9th Maths Objective type questions

Objective type questions

Chapter 1

Q1. Match the Columns

1. `sqrt(ab)`_______________ a) `sqrta/sqrtb`
2. `sqrt(a/b)`_______________ b) `sqrtasqrtb`
3. `(sqrta+sqrtb)(sqrta-sqrtb)`__c) `a^2-b`
4. `(a+sqrtb)(a-sqrtb)`________d) `a+2sqrt(ab)+b`

5. `(sqrta+sqrtb)^2`__________e) `a-b`

Answer: 

1.(b), 2.(a), 3.(e), 4.(c), 5.(d)

Q2. Match the Columns

1. `a^p.a^q`________________a) `a^(pq)`
2. `(a^p)^q`________________b) `a^(p+q)`
3. `a^p/a^q`________________c) `(ab)^p`
4. `a^pb^p`________________d)  `a^(p-q)`

Answer:

1.(b), 2.(a), 3.(d), 4.(c)

Q3. State whether the following statements are true or false. Give reasons for your answer :

i) Every natural number is a whole number.

ii) Every integer is a whole number.

iii) Every rational number is a whole number.

iv) Every whole number is a natural number.

v) Every integer is a rational number.

vi) Every rational number is an integer.

Answer :

i) True ii) False iii) False vi) False v) True vi) False 

Q4. State whether the following statements are true or false. 
(i) Every irrational number is a real number.
(ii) Every point on the number line is of the form √m, where m is a natural number.
(iii) Every real number is an irrational number.
Answer :
i) True ii) False  iii) False

Q5. Classify the following numbers as rational or irrational :

i) `2 - \sqrt5`

ii) (`3 - \sqrt23)  - \sqrt23` 

iii) `\frac{2\sqrt7}{7\sqrt7}`  

iv) `\frac{1}{\sqrt2}`

v) `2π`

Answer :

Rational numbers : (ii) and (iii)

Irrational numbers : (i), (iv) and (v)

Chapter 2

Q1. Which of the following expression are polynomials in one variable and which are not? 

i) `4x^2 - 3x + 7`   ii) `y^2 + sqrt2`

iii)  `3sqrtt + tsqrt2`   iv)  `y + frac{2}{y}`

v)  `x^(10) + y^3 + t^(50)`

Answer :

i) A polynomial in one 
ii) A polynomial in one 
iii) Not a polynomial 
iv) Not a polynomial 

v) A polynomial in three variables 

Q2. Write the coefficient of `x^2` in each of the following:

i) `2+x^2+x`   ii) `2 - x^2 + x^3`  

iii) `frac{π}{2}x^2 + x`  iv) `sqrt2x - 1`

Answer :

i) `1`  ii) `-1`  iii) `frac{π}{2}`  iv) `0`

Q3. Give one example of each of a binomial of degree `35` and of a monomial of degree `100`.

Answer :

Binomial of degree `35 = x^35 + 100`

Monomial of degree `100 = 10x^100`. 

Q4. Write the degree of each of the following polynomial:

i) `5x^3 + 4x^2 + 7x`  

ii) `4 - y^2`

iii) `5t - sqrt7`  

iv) `3`.

Answer :

i) `3`  ii) `2`  iii) `1`  iv) `0`

Q5. Classify the following as linear, quadratic and polynomial :

i) `x^2 + x`  

ii) `x - x^2`

iii) `y+y^2+4`  

iv) `1 + x`

v) `3t`  vi) `r^2`   

vii) `7x^3`.

Answer :

Linear:  iv),  v)
Quadratic: i),  iii),  vi)

Cubic: ii),  vii)

Chapter 3

Q1. Write the answer to each of the following questions :

i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

ii) What is the name of each part of the plane formed by these two lines?

iii) Write the name of each point where these two lines intersect.

Answer :

i) The x-axis and the y-axis.

ii) Quadrants.

iii) The Origin.

Chapter 4

Q1. Which one of the following options is true, and why?

`y=3x+5`has

i) a unique solution, ii) only two solutions, iii) infinitely many solutions.

Answer :

iii) because a linear equation in two variables has infinitely many solutions.

Chapter 6

Q1. Fill in the blanks:

1) If two lines intersect each other, then the vertically opposite angles are _____.

2) The sum of the three angles of a triangle is _____.

3) Lines which are parallel to a given line are ______ to each other.

Answer:

1) equal    2) `180^circ`    3) parallel

Chapter 7

1) Two circles of the same radii are ____.

2) In a triangle, the angle opposite to the longer side is ______.

3) Sum of any two sides of a triangle is greater than the _____ side.

4) Two figures are congruent if they are of the same shape and of the same_____.

Answer:

1) Congruent    2) larger (greater)    3) third.    4) size.

Chapter 9

Q1. Fill in the blanks:

1) A median of a triangle divides it into two triangles of equal ____.

2) Area of a triangle is half the product of its base and the corresponding ____.

3) Area of a parallelogram is the product of its base and the corresponding ____.

Answer:

1) Area    2) Altitude    3) Altitude

Chapter 10

Q1. Fill in the blanks:

i) The centre of a circle lies in ____ of the circle. [exterior/ interior]

ii) A point, whose distance from the centre of a circle is greater than its radius lies in ____ of the circle. [exterior/interior]

iii) The longest chord of a circle is a ____ of the circle.

iv) An arc is a ____ when its ends are the ends of a diameter.

v) Segment of a circle is the region between an arc and ____ of the circle.

vi) A circle divides the plane, on which it lies, in _____ parts.

Answer: 

i) Interior,

ii) Exterior,

iii) Diameter,

iv) Semicircle,

v) The chord, 

vi) Three.

Q2. Write True or Fales: Give reasons for your answers.

i) Line segment joining the centre to any point on the circle is a radius of the circle.

ii) A circle has only finite number of equal chords.

iii) If a circle is divided into three equal arcs, each is a major arc.

iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.

v) Sector is the region between the chord and its corresponding arc.

vi) A circle is a plane figure.

Answer:

i) True,

ii) False,

iii) False,

iv) True,

v) False,

vi) True.

Chapter 12

Q1. Fill in the blanks:

1) Heron's formula is __________.

2) Semiperimeter `S =`__________.

3) Area of equilateral triangle `=`_______.

4) Area of  of rhombus `=`_________.

5) Area of parallelogram `=`_______.

Answer:

1) `sqrt(s(s-a)(s-b)(s-c))`    

2) `(a+b+c)/2`    

3) `sqrt3/4a^2`    

4) `1/2(d_1 times d_2)`    

5) base`times`height.