Math Quiz For Class 9th

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4x+3y-2 is an algebraic
- Expression
- Sentence
- Equation
- Inequation

About This Quiz

This Math Quiz for 9th grade covers fundamental concepts of matrices including their order, properties, and operations. It is designed to test and reinforce students' understanding of matrix theory.

Quiz Preview

2.

Bisection means to divide into ____________ equal parts:
- 2
- 3
- 4
- None of these
Correct Answer

A. 2

Explanation

Bisection means to divide into two equal parts.

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3.

A triangle having all sides equal is called:
- Isoscels
- Scalene
- Equilateral
- None of these
Correct Answer

A. Equilateral

Explanation

An equilateral triangle is a type of triangle where all three sides are equal in length. Therefore, the correct answer is "Equilateral".

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4.

Write 4^2/3with radical sign:
- ³√4²
- √4³
- ³√4³
- √4⁶
Correct Answer

A. ³√4²

Explanation

The correct answer is 3√42. This is because the radical sign (√) represents the square root of a number. In this case, 3√42 means the cube root of 42. Cube root is the number that when multiplied by itself three times gives the original number. Therefore, the cube root of 42 is 3√42.

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5.

Equality of two ratios is defined as:
- Ratio
- Proportion
- Congruent
- Equality
Correct Answer

A. Proportion

Explanation

Equality of two ratios is defined as proportion. A proportion is a statement that two ratios are equal. In other words, when two ratios are in proportion, the corresponding terms in the ratios are equal. This means that if we have two ratios, such as a:b and c:d, and they are in proportion, then we can say that a/b = c/d. Proportions are used in various mathematical applications, such as solving problems involving similar figures, scaling, and finding unknown values.

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6.

If three points lie on the same line, then these points are called:
- Collinear
- Non-collinear
- Parallel
- Unparallel
Correct Answer

A. Collinear

Explanation

When three points lie on the same line, they are called "collinear." This means that the three points can be connected by a straight line without any curves or bends. In other words, they lie on the same path and can be considered as being on the same line.

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7.

A line segment has __________ mid point:
- 1
- 2
- 3
- 4
Correct Answer

A. 1

Explanation

A line segment has one midpoint. The midpoint of a line segment is the point that divides the segment into two equal halves. It is the point that is equidistant from both ends of the segment.

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8.

When the number of rows is not equal to the number of columns, the matrix is called____________:
- Square matrix
- Rectangular matrix
- Symmetric matrix
- Row matrix
Correct Answer

A. Rectangular matrix

Explanation

A rectangular matrix is a matrix where the number of rows is not equal to the number of columns. In other words, it has a different number of rows and columns, creating a rectangular shape. This is in contrast to a square matrix, which has an equal number of rows and columns. A symmetric matrix is a square matrix that is equal to its transpose, and a row matrix is a matrix with only one row.

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9.

If x is no larger than 10, then __________
- X≥8
- X≤10
- X<10
- X>10
Correct Answer

A. X≤10

Explanation

If x is no larger than 10, it means that x cannot be greater than 10. The correct answer x≤10 indicates that x can be equal to 10 or any value less than 10.

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10.

Product of
- [2x+y]
- [x-2y]
- [2x-y]
- [x+2y]
Correct Answer

A. [2x-y]

Explanation

The given expression is a product of four terms: [2x+y], [x-2y], [2x-y], and [x+2y]. The correct answer, [2x-y], is obtained by multiplying the terms together. When multiplying the terms, we use the distributive property and combine like terms. The resulting expression simplifies to 4x^2 - 9y^2. Therefore, the correct answer is [2x-y].

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11.

Bisection of an angle mean to draw a ray to divide the given angle into ___________ equal parts:
- One
- Two
- Three
- Four
Correct Answer

A. Two

Explanation

Bisection of an angle means to draw a ray that divides the given angle into two equal parts. This is achieved by drawing a line that starts from the vertex of the angle and passes through the midpoint of the angle. By doing so, the angle is split into two smaller angles, each having the same measure.

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12.

The logaritm of any number to itself as base is ___________
- 1
- 0
- -1
- 10
Correct Answer

A. 1

Explanation

The logarithm of any number to itself as a base is always 1. This is because the logarithm of a number to a base is the exponent to which the base must be raised to obtain the number. When the number and the base are the same, the exponent is always 1.

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13.

How many lines can be drawn through two points?
- 1
- 2
- 3
- Unlimited
Correct Answer

A. 1

Explanation

Only one line can be drawn through two points. This is because two points determine a unique line. Any additional lines drawn through the same two points would be overlapping and therefore the same line.

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14.

In a triangle, there can be only one _______________
- Right angle
- Acute angle
- Supplementary angle
- None of these
Correct Answer

A. Right angle

Explanation

In a triangle, there can be only one right angle. This is because a right angle measures exactly 90 degrees, and the sum of the interior angles of a triangle is always 180 degrees. Therefore, if one angle is a right angle, the other two angles must add up to 90 degrees in order to satisfy the condition that the sum of the angles is 180 degrees. Any additional right angles would result in the sum of the angles exceeding 180 degrees, which is not possible in a triangle.

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15.

Log p - log q is same as _____________
- Log(p/q)
- Log(p-q)
- Log p/log q
- Log(q/p)
Correct Answer

A. Log(p/q)

Explanation

The given expression, log p - log q, is equivalent to log(p/q). This is because when subtracting logarithms with the same base, the result is the logarithm of the division of the corresponding values. Therefore, log p - log q simplifies to log(p/q).

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16.

Find m so that x²+4x+m is a complete square _____________
- 8
- -8
- 4
- 16
Correct Answer

A. 4

Explanation

To find m so that x^2 + 4x + m is a complete square, we can use the formula for completing the square. The formula states that if we have a quadratic equation in the form ax^2 + bx + c, then we can rewrite it as (x + (b/2a))^2 + (c - b^2/4a). In this case, a = 1, b = 4, and c = m. Plugging these values into the formula, we get (x + 2)^2 + (m - 4)/4. To make this a complete square, we want the second term to be equal to zero. Therefore, (m - 4)/4 = 0, which implies m = 4.

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17.

Distance between points (0,0) and (1,1) is:
- 0
- 1
- 2
- √2
Correct Answer

A. √2

Explanation

The distance between two points in a coordinate plane can be found using the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates. In this case, the x-coordinates are both 0 and the y-coordinates are both 1. Therefore, the distance is the square root of (0-0)^2 + (1-1)^2 = √2.

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18.

Log e = __________, where e ≈ 2.718
- 0
- 0.4343
- ∞
- 1
Correct Answer

A. 0.4343

Explanation

The value of the natural logarithm of e is approximately 0.4343. The natural logarithm is the logarithm to the base e, where e is a mathematical constant approximately equal to 2.718. Therefore, log e = 0.4343.

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19.

Symbol used for congruent is:
- ~
- ≅
- Δ
- ∥
Correct Answer

A. ≅

Explanation

The symbol used for congruent is "≅". This symbol signifies that two geometric figures or angles are congruent, meaning they have the same size and shape. It is commonly used in geometry to show that two triangles or other shapes are equal in size and shape.

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20.

The sign of ratio is:
- =
- ∥
- :
- : :
Correct Answer

A. :

Explanation

The given correct answer is ":". In mathematics, the ":" symbol is commonly used to represent the ratio between two quantities. It indicates the division of one quantity by another. For example, if we have a ratio of 2:3, it means that the first quantity is divided by the second quantity in a ratio of 2 to 3. Therefore, the correct answer for the sign of ratio is ":".

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21.

If (x,0)=(0,y), then (x,y) is :
- (0,1)
- (1,0)
- (0,0)
- (1,1)
Correct Answer

A. (0,0)

Explanation

If (x,0) = (0,y), it means that the x-coordinate of the first ordered pair is 0 and the y-coordinate of the second ordered pair is also 0. Therefore, the only possible value for (x,y) is (0,0).

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22.

Order of square matrix is:
- 2-by-2
- 1-by-2
- 2-by-1
- 3-by-2
Correct Answer

A. 2-by-2

Explanation

The order of a square matrix refers to the number of rows and columns it has. In this case, the correct answer is 2-by-2, which means the matrix has 2 rows and 2 columns. This is determined by the given options, where the other options have either different numbers of rows or columns, making them not square matrices.

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23.

Log (mⁿ) can be written as ________________
- (log m)ⁿ
- M log n
- N log m
- Log (mn)
Correct Answer

A. N log m

Explanation

The given expression, log (mn), can be written as n log m. This is because when we take the logarithm of a product, it can be split into the sum of the logarithms of the individual factors. So, log (mn) is equal to log m + log n. By rearranging the terms, we get n log m.

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24.

Two lines intersect each other at __________ points.
- 1
- 2
- 3
- 4
Correct Answer

A. 1

Explanation

Two lines intersect each other at one point. This is a fundamental property of lines in geometry. When two lines cross each other, they meet at a single point of intersection.

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25.

Point (-3,-3) lies in quadrant:
- I
- II
- III
- IV
Correct Answer

A. III

Explanation

The point (-3,-3) lies in quadrant III because the x-coordinate (-3) is negative and the y-coordinate (-3) is also negative. In quadrant III, both the x and y coordinates are negative.

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26.

The diagonal of a parallelogram ______________ each other:
- Bisect
- Trisect
- Bisect at right angled
- None of these
Correct Answer

A. Bisect

Explanation

The diagonal of a parallelogram bisect each other because they intersect at their midpoint. This is a property of parallelograms, where opposite sides are parallel and congruent. The diagonals of a parallelogram divide it into two congruent triangles, and since the triangles share a side, the diagonals must intersect at their midpoint.

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27.

(3+√ 2)(3-√ 2) is equal to
- 7
- -7
- -1
- 1
Correct Answer

A. 7

Explanation

The given expression can be simplified using the formula (a+b)(a-b) = a^2 - b^2. In this case, a = 3 and b = √2. Substituting these values into the formula, we get (3^2 - (√2)^2), which simplifies to (9 - 2), resulting in 7. Therefore, the correct answer is 7.

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28.

The idea of Matrices was given by
- Arthur Cayley
- Briggs
- Al-Khawarzmi
- John Napier
Correct Answer

A. Arthur Cayley

Explanation

Arthur Cayley is credited with the idea of matrices. He was a British mathematician who made significant contributions to the field of algebra and is considered one of the founders of modern matrix theory. Cayley introduced the concept of matrices in the mid-19th century, developing the algebraic notation and operations that are still used today. His work laid the foundation for the study of linear algebra and its applications in various fields of science and engineering.

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1
29.

In a ____________ opposite sides are congruent:
- Triangle
- Parallelogram
- Trapezium
- Rhombus
Correct Answer

A. Parallelogram

Explanation

In a parallelogram, opposite sides are congruent. This means that the lengths of the two pairs of opposite sides are equal. This property is unique to parallelograms and does not apply to triangles, trapeziums, or rhombuses. In a triangle, only the three sides can be congruent if it is an equilateral triangle. In a trapezium, only one pair of opposite sides are parallel and may or may not be congruent. In a rhombus, opposite sides are parallel, but they may not be congruent unless it is also a square.

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30.

Unit of ratio is
- No unit
- Second
- Meter
- Kilogram
Correct Answer

A. No unit

Explanation

The unit of ratio is "no unit" because a ratio is a comparison of two quantities and does not involve any specific physical measurement. Ratios are expressed as a quotient of two numbers and do not require any specific unit of measurement.

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31.

It is called ____________ matrix:
- Zero
- Unit
- Scalar
- Singular
Correct Answer

A. Scalar

Explanation

A scalar matrix is a special type of square matrix where all the elements on the main diagonal are equal and all other elements are zero. In this case, the given matrix is a scalar matrix because all the elements are zero except for the main diagonal, which contains the same value.

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32.

In ³√35 the radicand is
- 3
- 1/3
- 35
- (35)^1/3
Correct Answer

A. 35

Explanation

The radicand is the number under the radical symbol. In this case, the radical symbol is the cube root (∛) and the number under it is 35. Therefore, the radicand is 35.

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1
33.

The factors of x²-5x+6 are
- X+1, x-6
- X-2, x-3
- X+6, x-1
- X+2, x+3
Correct Answer

A. X-2, x-3

Explanation

The given quadratic equation is x^2 - 5x + 6. To find the factors of this equation, we need to determine two binomials that multiply together to give the original equation. By using the method of factorization, we can determine that the factors are (x-2) and (x-3).

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34.

H.C.F of a³+b³ and a²-ab+b² is _____________
- A+b
- A²-ab+b²
- (a-b)²
- A²+b²
Correct Answer

A. A²-ab+b²

Explanation

The given question asks for the highest common factor (H.C.F) of two expressions, a^3 + b^3 and a^2 - ab + b^2. The correct answer, a^2 - ab + b^2, is obtained by factoring the expressions and finding the common factors. The expressions can be factored as (a + b)(a^2 - ab + b^2) and (a + b)(a^2 - ab + b^2) respectively. The common factor is (a + b), and when simplified, we get a^2 - ab + b^2. Therefore, a^2 - ab + b^2 is the H.C.F of the given expressions.

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35.

Which ordered pair satisfies the equation y=2x?
- (1,2)
- (2,1)
- (2,2)
- (0,1)
Correct Answer

A. (1,2)

Explanation

The equation y = 2x represents a linear relationship where the y-coordinate is always twice the x-coordinate. Among the given options, only the ordered pair (1,2) satisfies this condition since when x is 1, y is indeed 2. Therefore, (1,2) is the correct answer.

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36.

Mid point of the points (2,2) and (0,0) is:
- (1,1)
- (1,0)
- (0,1)
- (-1,-1)
Correct Answer

A. (1,1)

Explanation

The mid point of two points can be found by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the x-coordinate of the mid point is (2+0)/2 = 1 and the y-coordinate is (2+0)/2 = 1. Therefore, the mid point of the given points is (1,1).

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37.

Similar triangles are of the same shape but ____________ in sizes.
- Same
- Different
- Both same and different
- None of these
Correct Answer

A. Different

Explanation

Similar triangles are of the same shape but different in sizes. This means that although the angles of similar triangles are equal, their side lengths are proportional and not equal. The corresponding sides of similar triangles are in the same ratio, which results in the triangles being different in size. Therefore, the correct answer is "different".

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38.

Congruent triangles are__________
- Parallel
- Similar
- Different
- None of these
Correct Answer

A. Similar

Explanation

Congruent triangles are similar. Congruent triangles have the same shape and size, meaning that their corresponding angles and sides are equal. Similar triangles, on the other hand, have the same shape but may have different sizes. Therefore, congruent triangles are a subset of similar triangles, as all congruent triangles are similar but not all similar triangles are congruent.

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39.

Each Hypotenuse of a parallelogram divides it into __________ congruent triangles:
- 2
- 3
- 4
- 5
Correct Answer

A. 2

Explanation

Each hypotenuse of a parallelogram divides it into two congruent triangles. This is because a parallelogram has two pairs of opposite sides that are equal in length and parallel to each other. The hypotenuse, which is the longest side of a right triangle, acts as a diagonal for the parallelogram and divides it into two congruent triangles. These triangles have the same shape and size, with corresponding angles and sides equal to each other. Therefore, the correct answer is 2.

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40.

If a^x=n, then:
- A=log_xa
- X=log_na
- X=log_an
- A=log_nx
Correct Answer

A. X=log_an

Explanation

The equation ax=n can be rewritten as x=logan. This is because the logarithm of a number to a base is the exponent to which the base must be raised to obtain that number. In this case, "a" is the base, "x" is the exponent, and "n" is the result of raising "a" to the power of "x". Therefore, x=logan is the correct answer.

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41.

(√a+√b)(√a-√b) is equal to
- A²+b²
- A²-b²
- A-b
- A+b
Correct Answer

A. A-b

Explanation

The expression (√a+√b)(√a-√b) can be simplified using the difference of squares formula, which states that (x+y)(x-y) is equal to x^2 - y^2. In this case, we can let x = √a and y = √b. Therefore, the expression simplifies to (√a)^2 - (√b)^2, which is equal to a - b.

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42.

In two triangles for (1-1) correspondence symbol used is____________
- =
- ≅
- ↔
- ~
Correct Answer

A. ↔

Explanation

The symbol "↔" is used to represent the concept of "if and only if" or "equivalent to" in mathematics. In the context of two triangles, "↔" signifies that the two triangles are congruent to each other. This means that they have the same shape and size, and all corresponding sides and angles are equal. Therefore, the correct answer is "↔".

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43.

How many end points has a ray?
- 1
- 2
- 3
- 4
Correct Answer

A. 1

Explanation

A ray has only one endpoint. A ray is a part of a line that starts at a specific point (the endpoint) and extends infinitely in one direction. It does not have a second endpoint like a line segment, which has two distinct endpoints. Therefore, the correct answer is 1.

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44.

If a:b=c:d then a,b,c and d are said to be in:
- Proportion
- Ratio
- Equal
- Unequal
Correct Answer

A. Proportion

Explanation

If a:b=c:d, it means that the ratio of a to b is equal to the ratio of c to d. In other words, the quantities a, b, c, and d are in proportion. Proportion refers to the relationship between two or more ratios that are equal. It is a mathematical concept used to compare quantities and determine their relative sizes. Therefore, the answer is proportion.

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45.

The value of i⁹ is ____________
- 1
- -1
- I
- -i
Correct Answer

A. I

Explanation

The value of i9 is i because i is the imaginary unit, which represents the square root of -1. When i is raised to the power of 9, it cycles through a pattern where the powers of i repeat every 4 terms: i, -1, -i, 1. Since 9 is equivalent to 8 + 1, the power of i can be simplified to i8 * i1. i8 is equal to 1, so the value of i9 is i.

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46.

(27x^-1)^-2/3
- ³√x²/9
- √x³/9
- ³√x²/8
- √x³/8
Correct Answer

A. ³√x²/9

Explanation

The given expression can be simplified by first simplifying the expression inside the parentheses. The expression (27x - 1) can be simplified further by distributing the -2/3 to both terms inside the parentheses. This gives us -54x/3 + 2/3. Simplifying this further, we get -18x + 2/3. Next, we need to simplify the expression outside the parentheses. Taking the cube root of x^2/9 gives us (x^2/9)^(1/3) which simplifies to (x^2)^(1/3)/(9)^(1/3). Simplifying this further, we get x^(2/3)/3. Therefore, the correct answer is 3√x^2/9.

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47.

A²-b² /a+b
- (a-b)²
- (a+b)²
- (a-b)
- (a+b)
Correct Answer

A. (a-b)

Explanation

The correct answer is (a-b) because when we simplify the expression (a2-b2)/(a+b), we can factor the numerator as (a-b)(a+b). Then, we can cancel out the (a+b) terms in the numerator and denominator, leaving us with (a-b) as the final answer.

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48.

A square matrix M is called to be skew symmetric, if:
- M^t=M^t
- M^t=1/M
- M^t=-M
- M^t = M
Correct Answer

A. M^t=-M

Explanation

A square matrix M is called skew symmetric if its transpose is equal to the negative of the matrix itself. In other words, if Mt = -M. This means that the elements above the main diagonal of M are equal to the corresponding elements below the main diagonal, but with opposite signs. The correct answer states that Mt=-M, which is the correct condition for a matrix to be skew symmetric.

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49.

If x=3 and y=-1 then the value of x³y is
- 27
- -27
- 9
- -9
Correct Answer

A. -27

Explanation

The given expression x3y means x cubed multiplied by y. Substituting the given values, we have 3 cubed multiplied by -1, which equals -27.

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Math Quiz For Class 9th

4x+3y-2 is an algebraic

Quiz Preview

Bisection means to divide into ____________ equal parts:

A triangle having all sides equal is called:

Write 42/3 with radical sign:

Equality of two ratios is defined as:

If three points lie on the same line, then these points are called:

A line segment has __________ mid point:

When the number of rows is not equal to the number of columns, the matrix is called____________:

If x is no larger than 10, then __________

Product of

Bisection of an angle mean to draw a ray to divide the given angle into ___________ equal parts:

The logaritm of any number to itself as base is ___________

How many lines can be drawn through two points?

In a triangle, there can be only one _______________

Log p - log q is same as _____________

Find m so that x2+4x+m is a complete square _____________

Distance between points (0,0) and (1,1) is:

Log e = __________, where e ≈ 2.718

Symbol used for congruent is:

The sign of ratio is:

If (x,0)=(0,y), then (x,y) is :

Order of square matrix is:

Log (mn) can be written as ________________

Two lines intersect each other at __________ points.

Point (-3,-3) lies in quadrant:

The diagonal of a parallelogram ______________ each other:

(3+√ 2)(3-√ 2) is equal to

The idea of Matrices was given by

In a ____________ opposite sides are congruent:

Unit of ratio is

It is called ____________ matrix:

In 3√35 the radicand is

The factors of x2-5x+6 are

H.C.F of a3+b3 and a2-ab+b2 is _____________

Which ordered pair satisfies the equation y=2x?

Mid point of the points (2,2) and (0,0) is:

Similar triangles are of the same shape but ____________ in sizes.

Congruent triangles are__________

Each Hypotenuse of a parallelogram divides it into __________ congruent triangles:

If ax=n, then:

(√a+√b)(√a-√b) is equal to

In two triangles for (1-1) correspondence symbol used is____________

How many end points has a ray?

If a:b=c:d then a,b,c and d are said to be in:

The value of i9 is ____________

(27x-1)-2/3

A2-b2 /a+b

A square matrix M is called to be skew symmetric, if:

If x=3 and y=-1 then the value of x3y is

Write 4^2/3with radical sign:

Find m so that x²+4x+m is a complete square _____________

Log (mⁿ) can be written as ________________

In ³√35 the radicand is

The factors of x²-5x+6 are

H.C.F of a³+b³ and a²-ab+b² is _____________

If a^x=n, then:

The value of i⁹ is ____________

(27x^-1)^-2/3

A²-b² /a+b

If x=3 and y=-1 then the value of x³y is