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Maths Mock Test- 3 - Class 9 MCQ

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30 Questions MCQ Test - Maths Mock Test- 3

Maths Mock Test- 3 for Class 9 2024 is part of Class 9 preparation. The Maths Mock Test- 3 questions and answers have been prepared according to the Class 9 exam syllabus.The Maths Mock Test- 3 MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Maths Mock Test- 3 below.

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Maths Mock Test- 3 - Question 1

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If a+b+c = 0, then a³+b³+c³is equal to

A.
1
B.
3abc
C.
abc
D.
2abc

Maths Mock Test- 3 - Question 2

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A rectangular sand box is 5 m wide and 2 m long. How many cubic metres of sand are needed to fill the box upto a depth of 10 cm ?

A.
1
B.
10
C.
100
D.
1000

Detailed Solution for Maths Mock Test- 3 - Question 2

To calculate the volume of sand needed to fill the rectangular sandbox, we can use the formula:Volume = Length × Width × DepthGiven:
Length = 2 m
Width = 5 m
Depth = 10 cm = 0.1 mSubstituting the values into the formula:Volume = 2 m × 5 m × 0.1 m
Volume = 1 cubic meterTherefore, the correct answer is A: 1 cubic meter.

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Maths Mock Test- 3 - Question 3

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In Parallelogram ABCD, bisectors of angles A and B intersect each other at O. The measure of ∠AOB is

A.
120^∘
B.
60^∘
C.
90^∘
D.
30^∘

Maths Mock Test- 3 - Question 4

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Three statements are given below:
(I) In a Rectangle ABCD, the diagonals AC bisects ∠A as well as ∠C.
(II) In a Square ABCD, the diagonals AC bisects ∠A as well as ∠C.
(III) In rhombus ABCD, the diagonals AC bisects ∠Aas well as ∠C.
Which is True?

A.
III
B.
I
C.
II and III
D.
II

Maths Mock Test- 3 - Question 5

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Chords AD and BC intersect each other at right angles at point P. ∠DAB = 35^o, then ∠ADC is equal to

A.
55^o
B.
45^o
C.
35^o
D.
65^o

Maths Mock Test- 3 - Question 6

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In the given figure, AB is a diameter of the circle APBR. APQ and RBQ are straight lines. If ∠A = 35^o and , then the measure of ∠PBR is

A.
165^o
B.
115^o
C.
155^o
D.
135^o

Maths Mock Test- 3 - Question 7

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The point which lies on y-axis at a distance of 6 units in the positive direction of y-axis is

A.
(-6, 0)
B.
(0, -6)
C.
(0, 6)
D.
(6, 0)

Maths Mock Test- 3 - Question 8

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The point B(-3, 4) lies in

A.
IV Quadrant
B.
II Quadrant
C.
I Quadrant
D.
III Quadrant

Detailed Solution for Maths Mock Test- 3 - Question 8

In a coordinate plane, the quadrants are defined as follows:
- I Quadrant: (x > 0, y > 0)
- II Quadrant: (x < 0, y > 0)
- III Quadrant: (x < 0, y < 0)
- IV Quadrant: (x > 0, y < 0)
The point B(-3, 4) has x-coordinate -3 and y-coordinate 4.
Since x is negative and y is positive, it lies in the II Quadrant.

Maths Mock Test- 3 - Question 9

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The length of the longest rod that can fit in a cubical vessel of side 10 cm, is

A.
10 cm
B.
10√2 cm
C.
10√3 cm
D.
20 cm

Detailed Solution for Maths Mock Test- 3 - Question 9

The length of the longest rod that can fit in a cubical vessel of side 10 cm is equal to the length of the diagonal of the cube. Using the Pythagorean theorem, the length of the diagonal of the cube can be found as:Diagonal = √(length² + breadth² + height²)
Diagonal = √(10² + 10² + 10²)
Diagonal = √300
Diagonal = 10√3 cmTherefore, the length of the longest rod that can fit in a cubical vessel of side 10 cm is 10√3 cm, which corresponds to option C.

Maths Mock Test- 3 - Question 10

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D and E are the mid-points of the sides AB and AC of △ABC and O is any point on the side BC, O is joined to A. If P and Q are the mid-points of OB and OC res, Then DEQP is

A.
A Rectangle
B.
A Triangle
C.
A Rhombus
D.
A Parallelogram

Maths Mock Test- 3 - Question 11

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Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA res. If length of a diagonal of Rectangle is 8cm, then the quadrilateral PQRS is a

A.
Rectangle with one side 4cm
B.
Parallelogram with one side 4cm
C.
Square with one side 4 cm
D.
Rhombus with each side 4cm

Maths Mock Test- 3 - Question 12

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Which of the following is an rational number?

A.
0.323223222322223…….
B.
√180
C.
√31
D.
√196

Detailed Solution for Maths Mock Test- 3 - Question 12

- A rational number is a number that can be expressed as a fraction where both the numerator and denominator are integers.
- √196 is a rational number because it simplifies to 14/1, which is a fraction where both the numerator and denominator are integers.
- Options B and C are irrational numbers because they cannot be expressed as fractions.
- Option A is a repeating decimal, which can be rational if it eventually settles into a repeating pattern, but without further information, it is not clear if this is the case.

Maths Mock Test- 3 - Question 13

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If 146! Is divisible by 5ⁿ, and then find the maximum value of n.

A.
34
B.
35
C.
36
D.
37
E.
Cannot be said

Detailed Solution for Maths Mock Test- 3 - Question 13

Required answer,

Note:
We have taken integral value only, not the fractional.
For example 146/5 = 29.2 but we have taken 29 and so on.

Maths Mock Test- 3 - Question 14

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A.
6
B.
2
C.
4
D.
8

Detailed Solution for Maths Mock Test- 3 - Question 14

Maths Mock Test- 3 - Question 15

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In the given figure, if ∠AOB = 80^o and ∠ABC = 30^o , then ∠CAO is equal to

A.
30^o
B.
60^o
C.
80^o
D.
40^o

Detailed Solution for Maths Mock Test- 3 - Question 15

2ACB=AOB
ACB=40
CAB+ACB+ABC=180
CAB=180-70
CAB=110
since,OA=OB(radius)
OAB=OBA

AOB+OAB+OBA=180
2OBA=100
OBA=50

CAO=CAB-OBA=110-5O
CAO=60^o

Maths Mock Test- 3 - Question 16

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In the figure, O is the centre of eh circle and ∠AOB = 80^o. The value of x is :

A.
40^o
B.
160^o
C.
60^o
D.
30^o

Maths Mock Test- 3 - Question 17

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The consecutive class marks of a data having continuous class intervals having class width as 5, have a gap of ________ between them.

A.
2.5
B.
4.5
C.
5
D.
10

Maths Mock Test- 3 - Question 18

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The point which lies on x-axis at a distance of 3 units in the positive direction of x-axis is

A.
(-3, 0)
B.
(0, 3)
C.
(0, -3)
D.
(3, 0)

Maths Mock Test- 3 - Question 19

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The point D(3, -6) lies in

A.
II Quadrant
B.
III Quadrant
C.
IV Quadrant
D.
I Quadrant

Detailed Solution for Maths Mock Test- 3 - Question 19

The point D(3, -6) lies in the IV Quadrant.
Explanation: In the Cartesian plane, the X-axis and Y-axis divide the plane into four quadrants. The I Quadrant is where both x and y are positive. The II Quadrant is where x is negative and y is positive. The III Quadrant is where both x and y are negative. The IV Quadrant is where x is positive and y is negative.
The point D(3, -6) has a positive x-coordinate and a negative y-coordinate. Therefore, it lies in the IV Quadrant.

Maths Mock Test- 3 - Question 20

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Which is true?

A.
A triangle can have two obtuse angles
B.
A triangle can have two acute angles
C.
A triangle can have two right angles
D.
All is true

Maths Mock Test- 3 - Question 21

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If ABC and PQR are similar triangles in which ∠ A = 47⁰ and ∠ Q = 83⁰, then ∠ C is:

A.
50⁰
B.
70⁰
C.
60⁰
D.
80⁰

Detailed Solution for Maths Mock Test- 3 - Question 21

Maths Mock Test- 3 - Question 22

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Which of the following equations is not linear equation :

A.
2x + 3 = 7x – 2
B.
2/3x + 5 = 3x – 4
C.
x² + 3 = 5x – 3
D.
(x – 2)² = x² + 8

Maths Mock Test- 3 - Question 23

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If x = 1,y = 1 is a solution of equation 9ax + 12ay = 63 then, the value of a is :

A.
- 3
B.
3
C.
7
D.
5

Maths Mock Test- 3 - Question 24

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In the figure, ∠M = 82°, then O = ?

A.
52°
B.
98°
C.
35°
D.
45°

Maths Mock Test- 3 - Question 25

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A polynomial containing two nonzero terms is called a ________.

A.
binomial
B.
trinomial
C.
monomial
D.
none of these

Detailed Solution for Maths Mock Test- 3 - Question 25

A binomial is a mathematical expression with two terms.

Examples of binomials.

binomial

All of these examples are binomials. Study them for a bit, and see if you can spot a pattern. The following is a list of what binomials must have:

They must have two terms.

If the variables are the same, then the exponents must be different.

Exponents must be whole positive integers. They cannot be negatives or fractions.

A term is a combination of numbers and variables. In the example 3x + 5, our first term is 3x, and our second term is 5. Terms are separated by either addition or subtraction. In our first example, notice how the 3x and 5 are separated by addition. In the last example, we have a binomial whose two terms both have the same variable s. Notice how each term has its variable to a different exponent. The first term has an exponent of 5, and the second term has an exponent of 4. While we can have fractions for our numbers, we cannot have fractional exponents.

Here are some examples of expressions that are not binomials.

Maths Mock Test- 3 - Question 26

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The expanded form of (3x−5)³ is

A.
27x³−135x²+225x−125
B.
27x³+135x²−225x−125
C.
27x³+135x²+225x−125
D.
none of these

Detailed Solution for Maths Mock Test- 3 - Question 26

Let a = 3x and b = 5 (3x)³ - (5)³ - 3×3x×5(3x- 5) = 27x³ - 125 -45x ( 3x -5) = 27x³ -125 - 135x² + 225x = 27x³ - 135x² + 225x - 125

Maths Mock Test- 3 - Question 27

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A.
231
B.
320
C.
336
D.
322

Detailed Solution for Maths Mock Test- 3 - Question 27

X+ 1/x = 7 then,
cubing both side
= (x +1/x)³ = (7)³
= x³ + 1/x³ + 3×x×1/x×(x+1/x) = 343
= x³ +1/x³ +3(7) = 343
= x³ +1/x³ +21 =343
= x³ +1/x³ =343 - 21
= x³ +1/x³ = 322

Maths Mock Test- 3 - Question 28

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Opposite angles of a Quadrilateral ABCD are equal. If AB = 4cm, find the length of CD.

A.
4cm
B.
3cm
C.
5cm
D.
2cm

Maths Mock Test- 3 - Question 29

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In a Trapezium ABCD, if AB ║ CD, then (AC²+ BD²) = ?

A.
BC²+ AD²+ 2AB.CD
B.
BC²+ AD²+ 2BC.AD
C.
AB²+ CD²+ 2AB.CD
D.
AB²+ CD²+ 2AD.BC

Maths Mock Test- 3 - Question 30

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In quadrilateral ABCD, ∠B=90^∘, ∠C−∠D = 60^∘ and ∠A−∠C−∠D = 10^∘. Find ∠A, ∠C and ∠D.

A.
140^∘, 95^∘, 35^∘
B.
145^∘, 55^∘, 20^∘
C.
150^∘, 60^∘, 80^∘
D.
None of these

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