The sum of all rational terms in the expansion of $\left(2^{\frac15}+5^{\frac13}\right)^{15}$ is equal to:
Previous 10 Questions — JEE Main 2024 (4 April Morning Shift)
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Let the first three terms $2,\,p,\,q$ with $q\ne 2$ of a G.P. be respectively the $7^{\text{th}},\,8^{\text{th}}$ and $…
Topic: JEE Main 2024 (4 April Morning Shift)
If the solution $y = y(x)$ of the differential equation
$(x^{4}+2x^{3}+3x^{2}+2x+2)\,dy-(2x^{2}+2x+3)\,dx=0$
satisfies …
Topic: JEE Main 2024 (4 April Morning Shift)
Three urns $A$, $B$ and $C$ contain $(7\text{ red}, 5\text{ black})$, $(5\text{ red}, 7\text{ black})$ and $(6\text{ re…
Topic: JEE Main 2024 (4 April Morning Shift)
The vertices of a triangle are $A(-1,3)$, $B(-2,2)$ and $C(3,-1)$.
A new triangle is formed by shifting the sides of …
Topic: JEE Main 2024 (4 April Morning Shift)
Let the point, on the line passing through the points $P(1,-2,3)$ and $Q(5,-4,7)$,
farther from the origin and at a di…
Topic: JEE Main 2024 (4 April Morning Shift)
If the domain of the function
$\sin^{-1}\!\left(\dfrac{3x-22}{2x-19}\right)+\log_e\!\left(\dfrac{3x^2-8x+5}{x^2-3x-10}…
Topic: JEE Main 2024 (4 April Morning Shift)
Let a unit vector which makes an angle of $60^\circ$ with $\,2\hat i+2\hat j-\hat k\,$ and an angle of $45^\circ$ with …
Topic: JEE Main 2024 (4 April Morning Shift)
Let $f(x)=x^5+2e^{x/4}$ for all $x\in\mathbb R$.
Consider a function $g(x)$ such that $(g\circ f)(x)=x$ for all $x\in…
Topic: JEE Main 2024 (4 April Morning Shift)
Let $\alpha, \beta \in \mathbb{R}$.
Let the mean and the variance of 6 observations $-3,\, 4,\, 7,\,-6,\, \alpha,\, \…
Topic: JEE Main 2024 (4 April Morning Shift)
A square is inscribed in the circle $x^2 + y^2 - 10x - 6y + 30 = 0$.
One side of this square is parallel to $y = x + …
Topic: JEE Main 2024 (4 April Morning Shift)
Next 10 Questions — JEE Main 2024 (4 April Morning Shift)
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If $2$ and $6$ are roots of the equation $ax^{2}+bx+1=0$, then the quadratic equation whose roots are $\dfrac{1}{2a+b}$…
Topic: JEE Main 2024 (4 April Morning Shift)
Let the sum of the maximum and the minimum values of the function
$f(x)=\dfrac{2x^{2}-3x+8}{2x^{2}+3x+8}$ be $\dfrac{m…
Topic: JEE Main 2024 (4 April Morning Shift)
If the system of equations
$x+\big(\sqrt{2}\sin\alpha\big)y+\big(\sqrt{2}\cos\alpha\big)z=0$
$x+(\cos\alpha)y+(\sin\a…
Topic: JEE Main 2024 (4 April Morning Shift)
Let $\alpha$ and $\beta$ be the sum and the product of all the non-zero solutions of the equation
$(\overline{z})^2 + …
Topic: JEE Main 2024 (4 April Morning Shift)
Let $f:\mathbb{R}\to\mathbb{R}$ be a function given by
$
f(x)=
\begin{cases}
\dfrac{1-\cos 2x}{x^2}, & x0,
\end{cases}
…
Topic: JEE Main 2024 (4 April Morning Shift)
