Question Set A

CBSE 9th Standard Mathematics Number Systems Important Questions And Answers Study Material - QB365

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Questions:

Multiple Choice Question

20 x 1 = 20

The sides of a triangle are 7 cm, 24 cm, and 25 cm.Its area is

(a)

168 cm²

(b)

84 cm²

(c)

87.5 cm²

(d)

300 cm²

In figure value of x is

(a)

\(30^{ 0 }\)

(b)

\(40^{ 0 }\)

(c)

\(30^{ 0 }\)

(d)

\(50^{ 0 }\)

An angle which is greater than \(90^{ 0 }\) and less than \(180^{ 0 }\) is called

(a)

a right angle

(b)

a straight angle

(c)

an acute angle

(d)

an obtuse angle

Euclid stated that all right angles are equal to each other in the form of

(a)

an axiom

(b)

a definition

(c)

a postulate

(d)

a proof

The point of the from \(\left({p\over2},p\right)\) always lies on the graph of the equation:

(a)

2x=y

(b)

x=2y

(c)

x=y+2

(d)

x+2=y

Find the value of k if (4, 1) is a solution of 3x+2y=k

(a)

(b)

(c)

(d)

The line y=x passes through

(a)

(0,0)

(b)

(0,1)

(c)

(1,0)

(d)

91,-1)

The salary of Dr.Harikisham is thrice the salary of Manish Goyal.Write a linear equation in two variables to represent the statement.

(a)

x=3

(b)

x+3y=0

(c)

x=3y+3

(d)

x=y+3

The equation \(x+\sqrt{2}=0\) has

(a)

no solution

(b)

infinitely many solutions

(c)

only one solution

(d)

only two solution

10.

The line of intersection of III and IV quadrants is

(a)

y - axis

(b)

x - axis

(c)

horizontal axis

(d)

None of these

11.

If x is negative and y is positive, then the point (x,y) lies in

(a)

II quadrant

(b)

III quadrant

(c)

IV quadrant

(d)

I quadrant

12.

If the polynomial p(x) is divided by (x+3), then the remainder will be:

(a)

p(-1)

(b)

p(2)

(c)

p(-3)

(d)

p(3)

13.

If \(p(x)=7-3x+2x^2\) then value of p(-2) is:

(a)

(b)

(c)

(d)

14.

The coefficient of \(x^2\)in \((3x+x^3)(x+\frac{1}{x })\)

(a)

(b)

(c)

(d)

15.

\((1+3x)^3\) is an example of:

(a)

Monomial

(b)

Binomial

(c)

Trinomial

(d)

None of these

16.

A linear polynomial

(a)

has one and only one zero

(b)

may have no zero

(c)

may have one zero

(d)

may have more than one zero

17.

Rationalization of the denominator of \(\frac { 1 }{ \sqrt { 5 } +\sqrt { 2 } } \) gives:

(a)

\(\frac { 1 }{ \sqrt { 10 } } \)

(b)

\(\sqrt { 5 } +\sqrt { 2 } \)

(c)

\(\sqrt { 5 } -\sqrt { 2 } \)

(d)

\(\frac { \left( \sqrt { 5 } -\sqrt { 2 } \right) }{ 3 } \)

18.

\(\pi \) is:

(a)

a rational number

(b)

an integer

(c)

an irrational number

(d)

a whole number

19.

Which of the following numbers is an irrational number?

(a)

\(\sqrt { 23 } \)

(b)

\(\sqrt { 225 } \)

(c)

0.3796

(d)

\(7.\overline { 478 } \)

20.

Which one of the following is an irrational number?

(a)

0.14

(b)

\(0.\overline { 1416 } \)

(c)

\(0.\overline { 1416 } \)

(d)

0.401 4001 40001 4...

Generic 5

10 x 5 = 50

21.

Sarika participated in a drawing competition. She is required to make a design on a rectangular sheet of dimensions 50 cm x 70 cm. In the design she made 8 triangles, each of sides 26 cm, 17 cm and 25 cm as shown in the figure.

(i) Find the total area of the design.
(ii) Find the remaining area of the sheet.
(iii) By drawing a design in a competition, which value is depicted by Sarika?

22.

In a ΔABC, if ∠A + ∠B = 150° and ∠E + ∠C = 100. Find the measure of each angle of the triangle.

23.

In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius.
F =\(\left(\frac{9}{5}\right)\)C + 32
(i) If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what is the
(ii)temperature in Celsius?
Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

24.

Check whether 7 + 3x is a factor of 3x³ + 7x.

25.

KGB schools provide free education to girls students from weaker sections. The local body of a town want to open a KGB school in the town for which a rectangular plot ABCD, as shown in the following figure, is very suitable. But this plot belongs to Rati Ram. Rati Ram agrees to exchange it with triangular plot PQR as shown in the same figure. The co-ordinates of the vertices of both the plots are shown in the figure:

(i) Compare the areas of both the plots.
(ii) Which mathematical concept is used in the above problem?
(iii) By opening KGB school in the town, which value is depicted by the local body?

26.

Show that: \(\frac { 1 }{ 1+{ x }^{ a-b } } +\frac { 1 }{ 1+{ x }^{ b-a } } =1\)

27.

If \({ z }^{ 2 }+\frac { 1 }{ { z }^{ 2 } } =47,\) find the value of \({ z }^{ 3 }+\frac { 1 }{ { z }^{ 3 } } ,\)using only the positive value of \(z+\frac { 1 }{ z } \) .

28.

Factorise 6x³ - 7x² - 8x + 5.

29.

Without actually calculating the cubes, find the calue of \({ \left( \frac { 1 }{ 2 } \right) }^{ 3 }+{ \left( \frac { 1 }{ 3 } \right) }^{ 3 }-{ \left( \frac { 5 }{ 6 } \right) }^{ 3 }\)

30.

If the point (3,4) lies on the graph of the equation 3y = ax + 7, then find the value of a.

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Answers Key:

Multiple Choice Question

20 x 1 = 20

\(\because \) 7²+24²=25²
\(\therefore \) Triangle is right angled with hypotenuse 25 cm.
\(\therefore \) Area =\(\frac { 7\times 24 }{ 2 } \)= 84 cm²

\(4x+2x=180^{ 0 }\)

Definition of an obuse angle

(a)
an axiom

\(\left({p\over2},p\right)\) satisfies 2x=y

3(4)+2(1)=k ⇒ k=14

O(0,0) satisfies y=x

(a)
x=3

10.

(a)
y - axis

11.

(a)
II quadrant

12.

x+3=0
\(\Rightarrow\) x=-3
\(\therefore\) Remainder=p(-3)

13.

\(p(-2)=7-3(-2)+2(-2)^2=21\)

14.

Coefficient of \(x^2=3+1=4\)

15.

\((1+3x)^3\) \(=1+27x^3+9x+27x^2\) It has 4 terms

16.

A characteristic of a linear polynomial

17.

(d)
\(\frac { \left( \sqrt { 5 } -\sqrt { 2 } \right) }{ 3 } \)

18.

19.

(a)
\(\sqrt { 23 } \)

20.

(d)
0.401 4001 40001 4...

Generic 5

10 x 5 = 50

21.

(i) Sides of a triangle are:
a = 26 cm, b = 17 cm and c = 25 cm
∴ \(s=\frac{a+b+c}{2}\)
⇒ \(s=\frac{26+17+25}{2}\) = 34 cm
Using, Hero's formula,
Area of a Δ = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{34(34-26)(34-17)(34-25)}\) cm²
= \(\sqrt{34 \times 8 \times 17 \times 9}\) cm²
= \(\sqrt{2 \times 17 \times 2 \times 4 \times 17 \times 3 \times 3}\) cm²
= \(\sqrt{2^{2} \times 17^{2} \times 2^{2} \times 3^{2}}\) cm²
= 2 x 17 x 2 x 3 cm² = 204 cm²
∵ The design is having 8 equal (congruent) triangles.
∴ Total area of the design
= 8 x (Area of one triangle)
= 8 x 204 cm² = 1632 cm²
(ii) Total area of the sheet =70 cm x 50 cm = 3500 cm²
∴ Remaining area of the sheet = (3500 - 1632) cm² = 1868 cm²
(iii) Creativity.

22.

We have ∠A + ∠B = 150° ...(1)
∠B + ∠C = 100° ...(2)
Adding (1) and (2), we get
∴ ∠A + 2∠B + ∠C = 150 + 100° = 250°
⇒ (∠A + ∠B + ∠C) + ∠B = 250°
⇒ 180° + ∠B = 250° [∴ ∠A + ∠E + ∠C = 180°]
∴ ∠B = 250° - 180° = 70°.
Now, ∠A + ∠B = 150°
⇒ ∠A = 150° - ∠B = 150° - 70° = 80°
Also ∠B + ∠C = 100°
⇒ ∠C = 100 - ∠B = 100 - 70° = 30°
Thus, ∠A = 80°, ∠B = 70° and ∠C = 30°.

23.

(i) From the graph, we have
0°C = 32°F
and 0°F = 17.8°C
(ii) Yes, from the graph, we have
40°F = -40°C

24.

We have p(x) = 3x³ + 7x and zero of 7 + 3x is \(\frac{-7}{3}\)
[∵7 + 3x = 0 ⇒ x = \(\frac{-7}{3}\)]
∴ p\(\left(\frac{-7}{3}\right)\) = 3\(\left(\frac{-7}{3}\right)\)+7\(\left(\frac{-7}{3}\right)\) = 3\(\left(\frac{-343}{27}\right)\) + \(\left(\frac{-49}{3}\right)\)
= -\(\frac{343}{9}\) - \(\frac{49}{3}\) = \(\frac{-490}{9}\)
Since \(\left(\frac{-490}{9}\right)\) ≠ 0
i.e. the remainder is not 0.
∴ 3x³ - 7x is not divisible by 7 + 3x.
Thus, (7 + 3x) is not a factor of 3x³ - 7x.

25.

(i) For rectangle ABCD:
AB = 8 - 2 = 6 units ← Length
AD = 12 - 8 = 4 units ← Breadth
∴ Area of rectangle ABCD = AB x AD
= 6 units x 4 units
= 24 sq. units.
For triangle PQR:
QR = 12 - 4 = 8 units ← Base
SP = 6 - 0 = 6 units ← Height
∴ Area of ΔPQR = \(\frac{1}{2}\) base x height
= \(\frac{1}{2}\) x 8 x 6 sq. units
= 24 sq. units.
⇒ \(\left[\begin{array}{l} \text { area of } \\ \text { rect. } \mathrm{ABCD} \end{array}\right]=\left[\begin{array}{l} \text { area of } \\ \Delta \mathrm{PQR} \end{array}\right]\)
(ii) Co-ordinate Geometry.
(iii) Community or social upliftment.

26.

\(\frac { 1 }{ 1+{ x }^{ a-b } } +\frac { 1 }{ 1+{ x }^{ b-a } } =\frac { { x }^{ b } }{ { x }^{ b }+{ x }^{ a } } +\frac { { x }^{ a } }{ { x }^{ a }+{ x }^{ b } } \)
\(=\frac { { x }^{ b }+{ x }^{ a } }{ { x }^{ a }+{ x }^{ b } } \)

27.

322

28.

(x +1)(3x - 5)(2x - 1)

29.

30.

Since, the point (3, 4) lies on the graph, then it will satisfy its equation.
On putting x = 3 and y = 4 in given equation, we get
3(4)=a(3)+7
\(\Rightarrow 13+3a+7\)
\(\Rightarrow 12-7=3a\)
\(\Rightarrow 3a=5\)
\(\Rightarrow a=\frac{5}{3}\)

CBSE 9th Standard Mathematics Number Systems Important Questions And Answers Study Material - QB365 Set A

QB365 Student Learing Managemnet System

Std: 9th Standard CBSE - Mathematics

chapter: Number Systems - Important Questions And Answers

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Questions:

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Answers Key:

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