JEE Mains · Maths · STD 11 - 1. set theory
The number of elements in the set \(\left\{n \in Z :\left|n^2-10 n+19\right| < 6\right\}\) is \(...........\)
- A \(12\)
- B \(18\)
- C \(24\)
- D \(6\)
Answer & Solution
Correct Answer
(D) \(6\)
Step-by-step Solution
Detailed explanation
\(-6 < n ^2-10 n +19 < 6\) \(\Rightarrow n^2-10 n+25 > 0 \text { and } n ^2-10 n +13 < ( n -5)^2 >\) \(0 n \in[5-2 \sqrt{3}, 5+2 \sqrt{3}]\) \(n \in R-[5]\) \(\therefore n \in[1.3,8.3]\) \(\Rightarrow n=2,3,4,6,7,8\)
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
- For \(x \in \left( {0,\frac{3}{2}} \right)\), let \(f\left( x \right) = \sqrt x \), \(g\left( x \right) = \tan \,x\) and \(h\left( x \right) = \frac{{1 - {x^2}}}{{1 + {x^2}}}\). If \(\phi \left( x \right) = \left( {\left( {hof} \right)og} \right)\left( x \right)\), then \(\phi \left( {\frac{\pi }{3}} \right)\) is equal toJEE Mains 2019 Hard
- If one end of a focal chord of the parabola, \(y^2 = 16x\) is at \((1, 4),\) then the length of this focal chord isJEE Mains 2019 Hard
- The probabilities that players \(A\) and \(B\) of a team are selected for the captaincy for a tournament are \(0.6\) and \(0.4\), respectively. If \(A\) is selected the captain, the probability that the team wins the tournament is \(0.8\) and if \(B\) is selected the captain, the probability that the team wins the tournament is \(0.7\). Then the probability, that the team wins the tournament, is :JEE Mains 2026 Easy
- If \({ }^{2 n+1} P_{n-1}:{ }^{2 n-1} P_n=11: 21\), then \(n^2+n+15\) is equal to:JEE Mains 2023 Hard
- If the sum of the first \(20\) terms of the series \(\log _{\left(7^{\frac{1}{2}}\right)} x+\log _{\left(7^{\frac{1}{3}}\right)} x+\log _{\left(7^{\frac{1}{4}}\right)} x+\ldots\) is \(460,\) then \(x\) is equal toJEE Mains 2020 Hard
- The shortest distance between the lines \(x+1=2 y=-\) \(12 z\) and \(x=y+2=6 z-6\) isJEE Mains 2023 Easy
More PYQs from JEE Mains
- Let the system of linear equations \(4 x+\lambda y+2 z=0\) ; \(2 x-y+z=0\) ; \(\mu x +2 y +3 z =0, \lambda, \mu \in R\) has a non-trivial solution. Then which of the following is true?JEE Mains 2021 Hard
- If the range of the function \(f(x)=\frac{5-x}{x^2-3 x+2}\), \(x \neq 1,2\), is \((-\infty, \alpha] \cup[\beta, \infty)\), then \(\alpha^2+\beta^2\) is equal to:JEE Mains 2025 Medium
- If the tangents drawn at the point \(O (0,0)\) and \(P (1+\sqrt{5}, 2)\) on the circle \(x ^{2}+ y ^{2}-2 x -4 y =0\) intersect at the point \(Q\), then the area of the triangle \(OPQ\) is equal toJEE Mains 2022 Hard
- The term independent of \(x\) in the expansion of \(\left(\frac{(x+1)}{\left(x^{2 / 3}+1-x^{1 / 3}\right)}-\frac{(x+1)}{\left(x-x^{1 / 2}\right)}\right)^{10}, x\gt1\) is:JEE Mains 2025 Medium
- If the line \(3 x-2 y+12=0\) intersects the parabola \(4 y=3 x^2\) at the points \(A\) and \(B\), then at the vertex of the parabola, the line segment \(A B\) subtends an angle equal toJEE Mains 2025 Medium
- \( \text { If } S(x)=(1+x)+2(1+x)^2+3(1+x)^3+\ldots . \) \( +60(1+x)^{60}, x \neq 0 \text {, and }(60)^2 S(60)=a(b)^b+b\) where \(a, b N\), then \((a+b)\) equal to ...............JEE Mains 2024 Hard