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JEE Mathematics / Practice

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Showing 51-55 of 5539 questions.

JEE Main 2021 (Online) 24th February Morning ShiftQuestion 51
If $e^{\left(\cos^{2}x+\cos^{4}x+\cos^{6}x+\ldots\infty\right)\log_e2}$ satisfies the equation $t^{2}-9t+8=0$, then the value of $\frac{2\sin x}{\sin x+\sqrt{3}\cos x}\left(0<x<\frac{\pi}{2}\right)$ is :
Trigonometric Ratio & Identities
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JEE Main 2020 (Online) 3rd September Evening ShiftQuestion 52
Let $R_1$ and $R_2$ be two relations defined as follows : $R_1=\{(a,b)\in\mathbf{R}^2:a^2+b^2\in\mathbf{Q}\}$ and $R_2=\{(a,b)\in\mathbf{R}^2:a^2+b^2\notin\mathbf{Q}\}$, where $\mathbf{Q}$ is the set of all rational numbers. Then :
Sets, Relations and Function
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JEE Main 2020 (Online) 2nd September Evening ShiftQuestion 53
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) 25th February Morning ShiftQuestion 54
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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JEE Main 2021 (Online) 22nd July Evening ShiftQuestion 55
The number of solutions of $\sin^{7}x+\cos^{7}x=1$, $x\in[0,4\pi]$ is equal to :
Trigonometric Ratio & Identities
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