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### XYZ SCHOOL

### PERIODIC TEST -1
EXAMINATION-(2022-23)

### SUBJECT: MATHEMATICS MAX. MARKS : 10

**CLASS : X DURATION : 1 HRS**

### General Instructions:

(i).
**All **questions are compulsory.

(ii). This question paper contains
11** **questions divided into three Sections
A, B and C.

(iii). **Section A **comprises of 04 questions of **1/2
mark **each. **Section B **comprises
of 06 questions of **1 marks **each. **Section C **comprises of 01 question of **2 marks **.

__SECTION – A__

**Questions 1 to 4 carry 1/2 mark each.**

1.
If
two positive integers a and b are written as a = x^{3}y^{2} and
b = xy^{3 }; x, y are prime numbers, then HCF (a, b) is

(A)xy (B)xy^{2} (C)x^{3}y^{3} (D)x^{2}y^{2}

2.
The
least number that is divisible by all the numbers from 1 to 10 (both inclusive)
is

(A)10 (B)100 (C)504 (D)2520

3.
A
quadratic polynomial, whose zeroes are –3 and 4, is

4.
The
zeroes of the quadratic polynomial x^{2} + 99x + 127 are

(A)
both positive (B) both
negative (C) one positive and one negative

(D) both equal

__SECTION – B__

**Questions 5 to 8 carry 1 mark each.**

5.
Given
that HCF (306, 657) = 9, find LCM (306, 657).

6.
Prove
that is
irrational.

7.
Find
the zeroes of the following quadratic polynomial and verify the relationship
between the zeroes and the coefficients: 4s^{2} – 4s + 1

8.
Find
a quadratic polynomial each with the given numbers as the sum and product of
its zeroes respectively: and .

9.
Half
the perimeter of a rectangular garden, whose length is 4 m more than its width,
is 36 m. Find the dimensions of the garden.

10.
Solve
2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y =
mx + 3.

__SECTION – C__

**Question 11 carry
2 marks**

11.
.
Solve the following pair of linear equations by the elimination method:

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