>
Exams
>
Mathematics
>
Principle of Mathematical Induction
>
if n 10 100 and n n then how many such n are possi
Question:
If n
\(\in\)
[10,100] and n
\(\in\)
N, then how many such n are possible where 3n - 3 is divisible by 7?
JEE Main - 2023
JEE Main
Updated On:
Mar 21, 2025
Hide Solution
Verified By Collegedunia
Solution and Explanation
Correct answer is 15.
Download Solution in PDF
Was this answer helpful?
1
8
Top Questions on Principle of Mathematical Induction
Sum of the series
\(\frac {1}{1-3.1^2+1^4}+\frac {2}{1-3.2^2+2^4}+\frac {3}{1-3.3^2+3^4}\)
upto
\(10\)
terms is _____ .
JEE Main - 2024
Mathematics
Principle of Mathematical Induction
View Solution
The given series
\(\frac{x}{1.3}+\frac{x^2}{2.4}+\frac{x^3}{3.5}+......,(x\gt0)\)
is convergent in the interval
CUET (PG) - 2023
Mathematics
Principle of Mathematical Induction
View Solution
If
\(f(z)=\frac{1}{z^2-3z+2}\)
is expanded in the region |z|<1, then
CUET (PG) - 2023
Mathematics
Principle of Mathematical Induction
View Solution
The infinite series
\(\displaystyle\sum_{n=1}^{∞} \frac{3^n}{4^{n+2}}\)
is:
CUET (PG) - 2023
Mathematics
Principle of Mathematical Induction
View Solution
The value of
\(\lim\limits_{n \to \infty} \frac{1}{n} [1+2^{\frac{1}{2}}+3^{\frac{1}{3}}+...n^{\frac{1}{n}}]\)
is
CUET (PG) - 2023
Mathematics
Principle of Mathematical Induction
View Solution
View More Questions
Questions Asked in JEE Main exam
The product B formed in the following reaction sequence is:
\[ {C}_6{H}_5{CN} \xrightarrow{{HCl}} (A) \xrightarrow{{AgCN}} (B) \]
JEE Main - 2025
Organic Chemistry
View Solution
What are the units of viscosity, intensity of wave, and pressure gradient?
JEE Main - 2025
Units and measurement
View Solution
If the system of equations
\[ (\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 \] \[ \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 \] \[ (\lambda + 1)x + (\lambda + 2)y - (\lambda + 2)z = 9 \]
has infinitely many solutions, then \( \lambda^2 + \lambda \) is equal to:
JEE Main - 2025
Matrices and Determinants
View Solution
Let \( P_n = \alpha^n + \beta^n \), \( P_{10} = 123 \), \( P_9 = 76 \), \( P_8 = 47 \), and \( P_1 = 1 \). The quadratic equation whose roots are \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \) is:
JEE Main - 2025
Sequences and Series
View Solution
The distance of the point \( P(1, 2, 3) \) from the plane \( 3x - 4y + 12z - 7 = 0 \) is:
JEE Main - 2025
Geometry and Vectors
View Solution
View More Questions