Let g(x) = $\int_0^x {f(t)dt} $, where f is continuous function in [ 0, 3 ] such that ${1 \over 3}$ $ \le $ f(t) $ \le $ 1 for all t$\in$ [0, 1] and 0 $ \le $ f(t) $ \le $ ${1 \over 2}$ for all t$\in$ (1, 3]. The largest possible interval in which g(3) lies is :
Previous 10 Questions — JEE Main 2021 (18 March Evening Shift)
Nearest first
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Let \; f:\mathbb{R}\to\mathbb{R} \text{ be defined as}
\[
f(x) =
\begin{cases}
\dfrac{\sin\!\big((a+1)x\big)+\sin 2x}{2…
Topic: JEE Main 2021 (18 March Evening Shift)
Let a complex number be w = 1 $-$ ${\sqrt 3 }$i. Let another complex number z be such that |zw| = 1 and arg(z) $-$ arg(…
Topic: JEE Main 2021 (18 March Evening Shift)
Let $\overrightarrow a $ and $\overrightarrow b $ be two non-zero vectors perpendicular to each other and $|\overrighta…
Topic: JEE Main 2021 (18 March Evening Shift)
If 15sin4$\alpha$ + 10cos4$\alpha$ = 6, for some $\alpha$$\in$R, then the value of 27sec6$\alpha$ + 8cosec6$\alpha$ is…
Topic: JEE Main 2021 (18 March Evening Shift)
The area bounded by the curve 4y2 = x2(4 $-$ x)(x $-$ 2) is equal to :
Topic: JEE Main 2021 (18 March Evening Shift)
Let the system of linear equations4x + $\lambda$y + 2z = 0 ,2x $-$ y + z = 0 , $\mu$x + 2y + 3z = 0, $\lambda$, $\mu$$\…
Topic: JEE Main 2021 (18 March Evening Shift)
If 15sin4$\alpha$ + 10cos4$\alpha$ = 6, for some $\alpha$$\in$R, then the value of 27sec6$\alpha$ + 8cosec6$\alpha$ is …
Topic: JEE Main 2021 (18 March Evening Shift)
Next 10 Questions — JEE Main 2021 (18 March Evening Shift)
Ascending by ID
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Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $-$a. Also by adding a …
Topic: JEE Main 2021 (18 March Evening Shift)
In a triangle ABC, if $|\overrightarrow {BC} | = 8,|\overrightarrow {CA} | = 7,|\overrightarrow {AB} | = 10$, then the …
Topic: JEE Main 2021 (18 March Evening Shift)
Define a relation R over a class of n $\times$ n real matrices A and B as "ARB iff there exists a non-singular matrix P…
Topic: JEE Main 2021 (18 March Evening Shift)
Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be a…
Topic: JEE Main 2021 (18 March Evening Shift)
Let f : R $-$ {3} $ \to $ R $-$ {1} be defined by f(x) = ${{x - 2} \over {x - 3}}$.Let g : R $ \to $ R be given as g(x)…
Topic: JEE Main 2021 (18 March Evening Shift)
Let S1 be the sum of first 2n terms of an arithmetic progression. Let S2 be the sum of first 4n terms of the same arith…
Topic: JEE Main 2021 (18 March Evening Shift)
