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JEE Mathematics / Practice

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Showing 7506-7510 of 7517 questions.

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7506
Let $r_1$ and $r_2$ be the radii of the largest and smallest circles, respectively, which pass through the point $(-4,1)$ and having their centres on the circumference of the circle $x^2+y^2+2x+4y-4=0$. If $\dfrac{r_1}{r_2}=a+b\sqrt{2}$, then $a+b$ is equal to :
Circle
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JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7507
Let $A$, $B$ and $C$ be three events such that the probability that exactly one of $A$ and $B$ occurs is $(1-k)$, the probability that exactly one of $B$ and $C$ occurs is $(1-2k)$, the probability that exactly one of $C$ and $A$ occurs is $(1-k)$ and the probability of all $A$, $B$ and $C$ occur simultaneously is $k^2$, where $0<k<1$. Then the probability that at least one of $A$, $B$ and $C$ occur is :
Probability
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JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7508
The value of $\tan\left(2\tan^{-1}\left(\dfrac{3}{5}\right)+\sin^{-1}\left(\dfrac{5}{13}\right)\right)$ is equal to :
Inverse Trigonometric Functions
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JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7509
If $f:\mathbf{R}\to\mathbf{R}$ is given by $f(x)=x+1$, then the value of $\displaystyle\lim_{n\to\infty}\dfrac{1}{n}\left[f(0)+f\left(\dfrac{5}{n}\right)+f\left(\dfrac{10}{n}\right)+\cdots+f\left(\dfrac{5(n-1)}{n}\right)\right]$ is :
Definite Integration
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JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7510
Let $f:\mathbf{R}-\left\{\dfrac{\alpha}{6}\right\}\to\mathbf{R}$ be defined by $f(x)=\dfrac{5x+3}{6x-\alpha}$. Then the value of $\alpha$ for which $(f\circ f)(x)=x$, for all $x\in\mathbf{R}-\left\{\dfrac{\alpha}{6}\right\}$, is :
Functions
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