Practice Test

Q1) The largest no which divides 70 and 125, leaving remainders 5 and 8, respectively , is: Show Answer

Q2) If the HCF of 65 and 117 is expressible in the form 65m-117, then the value of m is Show Answer

Q3) The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is Show Answer

Q4) The product of a non-zero rational and an irrational number is: Show Answer

Q5) The number 1.732 is: Show Answer

Q6) 2.1311 3111 311113....is Show Answer

Q7) Which of the following rational numbers is expressible as a terminating decimal? Show Answer

Q8) - In the following questions, A statement of Assertion (A) is followed by a statement of Reason(R), Mark the correct choice as.
Assertion(A):(7x13x11)+11 and (7x6x5x4x3x2x1)+3 have exactly composite numbers.
Reason(R): (3x12x101)+4 is not a composite number.
Show Answer

Q9) In the following questions, A statement of Assertion (A) is followed by a statement of Reason(R), Mark the correct choice as.
Assertion(A):If HCF (336,54) =6, then LCM (336,54)=3000
Reason(R):The sum of exponents of prime factors in the prime factorisation of 196 is 4. Show Answer

Q10) In the following questions, A statement of Assertion (A) is followed by a statement of Reason(R), Mark the correct choice as.
Assertion(A):HCF of two or more numbers = Product of the smallest power of each common prime factor, involved in the numbers.
Reason(R): The HCF of 12,21 and 15 is 3. Show Answer

Q11) - In the following questions, A statement of Assertion (A) is followed by a statement of Reason(R), Mark the correct choice as.
Assertion(A): The product of two consecutive positive integers is divisible by 2.
Reason(R): 13233343563715 is a composite number. Show Answer

Q12) Find the greatest number of 5 digits, that will give us reminder of 5, when divided by 8 and 9 respectively. Show Answer

Q13) For some integers p and 5, there exist unique integers q and r such that p = 5q + r. Possible values of r are Show Answer

Q14) The ratio between the LCM and HCF of 5, 15, 20 is : Show Answer

Q15) Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds. If they first beep together at 12 noon, at what time will they beep again for the first time ? Show Answer

Q16) If A = 2n + 13, B = n +7, where n is a natural number, then HCF of A and B is : Show Answer

Q17) There are 576 boys and 448 girls in a school that are to be divided into equal sections of either boys or girls alone. The total number of sections thus formed are : Show Answer

Q18) Two natural numbers whose difference is 66 and the least common multiple is 360, are : Show Answer

Q19) 4 Bells toll together at 9.00 am. They toll after 7,8,11 and 12 seconds respectively. How many times will they toll together again in the next 3 hours ? Show Answer

Q20) Which of the following rational numbers have a terminating decimal expansion ? Show Answer

Q21) From the following, the rational number whose decimal expansion terminating is : Show Answer

Q22) The sum of exponents of prime factors in the prime-factorisation of 196 is: Show Answer

Q23) A rational number in its decimal expansion is 327.7081. What would be the prime factors of q when the number is expressed in the p/q form? Show Answer

Q24) The total number of factors of a prime number is: Show Answer

Q25) The HCF and the LCM of 12, 21, 15 respectively are: Show Answer

Q26) What is the product or sum of a rational and irrational numbers? Show Answer

Q27) HCF of 2 numbers is 113, and their LCM is 56952. If one number is 904, then the other number is: Show Answer

Q28) The H.C.F. of 306 and 1314 is: Show Answer

Q29) If HCF (18, 72) = 18, then LCM (18, 72) is: Show Answer

Q30) If the HCF of two numbers is 1, then the two numbers are called: Show Answer

Q31) Which of the following is the smallest composite number? Show Answer

Q32) The HCF of smallest prime number and the smallest composite number is ........... . Show Answer

Q33) If b = 3, then any integer can be expressed as: Show Answer

Q34) For some integer m, every even integer is of the form: Show Answer

Q35) For some integer q, every odd integer is of the form: Show Answer

Q36) The total number of participants is: Show Answer

Q37) The LCM of 60, 84, and 108 is: Show Answer

Q38) The HCF of 60, 84, and 108 is: Show Answer

Q39) The minimum number of rooms required, if in each room, the same number of participants are to be seated and all of them being in the same subject is: Show Answer

Q40) The minimum number of rooms required, if in each room, the same number of participants are to be seated and all of them being in the same subject, find the minimum number of rooms required for all the participants and officials. Show Answer

Q41) Who reaches the nearest point? Show Answer

Q42) How many times can they meet in between same steps? Show Answer

Q43) Who takes least number of steps to reach near 100? Show Answer

Q44) What is the first stair where any two out of 3 will meet together? Show Answer

Q45) What is the second stair where any two out of three will meet together? Show Answer

Q46) How many maximum guests Venika can invite?
Show Answer

Q47) How many apples and bananas will each guest
get? Show Answer

Q48) Venika decide to add 42 mangoes also. In this
case how many maximum guests Venika can invite? Show Answer

Q49) If Venika decide to add 3 more mangoes and
remove 6 apple in total fruits, in this case how
many maximum guests Venika can invite? Show Answer

Q50) How many total fruits will each guest get? Show Answer

Q51) What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B? Show Answer

Q52) If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32, 36) is....... Show Answer

Q53) 36 can be expressed as a product of its primes as: Show Answer

Q54) In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are: Show Answer

Q55) What is the minimum number of rooms required during the event? Show Answer

Q56) The LCM of 60, 84 and 108 is: Show Answer

Q57) The product of HCF and LCM of 60, 84 and 108 is: Show Answer

Q58) 108 can be expressed as a product of its primes as: Show Answer

Q59) What is the maximum number of columns in which they can be planted? Show Answer

Q60) Find the total number of plants Show Answer

Q61) Find the sum of exponents of the prime factors of the maximum number of columns in which they can be planted. Show Answer

Q62) What is the total numbers of row in which they can be planted? Show Answer

Q63) Find the sum of exponents of the prime factors of total number of plants. Show Answer

Q64) What will be the value of x? Show Answer

Q65) What will be the value of y? Show Answer

Q66) What will be the value of z? Show Answer

Q67) According to Fundamental Theorem of Arithmetic 13915 is a Show Answer

Q68) The prime factorisation of 13915 is Show Answer

Q69) For positive integers a and 3, there exist unique integers q and r such that a=3q + r, where r must satisfy: Show Answer

Q70) Find the greatest number of 5 digits, that will give us reminder of 5, when divided by 8 and 9 respectively. Show Answer