New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Limits Continuity and Differentiability question

2021 · 17 Mar · Shift 2 · Q31

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 17 Mar · Shift 2 · Q31

Limits Continuity and Differentiability question

2021 · 17 Mar · Shift 2 · Q31

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

The value of

\mathop {\lim }\limits_{n \to \infty } {{[r] + [2r] + ... + [nr]} \over {{n^2}}}

, where r is a non-zero real number and [r] denotes the greatest integer less than or equal to r, is equal to :

A
r
B
${r \over 2}$
C
0
D
2r

More from Limits Continuity and Differentiability

If $x \to 0 lim \frac{s i n ^{- 1} x - t a n ^{- 1} x}{3 x ^{3}}$ is equal to L, then the value of (6L + 1) is2021 · MCQ
If $f (x) = {\frac{1}{∣ x ∣} a x^{2} + b; ∣ x ∣ \geq 1; ∣ x ∣ < 1$ is differentiable at every point of the domain, then the values of a and b are respectively :2021 · MCQ
Let $f : R \to R$ be a function defined as $f (x) = ⎩ ⎨ ⎧ \frac{sin ( a + 1 ) x + sin 2 x}{2 x} b \frac{x + b x ^{3} - x}{b x ^{5/2}} if x < 0 if x = 0 if x > 0$ …2021 · MCQ
Let f : R $\to$ R satisfy the equation f(x + y) = f(x) . f(y) for all x, y $\in$ R and f(x) $e$ 0 for any x $\in$ R. If the function f is differentiable at x = 0 and f'(0) = 3, then $$\mathop {\lim }\limits_{h \to 0} {1 \over h}(f(h) -…2021 · Numerical
Let a function f : R $\to$ R be defined as $f (x) = ⎩ ⎨ ⎧ sin x - e^{x} a + [- x] 2 x - b i f i f i f x \leq 0 0 < x < 1 x \geq 1$ …2021 · MCQ
If the value of $x \to 0 lim (2 - cos x cos 2 x)^{(\frac{x + 2}{x ^{2}})}$ is equal to ea, then a is equal to .2021 · Numerical
If $f : R \to R$ is given by $f (x) = x + 1$ , then the value of $n \to \infty lim \frac{1}{n} [f (0) + f (\frac{5}{n}) + f (\frac{10}{n}) + ...... + f (\frac{5 ( n - 1 )}{n})]$ …2021 · MCQ
Let a function $g : [0, 4] \to R$ be defined as $g (x) = {0 \leq t \leq x max {t^{3} - 6 t^{2} + 9 t - 3} 4 - x 0 \leq x \leq 3 3 < x \leq 4$ then the number of…2021 · Numerical