JEE Mains · Maths · STD 11 - 8. sequence and series
The sum of all natural numbers \(‘n’\) such that \(100 < n < 200\) and \(H.C. F\, (91, n) > 1\) is
- A \(3221\)
- B \(3303\)
- C \(3203\)
- D \(3121\)
Answer & Solution
Correct Answer
(D) \(3121\)
Step-by-step Solution
Detailed explanation
\({S_A} = \) sum of numbers between \(100\) and \(200\) which are divisible by \(7\). \( \Rightarrow {S_A} = 105 + 112 + ..... + 196\) \({S_A} = \frac{{14}}{2}\left[ {105 + 196} \right] = 2107\) \({S_B} = \) Sum of number between \(100\) and \(200\) which are divisible by…
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
- A board has 16 squares as shown in the figure:
Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :JEE Mains 2025 Easy - Let the coefficients of \(x ^{-1}\) and \(x ^{-3}\) in the expansion of \(\left(2 x^{\frac{1}{5}}-\frac{1}{x^{\frac{1}{5}}}\right)^{15}, x>0\), be \(m\) and \(n\) respectively. If \(r\) is a positive integer such \(m n^{2}={ }^{15} C _{ r } .2^{ r }\), then the value of \(r\) is equal toJEE Mains 2022 Medium
- Let f: \(\mathrm{R} \rightarrow \mathrm{R}\) be defined as \(f(x) \rightarrow \frac{\lambda\left|x^{2}-5 x+6\right|}{\mu\left(5 x-x^{2}-6\right)}, x<2\) \(\quad\quad\quad\quad e^{\frac{\tan (x-2)}{x-[x]}}, \quad x>2\) \(\quad\quad\quad\quad \mu \quad\quad\quad\quad x=2\) Where \([x]\) is the greatest integer less than or equal to \(x\). If \(f\) is continuous at \(x=2\), then \(\lambda+\mu\) is equal to:JEE Mains 2021 Hard
- Let S be the set of the first 11 natural numbers. Then the number of elements in \( A=\{B\subseteq S:n(B)\ge2 \) and the product of all elements of B is even} is ___ .JEE Mains 2026 Medium
- The area of the region, inside the ellipse \( x^{2}+4y^{2}=4 \) and outside the region bounded by the curves \( y=|x|-1 \) and \( y=1-|x| \), is:JEE Mains 2026 Medium
- If the shortest distance between the straight lines \(3(x-1)=6(y-2)=2(z-1)\) and \(4(\mathrm{x}-2)=2(\mathrm{y}-\lambda)=(\mathrm{z}-3), \lambda \in \mathrm{R}\) is \(\frac{1}{\sqrt{38}}\), then the integral value of \(\lambda\) is equal to :JEE Mains 2021 Medium
More PYQs from JEE Mains
- Let \(f : R \rightarrow R\) be defined as \(f ( x )= x ^{3}+ x -5\). If \(g ( x )\) is a function such that \(f ( g ( x ))= x\), \(\forall x \in R\), then \(g ^{\prime}(63)\) is equal toJEE Mains 2022 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(d y=e^{a x+y} d x ; \alpha \in N\). If \(y\left(\log _{e} 2\right)=\log _{e} 2\) and \(y(0)=\log _{e}\left(\frac{1}{2}\right)\), then the value of \(\alpha\) is equal to \(.....\)JEE Mains 2021 Medium
- If \(\alpha \) and \(\beta \) be the roots of the equation \(x^2 - 2x + 2 = 0\) , then the least value of \(n\) for \({\left( {\frac{\alpha }{\beta }} \right)^n} = 1\) isJEE Mains 2019 Hard
- If for some \(p , q , r \in R\), not all have same sign, one of the roots of the equation \(\left(p^{2}+q^{2}\right) x^{2}-2 q(p+r) x\) \(+q^{2}+r^{2}=0\) is also a root of the equation \(x^{2}+2 x-8=0\), then \(\frac{q^{2}+r^{2}}{p^{2}}\) is equal to-JEE Mains 2022 Hard
- If \(A = \left[ {\begin{array}{*{20}{c}}
{\cos \,\theta }&{ - \sin \,\theta }\\
{\sin \,\theta }&{\cos \,\theta }
\end{array}} \right]\), then the matrix \({A^{ - 50}}\) when \(\theta = \frac{\pi }{{12}}\) is equal toJEE Mains 2019 Hard - Let \(f(x)\) be a quadratic polynomial such that \(f(-2)\) \(+f(3)=0\). If one of the roots of \(f(x)=0\) is \(-1\), then the sum of the roots of \(f(x)=0\) is equal toJEE Mains 2022 Hard