Let $f(x)=x^{2},\ x\in\mathbb{R}$. For any $A\subseteq\mathbb{R}$, define $g(A)={,x\in\mathbb{R}:\ f(x)\in A,}$. If $S=[0,4]$, then which one of the following statements is not true?
Previous 10 Questions — JEE Main 2019 (10 April Morning Shift)
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If $\displaystyle \lim_{x\to1}\frac{x^{4}-1}{x-1}=\lim_{x\to k}\frac{x^{3}-k^{3}}{x^{2}-k^{2}}$, then $k$ is:
Topic: JEE Main 2019 (10 April Morning Shift)
If a directrix of a hyperbola centred at the origin and passing through the point $(4,-2\sqrt{3})$ is $5x=4\sqrt{5}$ an…
Topic: JEE Main 2019 (10 April Morning Shift)
If$f(x) = \left\{ {\matrix{
{{{\sin (p + 1)x + \sin x} \over x}} & {,x < 0} \cr
q & {,x = 0} \cr
…
Topic: JEE Main 2019 (10 April Morning Shift)
If $\displaystyle \int \frac{dx}{(x^{2}-2x+10)^{2}} = A\left(\tan^{-1}\left(\frac{x-1}{3}\right) + \frac{f(x)}{x^{2}-2x…
Topic: JEE Main 2019 (10 April Morning Shift)
The value of $\displaystyle \int_{0}^{2\pi}\big\lfloor \sin 2x,(1+\cos 3x)\big\rfloor,dx$, where $[\cdot]$ denotes the …
Topic: JEE Main 2019 (10 April Morning Shift)
Let $f:\mathbb{R}\to\mathbb{R}$ be differentiable at $c\in\mathbb{R}$ and $f(c)=0$. If $g(x)=|f(x)|$, then at $x=c$, $g…
Topic: JEE Main 2019 (10 April Morning Shift)
Let $A(3,0,-1),; B(2,10,6)$ and $C(1,2,1)$ be the vertices of a triangle and $M$ be the midpoint of $AC$. If $G$ divide…
Topic: JEE Main 2019 (10 April Morning Shift)
If the system of linear equations$x+y+z=5$$x+2y+2z=6$$x+3y+\lambda z=\mu,; (\lambda,\mu\in\mathbb{R})$has infinitely ma…
Topic: JEE Main 2019 (10 April Morning Shift)
If for some $x\in\mathbb{R}$, the frequency distribution of the marks obtained by $20$ students in a test is:then the m…
Topic: JEE Main 2019 (10 April Morning Shift)
The number of $6$-digit numbers that can be formed using the digits $0,1,2,5,7,9$ which are divisible by $11$ and no di…
Topic: JEE Main 2019 (10 April Morning Shift)
