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9th Mathematics Model Exam -2

MABS Institution

9th Mathematics Model Exam -2-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

The sum of \({ 5x }^{ 2 };-7x^{ 2 };8x^{ 2 };11x^{ 2 }\quad and\quad -9x^{ 2 }\) is _________________________

\(2{ x }^{ 2 }\)
\(4{ x }^{ 2 }\)
\(6{ x }^{ 2 }\)
\(8{ x }^{ 2 }\)

In the given figure CE || DB then the value of x⁰ is

45°
30°
75°
85°

If \(\frac { 1 }{ 7 } \)= 0.142857, then the value of is______________.

0.285741
0.428571
0.285714
0.574128

\(\sqrt{27}\)+\(\sqrt{12}\)=

\(\sqrt{39}\)
5\(\sqrt{6}\)
5\(\sqrt{3}\)
3\(\sqrt{5}\)

The perpendicular line from the centre of the circle to the chord divided the chord in the ratio________

1: 1
1: 2
2: 1
1: 3

The probability of all possible outcomes of a random experiment is always equal to

One
Zero
Infinity
All of the above

The set does not have a proper subset is __________

Finite set
Infinite set
Null set
Singleton set

If x⁵¹ + 51 is divided by x + 1, then the remainder is

0
1
49
50

Which of the following is a linear equation

\(x+\frac { 1 }{ x } =2\)
x(x −1) = 2
3x+5=\(\frac { 2 }{ 3 } \)
x³ - x =5

If one angle of a cyclic quadrilateral is 75° , then the opposite angle is

100°
105°
85°
90°

Part - B

Generic 2 - Answer All Question

Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and ·recurring.
\(7\over 16\)

Draw an equilateral triangle of side 6.5 cm and locate its incentre. Also draw the incircle

Draw a Venn diagram similar to one at the side and shade the region representing the following sets

A′

The radius of a circle 15 em and the length of one of its chord is 24 cm. Find the distance of the chord from the centre.

Represent the following sets in set builder form.
E = The set of odd Whole numbers less than 9.

List the set of letters of the following words in Roster form.
PARALLELOGRAM

Find the cardinal number of the following sets.
R = {x : x is an integers, x∈Z and –5 ≤ x <5}

In a week, temperature of a certain place is measured during winter are as follows 26⁰C,24⁰C,28⁰C,31⁰C,26⁰C.Find the mean temperatureof the week.

Express the following in the form \({p\over q},\) where p and q are integers and q \(\ne\) 0.
\(0.2\overline{45}\)

Find the value of \(\left( 8 \right) ^{ \frac { 5 }{ 3 } }\)

Part - C

Generic 3 - Answer All Question

Team I and Team II play 10 cricket matches each of 20 overs. Their total scores in each match are tabulated in the table as follows:

Match numbers 1 2 3 4 5 6 7 8 9 10

Team I 200 122 111 88 156 184 99 199 121 156

Team II 143 123 156 92 164 72 100 201 98 157

What is the relative frequency of Team I winning?

Add the following polynomials and find the degree of the resultant polynomial.
h(x)=7x³-6x+1 f(x)=7x²+17x-9

Find the GCD of 3x²- 48 and x² -7x +12

What must be subtracted from \({ y }^{ 4 }+{ 2y }^{ 3 }-3y+8\quad to\quad get\quad { y }^{ 4 }-{ 2y }^{ 3 }+6?\)

Express the following decimal expression into rational numbers. 0.86

Find the value of k, if (x-3) is a factor of polynomial x³- 9x²+ 26x + k

Let m || n and l is a transversal Such that ∠1 : ∠2 = 11 : 7. Determine all the eight angles.
Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:

Three different triangular plots are available for sale in a locality. Each plot has a perimeter of 120 m. The side lengths are also given:

Shape of plot Perimeter Length of sides

Right angled triangle 120m 30m, 40m, 50m

Acute angled triangle 120 m 35 m, 40 m, 45 m

Equilateral triangle 120 m 40 m, 40 m, 40 m

Help the buyer to decide which among these will be more spacious.

Is (2x -3) a factor of p(x)=2x³-9x²+x+12?

Express the following decimal expression into rational numbers. \(2.\overline { 327 } \)

Part - D

Generic 5 - Answer All Question(Question No 6 compualsary)

Construct the centroid of ΔPQR whose sides are PQ = 8cm; QR = 6cm; RP = 7cm

If A, Band C are overlapping sets, draw venn diagram for:\(A\cap B\)

In a school,80 students like Maths,90 students like Science 82 students like History, 21 like both Maths and Science 19 like both science and History 20 like both Maths and History and 8 liked all the three subjects. If each student like atleast one subject, then find (i) the number of students in the school (ii)the number of students who like only one subject.

Find the product (4x – 5), (2x² + 3x – 6).

Factorise 2x³- x² - 12x - 9 into linear factors

Express the following rational numbers into decimal and state the kind of decimal expansion
(i) \(\frac { 2 }{ 7 } \)
(ii) \(\frac { 35 }{ 100 } \)
(iii) \(-5\frac { 3 }{ 11 } \)
(iv) \(\frac { 22 }{ 3 } \)
(v) \(\frac { -9 }{ 32 } \)
(vi) \(\frac { 327 }{ 200 } \)

Construct the centroid of \(\triangle\)PQR such that PQ = 9 cm, PQ = 7cm, RP = 8 cm.

Solve graphically
2x + y = 4; 4x + 2y = 8

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