JEE Mains · Maths · STD 11 - 8. sequence and series
The mean of \(10\) numbers \(7 \times 8,10 \times 10,13 \times 12,16 \times 14, \ldots .\) is ....... .
- A \(3980\)
- B \(213\)
- C \(313\)
- D \(398\)
Answer & Solution
Correct Answer
(D) \(398\)
Step-by-step Solution
Detailed explanation
\(7 \times 8,10 \times 10,13 \times 12,16 \times 14 \ldots \ldots\) \(\mathrm{T}_{\mathrm{n}}=(3 \mathrm{n}+4)(2 \mathrm{n}+6)=2(3 \mathrm{n}+4)(\mathrm{n}+3)\) \(=2\left(3 \mathrm{n}^{2}+13 \mathrm{n}+12\right)=6 \mathrm{n}^{2}+26 \mathrm{n}+24\)…
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
- Let the distance between two parallel lines be 5 units and a point \(P\) lie between the lines at a unit distance from one of them. An equilateral triangle \(P Q R\) is formed such that \(Q\) lies on one of the parallel lines, while \(R\) lies on the other. Then \((Q R)^2\) is equal to _______ -.JEE Mains 2025 Medium
- If \(10\) different balls are to be placed in \(4\) distinct boxes at random, then the probability that two of these boxes contain exactly \(2\) and \(3\) balls isJEE Mains 2020 Hard
- Let \(f(x)=2+|x|-|x-1|+|x+1|, x \in R\). Consider \((S1)\): \(f^{\prime}\left(-\frac{3}{2}\right)+f^{\prime}\left(-\frac{1}{2}\right)+f^{\prime}\left(\frac{1}{2}\right)+f^{\prime}\left(\frac{3}{2}\right)=2\) \(( S 2): \int_{-2}^{2} f ( x ) dx =12\)Then,JEE Mains 2022 Hard
- Two marbles are drawn in succession from a box containing \(10\) red, \(30\) white, \(20\) blue and \(15\) orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, isJEE Mains 2024 Medium
- For some \(\mathrm{a}, \mathrm{b}\), let \(f(x)=\left|\begin{array}{ccc}\mathrm{a}+\frac{\sin x}{x} & 1 & \mathrm{~b} \\ \mathrm{a} & 1+\frac{\sin x}{x} & \mathrm{~b} \\ \mathrm{a} & 1 & \mathrm{~b}+\frac{\sin x}{x}\end{array}\right|, x \neq 0, \lim _{x \rightarrow 0} f(x)=\lambda+\mu \mathrm{a}+\nu \mathrm{b}\). Then \((\lambda+\mu+v)^2\) is equal to :JEE Mains 2025 Medium
- Let the function,
\(f(x)= \begin{cases}-3 a x^2-2, & x \lt 1 \\ a^2+b x, & x \geqslant 1\end{cases}\)
be differentiable for all \(x \in \mathbf{R}\), where \(\mathbf{a}\gt1, \mathbf{b} \in \mathbf{R}\). If the area of the region enclosed by \(y=f(x)\) and the line \(y=-20\) is \(\alpha+\beta \sqrt{3}, \alpha, \beta \in Z\), then the value of \(\alpha+\beta\) is ________JEE Mains 2025 Hard
More PYQs from JEE Mains
- If \(m\) and \(M\) are the minimum and the maximum values of \(4 + \frac{1}{2}\,{\sin ^2}\,2x - 2\,{\cos ^4}\,x\,,x\, \in R,\) then \(M - m\) is equal toJEE Mains 2016 Hard
- The mean and variance of \(n\) observations are \(8\) and \(16\), respectively. If the sum of the first \((n-1)\) observations is \(48\) and the sum of squares of the first \((n-1)\) observations is \(496\), then the value of \(n\) is:JEE Mains 2026 Medium
- Let \(g: R \rightarrow R\) be a non constant twice differentiable such that \(g^{\prime}\left(\frac{1}{2}\right)=g^{\prime}\left(\frac{3}{2}\right)\). If a real valued function \(f\) is defined as \(\mathrm{f}(\mathrm{x})=\frac{1}{2}[\mathrm{~g}(\mathrm{x})+\mathrm{g}(2-\mathrm{x})]\), thenJEE Mains 2024 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
- The tangent and normal to the ellipse \(3x^2 + 5y^2 = 32\) at the point \(P(2, 2)\) meet the \(x-\) axis at \(Q\) and \(R,\) respectively. Then the area(in sq. units) of the triangle \(PQR\) isJEE Mains 2019 Hard
- If \(\sum_{r=1}^{30} \frac{r^2\left({ }^{30} C_r\right)^2}{{ }^{30} C_{r-1}}=\alpha \times 2^{29}\), then \(\alpha\) is equal to ______JEE Mains 2025 Hard