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JEE Mathematics / Practice

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Showing 61-65 of 7517 questions.

JEE Main 2023 (Online) 13th April Evening ShiftQuestion 61
Let $A=\{-4,-3,-2,0,1,3,4\}$ and $R=\{(a,b)\in A\times A:b=|a|\text{ or }b^{2}=a+1\}$ be a relation on $A$. Then the minimum number of elements, that must be added to the relation $R$ so that it becomes reflexive and symmetric, is $\_\_\_\_\_\_$ .
Sets, Relations and Function
JEE Main 2020 (Online) 2nd September Evening ShiftQuestion 62
Let $f:\mathbf{R}\to\mathbf{R}$ be a function which satisfies $f(x+y)=f(x)+f(y)$ $\forall x,y\in\mathbf{R}$. If $f(1)=2$ and $g(n)=\sum_{k=1}^{(n-1)}f(k)$, $n\in\mathbf{N}$ then the value of $n$, for which $g(n)=20$, is :
Sets, Relations and Function
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JEE Main 2021 (Online) 27th July Evening ShiftQuestion 63
Let $A=\{n\in\mathbf{N}\mid n^2\le n+10{,}000\}$, $B=\{3k+1\mid k\in\mathbf{N}\}$ and $C=\{2k\mid k\in\mathbf{N}\}$, then the sum of all the elements of the set $A\cap(B-C)$ is equal to ________.
Sets, Relations and Function
JEE Main 2021 (Online) 27th July Morning ShiftQuestion 64
If $\log_32$, $\log_3(2^x-5)$, $\log_3\left(2^x-\frac72\right)$ are in an arithmetic progression, then the value of $x$ is equal to ________.
Sets, Relations and Function
JEE Main 2021 (Online) 25th February Morning ShiftQuestion 65
A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point $A$, with uniform speed. At that point, angle of depression of the boat with the man's eye is $30^{\circ}$ (Ignore man's height). After sailing for $20$ seconds, towards the base of the tower (which is at the level of water), the boat has reached a point $B$, where the angle of depression is $45^{\circ}$. Then the time taken (in seconds) by the boat from $B$ to reach the base of tower is :
Trigonometric Ratio & Identities
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