MATH QUIZ FOR CLASS 9th

1) Bisection means to divide into ____________ equal parts:

2

3

4

None of these

Bisection means to divide into two equal parts.

Explanation

Bisection means to divide into two equal parts.

2) 4x+3y-2 is an algebraic

Expression

Sentence

Equation

Inequation

The given expression, 4x+3y-2, is a combination of variables (x and y) and constants (4, 3, and 2) connected by mathematical operations (+ and -). It does not have an equal sign, so it is not an equation. It also does not have any inequality symbols (such as > or <), so it is not an inequation. Therefore, the correct answer is expression.

Explanation

The given expression, 4x+3y-2, is a combination of variables (x and y) and constants (4, 3, and 2) connected by mathematical operations (+ and -). It does not have an equal sign, so it is not an equation. It also does not have any inequality symbols (such as > or <), so it is not an inequation. Therefore, the correct answer is expression.

3) Unit of ratio is

No unit

Second

Meter

Kilogram

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.

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.

4) A triangle having all sides equal is called:

Isoscels

Scalene

Equilateral

None of these

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

Explanation

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

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

One

Two

Three

Four

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.

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.

6) Equality of two ratios is defined as:

Ratio

Proportion

Congruent

Equality

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.

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.

7) The sign of ratio is:

=

∥

:

: :

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 ":".

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 ":".

8) The diagonal of a parallelogram ______________ each other:

Bisect

Trisect

Bisect at right angled

None of these

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.

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.

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

(1,1)

(1,0)

(0,1)

(-1,-1)

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).

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).

10) In a triangle, there can be only one _______________

Right angle

Acute angle

Supplementary angle

None of these

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.

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.

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

2

3

4

5

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.

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.

12) A line segment has __________ mid point:

1

2

3

4

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.

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.

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

Collinear

Non-collinear

Parallel

Unparallel

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.

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.

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

Same

Different

Both same and different

None of these

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".

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".

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

(0,1)

(1,0)

(0,0)

(1,1)

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).

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).

16) Order of square matrix is:

2-by-2

1-by-2

2-by-1

3-by-2

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.

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.

17) 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

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.

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.

18) Two lines intersect each other at __________ points.

1

2

3

4

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.

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.

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

I

II

III

IV

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.

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.

20) Log e = __________, where e ≈ 2.718

0

0.4343

∞

1

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.

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.

21) Write 4^2/3with radical sign:

3√42

√43

3√43

√46

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.

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.

22) The idea of Matrices was given by

Arthur Cayley

Briggs

Al-Khawarzmi

John Napier

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.

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.

23) The factors of x²-5x+6 are

X+1, x-6

X-2, x-3

X+6, x-1

X+2, x+3

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).

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).

24) Product of

[2x+y]

[x-2y]

[2x-y]

[x+2y]

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].

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].

25) How many end points has a ray?

1

2

3

4

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.

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.

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

Proportion

Ratio

Equal

Unequal

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.

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.

27) The logaritm of any number to itself as base is ___________

1

0

-1

10

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.

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.

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

A+b

A2-ab+b2

(a-b)2

A2+b2

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.

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.

29) The point (-2,-3) lies in quadrant ______________

I

II

III

IV

The point (-2,-3) lies in quadrant III because the x-coordinate (-2) is negative and the y-coordinate (-3) is also negative. In quadrant III, both the x and y coordinates are negative.

Explanation

The point (-2,-3) lies in quadrant III because the x-coordinate (-2) is negative and the y-coordinate (-3) is also negative. In quadrant III, both the x and y coordinates are negative.

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

8

-8

4

16

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.

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.

31) If x is no larger than 10, then __________

X≥8

X≤10

X<10

X>10

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.

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.

32) Ifx,y,z ∈ R, z<0 then, x<y⇒ _____________:

Xz

Xz>yz

Xz=yz

None of these

If x, y, and z are real numbers and z is less than 0, then x < y implies that xz > yz. This can be explained by considering that when z is negative, multiplying both sides of the inequality x < y by z will result in a reversal of the inequality sign. Therefore, xz will be greater than yz.

Explanation

If x, y, and z are real numbers and z is less than 0, then x < y implies that xz > yz. This can be explained by considering that when z is negative, multiplying both sides of the inequality x < y by z will result in a reversal of the inequality sign. Therefore, xz will be greater than yz.

33) log (mⁿ) can be written as ________________

(log m)n

M log n

N log m

Log (mn)

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.

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.

34) If y=2x+1, x=2 then y is:

2

3

4

5

Given the equation y=2x+1, we are asked to find the value of y when x=2. Plugging in x=2 into the equation, we get y=2(2)+1=4+1=5. Therefore, the value of y when x=2 is 5.

Explanation

Given the equation y=2x+1, we are asked to find the value of y when x=2. Plugging in x=2 into the equation, we get y=2(2)+1=4+1=5. Therefore, the value of y when x=2 is 5.

35) a²-b² /a+b

(a-b)2

(a+b)2

(a-b)

(a+b)

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.

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.

36) Symbol used for congruent is:

~

≅

Δ

∥

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.

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.

37) In a ____________ opposite sides are congruent:

Triangle

Parallelogram

Trapezium

Rhombus

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.

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.

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

0

1

2

√2

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.

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.

39) The relation y=log_zx implies

Xy=z

Zy=x

Xz=y

Yz=x

The relation y=logzx implies that taking the logarithm of z to the base x will give us y. In other words, if we raise x to the power of y, we will get z. Therefore, zy=x is the correct answer.

Explanation

The relation y=logzx implies that taking the logarithm of z to the base x will give us y. In other words, if we raise x to the power of y, we will get z. Therefore, zy=x is the correct answer.

40) In a triangle, there can be ______________ right angle.

1

2

3

4

In a triangle, there can only be one right angle. A right angle is an angle that measures exactly 90 degrees. Since the sum of the interior angles of a triangle is always 180 degrees, if one angle is a right angle, the other two angles must be acute angles (less than 90 degrees) in order for the sum to be 180 degrees. Therefore, there can only be one right angle in a triangle.

Explanation

In a triangle, there can only be one right angle. A right angle is an angle that measures exactly 90 degrees. Since the sum of the interior angles of a triangle is always 180 degrees, if one angle is a right angle, the other two angles must be acute angles (less than 90 degrees) in order for the sum to be 180 degrees. Therefore, there can only be one right angle in a triangle.

41) (3+√ 2)(3-√ 2) is equal to

7

-7

-1

1

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.

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.

42) The value of i⁹ is ____________

1

-1

I

-i

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.

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.

43) It is called ____________ matrix:

Zero

Unit

Scalar

Singular

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.

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.

44) Congruent triangles are__________

Parallel

Similar

Different

None of these

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.

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.

45) The square root of a²-2a+1 is

±(a+1)

±(a-1)

A-1

A+1

The square root of a^2 - 2a + 1 can be written as √(a-1)^2. Taking the square root of a perfect square gives us the positive and negative value of the square root. Therefore, the answer is ±(a-1).

Explanation

The square root of a^2 - 2a + 1 can be written as √(a-1)^2. Taking the square root of a perfect square gives us the positive and negative value of the square root. Therefore, the answer is ±(a-1).

46) How many lines can be drawn through two points?

1

2

3

Unlimited

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.

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.

47) The point (-4,3) lies in the quadrant __________

I

II

III

IV

The point (-4,3) lies in the quadrant II because the x-coordinate (-4) is negative and the y-coordinate (3) is positive. In quadrant II, the x-coordinate is negative and the y-coordinate is positive.

Explanation

The point (-4,3) lies in the quadrant II because the x-coordinate (-4) is negative and the y-coordinate (3) is positive. In quadrant II, the x-coordinate is negative and the y-coordinate is positive.

48) x is equal to _______________ if :

9

-6

6

-9

If x is equal to 9, then it satisfies the given conditions because 9 is the only number in the list that is equal to itself. The other numbers (-6, 6, -9) are not equal to 9, so they do not satisfy the condition. Therefore, the correct answer is 9.

Explanation

If x is equal to 9, then it satisfies the given conditions because 9 is the only number in the list that is equal to itself. The other numbers (-6, 6, -9) are not equal to 9, so they do not satisfy the condition. Therefore, the correct answer is 9.

49) (27x^-1)^-2/3

3√x2/9

√x3/9

3√x2/8

√x3/8

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.

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.

50) Which ordered pair satisfies the equation y=2x?

(1,2)

(2,1)

(2,2)

(0,1)

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.

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.

51) log p - log q is same as _____________

Log(p/q)

Log(p-q)

Log p/log q

Log(q/p)

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).

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).

52) If a^x=n, then:

A=logxa

X=logna

X=logan

A=lognx

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.

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.

53) The degree of polynomial 4x⁴+2x²y is ____________

1

2

3

4

The degree of a polynomial is determined by the highest power of the variable in the polynomial. In this case, the polynomial is 4x^4 + 2x^2y. The highest power of x is 4, which means the degree of the polynomial is 4.

Explanation

The degree of a polynomial is determined by the highest power of the variable in the polynomial. In this case, the polynomial is 4x^4 + 2x^2y. The highest power of x is 4, which means the degree of the polynomial is 4.

54) In a parallelogram congruent parts are ______________

Opposite sides

Opposite angles

Opposite sides and angles

Diagonals

In a parallelogram, the opposite sides are congruent (equal in length) and the opposite angles are congruent (equal in measure). This means that if we have a parallelogram, we can say that the two pairs of opposite sides are congruent and the two pairs of opposite angles are congruent. Therefore, the correct answer is "opposite sides and angles".

Explanation

In a parallelogram, the opposite sides are congruent (equal in length) and the opposite angles are congruent (equal in measure). This means that if we have a parallelogram, we can say that the two pairs of opposite sides are congruent and the two pairs of opposite angles are congruent. Therefore, the correct answer is "opposite sides and angles".

55) If the bisector of an angle of a triangle bisects the side opposite to it, the triangle is __________:

Scalene

Isosceles

Any triangle

None of these

If the bisector of an angle of a triangle bisects the side opposite to it, then the triangle is an isosceles triangle. In an isosceles triangle, two sides are equal in length, and since the bisector of an angle bisects the side opposite to it, it divides that side into two equal parts. Therefore, the triangle must have two equal sides, making it an isosceles triangle.

Explanation

If the bisector of an angle of a triangle bisects the side opposite to it, then the triangle is an isosceles triangle. In an isosceles triangle, two sides are equal in length, and since the bisector of an angle bisects the side opposite to it, it divides that side into two equal parts. Therefore, the triangle must have two equal sides, making it an isosceles triangle.

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

27

-27

9

-9

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

57) In ³√35 the radicand is

3

1/3

35

(35)1/3

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.

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.

58) Order of transpose is _____________:

3-by-2

2-by-3

3-by-1

1-by-3

The order of transpose is determined by the dimensions of the original matrix. In this case, the original matrix is 2-by-3, which means it has 2 rows and 3 columns. When we take the transpose of this matrix, the rows become columns and the columns become rows, resulting in a matrix with dimensions 3-by-2.

Explanation

The order of transpose is determined by the dimensions of the original matrix. In this case, the original matrix is 2-by-3, which means it has 2 rows and 3 columns. When we take the transpose of this matrix, the rows become columns and the columns become rows, resulting in a matrix with dimensions 3-by-2.

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

(2,2)

(-2,-2)

(0,0)

(1,1)

The midpoint of two points can be found by averaging their x-coordinates and averaging their y-coordinates. In this case, the x-coordinate of the midpoint is (2 + (-2))/2 = 0, and the y-coordinate of the midpoint is (-2 + 2)/2 = 0. Therefore, the midpoint of the points (2,-2) and (-2,2) is (0,0).

Explanation

The midpoint of two points can be found by averaging their x-coordinates and averaging their y-coordinates. In this case, the x-coordinate of the midpoint is (2 + (-2))/2 = 0, and the y-coordinate of the midpoint is (-2 + 2)/2 = 0. Therefore, the midpoint of the points (2,-2) and (-2,2) is (0,0).

60) The median of a triangle cut each other in the ratio _______________

4:1

3:1

2:1

1:1

The median of a triangle divides each other in the ratio of 2:1. This means that the length of the line segment from the vertex to the midpoint of the opposite side is twice as long as the length of the line segment from the midpoint to the other side. This ratio is consistent for all three medians of a triangle.

Explanation

The median of a triangle divides each other in the ratio of 2:1. This means that the length of the line segment from the vertex to the midpoint of the opposite side is twice as long as the length of the line segment from the midpoint to the other side. This ratio is consistent for all three medians of a triangle.

61) H.C.F of 5x²y² and 20x³y³ is _____________

5x2y2

20x3y3

100x5y5

5xy

The H.C.F (Highest Common Factor) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, the given numbers are 5x^2y^2 and 20x^3y^3. To find the H.C.F, we need to find the highest power of each variable that is common to both numbers. The highest power of x that is common to both numbers is x^2, and the highest power of y that is common to both numbers is y^2. Therefore, the H.C.F is 5x^2y^2.

Explanation

The H.C.F (Highest Common Factor) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, the given numbers are 5x^2y^2 and 20x^3y^3. To find the H.C.F, we need to find the highest power of each variable that is common to both numbers. The highest power of x that is common to both numbers is x^2, and the highest power of y that is common to both numbers is y^2. Therefore, the H.C.F is 5x^2y^2.

62) What will be added to complete the square of 9a²-12ab?

-16b2

16b2

4b2

-4b2

To complete the square of 9a^2 - 12ab, we need to add a term that will make the expression a perfect square trinomial. The coefficient of the middle term is -12ab, so we want to find a term that, when squared, will give us (12ab/2)^2 = (6ab)^2 = 36a^2b^2. This term is 36a^2b^2. However, since we want to add this term to the expression, we need to subtract it to maintain the equality. Therefore, the term that needs to be added to complete the square is -36a^2b^2. Simplifying, we get 9a^2 - 12ab - 36a^2b^2. Factoring out a common factor, we have (3a - 6ab)^2. Notice that the middle term is -12ab, which matches the original expression. Therefore, the correct answer is 4b^2.

Explanation

To complete the square of 9a^2 - 12ab, we need to add a term that will make the expression a perfect square trinomial. The coefficient of the middle term is -12ab, so we want to find a term that, when squared, will give us (12ab/2)^2 = (6ab)^2 = 36a^2b^2. This term is 36a^2b^2. However, since we want to add this term to the expression, we need to subtract it to maintain the equality. Therefore, the term that needs to be added to complete the square is -36a^2b^2. Simplifying, we get 9a^2 - 12ab - 36a^2b^2. Factoring out a common factor, we have (3a - 6ab)^2. Notice that the middle term is -12ab, which matches the original expression. Therefore, the correct answer is 4b^2.

63) Factors of 3x²-x-2 are ____________

(x+1),(3x-2)

(x+1),(3x+2)

(x-1),(3x-2)

(x-1),(3x+2)

The factors of a quadratic expression can be found by factoring it into two binomials. In this case, we need to find two binomials that when multiplied together, result in 3x^2-x-2. By trial and error or using the quadratic formula, we can determine that the correct factors are (x-1) and (3x+2). Multiplying these two binomials together will give us the original quadratic expression.

Explanation

The factors of a quadratic expression can be found by factoring it into two binomials. In this case, we need to find two binomials that when multiplied together, result in 3x^2-x-2. By trial and error or using the quadratic formula, we can determine that the correct factors are (x-1) and (3x+2). Multiplying these two binomials together will give us the original quadratic expression.

64) (√a+√b)(√a-√b) is equal to

A2+b2

A2-b2

A-b

A+b

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.

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.

65) ___________ points are said to be collinear if they lie on same line:

Two

Three

Four

Five

Three points are said to be collinear if they lie on the same line. In other words, if three points can be connected by a straight line without any bends or curves, then they are collinear. This is a fundamental concept in geometry and is used to describe the relationship between points in a coordinate system.

Explanation

Three points are said to be collinear if they lie on the same line. In other words, if three points can be connected by a straight line without any bends or curves, then they are collinear. This is a fundamental concept in geometry and is used to describe the relationship between points in a coordinate system.

66) x= ___________ is a solution of the inequality -2<x<3/2

-5

3

0

3/2

The correct answer is 0 because it falls within the given range of -2 < x < 3/2. Any value between -2 and 3/2, excluding the endpoints, would be a solution to the inequality. Since 0 satisfies this condition, it is the correct answer.

Explanation

The correct answer is 0 because it falls within the given range of -2 < x < 3/2. Any value between -2 and 3/2, excluding the endpoints, would be a solution to the inequality. Since 0 satisfies this condition, it is the correct answer.

67) Real part of 2ab(i+i²) is ______________

-2ab

2ab

3ab

-3ab

The expression 2ab(i+i^2) can be simplified as 2ab(i-1), since i^2 is equal to -1. The real part of a complex number is the part without the imaginary unit, so the real part of 2ab(i-1) is -2ab.

Explanation

The expression 2ab(i+i^2) can be simplified as 2ab(i-1), since i^2 is equal to -1. The real part of a complex number is the part without the imaginary unit, so the real part of 2ab(i-1) is -2ab.

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

0

1

√ 2

2

The distance between two points can be calculated using the distance formula, which is derived from the Pythagorean theorem. In this case, the distance between the points (1,0) and (0,1) can be found using the formula: √((x2 - x1)^2 + (y2 - y1)^2). Plugging in the coordinates, we get: √((0 - 1)^2 + (1 - 0)^2) = √(1 + 1) = √2. Therefore, the correct answer is √2.

Explanation

The distance between two points can be calculated using the distance formula, which is derived from the Pythagorean theorem. In this case, the distance between the points (1,0) and (0,1) can be found using the formula: √((x2 - x1)^2 + (y2 - y1)^2). Plugging in the coordinates, we get: √((0 - 1)^2 + (1 - 0)^2) = √(1 + 1) = √2. Therefore, the correct answer is √2.

69) For ______ value of x, will be singular matrix.

3

-4

3

4

not-available-via-ai

Explanation

not-available-via-ai

70) Perpendicular distance to base from its opposite vertex is called _________

Median

Altitude

Orthocentre

Centroid

The perpendicular distance from the base to the opposite vertex is called the altitude. The altitude is a line segment that forms a right angle with the base of a triangle and extends from the base to the opposite vertex. It is used to calculate various properties of a triangle, such as the area and the length of other line segments within the triangle. The altitude plays an important role in geometric constructions and can help determine the height or distance of an object in real-world applications.

Explanation

The perpendicular distance from the base to the opposite vertex is called the altitude. The altitude is a line segment that forms a right angle with the base of a triangle and extends from the base to the opposite vertex. It is used to calculate various properties of a triangle, such as the area and the length of other line segments within the triangle. The altitude plays an important role in geometric constructions and can help determine the height or distance of an object in real-world applications.

71) H.C.F of x-2 and x²+x-6 is ________________

X2+x-6

X+3

X-2

X+2

The given question asks for the highest common factor (H.C.F) of the expressions x-2 and x^2+x-6. To find the H.C.F, we need to factorize both expressions. The expression x^2+x-6 can be factored as (x+3)(x-2). The common factor between x-2 and (x+3)(x-2) is x-2. Therefore, the correct answer is x-2.

Explanation

The given question asks for the highest common factor (H.C.F) of the expressions x-2 and x^2+x-6. To find the H.C.F, we need to factorize both expressions. The expression x^2+x-6 can be factored as (x+3)(x-2). The common factor between x-2 and (x+3)(x-2) is x-2. Therefore, the correct answer is x-2.

72) Arthur Cayley introduced the "Theory of Matrices" in ____________

1854

1856

1858

1860

not-available-via-ai

Explanation

not-available-via-ai

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

=

≅

↔

~

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 "↔".

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 "↔".

74) If the capacity c of an elevator is at most 1600 pounds, then:

C<1600

C≥1600

C≤1600

C>1600

If the capacity c of an elevator is at most 1600 pounds, it means that the maximum weight the elevator can carry is 1600 pounds or less. Therefore, the correct answer is c≤1600, which indicates that the capacity is less than or equal to 1600 pounds.

Explanation

If the capacity c of an elevator is at most 1600 pounds, it means that the maximum weight the elevator can carry is 1600 pounds or less. Therefore, the correct answer is c≤1600, which indicates that the capacity is less than or equal to 1600 pounds.

75) The point of concurrency of the three altitudes of a triangle is called:

Centriod

Orthocentre

Circumcentre

Incentre

The orthocentre is the point of concurrency of the three altitudes of a triangle. An altitude is a line segment drawn from a vertex of a triangle perpendicular to the opposite side. The orthocentre is the point where all three altitudes intersect. It is an important point in a triangle as it has several unique properties and is often used in geometric constructions and proofs.

Explanation

The orthocentre is the point of concurrency of the three altitudes of a triangle. An altitude is a line segment drawn from a vertex of a triangle perpendicular to the opposite side. The orthocentre is the point where all three altitudes intersect. It is an important point in a triangle as it has several unique properties and is often used in geometric constructions and proofs.

76) Factors of a⁴-4b⁴ are ____________

(a-b),(a+b),(a2+4b2)

(a2-2b2), (a2+2b2)

(a-b),(a+b),(a2-4b2)

(a-2b),(a2+2b2)

The given expression is a^4 - 4b^4. This can be factored using the difference of squares formula, which states that a^2 - b^2 = (a - b)(a + b). In this case, we can rewrite the expression as (a^2)^2 - (2b^2)^2, which can be factored as (a^2 - 2b^2)(a^2 + 2b^2). Therefore, the factors of a^4 - 4b^4 are (a^2 - 2b^2) and (a^2 + 2b^2).

Explanation

The given expression is a^4 - 4b^4. This can be factored using the difference of squares formula, which states that a^2 - b^2 = (a - b)(a + b). In this case, we can rewrite the expression as (a^2)^2 - (2b^2)^2, which can be factored as (a^2 - 2b^2)(a^2 + 2b^2). Therefore, the factors of a^4 - 4b^4 are (a^2 - 2b^2) and (a^2 + 2b^2).

77) The order of matrix [ 2 1] is __________

2-by-1

1-by-2

1-by-1

2-by-2

The order of a matrix is determined by the number of rows and columns it has. In this case, the matrix is given as [2 1], which means it has 1 row and 2 columns. Therefore, the order of the matrix is 1-by-2.

Explanation

The order of a matrix is determined by the number of rows and columns it has. In this case, the matrix is given as [2 1], which means it has 1 row and 2 columns. Therefore, the order of the matrix is 1-by-2.

78) One angle of parallelogram is 130^o, the remaining angles are of measures _____________

50o,130o,130o

50o,100o,130o

50o,65o,65o

50o,50o,130o

The sum of the angles in a parallelogram is always 360 degrees. If one angle is given as 130 degrees, the remaining angles must add up to 360 - 130 = 230 degrees. The only option that satisfies this condition is 50o, 50o, 130o.

Explanation

The sum of the angles in a parallelogram is always 360 degrees. If one angle is given as 130 degrees, the remaining angles must add up to 360 - 130 = 230 degrees. The only option that satisfies this condition is 50o, 50o, 130o.

79) Adjoint of

Option

not-available-via-ai

Explanation

not-available-via-ai

80) **The solution set of | x-4 |=-4 is:**

-8

-16

{ }

4

not-available-via-ai

Explanation

not-available-via-ai

81) If (x-2) is a factor of P(x) = x²+2kx+8, then the value of k is _____________

3

-3

2

-2

If (x-2) is a factor of P(x), it means that when we substitute x=2 into P(x), the result will be zero. Therefore, we can substitute x=2 into P(x) and solve for k. By substituting x=2 into P(x)=x^2+2kx+8, we get 2^2+2k(2)+8=0. Simplifying this equation, we get 4+4k+8=0. Combining like terms, we have 4k+12=0. Subtracting 12 from both sides, we get 4k=-12. Dividing both sides by 4, we find that k=-3.

Explanation

If (x-2) is a factor of P(x), it means that when we substitute x=2 into P(x), the result will be zero. Therefore, we can substitute x=2 into P(x) and solve for k. By substituting x=2 into P(x)=x^2+2kx+8, we get 2^2+2k(2)+8=0. Simplifying this equation, we get 4+4k+8=0. Combining like terms, we have 4k+12=0. Subtracting 12 from both sides, we get 4k=-12. Dividing both sides by 4, we find that k=-3.

82) x=0 is a solution of the inequality:

X>0

3x+5<0

X+2<0

X-2<0

The inequality x-2<0 represents all the values of x that are less than 2. Since the inequality is asking for values of x that are less than 0, we can see that x=0 satisfies this condition. Therefore, x=0 is a solution of the inequality x-2<0.

Explanation

The inequality x-2<0 represents all the values of x that are less than 2. Since the inequality is asking for values of x that are less than 0, we can see that x=0 satisfies this condition. Therefore, x=0 is a solution of the inequality x-2<0.

83) Which of the following is the solution of the inequality 3-4x≤11?

-8

-2

- 14/4

None of these

To find the solution of the inequality 3-4x≤11, we need to isolate the variable x. We can do this by subtracting 3 from both sides of the inequality, which gives us -4x≤8. Next, we divide both sides of the inequality by -4, remembering to reverse the inequality sign since we are dividing by a negative number. This gives us x≥-2. Therefore, the solution to the inequality is x=-2.

Explanation

To find the solution of the inequality 3-4x≤11, we need to isolate the variable x. We can do this by subtracting 3 from both sides of the inequality, which gives us -4x≤8. Next, we divide both sides of the inequality by -4, remembering to reverse the inequality sign since we are dividing by a negative number. This gives us x≥-2. Therefore, the solution to the inequality is x=-2.

84) L.C.M of 15x², 45xy and 30xyz is ____________

90xyz

90x2yz

15xyz

15x2yz

The L.C.M (Least Common Multiple) of three numbers is the smallest number that is divisible by each of the given numbers. To find the L.C.M of 15x^2, 45xy, and 30xyz, we need to find the highest power of each variable (x, y, and z) that appears in any of the given numbers. In this case, the highest power of x is 2, the highest power of y is 1, and the highest power of z is 1. Therefore, the L.C.M is 90x^2yz.

Explanation

The L.C.M (Least Common Multiple) of three numbers is the smallest number that is divisible by each of the given numbers. To find the L.C.M of 15x^2, 45xy, and 30xyz, we need to find the highest power of each variable (x, y, and z) that appears in any of the given numbers. In this case, the highest power of x is 2, the highest power of y is 1, and the highest power of z is 1. Therefore, the L.C.M is 90x^2yz.

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

Mt=Mt

Mt=1/M

Mt=-M

Mt = M

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.

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.

86) x is equal to, If

Option

not-available-via-ai

Explanation

not-available-via-ai

87) 1/a-b - 1/a+b

2a/a2-b2

2b/a2-b2

-2a/a2-b2

-2b/a2-b2

The given expression can be simplified by finding the common denominator, which is (a^2 - b^2). By multiplying the first term (1/a - b) by (a + b)/(a + b), we get (a + b)/(a^2 - b^2). Simplifying further, we have (2b)/(a^2 - b^2), which matches the given answer 2b/a^2 - b^2.

Explanation

The given expression can be simplified by finding the common denominator, which is (a^2 - b^2). By multiplying the first term (1/a - b) by (a + b)/(a + b), we get (a + b)/(a^2 - b^2). Simplifying further, we have (2b)/(a^2 - b^2), which matches the given answer 2b/a^2 - b^2.

88) Point (2,-3) lies in quadrant:

I

II

III

IV

The point (2,-3) lies in quadrant IV because the x-coordinate is positive (2) and the y-coordinate is negative (-3). In quadrant IV, the x-coordinate is positive and the y-coordinate is negative, which matches the given point.

Explanation

The point (2,-3) lies in quadrant IV because the x-coordinate is positive (2) and the y-coordinate is negative (-3). In quadrant IV, the x-coordinate is positive and the y-coordinate is negative, which matches the given point.

89) A triangular region means the ___________ of triangle and its interior.

Compliment

Intersection

Union

Outlines

A triangular region refers to the combination or joining together of both the triangle and its interior. It implies that the region includes both the boundary or outline of the triangle as well as the space within it. Therefore, the correct answer is "union."

Explanation

A triangular region refers to the combination or joining together of both the triangle and its interior. It implies that the region includes both the boundary or outline of the triangle as well as the space within it. Therefore, the correct answer is "union."

90) If (x-1, y+1)=(0,0), then (x,y) is :

(1,-1)

(-1,1)

(1,1)

(-1,-1)

If (x-1, y+1) = (0,0), it means that x-1 = 0 and y+1 = 0. Solving these equations, we find that x = 1 and y = -1. Therefore, the value of (x,y) is (1,-1).

Explanation

If (x-1, y+1) = (0,0), it means that x-1 = 0 and y+1 = 0. Solving these equations, we find that x = 1 and y = -1. Therefore, the value of (x,y) is (1,-1).

91) Medians of a triangle are___________

Same

Different

Concurrent

Equal

The medians of a triangle are concurrent, meaning they all intersect at a single point called the centroid. The centroid is the point of balance of the triangle, where the medians divide each other into segments with a ratio of 2:1. This property holds true for all triangles, making the statement that the medians are concurrent correct.

Explanation

The medians of a triangle are concurrent, meaning they all intersect at a single point called the centroid. The centroid is the point of balance of the triangle, where the medians divide each other into segments with a ratio of 2:1. This property holds true for all triangles, making the statement that the medians are concurrent correct.

92) The square root of x²-1+1/4x² is __________

±(x-1/2x)

±(x+1/2x)

(x-1/2x)

√(x-1/2x)

The given expression is the square root of x^2 - 1 + 1/4x^2. By factoring out a common factor of 1/4 from the two terms inside the square root, we get (1/4)(4x^2 - 1 + x^2). Simplifying further, we have (1/4)(5x^2 - 1). Taking the square root of this expression gives us ±√(1/4)(5x^2 - 1), which simplifies to ±√(5x^2 - 1)/2. Rearranging the terms, we get ±(x - 1/2x), which matches the given answer.

Explanation

The given expression is the square root of x^2 - 1 + 1/4x^2. By factoring out a common factor of 1/4 from the two terms inside the square root, we get (1/4)(4x^2 - 1 + x^2). Simplifying further, we have (1/4)(5x^2 - 1). Taking the square root of this expression gives us ±√(1/4)(5x^2 - 1), which simplifies to ±√(5x^2 - 1)/2. Rearranging the terms, we get ±(x - 1/2x), which matches the given answer.

93) In a parallelogram opposite sides are:

Congruent

Parallel

Both congruent and parallel

None of these

In a parallelogram, opposite sides are both congruent and parallel. This means that the lengths of the opposite sides are equal, and the opposite sides never intersect. This property is what defines a parallelogram and distinguishes it from other quadrilaterals.

Explanation

In a parallelogram, opposite sides are both congruent and parallel. This means that the lengths of the opposite sides are equal, and the opposite sides never intersect. This property is what defines a parallelogram and distinguishes it from other quadrilaterals.

94) Factors of 5x²-17xy-12y² are ______________

(x+4y),(5x+3y)

(x-4y),(5x-3y)

(x-4y),(5x+3y)

(5x-4y),(x+3y)

The given expression is a quadratic expression in two variables, x and y. To find the factors, we can use the factoring method. The expression can be factored as (x-4y)(5x+3y). This means that when we multiply these two factors, we will get the original expression. Therefore, the correct answer is (x-4y),(5x+3y).

Explanation

The given expression is a quadratic expression in two variables, x and y. To find the factors, we can use the factoring method. The expression can be factored as (x-4y)(5x+3y). This means that when we multiply these two factors, we will get the original expression. Therefore, the correct answer is (x-4y),(5x+3y).

95) Imaginary part of -i(3i+2) is ___________

-2

2

3

-3

To find the imaginary part of -i(3i+2), we need to simplify the expression. Distributing -i to both terms inside the parentheses, we get -i(3i) - i(2). Simplifying further, -i(3i) becomes 3i^2, and since i^2 is equal to -1, 3i^2 becomes -3. -i(2) simplifies to -2i. Combining the two terms, we have -3 - 2i. The imaginary part of this expression is the coefficient of i, which is -2. Therefore, the correct answer is -2.

Explanation

To find the imaginary part of -i(3i+2), we need to simplify the expression. Distributing -i to both terms inside the parentheses, we get -i(3i) - i(2). Simplifying further, -i(3i) becomes 3i^2, and since i^2 is equal to -1, 3i^2 becomes -3. -i(2) simplifies to -2i. Combining the two terms, we have -3 - 2i. The imaginary part of this expression is the coefficient of i, which is -2. Therefore, the correct answer is -2.

96) L.C.M of a²+b² and a⁴-b⁴ is :

A2+b2

A2-b2

A4-b4

A-b

The L.C.M (Least Common Multiple) of a2+b2 and a4-b4 can be found by factoring both expressions. When we factor a2+b2, it cannot be further simplified. However, when we factor a4-b4, we can use the difference of squares formula to simplify it as (a2+b2)(a2-b2). Therefore, the L.C.M of a2+b2 and a4-b4 is a4-b4.

Explanation

The L.C.M (Least Common Multiple) of a2+b2 and a4-b4 can be found by factoring both expressions. When we factor a2+b2, it cannot be further simplified. However, when we factor a4-b4, we can use the difference of squares formula to simplify it as (a2+b2)(a2-b2). Therefore, the L.C.M of a2+b2 and a4-b4 is a4-b4.

97) The logarithm of unity to any base is:

1

10

E

0

The logarithm of unity to any base is 0 because any number raised to the power of 0 is always equal to 1. This means that the logarithm of 1 to any base will always be 0.

Explanation

The logarithm of unity to any base is 0 because any number raised to the power of 0 is always equal to 1. This means that the logarithm of 1 to any base will always be 0.

98) Altitudes of a triangle means perpendicular from _____ to the opposite side.

Vertex

Side

Mid point

None of these

Altitudes of a triangle means perpendicular from each vertex to the opposite side. This means that for each vertex of the triangle, there is a line segment drawn perpendicular to the side opposite to that vertex. These perpendicular lines are called altitudes and they intersect the opposite sides at right angles. Therefore, the correct answer is "vertex".

Explanation

Altitudes of a triangle means perpendicular from each vertex to the opposite side. This means that for each vertex of the triangle, there is a line segment drawn perpendicular to the side opposite to that vertex. These perpendicular lines are called altitudes and they intersect the opposite sides at right angles. Therefore, the correct answer is "vertex".

99) Antilogarithm table was prepared by

John Napier

Henry Briggs

Jobst Burgi

Arthur Cayley

Jobst Burgi is the correct answer because he was a Swiss mathematician who worked closely with John Napier and Henry Briggs in the development of logarithms. While Napier is credited with the invention of logarithms, Burgi played a significant role in their practical application and calculation. He collaborated with Napier and Briggs to create logarithm tables, which were used for various mathematical calculations. Therefore, Burgi's contribution to the preparation of antilogarithm tables makes him the correct answer for this question.

Explanation

Jobst Burgi is the correct answer because he was a Swiss mathematician who worked closely with John Napier and Henry Briggs in the development of logarithms. While Napier is credited with the invention of logarithms, Burgi played a significant role in their practical application and calculation. He collaborated with Napier and Briggs to create logarithm tables, which were used for various mathematical calculations. Therefore, Burgi's contribution to the preparation of antilogarithm tables makes him the correct answer for this question.

100) Which of the solution set of the inequality 9-7x>19-2x?

19

-7

2

-2

The correct answer is -7 because when we simplify the inequality, we get -7x > 10. To isolate x, we divide both sides by -7, which reverses the inequality sign, giving us x < -10/7. Therefore, the solution set is x < -10/7, and the only option that represents a number less than -10/7 is -7.

Explanation

The correct answer is -7 because when we simplify the inequality, we get -7x > 10. To isolate x, we divide both sides by -7, which reverses the inequality sign, giving us x < -10/7. Therefore, the solution set is x < -10/7, and the only option that represents a number less than -10/7 is -7.

Math Quiz For Class 9th

1) Bisection means to divide into ____________ equal parts:

2)

What first name or nickname would you like us to use?

2) 4x+3y-2 is an algebraic

3) Unit of ratio is

4) A triangle having all sides equal is called:

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

6) Equality of two ratios is defined as:

7) The sign of ratio is:

8) The diagonal of a parallelogram ______________ each other:

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

10) In a triangle, there can be only one _______________

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

12) A line segment has __________ mid point:

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

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

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

16) Order of square matrix is:

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

18) Two lines intersect each other at __________ points.

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

20) Log e = __________, where e ≈ 2.718

21) Write 42/3 with radical sign:

22) The idea of Matrices was given by

23) The factors of x2-5x+6 are

24) Product of

25) How many end points has a ray?

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

27) The logaritm of any number to itself as base is ___________

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

29) The point (-2,-3) lies in quadrant ______________

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

31) If x is no larger than 10, then __________

32) Ifx,y,z ∈ R, z<0 then, x<y⇒ _____________:

33) log (mn) can be written as ________________

34) If y=2x+1, x=2 then y is:

35) a2-b2 /a+b

36) Symbol used for congruent is:

37) In a ____________ opposite sides are congruent:

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

39) The relation y=logzx implies

40) In a triangle, there can be ______________ right angle.

41) (3+√ 2)(3-√ 2) is equal to

42) The value of i9 is ____________

43) It is called ____________ matrix:

44) Congruent triangles are__________

45) The square root of a2-2a+1 is

46) How many lines can be drawn through two points?

47) The point (-4,3) lies in the quadrant __________

48) x is equal to _______________ if :

49) (27x-1)-2/3

50) Which ordered pair satisfies the equation y=2x?

51) log p - log q is same as _____________

52) If ax=n, then:

53) The degree of polynomial 4x4+2x2y is ____________

54) In a parallelogram congruent parts are ______________

55) If the bisector of an angle of a triangle bisects the side opposite to it, the triangle is __________:

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

57) In 3√35 the radicand is

58) Order of transpose is _____________:

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

60) The median of a triangle cut each other in the ratio _______________

61) H.C.F of 5x2y2 and 20x3y3 is _____________

62) What will be added to complete the square of 9a2-12ab?

63) Factors of 3x2-x-2 are ____________

64) (√a+√b)(√a-√b) is equal to

65) ___________ points are said to be collinear if they lie on same line:

66) x= ___________ is a solution of the inequality -2<x<3/2

67) Real part of 2ab(i+i2) is ______________

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

69) For ______ value of x, will be singular matrix.

70) Perpendicular distance to base from its opposite vertex is called _________

71) H.C.F of x-2 and x2+x-6 is ________________

72) Arthur Cayley introduced the "Theory of Matrices" in ____________

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

74) If the capacity c of an elevator is at most 1600 pounds, then:

75) The point of concurrency of the three altitudes of a triangle is called:

76) Factors of a4-4b4 are ____________

77) The order of matrix [ 2 1] is __________

21) Write 4^2/3with radical sign:

23) The factors of x²-5x+6 are

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

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

33) log (mⁿ) can be written as ________________

35) a²-b² /a+b

39) The relation y=log_zx implies

42) The value of i⁹ is ____________

45) The square root of a²-2a+1 is

49) (27x^-1)^-2/3

52) If a^x=n, then:

53) The degree of polynomial 4x⁴+2x²y is ____________

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

57) In ³√35 the radicand is

61) H.C.F of 5x²y² and 20x³y³ is _____________

62) What will be added to complete the square of 9a²-12ab?

63) Factors of 3x²-x-2 are ____________

67) Real part of 2ab(i+i²) is ______________

71) H.C.F of x-2 and x²+x-6 is ________________

76) Factors of a⁴-4b⁴ are ____________

78) One angle of parallelogram is 130^o, the remaining angles are of measures _____________

80) **The solution set of | x-4 |=-4 is:**

81) If (x-2) is a factor of P(x) = x²+2kx+8, then the value of k is _____________

84) L.C.M of 15x², 45xy and 30xyz is ____________

92) The square root of x²-1+1/4x² is __________

94) Factors of 5x²-17xy-12y² are ______________

96) L.C.M of a²+b² and a⁴-b⁴ is :