Equations in One Variable Test

Result

Equations in One Variable Test - 10

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Which of the following figures are not trapeziums?

A
Only (ii), (vi) and (iii)

B
Only (i), (iv) and (v)

C
Only (i), (ii), (iii) and (v)

D
Only (iv), (vi) and (v)

Solution

A trapezium is a quadrilateral with a pair of parallel sides.
So, the following figures are not trapeziums:

Hence, (2) is the correct option.
Question 2
1 / -0

What will be the sum of all the interior angles of a nonagon?

A
1360°

B
1260°

C
1620°

D
1460°

Solution

A nonagon has 9 sides.
We know,
Sum of interior angles of a polygon = (n - 2) 180°
Here, n = number of sides
Sum of angles of a nonagon
= (9 - 2) 180°
= 7 180°
= 1260°
Hence, (2) is the correct option.
Question 3
1 / -0

Which of the following statements is/are true?

(i) A parallelogram with sides of equal length is called a rhombus.
(ii) If the diagonals of a quadrilateral are of equal length, then it is a rectangle.

A
Both (i) and (ii)

B
Only (i)

C
Only (ii)

D
Neither (i) nor (ii)

Solution

(i) If all the sides of a parallelogram are equal in length, then it is called a rhombus.
(ii) If the diagonals of a quadrilateral are of equal length, then it is a rectangle or a square. A square is also a special rectangle.
Hence, both (i) and (ii) are true.
Hence, (1) is the correct option.
Question 4
1 / -0

Which of the following statements is/are true?

(I) Polygon is a simple closed curve.
(II) Polygon is made up of line segments only.

A
Both (I) and (II)

B
Neither (I) nor (II)

C
Only (I)

D
Only (II)

Solution

(I) Polygon is a simple closed curve. (True)
(II) Polygon is made up of line segments only. (True)

A simple closed curve is closed from all sides, i.e. all its adjacent sides are joined. The properties of a polygon are same as those of a simple closed curve because it is also closed from all sides. So, we can say that polygons are simple closed curves.
Also, a polyygon is made up of line segments only.
Example: Square, Triangle, Pentagon, etc. all are polygons and are made up of line segments only.

Both (I) and (II) are true.
Question 5
1 / -0

ABCD is a rectangle, the diagonals of which meet at point O. What is the value of x, if OD = 2x + 4 and OA = 3x + 1? (All dimensions are in cm)

A
5 cm

B
4 cm

C
3 cm

D
2 cm

Solution

OD = 2x + 4
OA = 3x + 1
BD = 2(OD) = 2(2x + 4) = 4x + 8
AC = 2(OA) = 2(3x + 1) = 6x + 2
AC and BD are diagonals and diagonals of a rectangle are equal.
Therefore,
4x + 8 = 6x + 2 6x - 4x = 8 - 2 = 2x = 6
x = 3 cm
Question 6
1 / -0

ABCD is a rhombus where AO = 12 cm, BO = 5 cm and one of its side measures 13 cm. What is the value of x + y + z?

A
12 cm

B
13 cm

C
25 cm

D
30 cm

Solution

x = 13 cm
y = AO = 12 cm
z = OD = OB = 5 cm (Because diagonals of a rhombus bisect each other)
Therefore,
x + y + z = (13 + 12 + 5) cm
= 30 cm
Question 7
1 / -0

What are the values of 'x' and 'y' in the given figure, where ABCD is a parallelogram? (All dimensions are in cm.)

A
x = 18 cm, y = 26 cm

B
x = 16 cm, y = 30 cm

C
x = 6 cm, y = 9 cm

D
x = 9 cm, y = 6 cm

Solution

3x = 18 cm
=> x = 6 cm (Opposite sides of a parallelogram are equal.)
3y - 1 cm = 26 cm
3y = 27 cm
y = 9 cm (Opposite sides of a parallelogram are equal.)
Therefore, x = 6 cm and y = 9 cm
Question 8
1 / -0

In the given figure, AE is parallel to DC. Find the measure of BCE.

A
20⁰

B
30⁰

C
40⁰

D
50⁰

Solution

Angle DCE = 50^o
So, angle BCE = 20^o
Question 9
1 / -0

Find the measure of CAB from the given figure.

A
103°

B
125°

C
213°

D
225°

Solution

In the given figure,
BDC + BDE = 180° (Supplementary angles)
BDC + 125° = 180°
BDC = 180° - 125°
BDC = 55°
In quadrilateral ABDC,
CAB + 38° + 55° + 142° = 360° (The sum of angles of a quadrilateral is 360°.)
CAB + 235° = 360°
CAB = 125°
Question 10
1 / -0

A parallelogram whose diagonals does not bisect each other at 90° but each angle measures 90° is called

A
square

B
rhombus

C
rectangle

D
kite

Solution

A parallelogram whose diagonals does not bisect each other at 90° but each angle measures 90° is called a rectangle.
Question 11
1 / -0

Which of the following is/are true?

(i) is a convex polygon.
(ii) is a concave polygon.

A
Both (i) and (ii)

B
Only (i)

C
Only (ii)

D
Neither (i) and (ii)

Solution

(i) A convex polygon is defined as a polygon with all its interior angles less than 180°. This means that all the vertices of the polygon will point outwards
∴ Figure (i) is not a polygon.
(i) is false.

(ii)

We know that some of the diagonals of a concave polygon will lie outside the polygon. The given figure is a concave polygon as its diagonal has a part in its exterior
Therefore, (ii) is true.

Hence, (3) is the correct option.
Question 12
1 / -0

How many diagonals does an octagon have?

A
18

B
20

C
8

D
14

Solution

An octagon has 8 sides.

Diagonal is a line segment connecting two non-consecutive vertices of a polygon.
Number of diagonals for a polygon is , where n is the number of sides of the polygon.
Now, n = 8 for an octagon.
Number of diagonals =
=
Hence, (2) is the correct option.
Question 13
1 / -0

In a quadrilateral ABCD, AC = AD, AC = BC, ACB = 40° and CDA = 50°. Find the measures of ABC and DAC, respectively.

A
20°, 40°

B
70°, 80°

C
50°, 40°

D
70°, 20°

Solution

In ACD,
(In a triangle, angles opposite to equal sides are equal.)

(Angle sum property of a triangle)

In ABC,

(In a triangle, angles opposite to equal sides are equal.)
(Angle sum property of a triangle)
Question 14
1 / -0

Which of the following statements is/are correct for diagonals?

(I) The diagonals of a square are of equal length.
(II) The diagonals of a square bisect each other at right angles.

A
Both (I) and (II)

B
Neither (I) nor (II)

C
Only (I)

D
Only (II)

Solution

(I) The diagonals of a square are of equal length. - True

Given above is a square ABCD with diagonals AC and BD equal in length.

(II) The diagonals of a square bisect each other at right angles. - True

Given above is a square ABCD, where diagonals bisect each other at right angles.
Both are the properties of the diagonals of a square.

Both statements (I) and (II) are true.
Question 15
1 / -0

Which of the following statements is false?

A
A rectangle is also a parallelogram.

B
A rhombus is also a kite.

C
A rhombus is also a parallelogram.

D
A trapezium is also a parallelogram.

Solution

A parallelogram has its opposite sides parallel as well as equal, whereas in a trapezium, only one pair of opposite sides is parallel.
Hence, (4) is the correct option.