Matric Notes Math 9th

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

1. ³√x² / 9
2. √x³ / 9
3. ³√x² / 8
4. √x² / 8

Write ⁷√x in exponential form:

1. x
2. x⁷
3. x^1/7
4. x^7/2

Write 4^2/3 with radical sign:

1. ³√4²
2. √4³
3. ²√4³
4. √4⁶

In ³√35 the radicand is:

(25/16)^-1/2

The conjugate of 5 + 4i is:

The value of i⁹ is:

Every real number is:

Real part of 2abi(i + i²) is:

Imaginary part of -i(3i + 2) is:

Which of the following sets have the closure property w.r.t addition:

Name the property of real numbers used in (-√5/2) x 1 = -√5/2:

If x, y, z ∈ R, z < 0, then x < y -->

If a, b ∈ R, then only one of a = b , or a < b or a > b holds is called:

A non-terminating, non-recurring decimal represents:

Division is not an associative operation.

Every whole number is a natural number.

Multiplicative inverse of 0.02 is 50.

π  is a rational number.

Every integer is a rational number.

Subtraction is a commutative operation.

Every real number is a rational number.

Decimal representation of a rational number is either terminating or recurring.

1.$\bar{8}$ = 1 +8/9

If a^x = n, then:

1. a = log_xn
2. x = log_na
3. x = log_an
4. a = log_nx

The relation y = log_zx implies.

1. x^y = z
2. z^y = x
3. x^z = y
4. y^z = x

The logarithm of unity to any base is:

The logarithm of any number to itself as base is:

log e = __ , where e ≈ 2.718

The value of log (p/q) is:

log p - log q is same as:

log (m)ⁿ can be written as:

1. (log m)ⁿ
2. m log n
3. n log m
4. log (mn)

log_b a x log_c b can be written as:

1. log_a c
2. log_c a
3. log_a b
4. log_b c

log_y x will be equal to:

1. log_z x / log_y z
2. log_x z / log_y z
3. log_z x / log_z y
4. log_z y / log_z x

4x + 3y - 2 is an algebraic:

The degree of polynomial 4x⁴ + 2x²y is:

a³ + b³ is equal to:

1. (a - b)(a² + ab + b²)
2. (a + b)(a² - ab + b²)
3. (a - b)(a² - ab + b²)
4. (a - b)(a² + ab - b²)

(3 + √2)(3 - √2) is equal to:

Conjugate of such a + √b is:

1/(a-b) - 1/(a+b) is equal to:

1. 2a/(a²-b²)
2. 2b/(a²-b²)
3. -2a/(a²-b²)
4. -2b/(a²-b²)

(a²-b²)/(a+b) equal to:

1. (a-b)²
2. (a+b)²
3. a + b
4. a - b

(√a + √b)(√a - √b) is equal to:

1. a² + b²
2. a² - b²
3. a - b
4. a + b

The factors of x² - 5x + 6 are:

Factors of 8x³ + 27y³ are:

1. (2x + 3y), (4x² + 9y²)
2. (2x - 3y), (4x² - 9y²)
3. (2x + 3y), (4x² - 6xy + 9y²)
4. (2x - 3y), (4x² + 6xy + 9y²)

Factors of 3x² - x- 2 are:

Factors of a⁴ - 4b⁴ are:

1. (a - b), (a + b), (a² + 4b²)
2. (a² - 2b²), (a² + 2b²)
3. (a - b), (a + b), (a² - 4b²)
4. (a - 2b), (a² + 2b²)

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

1. -16b²
2. 16b²
3. 4b²
4. -4b²

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

Factors of 5x² - 17xy - 12y² are:

Factors of 27x³ - 1/x³ are:

1. (3x - 1/x)(9x² + 3 + 1/x²)
2. (3x + 1/x)(9x² + 3 + 1/x²)
3. (3x - 1/x)(9x² - 3 + 1/x²)
4. (3x + 1/x)(9x² - 3 + 1/x²)

H.C.F. of p³q-pq³ and p5q² - p²q⁵ is:

1. pq(p²-q²)
2. pq(p-q)
3. p²q²(p-q)
4. pq(p³-q³)

H.C.F. of 5x²y² and 20x³y³ is:

1. 5x²y²
2. 20x³y³
3. 100x⁵y⁵
4. 5xy

H.C.F. of x-2 and x² + x - 6 is:

1. x² + x -6
2. x + 3
3.  x - 2
4. x + 2

H.C.F. a³ + b³ and a² - ab + b² is:

1. a + b
2. a² - ab + b²
3. (a-b)²
4. a² + b²

H.C.F. of x² - 5x + 6 and x² - x -6 is:

1. x - 3
2. x + 2
3. x² - 4
4. x - 2

H.C.F. of a² - b² and a³ - b³ is:

1. a - b
2.  a + b
3. a² + ab + b²
4. a² - ab + b²

H.C.F. of x² + 3x + 2, x² +4x + 3 and x² + 5x +4 is:

L.C.M. of 15x², 45xy and 30xyz is:

1. 90xyz
2. 90x²yz
3. 15xyz
4. 15x²yz

L.C.M. of a² + b² and a⁴ - b⁴ is:

1. a² + b²
2. a² - b²
3. a⁴ - b⁴
4. a - b

The product of two algebraic expressions is equal to the __ of their H.C.F. and L.C.M.

Simplify (a / (9a² - b²)) + (1 / (3a - b)) =:

1. 4a / ( 9a² -b²)
2. (4a - b) / ( 9a² -b²)
3. (4a + b) / ( 9a² -b²)
4. b / ( 9a² -b²)

Simplify (a²+5a-14)/(a²-3a-18) x (a+3)/(a-2) =:

Simplify (a³-b³)/(a⁴-b⁴) ÷ (a²+ab+b²)/(a²+b²) =:

1. 1/(a+b)
2. 1/(a-b)
3. (a-b)/(a²-b²)
4. (a+b)/(a²+b²)

Simplify ((2x+y)/(x+y) - 1) ÷ (1 - x/(x+y)) =:

The square root of a² - 2a + 1 is:

What should be added to complete the square of x⁴ + 64?

1. 8x²
2. -8x²
3. 16x²
4. 4x²

The square root of x⁴ + 1/x⁴ + 2 is:

1. ±(x + 1/x)
2. ±(x² + 1/x²)
3. ±(x- 1/x)
4. ±(x² - 1/x²)

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

A statement involving any of the symbols <, >, ≤, ≥ is called __.

x = __ is a solution of the inequality -2 < x < 3/2.

If x is no larger than 10, then ...

If the capacity c of an elevator is at most 1600 pounds, then __.

x = 0 is solution of the in equality.

The equation 3x - 5 = 7 - x is a linear equation.

The equation x - 0.3x = 0.7x is an identity.

The equation -2x + 3 = 8 is equivalent to -2x = 11.

To eliminate fractions, we multiply each side of a equation by the L.C.M. of denominators.

4(x + 3) = x + 3 is a conditional equation.

The equation 2(3x + 5) = 6x + 12 is an inconsistent equation.

To solve 2x / 3 = 12, we should multiply each side by 2 / 3.

Equations having exactly the same solution are called equivalent equations.

A solution that does not satisfy the original equation is called extraneous solution.

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

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

Point (2,-3) lies in quadrant.

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

If y=2x+1, x=2 then y is.

Which ordered pair satisfies the equation y=2x?

The point O (0,0) is in quadrant II.

The point P (2,0) lies on x-axis.

The graph of x=-2 is a vertical line.

3-y=0 is a horizontal line.

The point Q (-1,2) is in quadrant III.

The point R (-1,-2) is in quadrant IV.

y = x is a line on which origin lies.

The point P (1,1) lies on the line x + y =0.

The point S (1,-3) lies in quadrant III.

The point R (0,1) lies on the x-axis.

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

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

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

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

A triangle having all sides equal is called:

A triangle having all sides different is called:

A __ has two end points.

A line segment has __ midpoint.

A line has two end points.

A line segment has one end point.

A triangle is formed by three collinear points.

Each side of a triangle has two collinear vertices.

The end points of each side of a rectangular are collinear.

All the points that lie on the x-axis are collinear.

Origin is the only point collinear with the points of both the axes separately.

A ray has two end points.

In a triangle, there can be only one right angle.

Three points are said to be collinear, if they lie on same line.

Two parallel lines intersect at a point.

Two lines can intersect only at one point.

A triangle of congruent sides has non-congruent angles.

In a triangle there can only be one:

In a parallelogram opposite sides are

In a parallelogram opposite angle are

Diagonals of a parallelogram _____ each other at a point.

Medians of a triangle are

Diagonal of parallelogram divides the parallelogram into two _____ triangles.

Diagonals of a parallelogram divides parallelogram into __ triangles.

In parallelogram congruent parts are:

Bisection means to divide into two equal parts.

Right bisection of line segment means to draw perpendicular which passes through the mid-point of line segment.

Any point on the right bisector of a line segment is not equidistant from its end points.

Any point equidistant from the end points of a line segment is on the right bisector of it.

The right bisectors of the sides of a triangle are not concurrent.

The bisectors of the angles of a triangle are concurrent.

Any point on the bisector of an angle is not equidistant from its arms.

Any point inside an angle, equidistant from its arms, is on the bisector of it.

Bisection means to divide into __ equal parts.

The bisectors of the angles of a  triangle are:

The right bisectors of the sides of an acute triangle intersects each other __ the triangle.

The right bisectors of the sides of a right triangle intersect each other on the:

The right bisectors of the sides of an obtuse triangle intersects each other __ the triangle.

Congruent triangle are of same size and shape.

Similar triangles are of same shape but different sizes.

Symbol used for congruent is '≅'.

Symbol used for similarity is '∼'.

Congruent triangles are similar.

Similar triangles are congruent.

A line segment has only one mid-point.

One and only one line can be drawn through two points.

Proportion is non-equality of two rations.

Ratio has no unit.

The ratio between two alike quantities has no:

Proportion is a equality of __ ratios.

Similar triangles are of the same shape but __ in size.

⊥ is the symbol of:

In a right angled triangle greater angle is of 90^o.

In a right angled triangle right angle is of 60^o.

In a right angled triangle hypotenuse is a side opposite to right angle.

If a, b, c are sides of right angled triangle with c as longer side, then c² = a² + b².

If 3 cm and 4 cm are two sides of a right angled triangle, then hypotenuse is 5 cm.

If hypotenuse of an isosceles right triangle is √2 cm. then each of other side is of length 2cm.

Area of figure means region enclosed by boundary lines of closed figure.

Similar figures have same area.

Congruent figures have same area.

A diagonal of a parallelogram divides it into two non-congruent triangles.

Altitude of a triangle means perpendicular from vertex to the opposite side(base).

Area of parallelogram is equal to the product of base and height.

A triangle having two sides congruent is called.

A quadrilateral having each angle equal to 90^o is called.

The right bisectors of the three sides of a triangle are.

The __ altitudes of an isosceles triangle are congruent.

A point equidistant from the end points of a line-segment is on its.

__ congruent triangles can be made by joining the mid-points of the sides of a triangle.

The diagonals of a parallelogram __ each other.

The medians of a triangle cut each other in the ratio.

One angle on the base of an isosceles triangle is 30⁰. What is the measure of its vertical angle.

If the three altitudes of a triangle are congruent, then the triangle is.

If two medians of triangle are congruent then the triangle will be.

Sum of interior angles of a triangle is: (Extra)