JEE Mains · Maths · STD 11 - 14. probability
Let \(S=\{1,2,3, \ldots, 2022\}\). Then the probability, that a randomly chosen number \(n\) from the set \(S\) such that \(\operatorname{HCF}( n , 2022)=1\), is.
- A \(\frac{128}{1011}\)
- B \(\frac{166}{1011}\)
- C \(\frac{127}{337}\)
- D \(\frac{112}{337}\)
Answer & Solution
Correct Answer
(D) \(\frac{112}{337}\)
Step-by-step Solution
Detailed explanation
Total number of elements \(=2022\) \(2022=2 \times 3 \times 337\) \(\operatorname{HCF}( n , 2022)=1\) is feasible when the value of ' \(n\) ' and \(2022\) has no common factor. \(A=\) Number which are divisible by \(2\) from \(\{1,2,3 \ldots . .2022\}\) \(n ( A )=1011\) \(B =\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls isJEE Mains 2019 Hard
- Let \(A = \left\{ {\left( {x,y} \right):{y^2} \le 4x,y - 2x \ge - 4} \right\}\) .The area of the region \(A\) isJEE Mains 2014 Hard
- A plane \(E\) is perpendicular to the two planes \(2 x -2 y + z =0\) and \(x - y +2 z =4\), and passes through the point \(P (1,-1,1)\). If the distance of the plane \(E\) from the point \(Q(a, a, 2)\) is \(3 \sqrt{2}\), then \(( PQ )^{2}\) is equal toJEE Mains 2022 Hard
- For three events \(A,B \) and \(C\) ,\(P (\) Exactly one of \(A\) or \(B\) occurs\()\, =\, P (\) Exactly one of \(C\) or \(A\) occurs \() =\) \(\frac{1}{4}\) and \(P (\) All the three events occur simultaneously \() =\) \(\frac{1}{16}\) Then the probability that at least one of the events occurs is :JEE Mains 2017 Hard
- Let the slope of the tangent to a curve \(y=f(x)\) at \((x, y)\) be given by \(2 \tan x(\cos x-y)\). if the curve passes through the point \((\frac{\pi}{4},0)\), then the value of \(\int \limits_{0}^{\pi / 2} y d x\) is equal toJEE Mains 2022 Hard
- Let the solution curve of the differential equation \(x \frac{d y}{d x}-y=\sqrt{y^{2}+16 x^{2}}, y(1)=3\) be \(y=y(x)\). Then \(y (2)\) is equal toJEE Mains 2022 Medium
More PYQs from JEE Mains
- Two tangents are drawn from a point \(P\) to the circle \(x^{2}+y^{2}-2 x-4 y+4=0\), such that the angle between these tangents is \(\tan ^{-1}\left(\frac{12}{5}\right)\), where \(\tan ^{-1}\left(\frac{12}{5}\right) \in(0, \pi)\). If the centre of the circle is denoted by \(C\) and these tangents touch the circle at points \(A\) and \(B\), then the ratio of the areas of \(\Delta PAB\) and \(\Delta CAB\) is :JEE Mains 2021 Hard
- \(\lim _{x \rightarrow \infty} \frac{\left(2 x^2-3 x+5\right)(3 x-1)^{\frac{x}{2}}}{\left(3 x^2+5 x+4\right) \sqrt{(3 x+2)^x}}\) is equal to :JEE Mains 2025 Medium
- Two parabolas with a common vertex and with axes along \(x-\) axis and \(y-\) axis, respectively, intersect each other in the first quadrant. if the length of the latus rectum of each parabola is \(3\) , then the equation of the common tangent to the two parabolas is?JEE Mains 2018 Hard
- \(\smallint \left( {1 + x - \frac{1}{x}} \right){e^{x + \frac{1}{x}}}\;dx = \)JEE Mains 2014 Hard
- Let the slope of the line \(45 x+5 y+3=0\) be \(27 r_1+\frac{9 r_2}{2} \quad\) for some \(r_1, \quad r_2 \in R\). Then \(\operatorname{Lim}_{x \rightarrow 3}\left(\int_3^\pi \frac{8 t^2}{\frac{3 r_2 x}{2}-r_2 x^2-r_1 x^3-3 x} d t\right)\) is equal to ...........JEE Mains 2024 Hard
- Equation of the tangent to the circle, at the point \((1 , -1)\) whose centre is the point of intersection of the straight lines \(x - y = 1\) and \(2x + y= 3\) isJEE Mains 2016 Hard