Math Quiz For Class 9th

  • CCSS.Math.Content.HSA-REI.C.9
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| Attempts: 404 | Questions: 100 | Updated: Mar 20, 2025
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1) 4x+3y-2 is an algebraic

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

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About This Quiz
Math Quiz For Class 9th - 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.

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2) A triangle having all sides equal is called:

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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3) Bisection means to divide into ____________ equal parts:

Explanation

Bisection means to divide into two equal parts.

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

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

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

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

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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8) A line segment has __________ mid point:

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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9) 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 ":".

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10) Unit of ratio is

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

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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12) Equality of two ratios is defined as:

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

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

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

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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16) The diagonal of a parallelogram ______________ each other:

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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17) Write 42/3 with radical sign:

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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18) Two lines intersect each other at __________ points.

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

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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20) Order of square matrix is:

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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21) Product of    

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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22) How many end points has a ray?

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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23) The idea of Matrices was given by

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

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

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

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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27) Log e = __________, where e ≈ 2.718

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

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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29) (3+√ 2)(3-√ 2) is equal to

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

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

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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32) log (mn) can be written as ________________

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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33) In a ____________ opposite sides are congruent:

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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34) It is called ____________ matrix:

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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35) (√a+√b)(√a-√b) is equal to

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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36) If ax=n, then:

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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37) a2-b2 /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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38) If a:b=c:d then a,b,c and d are said to be in:

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

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.

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

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

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.

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

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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43) Congruent triangles are__________

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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44) The value of i9 is ____________

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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45) The relation y=logzx implies

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.

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

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.

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47) (27x-1)-2/3

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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48) log p - log q is same as _____________

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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49) In 3√35 the radicand is

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

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.

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

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).

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52) Symbol used for congruent is:

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

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.

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54) Order of transpose   is _____________:

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.

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

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.

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56) In two triangles for (1-1) correspondence symbol used 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 "↔".

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57) In a parallelogram congruent parts are ______________

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".

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

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.

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

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.

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

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.

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

Explanation

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

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.

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63) x is equal to _______________ if :

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.

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

Explanation

If x, y, and z are real numbers and z is less than 0, then x yz. This can be explained by considering that when z is negative, multiplying both sides of the inequality x

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

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.

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66) The square root of a2-2a+1 is 

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).

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

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.

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

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.

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

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

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.

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

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.

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

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.

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

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

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.

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

Explanation

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

Explanation

The correct answer is 0 because it falls within the given range of -2

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77) Factors of a4-4b4 are ____________

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).

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78)  x is equal to, If 

Explanation

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

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.

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

Explanation

The inequality x-2

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

Explanation

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

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.

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

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.

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

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.

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

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.

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

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."

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

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.

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88) Medians of a triangle are___________

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.

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89) In a parallelogram opposite sides are:

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.

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

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).

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91) Adjoint of

Explanation

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

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).

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93) L.C.M of a2+b2 and a4-b4 is :

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.

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

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.

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

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.

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96) The logarithm of unity to any base is:

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.

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97) 1/a-b - 1/a+b

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.

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98) Antilogarithm table was prepared by

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.

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

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".

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

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

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4x+3y-2 is an algebraic
A triangle having all sides equal is called:
Bisection means to divide into ____________ equal parts:
If three points lie on the same line, then these points are called:
Bisection of an angle mean to draw a ray to divide the given angle...
If (x,0)=(0,y), then (x,y) is :
Mid point of the points (2,2) and (0,0) is:
A line segment has __________ mid point:
The sign of ratio is:
Unit of ratio is
When the number of rows is not equal to the number of columns, the...
Equality of two ratios is defined as:
In a triangle, there can be only one _______________
If x is no larger than 10, then __________
Each Hypotenuse of a parallelogram divides it into __________...
The diagonal of a parallelogram ______________ each other:
Write 42/3 with radical sign:
Two lines intersect each other at __________ points.
Point (-3,-3) lies in quadrant:
Order of square matrix is:
Product of    
How many end points has a ray?
The idea of Matrices was given by
Find m so that x2+4x+m is a complete square _____________
Similar triangles are of the same shape but ____________ in sizes.
The logaritm of any number to itself as base is ___________
Log e = __________, where e ≈ 2.718
The factors of x2-5x+6 are
(3+√ 2)(3-√ 2) is equal to
Distance between points (0,0) and (1,1) is: 
H.C.F of a3+b3 and a2-ab+b2 is _____________
Log (mn) can be written as ________________
In a ____________ opposite sides are congruent:
It is called ____________ matrix:
(√a+√b)(√a-√b) is equal to
If ax=n, then:
A2-b2 /a+b
If a:b=c:d then a,b,c and d are said to be in:
The point (-4,3) lies in the quadrant __________
How many lines can be drawn through two points?
Factors of 3x2-x-2 are ____________
Which ordered pair satisfies the equation y=2x?
Congruent triangles are__________
The value of i9 is ____________
The relation y=logzx implies
If y=2x+1, x=2 then y is:
(27x-1)-2/3
Log p - log q is same as _____________
In 3√35 the radicand is
The degree of polynomial 4x4+2x2y is ____________
Mid point of the points (2,-2) and (-2,2) is:
Symbol used for congruent is:
If the bisector of an angle of a triangle bisects the side opposite to...
Order of transpose   is _____________:
The point (-2,-3) lies in quadrant ______________
In two triangles for (1-1) correspondence symbol used is____________
In a parallelogram congruent parts are ______________
Real part of 2ab(i+i2) is ______________
H.C.F of 5x2y2 and 20x3y3 is _____________
Perpendicular distance to base from its opposite vertex is called...
Arthur Cayley introduced the "Theory of Matrices" in...
H.C.F of x-2 and x2+x-6 is ________________
X is equal to _______________ if :
Ifx,y,z ∈ R, z<0 then, x<y⇒ _____________:
The median of a triangle cut each other in the ratio _______________
The square root of a2-2a+1 is 
The order of matrix [ 2   1] is __________
The point of concurrency of the three altitudes of a triangle is...
A square matrix M is called to be skew symmetric, if:
___________ points are said to be collinear if they lie on same line:
Distance between the points (1,0) and (0,1) is:
In a triangle, there can be ______________ right angle.
If x=3 and y=-1 then the value of x3y is
One angle of parallelogram is 130o, the remaining angles are of...
For ______ value of x,    will be singular matrix.
X=  ___________ is a solution of the inequality...
Factors of a4-4b4 are ____________
 x is equal to, If 
Which of the following is the solution of the inequality 3-4x≤11?
X=0 is a solution of the inequality:
The solution set of | x-4 |=-4 is:
If the capacity c of an elevator is at most 1600 pounds, then:
L.C.M of 15x2, 45xy and 30xyz is ____________
What will be added to complete the square of 9a2-12ab?
Imaginary part of -i(3i+2) is ___________
A triangular region means the ___________ of triangle and its...
If (x-2) is a factor of P(x) = x2+2kx+8, then the value of k is...
Medians of a triangle are___________
In a parallelogram opposite sides are:
Factors of 5x2-17xy-12y2 are ______________
Adjoint of
If (x-1, y+1)=(0,0), then (x,y) is :
L.C.M of a2+b2 and a4-b4 is :
Point (2,-3) lies in quadrant:
The square root of x2-1+1/4x2 is __________
The logarithm of unity to any base is:
1/a-b - 1/a+b
Antilogarithm table was prepared by
Altitudes of a triangle means perpendicular from _____ to the opposite...
Which of the solution set of the inequality 9-7x>19-2x?
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