If $\alpha=\cos^{-1}\left(\dfrac{3}{5}\right),\ \beta=\tan^{-1}\left(\dfrac{1}{3}\right)$ where $0<\alpha,\beta<\dfrac{\pi}{2}$, then $\alpha-\beta$ is equal to:
Next 10 Questions — JEE Main 2019 (8 April Morning Shift)
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The sum of the solutions of the equation $\left|\sqrt{x}-2\right|+\sqrt{x},(\sqrt{x}-4)+2=0\ \ (x>0)$ is equal to:
Topic: JEE Main 2019 (8 April Morning Shift)
Let $A$ and $B$ be two non-null events such that $A\subset B$. Then, which of the following statements is always correc…
Topic: JEE Main 2019 (8 April Morning Shift)
The sum of all natural numbers $n$ such that $100
Topic: JEE Main 2019 (8 April Morning Shift)
Let $A = \left( {\matrix{
{\cos \alpha } & { - \sin \alpha } \cr
{\sin \alpha } & {\cos \alpha } \cr
…
Topic: JEE Main 2019 (8 April Morning Shift)
If $f(x)=\log_e\left(\dfrac{1-x}{1+x}\right),\ |x|
Topic: JEE Main 2019 (8 April Morning Shift)
Let $O(0,0)$ and $A(0,1)$ be two fixed points. Then the locus of a point $P$ such that the perimeter of $\triangle AOP$…
Topic: JEE Main 2019 (8 April Morning Shift)
If $S_1$ and $S_2$ are respectively the sets of local minimum and local maximum points of the function $f(x)=9x^4+12x^3…
Topic: JEE Main 2019 (8 April Morning Shift)
If $f(x)=\dfrac{2-x\cos x}{2+x\cos x}$ and $g(x)=\log_e x,\ (x>0)$, then the value of the integral $\displaystyle \int_…
Topic: JEE Main 2019 (8 April Morning Shift)
The area (in sq. units) of the region $A={(x,y)\in\mathbb{R}\times\mathbb{R}\mid 0\le x\le3,\ 0\le y\le4,\ y\le x^2+3x}…
Topic: JEE Main 2019 (8 April Morning Shift)
The mean and variance of seven observations are $8$ and $16$, respectively. If five of the observations are $2,4,10,12,…
Topic: JEE Main 2019 (8 April Morning Shift)
