1
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let $f(x)=\max \{x+|x|, x-[x]\}$, where $[x]$ stands for the greatest integer not greater than $x$. Then $\int\limits_{-3}^3 f(x) d x$ has the value

A
$\frac{51}{2}$
B
$\frac{21}{2}$
C
1
D
0
2
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

If $a, b, c$ are in A.P. and if the equations $(b-c) x^2+(c-a) x+(a-b)=0$ and $2(c+a) x^2+(b+c) x=0$ have a common root, then

A
$a^2, b^2, c^2$ are in A.P.
B
$a^2, c^2, b^2$ are in A.P.
C
$c^2, a^2, b^2$ are in A.P.
D
$a^2, b^2, c^2$ are in G.P.
3
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let $x-y=0$ and $x+y=1$ be two perpendicular diameters of a circle of radius $R$. The circle will pass through the origin if $R$ is equal to

A
$\frac{1}{2}$
B
$\frac{1}{\sqrt{2}}$
C
$\frac{1}{\sqrt{3}}$
D
$\frac{1}{3}$
4
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let $f(x)=|x-\alpha|+|x-\beta|$, where $\alpha, \beta$ are the roots of the equation $x^2-3 x+2=0$. Then the number of points in $[\alpha,\beta]$ at which $f$ is not differentiable is

A
2
B
0
C
1
D
infinite
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