For $a\in R$ (the set of al real numbers), $a \ne 1$, $\lim _{{n}\rightarrow\infty}\frac{({1}^a+{2}^a+{\ldots+{n}^a})}{{(n+1)}^{a-1}\lbrack(na+1)+(na+2)+\ldots+(na+n)\rbrack}=\frac{1}{60}$ . Then one of the value of $a$ is
Previous 10 Questions — NIMCET 2022
Nearest first
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A four-digit number is formed using the
digits 1, 2, 3, 4, 5 without repetition. The
probability that is divisible by…
Topic: NIMCET 2022
Area of the parallelogram formed by the
lines y=4x, y=4x+1, x+y=0 and x+y=1
Topic: NIMCET 2022
If $D={\begin{vmatrix}{1} & 1 & {1} \\ 1 & {2+x} & {1} \\ {1} & {1} & {2+y}\end{vmatrix}}\, for\, x\ne0,\, y\ne0$ then …
Topic: NIMCET 2022
If ${{a}}_1,{{a}}_2,\ldots,{{a}}_n$ are any real numbers and $n$ is
any positive integer, then
Topic: NIMCET 2022
$f(x)=x+|x|$ is continuous for
Topic: NIMCET 2022
Which of the following is NOT true?
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If $0{\lt}P(A){\lt}1$ and $0{\lt}P(B){\lt}1$ and $P(A\cap B)=P(A)P(B)$, then
Topic: NIMCET 2022
The value of $\cot \Bigg{(}{cosec}^{-1}\frac{5}{3}+{\tan }^{-1}\frac{2}{3}\Bigg{)}$ is
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A survey is done among a population of 200 people who like either tea or coffee. It is found that 60% of the pop lation…
Topic: NIMCET 2022
The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distributio…
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Next 10 Questions — NIMCET 2022
Ascending by ID
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If $\vec{a}=\lambda \hat{i}+\hat{j}-2\hat{k}$ , $\vec{b}=\hat{i}+\lambda \hat{j}-2\hat{k}$ and $\vec{c}=\hat{i}+\hat{j}…
Topic: NIMCET 2022
The function $f(x)=\log (x+\sqrt[]{{x}^2+1})$ is
Topic: NIMCET 2022
The mean of 25 observations was found to be 38. It was later discovered that 23 and 38 were misread as 25 and 36, then…
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The area enclosed within the curve |x|+|y|=2 is
Topic: NIMCET 2022
If ${\Bigg{(}\frac{x}{a}\Bigg{)}}^2+{\Bigg{(}\frac{y}{b}\Bigg{)}}^2=1$, $(a{\gt}b)$ and ${x}^2-{y}^2={c}^2$ cut at righ…
Topic: NIMCET 2022
If $\alpha , \beta$ are the roots of $x^2-x-1=0$ and $A_n=\alpha^n+\beta^n$, the Arithmetic mean of $A_{n-1}$ and $A_n$…
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If $a_1, a_2, a_3,...a_n$, are in Arithmetic Progression
with common difference d, then the sum $(sind) (cosec a_1 . c…
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Solutions of the equation ${\tan }^{-1}\sqrt[]{{x}^2+x}+{\sin }^{-1}\sqrt[]{{x}^2+x+1}=\frac{\pi}{2}$ are
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In a Harmonic Progression, $p^{th}$ term is $q$ and
the $q^{th}$ term is $p$. Then $pq^{th}$ term is
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If the roots of the quadratic equation $x^2+px+q=0$ are tan 30° and tan 15°
respectively, then the value of 2 + p - q …
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