List of top Mathematics Questions on Real Numbers

Let \(S=\left\{a+b\sqrt2:a,b\in Z\right\},T_1=\left\{(-1+\sqrt2)^n:n\in \N\right\},\ \text{and}\ T_2=\left\{(1+\sqrt2)^n:n\in\N\right\}\). Then which of the following statements is (are) TRUE ?
If $[x]^2 - 5[x] + 6 = 0$, where $[x]$ denotes the greatest integer function, then:
If \( q \) is a positive integer, which of the following is an even positive integer?
Which of the following has a terminating decimal expansion?
The H.C.F. of two numbers is 15 and L.C.M. is 105. If one of the numbers is 5, then the other number is:
In \( L_2 \) form of 0.375, the form of \( q \) is:
In division algorithm \( a = bq + r \), \( b = 43 \), \( q = 31 \) and \( r = 32 \), the value of \( a \) will be:
The H.C.F. of two consecutive odd numbers is
\( \sqrt{10} \times \sqrt{15} \) is
The simplest form of \( 0.\overline{3} + 0.\overline{4} \) is
If \( 156 = 2^x \times 3^y \times 13^z \), then \( x + y + z = ? \)
In the form of \( \frac{p}{2^n \times 5^m} \), \( 0.105 \) can be written as
If H.C.F. of two numbers = 25 and L.C.M = 50, then the product of the numbers will be
If in division algorithm \( a = bq + r \), \( b = 61 \), \( q = 27 \), and \( r = 32 \), what is the value of \( a \)?
If \( q \) is a positive integer, which of the following is an odd positive integer?
\( \sqrt{\frac{64}{81}} + \sqrt{\frac{16}{9}} \) is
The product of two irrational numbers \( 3 + \sqrt{6} \) and \( 3 - \sqrt{5} \) will be a/an
Prove that \( (2+\sqrt{3})^2 \) is not a rational number.
Using Euclid division algorithm find the HCF of 148 and 185.
The HCF of two numbers is 15 and their LCM is 105. If one of the numbers is 5, the other number is:
If the Euclidean algorithm equation is given as \( a = bq + r \) where \( b = 43 \), \( q = 31 \), and \( r = 32 \), then the value of \( a \) is:
If \( q \) is a positive integer, which of the following is an even positive integer?
Which of the following has a terminating decimal expansion?
The given number \( 2:1311311311113 \dots \) is:
The product of a rational number and an irrational number is: