.

For Assertion: The given linear equation is 2x – y = 1
Substituting x = 2 and y = 3, we get
LHS = 2 x 2 – 3 = 4 – 3 = 1 = RHS
Since (3, 0) satisfies the equation 4x + 3y = 12, therefore graph of the linear equation 2x – y = 1 passes through the point (2, 3).
So, Assertion is correct.
But Reason is not correct as every point lying on graph is a solution of 2x – y = 1.
Correct option is (c) Assertion (A) is true but reason (R) is false.

36.

We know that a linear equation in two variables has infinitely many solutions. So, Reason is correct.
Through a point infinite lines can be drawn.
Through (3, 2) infinite number of lines can be drawn.
Hence, Assertion is also correct.
But reason (R) is not the correct explanation of assertion (A).
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).

37.

We know that Point (-1, 2) lies in II-quadrant and (2,- 1) lies in IV quadrant
So, Reason is correct.
Hence the points (-1, 2) and (2,- 1) are at different positions in the coordinate plane.
So, Assertion is also correct
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

38.

We know that the perpendicular distance of a point from y-axis is called its x-coordinate or abscissa.
So, Reason is correct.
Point (4, -2) lies in IV quadrant.
So, Assertion is also correct but Reason is not the correct explanation of Assertion.
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).

CBSE 9th Standard Mathematics Lines and Angles Important Questions And Answers Study Material - QB365 Set B

QB365 Student Learing Managemnet System

Std: 9th Standard CBSE - Mathematics

chapter: Lines and Angles - Important Questions And Answers

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Questions:

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Answers Key:

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