10 MATHS PWT-1 Pratice Paper

MODEL PRATICE PAPER
PERIODIC WRITTEN TEST – I (2024 – 25)

MATHEMATICS
(FOR CBSE AFFILIATED SCHOOL)
Class: X (Max . Marks: 40) [Time: 1.45 Mints.
Name of the Student: …………………………………………………………… Roll No:
General Instructions:
1.This question paper has 5 sections A,B,C,D and E.
2.Section A has 11 MCQS carrying 1 mark each
3.Section B has 3 questions carrying 2 marks each.
4.Section C has 3 questions carrying 3 marks each.
5.Section D has 2 questions carrying 5 marks each.
6.Section E has 1 case based integrated units of assessment 4marks each.
7.First 15 minutes are allotted only for reading the question paper.
SECTION – A
1. If 3825 = 3𝑥 𝑋 5𝑦 𝑋 17𝑧 , then the value of 𝑥 + 𝑦 − 2𝑧is
A) 0 B)1 C) 2 D) 3
2.A quadratic polynomial, one of whose zeroes is 2 + √5and the sum of whose zeroes is 4,
is
A) 𝑥 2 + 4𝑥 + 1 B) 𝑥 2 − 4𝑥 − 1 C) 𝑥 2 − 4𝑥 + 1 D) 𝑥 2 + 4𝑥 − 1
3. The ratio of the sum and product of the roots of the quadratic equation 5𝑥 2 − 6𝑥 + 21 = 0
is
A) 5:21 B) 2:7 C) 21:5 D) 7:2
4. Which out of the following type of straight lines will be represented by the system of
equations 3𝑥 + 4𝑦 = 5and 6𝑥 + 8𝑦 = 10
A) parallel B) Interesting
C) coincident D) perpendicular to each other
5. A: Degree of a zero polynomial is not defined
R: Degree of non-zero constant polynomial is 0
A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation
of Assertion (A).
B) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct
explanation of Assertion (A).
C) Assertion (A) is true but Reason (R) is false.
D) Assertion (A) is true but Reason (R) is true.
6. If 𝛼and 𝛽 are the zeroes of the polynomial 𝑃(𝑥) = 𝑘𝑛2 − 30𝑥 + 45𝑘 and 𝛼 + 𝛽 =
𝛼𝛽then the
value of k is
A) −2
3
B) −3
2
C) 32 D) 23
7. The fourth vertex D of a parallelogram ABCD Whose three vertices are

𝐴(−2,3), 𝐵(6,7)𝑎𝑛𝑑𝐶(8,3) is
A) (0,1) B) (0, −1) C) (−1,0) D) (1,0)
8. If the roots of equation 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0, 𝑎 ≠ 0are real and equal then which of the
following relation is true?
𝑏2 𝑏2 𝑏2
A) 𝑎 = B) 𝑏 2 = 𝑎𝑐 C) 𝑎𝑐 = D) 𝑐 =
𝑐 4 𝑎
9. If the distance between the points (3,-5) and (x,-5) is 15 units, then the values of x are :
A) 12,-18 B)-12:18 C) 18,5 D) -9,-12
10. The pair of linear equations 𝑥 + 2𝑦 + 5 = 0 and −3𝑥 = 6𝑦 − 1 has
A) Unique Solution B) Exactly two solutions
C) Infinitely many solutions D) No Solution.
11. A: Mid-point of a line segment divides the segment in the ratio 1:1
R : The ratio in which the point (-3,k) divides the line segment joining the points (-5,4)
and (-2,3) is 1:2
A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation
of Assertion (A).
B) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct
explanation of Assertion (A).
C) Assertion (A) is true but Reason (R) is false.
D) Assertion (A) is true but Reason (R) is true.
SECTION – B
12. A) In teacher’s workshop, the number of teachers teaching French, Hindi and English are
48, 80 and 144 respectively Find the minimum number of rooms required if in each
room the same number of teachers are seated and all of them are of the same
subject.
(or)
12. B) Three bells toll at intervals of 9,12 and 15 minutes respectively. If they start tolling
together, after what time will they next toll together.
13. Solve the following system of linear equations 7𝑥 − 2𝑦 = 5 and 8𝑥 + 7𝑦 = 15 and
verify your
answer
2
14.If is a root of the quadratic equation 𝑘𝑥 2 − 𝑥 − 2 = 0 then find the value of K.
3
SECTION – C
15. Prove that √3 is an irrational number.
16. A) Find the zeroes of the polynomial 3𝑥 2 − 5𝑥 − 2 and verify the relationship
between the zeroes and the coefficients of the polynomial.
(or)
16. B) If 𝛼𝑎𝑛𝑑𝛽 are the zeroes of the Quadratic polynomial 𝑓(𝑥) = 6𝑥 2 + 11𝑥 − 10,
𝛼 𝛽
find the value of +
𝛽 𝛼
17. A) Find the coordinates of the points of trisection of the line segment joining
the points 𝐴(5, −3) and 𝐵(−4,3)
(or)
17. B) Find a relation between 𝑥𝑎𝑛𝑑𝑦such that the point (𝑥, 𝑦) is equidistant
from the point (3,6) and (-3,4)
SECTION – D
18.A) The denominator of a fraction is one more than twice the numerator. If the
sum of the fraction and its reciprocal is 2 16/21, Find the fraction.
(or)
18.B) In a flight of 2800 km , an aircraft was slowed due to bad weather. Its
average speed is reduced by 100 km/h and by ding so, the time of flight is
increased by 30 minutes. Find the original duration of the flight.
1 1 1 1
19.A) Solve for 𝑥: 𝑎+𝑏+𝑥 =𝑎+𝑏+𝑥 𝑎 ≠ 0, 𝑏 ≠ 0𝑎𝑛𝑑𝑎 + 𝑏 + 𝑥 = 0
(or)
19.B) If the equation (1 + 𝑚2 )𝑛2 𝑥 2 + 2𝑚𝑛𝑐𝑥 + (𝑐 2 − 𝑎2 ) = 0has equal roots, prove
that𝑐 2 = 𝑎2 (1 + 𝑚2 )
SECTION – E
20.
Based on the above ,answer the following questions

i) Find the mid-point of the segment joining F and G
ii) A) What is the distance between the points A and G?
(or)
B) Find the coordinates of the point which divides the line segment joining the
points A and B in the ratio 1: 3 internally.
iii) What are the coordinates of the point D?
PAPER PREPARED BY
RAJA RAO DEVARAPALLI
(CLUSTER RESOUCE PERSON(CRP))
TSUNDUR
BAPATLA DISTRICT
CONTACT NUMBER:9949479380

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MODEL PRATICE PAPER

PERIODIC WRITTEN TEST – I (2024 – 25)

7. The fourth vertex D of a parallelogram ABCD Whose three vertices are

Based on the above ,answer the following questions

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