Let S be the sample space of all five digit numbers. It p is the probability that a randomly selected number from S, is multiple of 7 but not divisible by 5, then 9p is equal to
Let S be the sample space of all five digit numbers. It p is the probability that a randomly selected number from S, is multiple of 7 but not divisible by 5, then 9p is equal to
- 1.0146
- 1.2085
- 1.0285
- 1.1521
The Correct Option is C
Solution and Explanation
The correct answer is (C):
Among the 5 digit numbers,
First number divisible by 7 is 10003 and last is 99995.
⇒ Number of numbers divisible by 7.
= \(\frac{99995-10003}{7} + 1\)
= 12875
First number divisible by 35 is 10010 and last is 99995.
⇒ Number of numbers divisible by 35 =\(\frac{ 99995-10010}{35}+1 = 2572\)
Hence number of number divisible by 7 but not by 5
= 12857 – 2572
= 10285
9P =\( \frac{10285}{90000} × 9\)
= 1.0285
Top Questions on types of differential equations
- If \( (1,1) \) is the vertex and \( x + y + 1 = 0 \) is the directrix of a parabola. If \( (a, b) \) is its focus and \( (c, d) \) is the point of intersection of the directrix and the axis of the parabola, then \( a + b + c + d \) is:
- TS EAMCET - 2024
- Mathematics
- types of differential equations
- A circle \( S \) passes through the points of intersection of the circles \( x^2 + y^2 - 2x - 3 = 0 \) and \( x^2 + y^2 - 2y = 0 \). If \( x + y + 1 = 0 \) is a tangent to the circle \( S \), then the equation of \( S \) is:
- TS EAMCET - 2024
- Mathematics
- types of differential equations
- If \( (2,3) \) is the focus and \( x - y + 3 = 0 \) is the directrix of a parabola, then the equation of the tangent drawn at the vertex of the parabola is:
- TS EAMCET - 2024
- Mathematics
- types of differential equations
- The equation of the common tangent to the parabola \(y^2 = 8x\) and the circle \(x^2 + y^2 = 2\) is \(ax + by + 2 = 0\). If \(-\frac{a}{b}>0\), then \(3a^2 + 2b + 1 =\)
- TS EAMCET - 2024
- Mathematics
- types of differential equations
- If \( m_1 \) and \( m_2 \) are the slopes of the direct common tangents drawn to the circles \[ x^2 + y^2 - 2x - 8y + 8 = 0 \quad \text{and} \quad x^2 + y^2 - 8x + 15 = 0 \] then \( m_1 + m_2 \) is:
- TS EAMCET - 2024
- Mathematics
- types of differential equations
Questions Asked in JEE Main exam
Match List-I with List-II.
Choose the correct answer from the options given below :- JEE Main - 2025
- Thermodynamics
- Let \( y = f(x) \) be the solution of the differential equation\[\frac{dy}{dx} + \frac{xy}{x^2 - 1} = \frac{x^6 + 4x}{\sqrt{1 - x^2}}, \quad -1 < x < 1\] such that \( f(0) = 0 \). If \[6 \int_{-1/2}^{1/2} f(x)dx = 2\pi - \alpha\] then \( \alpha^2 \) is equal to __________.
- JEE Main - 2025
- Differential equations
- Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is:
- JEE Main - 2025
- Statistics
- Let the system of equations $ x + 5y - z = 1 $ $ 4x + 3y - 3z = 7 $ $ 24x + y + \lambda z = \mu $ where $ \lambda, \mu \in \mathbb{R} $, have infinitely many solutions. Then the number of the solutions of this system, if $x, y, z$ are integers and satisfy $7 \leq x + y + z \leq 77$, is:
- JEE Main - 2025
- Linear Systems and Determinants
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
Concepts Used:
Types of Differential Equations
There are various types of Differential Equation, such as:
Ordinary Differential Equations:
Ordinary Differential Equations is an equation that indicates the relation of having one independent variable x, and one dependent variable y, along with some of its other derivatives.
\(F(\frac{dy}{dt},y,t) = 0\)
Partial Differential Equations:
A partial differential equation is a type, in which the equation carries many unknown variables with their partial derivatives.
Linear Differential Equations:
It is the linear polynomial equation in which derivatives of different variables exist. Linear Partial Differential Equation derivatives are partial and function is dependent on the variable.
Homogeneous Differential Equations:
When the degree of f(x,y) and g(x,y) is the same, it is known to be a homogeneous differential equation.
\(\frac{dy}{dx} = \frac{a_1x + b_1y + c_1}{a_2x + b_2y + c_2}\)
Read More: Differential Equations