 ### CBSE Class 9 Maths Sample Paper 2 # CBSE CLASS 9 MATHS SAMPLE PAPER – 2

CBSE 9th

Mathematics

Sample Paper 2

Time: 3-hour                                                                                                                  Total Marks: 80

General Instructions:

• All questions are compulsory.
• The question paper consists of 30 questions divided into four sections A, B, C and D.
• Section A contains 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each. Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4 marks each.
• There is no overall choice. However, an internal choice has been provided in four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternatives in all such questions.
• Use of calculators is not permitted.

Section-A

(Question numbers 1 to 6 carry 1 mark each)

Q. No.

1.

If \$mathrm{x}^{mathrm{a} / mathrm{b}}=1\$, then find the value of ‘a’.

2.

If \$mathrm{p}(mathrm{x})=2 mathrm{x}^{3}+5 mathrm{x}^{2}-3 mathrm{x}-2\$ is divided by \$mathrm{x}-1\$, then find the remainder.

3.

The distance of the point \$(0,-1)\$ from the origin is

4.

If the vertical angle of an isosceles triangle is \$100^{circ}\$, then find the measures of its base angles.

5.

The ratio of the whole surface area of a solid sphere and a solid hemisphere is

6.

There are 60 boys and 40 girls in a class. A student is selected at random. Find the probability that student is a girl.

Section B

(Question numbers 7 to 12 carry 2 marks each)

7.

If \$p=2-a\$, then prove that \$a^{3}+6\$ a \$p+p^{3}-8=0\$.

8.

In the adjoining figure, we have \$mathrm{AB}=mathrm{BC}, mathrm{BX}=mathrm{BY}\$. Show that \$mathrm{AX}=mathrm{CY}\$ (using appropriate Euclid’s axiom) 9.

If two opposite angles of a parallelogram are \$(63-3 x)^{circ}\$ and \$(4 x-7)^{circ} .\$ Find all the angles of the parallelogram.

10.

Three Schools situated at \$mathrm{P}, mathrm{Q}\$ and \$mathrm{R}\$ in the figure are equidistant from each other as shown in the figure. Find \$angle\$ QOR. 11.

The diameter of the two right circular cones are equal if their slant heights are in the

ratio \$3: 2\$, then what is the ratio of their curved surface areas?

12.

A batsman in his \$11^{text {th }}\$ innings makes a score of 68 runs and there by increases his average score by 2 . What is his average score after the \$11^{text {th }}\$ innings.

Section C

(Question numbers 13 to 22 carry 3 marks each)

13.

Represent \$sqrt{10}\$ on the number line.

14.

Simplify: \$frac{73 times 73 times 73+27 times 27 times 27}{73 times 73-73 times 27+27 times 27}\$

15.

Determine the point on the graph of the linear equation \$2 mathrm{x}+5 mathrm{y}=19\$, whose ordinate is \$1 frac{1}{2}\$ times its abscissa.

16.

Locate the points \$(3,0),(-2,3),(2,-3),(-5,4)\$ and \$(-2,-4)\$ in Cartesian plane. Also find the quadrant in which they lie.

OR

Observe the fig. given below and answer the following: i.

The coordinates of \$mathrm{B}\$.

ii.

The coordinates of \$mathrm{C}\$.

iii.

The point identified by the coordinate \$(-3,-5)\$.

iv.

The coordinates of \$mathrm{H}\$.

v.

The coordinates of origin

vi.

The abscissa of the point \$mathrm{D}\$.

17.

In figure, \$A C=A E, A B=A D\$ and \$angle B A D=angle E A C .\$ Show that \$B C=D E\$. OR \$mathrm{AB}\$ is a line segment and \$mathrm{P}\$ is its mid-point. D and \$mathrm{E}\$ are points on the same side of \$mathrm{AB}\$ such that \$angle mathrm{BAD}=angle mathrm{ABE}\$ and \$angle mathrm{EPA}=angle mathrm{DPB}\$. Show that:

i.

\$triangle mathrm{DAP} cong triangle mathrm{EBP}\$

ii.

18.

Show that the area of a rhombus is half the product of the lengths of its diagonals.

19.

\$mathrm{A}, mathrm{B}, mathrm{C}\$ and \$mathrm{D}\$ are the four points on a circle. AC and BD intersect at point \$mathrm{E}\$ such that \$angle\$ \$mathrm{BEC}=130^{circ}\$ and \$angle mathrm{ECD}=20^{circ} .\$ Find \$angle mathrm{BAC}\$. OR

Prove that equal chords of a circle subtend equal angles at the centre.

20.

Sides of a triangle are in the ratio \$12: 17: 25\$ and its perimeter is \$540 mathrm{~cm}\$. Find its area.

21.

The diameter of a garden roller is \$14 mathrm{~m}\$ and it is \$2 mathrm{~m}\$ long. How much area will it cover in 10 revolutions?

OR

The sum of height and radius of the base of a solid cylinder is \$37 mathrm{~cm}\$. If the total surface area of the cylinder is \$1628 mathrm{~cm}^{2}\$, then find its volume.

22.

Fifty seeds were selected at random from each 5 bags seeds and were kept under standardized conditions favorable to germination. After days, the number of seeds which

had germinated in each collection were counted and recorded as follows:

 Bag 1 2 3 4 5 Number of seeds generated 40 48 42 39 38

What is the probability of germination of

i.

More than 40 seeds in a bag

ii.

49 seeds in a bag

iii.

More than 35 seeds in a bag

Section D

(Question numbers 23 to 30 carry 4 marks each)

23.

If \$mathrm{x}=frac{6-sqrt{3} 2}{2}\$, then find the value of \$left(x^{3}+frac{1}{x^{3}}right)-6left(x^{2}+frac{1}{x^{2}}right)+left(x+frac{1}{x}right)\$.

OR

If \$x=frac{sqrt{3}+1}{sqrt{3}-1}, y=frac{sqrt{3}-1}{sqrt{3}+1}\$, find the value of \$x^{2}+x y-y^{2}\$

24.

Determine the value of \$mathrm{b}\$ ‘ for which the polynomial \$5 mathrm{x}^{3}-mathrm{x}^{2}+4 mathrm{x}+mathrm{b}\$ is divisible by \$1-5 mathrm{x}\$.

25.

Draw the graph of two lines whose equations are \$x+y-6=0\$ and \$x-y-2=0\$, on the same graph paper. Find the area of triangle formed by the two lines and y axis.

OR

The force exerted to pull a cart is directly proportional to the acceleration produced in the cart. Express the statement as a linear equation in two variables and draw the graph

for the same by taking the constant mass equal to \$6 mathrm{~kg}\$.

26.

In figure the sides \$A B\$ and AC of are produced to points \$E\$ and D respectively. If bisectors \$mathrm{BO}\$ and \$mathrm{CO}\$ of \$angle mathrm{CBE}\$ and \$angle mathrm{BCD}\$ respectively meet at point \$mathrm{O}\$, then prove that \$angle mathrm{BOC}=90^{circ}-frac{1}{2} angle mathrm{BAC}\$ 27.

In the adjoining figure, \$mathrm{P}\$ is the point in the interior of a parallelogram \$mathrm{ABCD}\$. Show that \$operatorname{ar}(triangle mathrm{APB})+operatorname{ar}(triangle mathrm{PCD})=frac{1}{2} operatorname{ar}(|| mathrm{gm} mathrm{ABCD})\$ 28.

Construct a right angled triangle whose base is \$5 mathrm{~cm}\$ and sum of its hypotenuse and other side is \$8 mathrm{~cm}\$.

29.

The floor of a rectangular hall has a perimeter \$300 mathrm{~cm}\$. Let the cost of painting of four walls at the rate of Rs.12 per \$mathrm{cm}^{2}\$ is Rs. 24,000 , then find the height of the hall.

30.

The marks obtained (out of 100) by a class of 80 students are given below:

 Marks 10-20 20-30 30-50 50-70 70-100 No. of students 6 17 15 16 26

Construct a histogram to represent the data above.

OR

Construct a frequency polygon for the following data:

 Ages (in years) 0-2 2-4 4-6 6-8 8-10 Frequency 4 7 12 5 2
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