Periodic Test-I — 2022-23
Subject — Mathematics
Class — X
Time : 1½ hrs.
MM : 40
Section – A (1×10=10)
Q.1 The LCM of smallest two digit composite number and smallest composite number is :
a) 12
b) 4
c) 20
d) 44
Q.2 The sum of exponents of prime factors in the prime factorisation of 196 is
a) 3
b) 4
c) 5
d) 2
Q.3 The least number that is divisible by all the numbers from 1 to 5 is :
a) 30
b) 20
c) 60
d) 120
Q.4 The degree of the polynomial having zeroes (-3) and 4 only is :
a) 2
b) 1
c) more than 3
d) 3
Q.5 Find the quadratic polynomial, the sum of whose zeroes is (-5) and their product is 6.
a) x²+5x+6
b) x²-5x+6
c) x²-5x-6
d) -x²+5x+6
Q.6 If 2 and α are zeroes of 2x²-6x+2 then the value of α is
a) 2
b) 3
c) 1
d) 5
Q.7 If an event cannot occur then its probability is :
a) 1
b) 3/4
c) 1/2
d) 0
Q.8 The probability of getting exactly one head in tossing a pair of coins is :
a) 0
b) 1
c) 1/3
d) 1/2
Q.9 A card is selected from a deck of 52 cards. The probability of being a red face card is :
a) 3/26
b) 3/13
c) 2/13
d) 1/2
Q.10 The median class of the following data is :
| Marks obtained | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| No. of students | 8 | 10 | 12 | 22 | 18 | 18 |
a) 20-30
b) 30-40
c) 40-50
d) 10-20
Section – B (2×3=6)
Q.11 A die is thrown once, the probability of getting a prime number is 2/3. Is it true? Justify your answer.
Q.12 Find the HCF and LCM by prime factorisation method. 306 and 1314
Q.13 If the product of zeroes of the polynomial ax²-6x-6 is 4 find the value of a.
Section – C (3×4=12)
Q.14 Find the zeroes of the following quadratic polynomial and verify the relation between the zeroes and its coefficients. 3x²-x-4
Q.15 Prove that √3-2 is an irrational number.
Q.16 Find the Mean of the following frequency distribution :
| Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| Frequency | 4 | 5 | 7 | 10 | 12 | 8 | 4 |
Q.17 A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bad. Find the probability that it bears.
a) a two digit number.
b) a number which is perfect square.
OR
A child game has 8 triangles of which 3 are blue and rest are red and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a :
a) triangle
b) square
c) square of blue colour
Section – D (4×3=12)
Q.18 Prove that √5 is an irrational number.
Q.19 Find the value of the missing frequency if the mean of the following data is 68
| Class Interval | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 | 75-85 | 85-95 |
| Frequency | 10 | 6 | 4 | f | 4 | 12 | 26 |
OR
Calculate the missing frequency f from the following data if median is 24
| Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 5 | 25 | f | 16 | 9 |
Q.20 If α and β are the zeroes of the polynomial x²-5x+k, such that α-β=1, find the value of k.