>
Exams
>
Mathematics
>
Sequence and series
>
if f x 1 nx n n 1 2 x 2 n n 1 n 2 6 x 3 x n then f
Question:
If f(x) = 1 + nx +
\(\frac{n(n-1)}{2}x^2+\frac{n(n-1)(n-2)}{6}x^3+...+x^n\)
then f"(1) =
KCET - 2023
KCET
Updated On:
Apr 17, 2024
n(n - 1) 2
n
(n - 1) 2
n-1
2
n-1
n(n - 1)2
n-2
Hide Solution
Verified By Collegedunia
The Correct Option is
D
Solution and Explanation
The correct answer is (D) : n(n - 1)2
n-2
.
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on Sequence and series
The function \( f(x) = 2x + 3(x)^{\frac{2}{3}}, x \in \mathbb{R} \), has
JEE Main - 2024
Mathematics
Sequence and series
View Solution
If three successive terms of a G.P. with common ratio $r \, (r>1)$ are the lengths of the sides of a triangle and $\lfloor r \rfloor$ denotes the greatest integer less than or equal to $r$, then $3\lfloor r \rfloor + \lfloor -r \rfloor$ is equal to:
JEE Main - 2024
Mathematics
Sequence and series
View Solution
Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10} = 390$ and the ratio of the tenth and the fifth terms is $15 : 7$, then $S_{15} - S_{5}$ is equal to:
JEE Main - 2024
Mathematics
Sequence and series
View Solution
Let \( x_1, x_2, x_3, x_4 \) be the solution of the equation \[ 4x^4 + 8x^3 - 17x^2 - 12x + 9 = 0 \] and \[ \left(4 + x_1^2\right)\left(4 + x_2^2\right)\left(4 + x_3^2\right)\left(4 + x_4^2\right) = \frac{125}{16} m.\] Then the value of \( m \) is ______.
JEE Main - 2024
Mathematics
Sequence and series
View Solution
Let \( \alpha, \beta \) be the distinct roots of the equation \[ x^2 - (t^2 - 5t + 6)x + 1 = 0, \, t \in \mathbb{R} \, \text{and} \, a_n = \alpha^n + \beta^n.\] Then the minimum value of \( \frac{a_{2023} + a_{2025}}{a_{2024}} \) is:
JEE Main - 2024
Mathematics
Sequence and series
View Solution
View More Questions
Questions Asked in KCET exam
The speed of sound in an ideal gas at a given temperature T is v. The rms speed of gas molecules at that temperature is v
rms
. The ratio of the velocities v and v
rms
for helium and oxygen gases are X and X' respectively. Then
\(\frac{X}{X'}\)
is equal to
KCET - 2023
Thermodynamics
View Solution
If
\(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\)
are in A.P., then p, q, r
KCET - 2023
Arithmetic Progression
View Solution
A stretched wire of a material whose Young's modulus Y = 2 × 10
11
Nm
-2
has Poisson's ratio of 0.25. Its lateral strain ε
l
= 10
-3
. The elastic energy density of the wire is
KCET - 2023
mechanical properties of solids
View Solution
A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth’s magnetic field B
H
= 3 × 10
-5
T. The emf induced in the rod at an instant t = 2s after it is released is ( Take g = 10 ms
-2
)
KCET - 2023
Faradays laws of induction
View Solution
A 60 W source emits monochromatic light of wavelength 662.5 nm. The number of photons emitted per second is
KCET - 2023
Quantum Physics
View Solution
View More Questions