CAREER FOUNDATION

SESSION 2022-23

YEARLY MOCK TEST

CLASS - X(CBSE) | All Phase
MATHEMATICS
Time : 3 Hrs. Date : 22-01-2023 Max. Marks : 80

GENERAL I NSTRUCTI ONS

Section A Has 20 MCQs carrying 1 Mark Each

Section B Has 5 Questions carrying 02 Marks Each.

Section C Has 6 Questions carrying 03 Marks Each.

Section D Has 4 Questions carrying 05 Marks Each.

Section E Has 3 case based integrated units of Assessment (04 marks Each)
 Mock Test |CBSE|MATH|CLASS 22.01.2023

SECTION - A
(MCQ BASED)
1. If one zero of the quadratic polynomial x 2 3x k is 2, then the value of k is
(A) 10 (B) – 10
(C) – 7 (D) – 2
2. Identify rational number among the given options
3
(A) 5 (B) 2

2 1
(C) 3 3 (D)
3 2 2
3. x and y are 2 different digits. If the sum of the two digit numbers formed by using both the digits
is a perfect square, then value of x + y is
(A) 10 (B) 11
(C) 12 (D) 13
4. The real roots of the equation x 2/3 x1/3 2 0 are
(A) 1, 8 (B) –1, –8
(C) –1, 8 (D) 1, –8
5. If the sum of the first 2n terms of 2, 5, 8, .......... is equal to the sum of the first n terms of 57,
59, 61, ..........,then n is equal to
(A) 10 (B) 12
(C) 11 (D) 13
6. In ABC, DE || BC , find the value of x

x x+3

D E

x+1 x+5

B C
(A) 3 (B) 2
(C) 4 (D) 1
7. The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of the first
triangle is 9 cm,then the corresponding side of second triangle is ...................
(A) 5.4 cm (B) 5.2 cm
(C) 4.9 cm (D) 5.1 cm
8. Two circles of radii 20 cm and 37 cm intersect in A and B. If O1 and O2 are their centres and
AB = 24 cm, then the distance O1O2 is equal to
(A) 44 cm (B) 51 cm
(C) 40.5 cm (D) 45 cm

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 Mock Test 22.01.2023

9. Find the value of (sin4 – cos4 +1) cosec2

(A) 1 (B) 2
(C) 0 (D) –1
10. A 6 m high tree cast a 4 m long shadow. At the same time, a flag pole cast a shadow 50 m long.
How long is the flag pole?
(A) 75 m (B) 100 m
(C) 150 m (D) 50 m
11. Find the distance of the point (5,-12) from the origin
(A) 13 units (B) 5 units
(C) 12 units (D) 200 units
12. It is proposed to build a single circular park equal in area to the sum of areas of two circular
parks of diameters 16 m and 12m in a locality. The radius of the new park would be
(A) 10 m (B) 15 m
(C) 20 m (D) 24 m
13. If the radius of the sphere is increased by 100%, the volume of the corresponding sphere is
increased by
(A) 200% (B) 500%
(C) 700% (D) 800%
14. The following figure shows the graph of y = p(x), where p(x) is polynomial in variable x. The
number of zeroes of the polynomial p(x) is

o x

(A) 1 (B) 2
(C) 3 (D) 4
15. Value of cos00.cos300.cos 450.cos60 0.cos90 0 is ____
(A) 0 (B) 1

1
(C) –1 (D)
2
16. The times, in seconds, taken by 150 athletes to run a 110 m hurdle race are tabulated below

Class Frequency
13.8-14 2
14-14.2 4
14.2-14.4 5
14.4-14.6 71
14.6-14.8 48
14.8-15 20

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 Mock Test |CBSE|MATH|CLASS 22.01.2023

The number of athletes who completed the race in less than 14.6 second is :
(A) 11 (B) 71
(C) 82 (D) 130
17. Which of the following cannot be the probability of an event?
1
(A) (B) 0.1
3
17
(C) 3% (D)
16
18. Out of one digit prime numbers, one number is selected at random. The probability of selecting an
even number is
1 1
(A) (B)
3 4
3 2
(C) (D)
4 3
19. Distance of point P(3, 4) from x -axis is
(A) 3 units (B) 4 units
(C) 5 units (D) 1 units
20. HCF of 144 and 198 is
(A) 9 (B) 18
(C) 6 (D) 12

SECTION - B
21. In the given figure, OA OB = OC OD , show that A= C and B= D
A
C

D O

[2]

B
22. In figure, a circle touches all the four sides of a quadrilateral ABCD. If AB = 6 cm, BC = 9 cm
and CD = 8 cm, then find the length of AD.
C

[2]
B
A
23. Find the value of sin30º cos 60º + cos 30º sin 60º, is it equal to sin 90º or cos 90º ? [2]
24. Two different dice are thrown together. Find the probability that the product of the number
appeared is less than 18.
OR
Harpreet tosses two different coins simultaneously. What is the probability that she gets :
(i) At least one head ? (ii) One head and one tail ? [2]

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 Mock Test 22.01.2023
25. In the given figure, if AB || DC, find the value of x.

D C
x-

3
x+
2

x-
5
x+

1
A B
OR
Water is flowing through a cylindrical pipe, of internal diameter 2cm, into a cylindrical tank of
base radius 40cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half
an hour. : [2]

SECTION - C
26. If one zero of a polynomial 3x 2 8x 2k 1 is seven times the other, find the value of k . [3]
27. Solve for x and y

a b
ax by
2
3x 5y 4 [3]
28. In the given figure, P and Q are the points on the sides AB and AC respectively of ABC, such
that AP = 3.5 cm, PB = 7 cm, AQ = 3 cm and QC = 6 cm. If PQ = 4.5 cm, find BC.

P Q

B C
OR
In the given figure, AB = AC. E is a point on CB produced. If AD is perpendicular to BC and
EF perpendicular to AC , prove that ABD is similar to CEF..
A

F
[3]

E B D C

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 Mock Test |CBSE|MATH|CLASS 22.01.2023

5cos 2 600 4 cos2 300 tan 2 450

29. Evaluate : [3]
sin 2 300 cos 2 600
30. A solid sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with
water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged into
water, by how much will the level of water rise in the cylindrical vessel ?
OR
A hemispherical tank, of diameter 3 m, is full of water. It is being emptied by a pipe at the rate of
4 22
3 litre per second. How much time will it take to make the tank half empty ?Use [3]
7 7
31. 144 cartons of Coke cans and 90 cartons of Pepsi cans are to be stacked in a canteen. If each
stack is of the same height and if it equal contain cartons of the same drink, what would be the
greatest number of cartons each stack would have? [3]

SECTION - D

x 1 2x 1 1
32. Solve for x : 2 where x ,1
2x 1 x 1 2
OR

Prove that 3 5 is an irrational number.. [5]

33. PB is a tangent to the circle with centre O at B.AB is a chord of length 24 cm at a distance of
5 cm from the centre. If the tangent is of length 20 cm, find the length of PO.
P

A B [5]
M

34. The arithmetic mean of the following frequency distribution is 53. Find the value of k .

Class 0-20 20-40 40-60 60-80 80-100

Frequency 12 15 32 k 13

OR
The following distribution gives the weights of 60 students of a class. Find the mean and mode
weights of the students

Weight(in kg) 40-44 44-48 48-52 52-56 56-60 60-64 64-68 68-72
[5]
Number of students 4 6 10 14 10 8 6 2

XA 2
35. Point A lies on the line segment XY joining X 6, 6 and Y 4, 1 in such a way that
XY 5

. If point A also lies on the line 3x k y 1 0 , find the value of k . [5]

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 Mock Test 22.01.2023

SECTION - E
Case based integrated units of Assessment
36. Overflow Pan : A metalworker makes an overflow pan by cutting equal squares with sides of
length x from the corners of a 30 cm by 20 cm piece of aluminium, as shown in the figure. The
sides are then folded up and the corners sealed.
(i) Find a polynomial function V(x) that gives the volume of the pan.
(ii) Find the volume of the pan if the height is 6 cm. Use remainder theorem.

[4]

37. Mr. RK Agrawal is owner of a famous amusement park in Delhi. The ticket charge for the park
is Rs 150 for children and Rs 400 for adult.

[4]
Generally he does not go to park and it is managed by team of staff. One day Mr Agrawal decided
to random check the park and went there. When he checked the cash counter, he found that 480
tickets were sold and Rs 134500 was collected.
(i) Let the number of children visited be x and the number of adults visited be y . Which of the
following is the correct system of equations that model the problem ?
(ii) How many children visited the park ? How many adults visited the park?
(iii) How much amount collected if 300 children and 350 adults visited the park?
(iv) One day total visited children and adults together is 750 and the total amount collected is
Rs 212500. What are the number of children and adults visited the park ?

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 Mock Test |CBSE|MATH|CLASS 22.01.2023

38. A bakery is an establishment that produces and sells flour-based food baked in an oven such as
bread, cookies, cakes, pastries, and pies. Some retail bakeries are also categorized as cafés,
serving coffee and tea to customers who wish to consume the baked goods on the premises.

[4]

Tania runs a bakery shop and her bakery is very famous for tasty biscuits. The amount of mixture
required to make one biscuit is 18 cu cm. Before it is cooked, the mixture is rolled into a sphere.
After the biscuit is cooked, the biscuit becomes a cylinder of radius 3 cm and height 0.7 cm. The
increase in volume is due to air being trapped in the biscuit. Biscuits are packed in a cylindrical card
box of height 14 cm. The arrangement of biscuits is shown below

(i) What is the volume of the biscuits after it is cooked ? What is the volume of air trapped, while
cooking the biscuit ?
(ii) How many biscuits will be there in a box ?
(iii) How much space is vacant in box after biscuits are packed ?
OR
(iv) If weight of 7 biscuits is 50 grams, what will be the weight of box of biscuits?