List of top Mathematics Questions on Number Theory asked in MET

Total number of even divisors of \(2079000\) which are divisible by \(15\) are:

If \( \frac{a}{b} = \frac{1}{3} \) and \( \frac{b}{c} = \frac{3}{4} \), then the value of \( \frac{a+2b}{b+2c} \) is:

Last two digits in \(9^{50}\) are _ _ _ _ _.

If \(x = \frac{2\sqrt{2}-\sqrt{7}}{2\sqrt{2}+\sqrt{7}}\), then \(x + x^{-1}\) is equal to

If \(x^{4/3} + x^{-1/3} = 1\), \(x^5 + 3x^2 - x\) is equal to

\[ 9^{-z} = \frac{1}{27^x \cdot 27^y} = (81)^{-y} \]

\[ \frac{5^{\frac{3}{2}} - 2^{\frac{3}{2}}}{\sqrt{5}-\sqrt{2}} + \frac{5^{\frac{3}{2}} + 2^{\frac{3}{2}}}{\sqrt{5}+\sqrt{2}} \]

The remainder obtained when \(5^{124}\) is divided by 124 is

Equation \(x * a = b\) has in group \((G, *)\)

The remainder obtained when \(1! + 2! + \cdots + 200!\) is divided by 14 is

Which of the following statement is not tautology?

The decimal equivalent of the binary number 10011.1 is

The binary representation of 60 is

If n be any integer, then \(n(n+1)(2n+1)\) is:

If $a$, $b$, $c$ are different integers such that $(a,b) = c$, which of the following statements is true?

The least positive remainder when $123 \times 125 \times 127$ is divided by 124 is

If $(3 - x) \equiv (2x - 5) \pmod{4}$, then one of the values of $x$ is

If $77 \equiv 88x \pmod{5}$, then x is equal to

When $5^{20}$ is divided by 7, the remainder is

The GCD of 364 and 462 is

If \(aN = \{an : n \in N\}\) and \(bN \cap cN = dN\), where \(a,b,c \in N\) and \(b,c\) are coprime, then

If all edges are directed in a graph then it is called as

\((p \wedge \neg q) \wedge (\neg p \wedge q)\) is

If \(G\) is an abelian group then for all \(a,b \in G\), \(b^{-1} * a^{-1} * b * a\) is equal to

If the scalar projection of the vector \(x\mathbf{i} - \mathbf{j} + \mathbf{k}\) on the vector \(2\mathbf{i} - \mathbf{j} + 5\mathbf{k}\) is \(\frac{1}{\sqrt{30}}\) then value of \(x\) is equal to