Real Numbers Te...

Which of the following is NOT a non-terminating repeating decimal?

A number (n) when divided by 7 leaves a remainder of 2. What will be the remainder if one more than square of the number is divided by 7?

The product of three numbers a, b and c is 15360. The values of H.C.F(a, b), H.C.F(a, c) and H.C.F(b, c) are 4, 4 and 8, respectively. What are the L.C.M. and H.C.F. of the three numbers if the product of L.C.M. and H.C.F. is 1920?

The fraction is equal to

Which of the following is a fractional form of ?

+ + = ?

If = a, then what is the value of a²?

Which of the following prime numbers should be the denominator to get a terminating decimal number?

+ + + ... + equals

What is the rationalising factor of ?

Which of the following is the greatest surd?

What will be the 8^th root of the 32^nd root of ?

If (a³ + k) is divisible by k, where 'a' is a positive integer and 'k' is a prime number, then which of the following is true?

A real number , where 'k' is a three-digit number with digits 2, 7 and 3 in any order, is expressed as a decimal number. Which of the following is true for the number?

Evaluate:

There are three watches, out of which one loses 4 seconds every minute and one gains 4 seconds every minute. If all the watches are set at 8 a.m. and an alarm is activated, each watch beeps for a second when the time turns 1 minute in that watch. At what time will they beep together again?

There are three wheels in three different machines A, B, and C. These three wheels are rotating at different speeds. The diameters of the wheels of these three machines are the same. A's wheels make a revolution in minutes, B's wheels in minutes, and C's wheels in minutes. Three markings, one on each wheel, are at the points of contact of the wheels with the plane when they start off. What is the shortest interval after which the markings on the wheels are again at the points of contact of all the 3 wheels simultaneously?

A and B think about two numbers 'a' and 'b'. They say that the sum of their numbers is 270. If the HCF of the two numbers is 18, then what is the maximum number of such pairs which will satisfy these conditions?

Sham had a certain number of chocolates which he wanted to share among students of a school. At first he tried to distribute equally between two students, then among three, four, five and six students, but every time he was left with one chocolate. When he tried to distribute them among 7 students, he succeeded. What is the smallest number of chocolates he could have?

There are three wheels A, B and C. Wheel A can complete 300 revolutions in 5 minutes. Wheel B can complete 72 revolutions in 2 minutes. Wheel C can complete 96 revolutions in 4 minutes. On completing one revolution, the starting point touches the ground. Two coins are tossed when the starting marks of all the wheels touch the ground together. How much time would have passed for the two coins to have been tossed 50 times each?

Which of the following statements is correct?

A. If number X = pⁿ × q^m × r and number Y = p^n-1 × q^m+1 × r, then L.C.M(X, Y) = pⁿ × q^m+1 × r
B. Square root of any non-square number would be an irrational number.
C. H.C.F(1970, 218) = H.C.F(218, 8)
D. The product of primes is equal to a composite number.

Find the correct terms which will replace the letters M, N, O, and P in the given sentences.

A. Zero is not included in the set of …M… numbers.
B. The product of the …N… power of each prime factor involved in the numbers is called …O….
C. Square of an irrational number is …P… a rational number.

Match the following:

Column I	Column II
1.	a.
2.	b.
3.	c.
4.	d.

A shop owner has four different types of chemicals A, B, C, and D. He has 806 litres of chemical A, 868 litres of chemical B, 930 litres of chemical C, and 992 litres of chemical D. He wants to fill these chemicals in containers to sell them. He prepares least number(a) of containers with equal amount of chemical in them, without mixing these chemicals. There is b litres of chemical in each container.

(1) What is the value of a?
(2) What is the value of b?

Read the statements carefully and state 'T' for true and 'F' for false.

(I)is an irrational number.
(II) The LCM of two numbers, 17²× 13²× 7 × 23 and 23³× 7 × 17, is in the form of 17^a× 13^b× 7^c × 23^d. So, the values of a, b, c, and d are 2, 2, 1 and 3, respectively.
(III) The fractional representation of is.
(IV) The product of two numbers is (a⁴ – b⁴). If the LCM of these two numbers is (a + b), then the HCF will be (a³ + ab² + a²b + b³).