x (x^ n-1 -n a^ n-1 ) a^n(n-1) is divisible by (x-a)^2 for - Vidyadip

MCQ

$x\left(x^{n-1}-n a^{n-1}\right) a^n(n-1)$ is divisible by $(x-a)^2$ for

A
$n > 1$
B
$n > 2$
✓
all $n \in N$
D
None of the above

✓

Answer

Correct option: C.

all $n \in N$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Principle of Mathematical Induction→Principle of Mathematical Induction — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Statement$-1:$ The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is $^9C_3 .$

Statement$-2:$ The number of ways of choosing any $3$ places from $9$ different places is $^9C_3 $.

There are $30$ questions in a multiple-choice test.$A$ student gets $1$ mark for each unattempted question, $0$ mark for each wrong answer and $4$ marks for each correct answer. A student answered $x$ questions correctly and scored $60$.Then, the number of possible value of $x$ is

The radius of circle $x^2+ y^2 - 6x - 8y = 0:$

The probability that $A$ speaks truth is $\frac{4}{5}$, while this probability for $B$ is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact

The period of the function $f(\theta ) = \sin \frac{\theta }{3} + \cos \frac{\theta }{2}$ is

If the straight line $y = mx$ is outside the circle ${x^2} + {y^2} - 20y + 90 = 0$, then

What is the equation of the locus of a point which moves such that $4$ times its distance from the $x$-axis is the square of its distance from the origin

Area of the triangle formed by the points $((a + 3)(a + 4), a + 3), ((a + 2)(a + 3), (a + 2))$ and $((a + 1)(a + 2), (a + 1))$ is:

A person write $4$ letters and addresses $4$ envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is

The means of five observations is $4$ and their variance is $5.2$. If three of these observations are $1, 2$ and $6$, then the other two are