List of top Mathematics Questions on Number Systems asked in JEE Main

The largest value of $n$, for which $40^n$ divides $60!$, is
Maximum value of $n$ for which $40^n$ divides $60!$ is
If \( a, b, c \) are in A.P. where \( a + b + c = 1 \) and \( a, 2b, c \) are in G.P., then the value of \( 9(a^2 + b^2 + c^2) \) is equal to:
Let \( \mathbf{a} = \sqrt{2} \hat{i} \) and \( \mathbf{b} = 5\hat{j} + \hat{k} \). If \( \mathbf{c} = \mathbf{a} \times \mathbf{b} \) and \( \mathbf{c} \) lies in the \( y \)-\( z \) plane such that \( |\mathbf{c}| = 2 \), then the maximum value of \( |\mathbf{c} \cdot \mathbf{d}| \) is equal to:
The largest \( n \in \mathbb{N} \), for which \( 7^n \) divides \( 101! \), is :
If \[ \int_0^6 \left( x^3 + \lfloor x^{1/3} \rfloor \right) \, dx = \alpha \] and \[ \int_0^{\frac{\pi}{2}} \frac{\sin^2 x}{\sin^6 x + \cos^6 x} \, dx = \beta, \] then the value of \( ab^2 \) is equal to:
Let \[ S = \{(m,n) : m,n \in \{1,2,3,\ldots,50\}\}. \] If the number of elements \((m,n)\) in \(S\) such that \(6^m + 9^n\) is a multiple of \(5\) is \(p\), and the number of elements \((m,n)\) in \(S\) such that \(m+n\) is a square of a prime number is \(q\), then \(p + q\) is equal to
Let the domain of the function \[ f(x) = \log_3 \log_5 \left( 7 - \log_2 \left( x^2 - 10x + 15 \right) \right) + \sin^{-1} \left( \frac{3x - 7}{17 - x} \right) \] be \( (\alpha, \beta) \), then \( \alpha + \beta \) is equal to:
Statement 1 : \(2^{513}+2^{013}+8^{13}+3^{13}\) is divisible by \(7\).
Statement 2 : The value of integral part of \((7+4\sqrt{3})^{25}\) is an odd number.
\[ x - ny + z = 6 \\ x - (n - 2)y + (n + 1)z = 8 \\ (n - 1)y + z = 1 \] Let \( n \) be the number on the die when rolled randomly. Then \( P \) (that system equation has a unique solution) = \( \frac{k}{6} \). Then sum of value of \( k \) and all possible values of \( n \) is:
Let $S$ be a set of $5$ elements and $P(S)$ denote the power set of $S$. Let $E$ be the event of choosing an ordered pair $(A,B)$ from $P(S)\times P(S)$ such that $A\cap B=\varnothing$. If the probability of the event $E$ is $\dfrac{3^p}{2^q}$, where $p,q\in\mathbb{N}$, then $p+q$ is equal to
The largest value of \( n \in \mathbb{N} \) such that \( 7^{n} \) divides \( (101)! \) is _____.
The sum of roots of the equation \[ |x - 1|^2 - 5|x - 1| + 6 = 0 \] is:
The largest value of \( n \in \mathbb{N} \) such that \( 7^n \) divides \( 101! \) is ______.
Maximum value of $n$ for which $40^n$ divides $60!$ is
Determine the largest value of \( n \) for which \[ 2^{n} \mid (75)! \]
Let \( A = \{1, 2, 3, \dots, 10\} \) and \( B = \left\{ \frac{m}{n} : m, n \in A, m <n \text{ and } \gcd(m, n) = 1 \right\} \). Then \( n(B) \) is equal to :

The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:

The remainder when $ \left( (64)^{64} \right)^{64} $ is divided by 7 is equal to:
The product of the last 2 digits of $ (1919)^{1919} $ is:
The greatest value of \( n \), where \( n \in \mathbb{N} \), such that \( 3^n \) divides \( 50! \) is:
The remainder, when \(7^{98}\) is divided by 23, is equal to:
The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is _____.
The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3, is equal to ______.
Let $[t]$ be the greatest integer less than or equal to t. Let A be the set of all prime factors of 2310 and $f: A \to \mathbb{Z}$ be the function $f(x) = \left[ \log_2 \left( x^2 + \left[ \frac{x^3}{5} \right] \right) \right]$. The number of one-to-one functions from A to the range of f is: